The Pennsylvania State University
The Graduate School
X-RAY, ULTRAVIOLET, AND OPTICAL FLARES IN
GAMMA-RAY BURST LIGHT CURVES
A Dissertation in
Astronomy and Astrophysics
by
Craig Arnel Swenson
c© 2014 Craig Arnel Swenson
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2014
The disseration of Craig Arnel Swenson was reviewed and approved∗ by the fol-
lowing:
Pete Roming
Adjunct Senior Research Associate in Astronomy and Astrophysics
Dissertation Advisor, Co-Chair of Committee
John Nousek
Professor of Astronomy and Astrophysics
Co-Chair of Committee
Eric Feigelson
Professor of Astronomy and Astrophysics
Derek Fox
Associate Professor of Astronomy and Astrophysics
Special Signatory
Stephane Coutu
Professor of Physics
Donald Schneider
Department Head
∗Signatures are on file in the Graduate School.
Abstract
One of the surprising results of the NASA Swift mission was the discovery of large
numbers of flares in gamma-ray burst (GRB) light curves. Though they had pre-
viously been seen, the Swift data showed that flares appear in approximately 50%
of X-ray GRB light curves. Many of these flares are very large and energetic, and
a number of studies have been performed analyzing the properties of the observed
X-ray flares. Flares in the UV and optical wavelengths have not received the
same attention due to the flares being smaller and more difficult to identify in the
UV/optical. This dissertation presents a new algorithm for detecting flares which
we employ on the data from the Second UVOT GRB Catalog, finding 119 flaring
periods, most of which are previously unreported. We also present our analysis of
the Swift X-ray data from 2005 January through 2012 December, where we find
498 flaring periods, many representing weaker flares that have not been included
in previous studies. Our analysis of these two catalogs shows that the our previous
understanding and assumptions about flare properties were very limited, particu-
larly in terms of flare duration, with many of our newly identified flares exhibiting
durations of ∆t/t > 1. Our correlation studies between the UV/optical and X-ray
flares shows that X-ray flares are generally larger, both in terms of duration and
flux, than their lower energy counterparts and we discuss possible reasons for this
trend. We further discuss whether the emission mechanism causing the observed
X-ray and UV/optical flares is the same, and contrast the potentially correlated
X-ray and UV/optical flares with flares that have no observed counterpart. The
broad range of flare properties observed and the number of UV/optical flares ob-
served without X-ray counterparts lead us to believe that the generally assumed
internal shock mechanism may not be correct for all GRB flares and that further
theoretical work is needed to explain the observed flare parameters.
iii
Table of Contents
List of Figures vii
List of Tables ix
Acknowledgments x
Chapter 1Introduction 11.1 Discovery of Gamma-Ray Bursts and Early Observations . . . . . . 11.2 Flares in Gamma-Ray Burst Light Curves . . . . . . . . . . . . . . 6
Chapter 2GRB 090926A 132.1 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Fermi data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.2 XRT data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.3 UVOT data . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.1 Comparing the Fermi LAT and Swift BAT GRB populations 162.2.2 Late time flares in GRB 090926A . . . . . . . . . . . . . . . 22
2.3 Astrophysical Interpretations . . . . . . . . . . . . . . . . . . . . . 25
Chapter 3Ultraviolet/Optical Flares 273.1 Flare Finding Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 273.2 UV/Optical Flares Table . . . . . . . . . . . . . . . . . . . . . . . . 343.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Chapter 4X-ray Flares 494.1 Modifications to Flare Finding Algorithm for X-ray Data . . . . . . 49
iv
4.2 X-ray Flares Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Chapter 5UV/Optical and X-ray Flare Correlation 925.1 Flares with potential counterparts . . . . . . . . . . . . . . . . . . . 935.2 Comparison to Flares with no potential counterpart . . . . . . . . . 105
Chapter 6Conclusions and Future Work 116
Bibliography 122
Appendix A: Flare Finding Algorithm with Simulated Examples 134
Appendix B: Step-by-Step Example of Flare Finding Algorithmon the X-ray Light Curve of GRB 090926A 141
v
List of Figures
1.1 BATSE 4G Catalog Skymap . . . . . . . . . . . . . . . . . . . . . . 31.2 BATSE 4G Catalog T90 distribution . . . . . . . . . . . . . . . . . . 31.3 GRB Fireball Model . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 The X-ray canonical light curve . . . . . . . . . . . . . . . . . . . . 71.5 GRB 050502B giant X-ray flare . . . . . . . . . . . . . . . . . . . . 81.6 GRB 060313 with UV/optical flares . . . . . . . . . . . . . . . . . . 11
2.1 Fermi GBM and LAT observations of GRB 090926A . . . . . . . . 142.2 Swift XRT and UVOT observations of GRB 090926A . . . . . . . . 152.3 Cumulative distribution curves for BAT detected GRBs . . . . . . . 202.4 X-ray and UV/Optical distribution curves for Swift observed GRBs 21
3.1 Flare Finding Algorithm Results for GRB 090926A . . . . . . . . . 333.2 Number distribution of Ultraviolet/Optical flares . . . . . . . . . . 443.3 Ultraviolet/Optical flares distribution of Tpeak . . . . . . . . . . . . 453.4 Ultraviolet/Optical flares distribution of ∆t/t . . . . . . . . . . . . 463.5 Ultraviolet/Optical flares flare flux ratio . . . . . . . . . . . . . . . 48
4.1 Number distribution of X-ray flares . . . . . . . . . . . . . . . . . . 834.2 X-ray flares distribution of Tpeak . . . . . . . . . . . . . . . . . . . . 844.3 X-ray flares distribution of ∆t/t . . . . . . . . . . . . . . . . . . . . 864.4 X-ray flares distribution of flare flux ratio . . . . . . . . . . . . . . . 874.5 X-ray flares Ioka et al. (2005) plot . . . . . . . . . . . . . . . . . . . 894.6 X-ray flares versus light curve canonical phase . . . . . . . . . . . . 91
5.1 X-ray Tstart versus UV/optical Tstart . . . . . . . . . . . . . . . . . . 985.2 X-ray Tpeak versus UV/optical Tpeak . . . . . . . . . . . . . . . . . . 995.3 X-ray Tstop versus UV/optical Tstop . . . . . . . . . . . . . . . . . . 1005.4 X-ray ∆t/t versus UV/optical ∆t/t . . . . . . . . . . . . . . . . . . 1035.5 X-ray ∆F/F versus UV/optical ∆F/F . . . . . . . . . . . . . . . . 1045.6 Counterpart verus no counterpart: UV/optical log(∆F/F ) . . . . . 1065.7 Counterpart verus no counterpart: UV/optical log(∆F/F )/Tpeak . . 107
vi
5.8 Counterpart verus no counterpart: UV/optical log(Fpeak) . . . . . . 1085.9 Counterpart verus no counterpart: UV/optical log(Fpeak/Tpeak) . . . 1085.10 Counterpart verus no counterpart: X-ray log(∆F/F ) . . . . . . . . 1095.11 Counterpart verus no counterpart: X-ray log(∆F/F )/Tpeak . . . . . 1105.12 Counterpart verus no counterpart: X-ray log(Fpeak) . . . . . . . . . 1115.13 Counterpart verus no counterpart: X-ray log(Fpeak/Tpeak) . . . . . . 1125.14 X-ray ∆F/F versus UV/optical ∆F/F with limits on unseen coun-
terparts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.15 X-ray (∆F/F )/Tpeak versus UV/optical (∆F/F )/Tpeak with limits
on unseen counterparts . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.1 Combined histogram of ∆t/t for X-ray flares . . . . . . . . . . . . . 1196.2 Combined X-ray flares Ioka et al. (2005) plot . . . . . . . . . . . . . 120
A.1 Simulated light curve with all breakpoints detected . . . . . . . . . 136A.2 Simulated light curve with short rise and undetected first breakpoint 138A.3 Simulated light curve with observing gaps . . . . . . . . . . . . . . 140
B.1 GRB 090926A X-ray light curve . . . . . . . . . . . . . . . . . . . . 142B.2 GRB 090926A fitted X-ray light curve residuals . . . . . . . . . . . 144B.3 GRB 090926A optimal number of additional breakpoints . . . . . . 146B.4 GRB 090926A: X-ray Flare 1 . . . . . . . . . . . . . . . . . . . . . 147B.5 GRB 090926A: X-ray Flare 2 . . . . . . . . . . . . . . . . . . . . . 149B.6 GRB 090926A: X-ray Flare 3 . . . . . . . . . . . . . . . . . . . . . 150
vii
List of Tables
2.1 Fermi LAT GRB parameters . . . . . . . . . . . . . . . . . . . . . 18
3.1 Ultraviolet/Optical GRB flares . . . . . . . . . . . . . . . . . . . . 36
4.1 X-ray GRB flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 Potentially correlated UV/optical and X-ray flare parameters . . . . 95
B.1 GRB 090926A, determination of optimal number of breakpoints . . 145B.2 Breakpoints detected in X-ray residuals of GRB 090926A . . . . . 146
viii
Acknowledgments
There are many people I must thank for their support and encouragement as Ihave pursued my Ph.D. My journey through graduate school has not followed thenormal pattern, with my dissertation advisor, Pete Roming, moving to Texas aftermy second year of graduate school. I thank him for continuing to advise me, despitethe long distance between us, and for his continual support and encouragement.Because of the freedom and latitude he provided me in my research (includingchasing a number of dead ends), I was able to learn and grow more as a researcherthan I otherwise may have. My rest of my dissertation committee (John Nousek,Eric Feigelson, Derek Fox and Stephane Coutu) provided invaluable guidance andI thank them for their time and generosity.
My thanks also goes to the wonderful Swift team at the Swift Mission Op-erations Center. They are individuals who are all dedicated to their work (asevidenced by the consistent high marks Swift receives) and I feel honored to havebeen a part of such a magnificent mission. My time at the MOC also allowed meto develop skills and take on responsibilities that are not afforded to most graduatestudents, and I am a more rounded person, researcher, and scientist as a result ofthose opportunities.
Lastly, and most importantly, I must thank my family. My loving wife, Katie,who has been nothing but supportive as we’ve made this journey together. I loveyou and look forward to the continued adventures we will have together. My sons,Lucas and Jaxson, you provide bring a joy and happiness to life that I can’t imageliving without. I love all of you!
ix
Chapter 1
Introduction
1.1 Discovery of Gamma-Ray Bursts and Early
Observations
Gamma-Ray Bursts (GRBs) are a relatively recent addition to the ever growing list
of observed astronomical sources, having been serendipitously discovered as a result
of observations made by the United States military Vela satellites monitoring Soviet
compliance to the Limited Nuclear Test Ban Treaty of 1963. The observations
made by the Vela satellites were classified and the existence of GRBs was not
publicly reported until six years after their initial detection when the data was
declassified and the first 16 GRBs were reported (Klebesadel et al. 1973). Due
to the orbital height and subsequent large distance between the individual Vela
satellites (done purposefully to enable monitoring of nuclear explosions behind the
moon), a rough localization of these initial 16 GRBs was constructed based on
photon arrival time. Strong et al. (1974) showed that there was no immediate
correlation between the observed positions of these first GRBs and the planes of
the solar system and Milk Way galaxy. GRBs continued to be detected throughout
2
the 1970s and 1980s as additional satellites and planetary missions were equipped
with γ-ray detectors, creating the InterPlanetary Network (IPN) (e.g. Hurley et al.
(2000)). However, the positional accuracy of these detections remained poor and
it was impossible to determine whether these phenomena were associated with an
already known class of objects, or whether GRBs represented an entirely new and
unknown class of astrophysical sources.
The first dedicated experiment to study GRBs was proposed in 1978 in the form
of the Burst and Transient Source Experiment (BATSE) onboard the Compton
Gamma-Ray Observatory (CGRO). Development of BATSE proceeded through
the 1980s and culminated in the successful launch of CGRO in April 1991 aboard
the Space Shuttle Atlantis. BATSE was in operation for 9 years (1991 - 2000) until
CGRO was successfully deorbited. During its active mission, BATSE discovered
more than 2700 GRBs and firmly established the isotropic nature of GRB positions
across the sky (Meegan et al. 1992) (Figure 1.1). An isotropic distribution lead to
two distinct possibilities: either 1) a galactic origin that extended into the halo of
the galaxy, or 2) a cosmological origin. The energy required to power a GRB at
cosmological distances was enormous, 1050−1052 ergs, which led many to question
whether this was a realistic option.
The large number of GRB detections also allowed for the discovery of two
distinct populations of GRBs. Kouveliotou et al. (1993) showed that GRBs were
observed to be one of two varieties either “short and hard”, or “long and soft”1
(Figure 1.2). The short GRBs have a duration of T902 < 2 seconds and a harder
observed spectrum, while the long GRBs have a softer spectrum and durations of
T90 > 2.
In spite of BATSE’s contribution to our understanding of the prompt γ-ray sig-
1‘soft’ and ‘hard’ refer to the relative energy of the observed emission, with soft being associ-ated with lower energy and hard with higher energy.
2Time over which GRB emits from 5% to 95% of its total measured γ-ray fluence.
3
+90
-90
-180+180
2704BATSE Gamma-RayBursts
Figure 1.1 Isotropic distribution of GRB positions as de-tected by BATSE. Taken from BATSE 4G catalog:http://www.batse.msfc.nasa.gov/batse/grb/skymap.
Figure 1.2 Distribution of T90 duration as seen by BATSE. Taken from BATSE 4Gcatalog: http://www.batse.msfc.nasa.gov/batse/grb/skymap.
4
nal associated with GRBs, the source of the observed emission was still a mystery.
It took the launch of the Italian BeppoSAX satellite in April 1996 to finally settle
the questions. BeppoSAX was crucial because it hosted two separate experiments,
the Gamma-Ray Burst Monitor (GRBM) and the Wide Field Cameras (WFC), a
set of four high resolution X-ray cameras, on the same satellite. This allowed for
detection of the initial γ-ray signal as well as subsequent follow-up in the X-ray
to localize the GRB to higher precision. The first X-ray afterglow was detected in
connection with GRB 970208 (Costa et al. 1997) and although an optical counter-
part was also detected its distance was uncertain for several years. Later that year,
in May 1997, BeppoSAX detected and localized GRB 970508, which was localized
early enough to allow for optical observations to be made while the afterglow was
still bright. These observations led to the first redshift measurement, placing GRB
970508 at 0.835 ≤ z ≤ 2.3 (Metzger et al. 1997) that settled the debate and place
GRBs at cosmological distances.
With GRBs occurring at cosmological distances, it became necessary to ac-
count for the previously mentioned energetics of 1050 − 1052 ergs that appeared
to be necessary to power these massive explosions. This was accomplished by in-
voking a compact “central engine” capable of accelerating the explosion ejecta to
relativistic speeds. The fireball model (Meszaros & Rees 1992; Meszaros & Rees
1993; Meszaros et al. 1994) described such a scenario in which the central engine is
likely a newly formed stellar-mass black hole surrounded by an accretion disk that
beams a highly relativistic jet of ejecta into the surrounding circumburst medium
(Figure 1.3). This model requires a number of emission mechanisms, all necessary
to explain the various components observed in GRB light curves. The prompt γ-
ray emission is the result of internal shocks caused by relativistic shells of material
moving at different relative velocities that collide with one another (we will also
5
Figure 1.3 Cartoon of GRB fireball model from Gomboc (2012).
invoke internal shocks as a potential candidate model for flares later in this work).
As these relativistic shells subsequently sweep up and collide with the external cir-
cumburst medium, a shock front forms, which is referred to as the forward shock.
This forward shock is believed to be the source of the long lived GRB afterglow
that is observed in the X-ray, optical and radio wavelengths. The creation of the
forward shock also results in a reverse shock, a front that propagates backward rel-
ative to the forward shock, that exists until the reverse shock front passes through
the thickness of the forward shock. The forward shock, reverse shock, and any
other collision with the circumburst medium are collectively know as “external
shocks”.
Despite having a theoretical explanation in hand and a growing number of
afterglow detections, the field of GRB research continued to be plagued by the
amount of time between the initial GRB prompt trigger and the subsequent local-
ization and follow-up in the X-ray and optical wavelengths. This led to large gaps
in the light curves of GRBs and no understanding of what happened during the
first few hours after the initial burst of γ-rays. Looking to remedy this problem,
6
the NASA Swift Gamma-Ray Burst Explorer (Gehrels et al. 2004) was selected in
1999 as part of the MIDEX program and was launched in November 2004.
1.2 Flares in Gamma-Ray Burst Light Curves
One of the many great advances made by the Swift mission was that of early
time GRB afterglow follow up. Swift was specifically designed with rapid GRB
afterglow observations in mind. Prior to the launch of Swift, GRB afterglow obser-
vations generally did not start until hours after the burst, and an X-ray position
was generally needed before any optical follow-up could occur. This meant that
most optical detections did not take place until days after the GRB. Swift would
solve this problem through the use of 3 separate instruments on the same space-
craft working together. After the detection of a GRB by the Burst Alert Telescope
(BAT; Barthelmy et al. 2005), Swift autonomously slews to the position, gener-
ally within ∼ 100 seconds, allowing the X-ray Telescope (XRT; Burrows et al.
2005a) and UV/Optical Telescope (UVOT; Roming et al. 2000, 2004, 2005) to be-
gin observations of the afterglow. Swift has proven to be invaluable in furthering
our understanding of GRB physics, having observed over 850 GRBs from 2004
December to 2014 May, and was specifically designed to be able to observe the
early afterglow evolution and transition from the prompt emission to the afterglow
stage. The early stages of the afterglow proved to be very exciting and led to the
discovery of a number of new features, including the “canonical” X-ray light curve
(Nousek et al. 2006; Zhang et al. 2006) (Figure 1.4) which has been observed in a
number of GRBs (e.g., Hill et al. 2006; Evans et al. 2009).
Another important feature seen early in the Swift mission was X-ray flares,
such as the giant X-ray flare of GRB 050502B (shown in Figure 1.5) (Burrows
et al. 2005b; Romano et al. 2006). Flares in X-ray light curves had been seen
7
Figure 1.4 The canonical X-ray light curve showing the decay in flux of the GRBafterglow with time, presented by Zhang et al. (2006) and Nousek et al. (2006).
prior to their discovery in XRT light curves (e.g., Piro et al. 1998, 2005), but had
only been observed a handful of times. It was quickly shown that they are quite
common, appearing in approximately 50% of XRT afterglows (O’Brien et al. 2006),
and are temporally displaced so as to be distinct from the prompt emission. Flares
are observed as superimposed deviations from the underlying light curve and have
been observed in all phases of the canonical X-ray light curve.
Early in the Swift mission, several studies were performed that highlighted
individual GRBs that exhibited either large numbers of flares or flares of unusually
high fluence. Each of these studies expanded our understanding of flares and the
physical processes whereby they are created. In particular, the studies of GRBs
050406 (Romano et al. 2006), 050502B (Falcone et al. 2006), 050713A (Morris
et al. 2007), 050724 (Campana et al. 2006) and 050904 (Cusumano et al. 2007)
established the fact that flares are likely caused by internal shocks because of
8
XRTCountRate(countss-1)
102
103
104
105
106
TimesinceBAT trigger (s)
0.0001
0.0010
0.0100
0.1000
1.0000
10.0000
100.0000
GRB 050502B
Figure 1.5 XRT light curve of GRB 050502B, showing the extreme X-ray flaringoccasionally observed (Burrows et al. 2005b).
their steep rise and decay slopes, though the actual source of the flares is still
debated and may be linked to instabilities in the ejecta or the release of stored
electromagnetic energy. These studies also showed that X-ray flares are observed
in both long and short GRBs, can contain energies as large as the prompt emission,
they appear to come from a distinct emission mechanism other than the afterglow,
and can be temporally separated from the prompt phase by hundreds of seconds.
Further studies have only reinforced these initial findings and have even shown
that significant flares can be created at times greater than 105s after the initial
prompt detection (e.g., Swenson et al. 2010).
Some attempts have been made to look at larger collections of flares and have
examined their properties on a more generalized basis. Falcone et al. (2007) and
Chincarini et al. (2007) examined the temporal and spectral properties, respec-
tively, from a collection of flares found in 33 of the first 110 GRBs observed by
9
Swift. The combined results from these two studies found that the late-time inter-
nal shocks were required to explain 10 of the observed flares and that central engine
activity was the preferred method for a majority of the bursts. However, Chincar-
ini et al. (2007) also state that more observations of flares over more energy bands
are needed. A follow-up study was performed (Chincarini et al. 2009) that limited
the data set to those GRBs which had redshifts, enabling a study of the actual
energetics of the flares and found some indication that the flare energy may be cor-
related to the GRB prompt energy, but was limited due to the number of bursts.
They once again confirmed that more observational work is needed. Additional
studies further confirmed earlier results showing that X-ray flares are likely caused
by late-time internal dissipation processes, which produces the prompt emission,
and also showed that flares evolve over time, becoming broader and flatter. How-
ever these studies limited their data to only the first 1000 seconds of the GRB
afterglow light curve (Chincarini et al. 2010) or a limited sample of 9 exceptionally
bright X-ray flares (Margutti et al. 2010).
An attempt at incorporating information from multiple energy bands was made
by Morris (2008) in which spectral energy distributions (SEDs) were created, using
BAT, XRT and UVOT data, for flares found in the same sample of 110 GRBs used
by Falcone et al. (2007) and Chincarini et al. (2007). The fits to the SEDs showed
that the flares, unlike the afterglow, could not be fit by a simple absorbed power
law.
The number of studies analyzing flares in the UV/optical are even more limited
than those for the X-ray (Roming et al. 2006a). The primary reason for this is
the lower significance of most flares in the softer energy bands. While the X-ray
flares are often easily identified by visual inspection of the light curves, potential
UV/optical flares are more often overlooked or dismissed as noise.
10
A notable example of flares detected by the UVOT is found in the light curve
of the short GRB 060313 (Roming et al. 2006b) in which late-time flaring was
observed by the UVOT, but not seen in the XRT (although an early-time X-
ray flare was observed), as shown in Figure 1.6. X-ray flares have often been
studied without an UV/optical counterpart, but this was one of the few cases
where the study focused on a UV/optical where an X-ray flare was not observed.
In the specific case of GRB 060313 the flares could be consistent with density
fluctuation in the circumstellar medium, provided that the cooling frequency, νc,
lies between the X-ray and UV/optical bands, which would explain why the flares
appeared in the UV/optical but not in the X-ray. However, the soft energy flares
can also be explained by central engine activity at late times, which is similar
to the explanation for X-ray flares as stated above. Another notable example is
that of GRB 090926A (Swenson et al. 2010) (see Figure 2.2 in Chapter 2). This
burst displayed the previously mentioned late time flares at times greater than 105
seconds, which can be explained by central engine activity at extremely late times,
but also because the flaring is simultaneously observed in the X-ray as well as the
UV/optical. Identifying the source of the flares and whether X-ray and UV/optical
flares have the same origin remains an important open question.
The common factor in all of the aforementioned studies is that the flares were
found by simple manual inspection of the light curves and were easily detectable
by eye. This method has allowed for a significant number of X-ray flares to be
detected and analyzed, but has yielded a very small number of UV/optical flares
due to the previously mentioned difficulty of identifying them due to their lower
significance. A blind, systematic search for flares in both X-ray and UV/optical
bands has not yet been performed and is necessary to provide an unbiased sample
of flares of all brightnesses. Such a sample would be able to address some of the
11
Time since trigger (sec)
.01 .1 1 10 100 1000 10000
BAT
XRT
UVOT
100 1000
(b)
Time since trigger (sec)
10000
(a)
Time since trigger (sec)
Figure 1.6 Combined BAT, XRT and UVOT light curve of GRB 060313 showingthe late-time UV/optical flares with no X-ray counterparts (inset a). Early X-rayflaring with no UV/optical counterpart is also shown in inset b. From Rominget al. (2006b).
limitations mentioned in the previous X-ray studies and would provide access to a
relatively untapped source of knowledge with additional UV/optical flares.
The complementary nature of two such flare catalogs would allow for more
stringent constraints on the origin of flares in GRBs through cross-correlation
of the two energy regimes. The precise nature of the GRB central engine still
remains largely unknown and, because flaring is most likely related to central
engine activity, the study of flares is crucial to our unlocking of that mystery.
In this work we present the results of a blind, systematic search for flares in
UVOT and XRT GRB light curves. Using Monte Carlo simulations and a dynamic
programming algorithm that makes use of the likelihood-based Bayesian Informa-
tion Criterion, we have constructed the most complete catalog of UV/optical and
12
X-ray flares to date, and provide the temporal details of each flare, including3,4,5
Tpeak, ∆t/t defined as (Tstop−Tstart)/Tpeak, and the strength of the flare relative to
the underlying light curve. In Chapter 2 we examine GRB 090926A as a case study
of an exceptionally bright Fermi LAT detected GRB with late-time UV/optical
and X-ray flares, and discuss the potential implications of these flares as they re-
late to the cause of the sustained flux levels at late-times seen in this GRB. More
broadly, in Chapter 3 we outline the methodology we use for identifying flare in a
large sample of GRB light curves, and present the flares found in the UVOT light
curves and discuss their properties. Chapter 4 details the modifications made to
the methodology for the case of the XRT light curves and presents the identified
flares. Chapter 5 examines the relationship between potentially correlated X-ray
and UV/optical flares, while also examining how these potentially correlated flares
differ from flares without counterparts. Finally, in Chapter 6 we summarize and
present ideas for future work and the need for further data.
3Tstart: The time at which the slope of the light curve changes, signifying the beginning ofthe flare
4Tpeak: The time after GRB trigger of the peak of the flare5Tstop: The time at which the light curve returns to the normal underlying decay slope
Chapter 2
GRB 090926A
2.1 Observations
2.1.1 Fermi data
At 04:20:26.99 UT on 2009 September 26, the Fermi Gamma-ray Burst Monitor
(GBM) triggered on GRB 090926A (Uehara et al. 2009), which was unfortunately
outside the BAT field of view. The GBM light curve, Figure 2.1, consisted of
a single pulse with T90 of 20±2 s (8-1000 keV). The time-averaged, combined
GBM/LAT spectrum from T0 to T0+20.7 s, where T0 is the trigger time, is
best fit by a Band function (Band et al. 1993), with Epeak = 268±4 keV, α =
-0.693±0.009 and β = -2.342±0.011 (with α being the spectral slope at E < Epeak
and β the spectral slope at E > Epeak). The fluence (10 keV - 10 GeV) during
this interval is (2.47±0.03)×10−4 ergs cm−2, bright enough to result in a Fermi
repointing. In the first 300 s, LAT observed 150 and 20 photons above 100 MeV
and 1 GeV, respectively. Possible extended emission continued out to a few kilo-
seconds. The highest energy photon, 19.6 GeV, was observed 26 s after the trigger.
The LAT light curve, Figure 2.1, is fit by a power-law of α = -2.17±0.14. We fit
14
Figure 2.1 Fermi GBM (upper) and LAT (lower) light curves.
the LAT spectrum, from 100 - 1000 s, with a power-law of β = −1.26+0.24−0.22.
2.1.2 XRT data
XRT began observing GRB 090926A ∼46.6 ks after the Fermi trigger, in Pho-
ton Counting (PC) mode. The light curve, Figure 2.2 (taken from the XRT light
curve repository; Evans et al. (2007, 2009)), shows a decaying behavior with some
evidence of variability, and is fit with a single power-law, decaying with α = -
1.40±0.05 (90% confidence level). The average spectrum from 46.6 ks – 149 ks
is best fit by an absorbed power-law model with β = −1.6+0.3−0.2 and an absorption
column density of 1.0+0.5−0.3 × 1021 cm−2 in excess of the galactic value of 2.7×1020
cm−2 (Kalberla et al. 2005). The counts to observed flux conversion factor de-
15
Figure 2.2 Light curves for the XRT (bottom) and UVOT (top). Shaded regionsindicate periods of flaring. Solid lines show the best fit parameters calculated foreach burst.
duced from this spectrum is 3.5×10−11 ergs cm−2 count−1. The average observed
(unabsorbed) fluxes are 1.3(1.9)×10−12 ergs cm−2 s−1.
2.1.3 UVOT data
UVOT began settled observations of GRB 090926A at T0+∼47 ks, and the optical
afterglow was immediately detected (Gronwall & Vetere 2009). The resulting opti-
cal afterglow light curve is shown in Figure 2.2. The underlying optical light curve
is well fit (χ2red = 0.92/82 d.o.f.) by a broken powerlaw. The best fit parameters
are: αOpt,1 = −1.01+0.07−0.03, tbreak = 351+70.2
−141.9 ks, αOpt,2 = −1.77+0.21−0.26. X-shooter,
16
mounted on the Very Large Telescope UT2, found a spectroscopic redshift of z =
2.1062 (Malesani et al. 2009).
2.2 Discussion
GRB 090926A was a remarkable burst for a number of reasons, including the
detection of more than 20 photons in the GeV range, the ease of detection by the
Swift XRT and UVOT nearly 13 hrs after the initial trigger and the presence of
late time flares in both the XRT and UVOT light curves. The overall brightness
and behavior of the optical afterglow are more reminiscent of afterglows observed
immediately after the trigger, as opposed to observations starting at 47 ks after
the trigger (Oates et al. 2009; Roming et al. 2009, 2014). The late time light curve
properties could be due to a LAT selection effect of caused by late time energy
injection, supported by the presence of flares in the light curve. We explore both
of these possibilities.
2.2.1 Comparing the Fermi LAT and Swift BAT GRB
populations
Despite its remarkably bright, late detection, GRB 090926A is not the first optical
counterpart to be found at such late times. From the launch of the Fermi satellite
in June 2008 through December 2009, Swift performed follow-up observations on
8 GBM triggered bursts with LAT detections: GRBs 080916C, 081024B, 090217,
090323, 090328, 090902B, 090926A, and 091003, all of which are long GRBs. None
of these bursts were observed before ∼39 ks. Although Swift observations were
performed as soon as possible, the error circle of the GBM (typical error radius of
a few degrees) is too large to be effectively observed by Swift, and the more precise
17
LAT position was required to better constrain the error radius before observations
could take place. Despite these delays, an X-ray counterpart was discovered by
XRT for 6 of the 8 bursts with follow-up observations. UVOT detected an op-
tical afterglow associated with 5 of the X-ray counterparts. In addition to these
follow-up observations, the short GRB 090510A was a coincident trigger between
GBM/LAT and BAT, raising the total number of Swift observed LAT bursts to 9.
GRB 090510A had both an X-ray and UV/optical counterpart.
The high percentage of LAT-detected bursts with optical afterglows, when com-
pared to the sample of Swift triggered bursts, raises questions about the nature
of the bursts themselves. Is the LAT instrument preferentially sensitive to bursts
that are brighter overall, resulting in a higher probability of detecting a bright,
long-lived optical counterpart, or are the bursts themselves different, with a late
time brightening causing the optical afterglows?
To investigate the former possibility, we calculated the fluence that would have
been observed by the BAT for the bursts that were triggered by Fermi/LAT and
later detected by XRT. Because we are assuming, for the purpose of this test, that
the spectrum is brighter at all wavelengths, a bright LAT burst corresponds to
a bright GBM burst. Under this assumption, we use the GBM spectral param-
eters provided by Ghisellini et al. (2010) to predict what would have been seen
by the BAT over the 15-150 keV range. We check our results and estimate our
error by comparing the predicted and observed fluence for the simultaneously ob-
served Fermi/Swift GRB 090510A. The GBM spectral parameters, as well as the
predicted BAT fluence between 15-150 keV are shown in Table 2.1.
We limit our error in the calculation of the expected BAT fluence to the error
introduced from the GBM parameters. Comparing the T90 of GRB 090510A as
observed by the GBM and BAT (1 s and 0.3 s, respectively), we realize that a
18
Tab
le2.
1.Fermi
LA
TG
RB
par
amet
ers
Sou
rce
Nam
eSGBM
T90
β1GBM
β2GBM
EPeak
SBAT
8−
104
keV
(s)
keV
15-1
50
keV
erg
cm−2
erg
cm−2
GR
B080916C
(1.6±
0.2
)×10−4
66
-0.9
1±
0.0
2-2
.08±
0.0
6424±
24
1.7
35×
10−5
GR
B090323
(1.3
2±
0.0
3)×
10−4
∼150
-0.8
9±
0.0
3.
..
697±
51
2.0
8×
10−5
GR
B090328
(1.5
2±
0.0
2)×
10−4
∼25
-0.9
3±
0.0
2-2
.2±
0.1
653±
45
1.4
15×
10−5
GR
B090510A
(2.3±
0.2
)×10−4
1-0
.80±
0.0
3-2
.6±
0.3
4400±
400
3.2
5×
10−7(5.5
7×
10−7)a
GR
B090902B
(5.4±
0.0
4)×
10−4
∼21
-0.6
96±
0.0
12
-3.8
5±
0.2
5775±
11
6.0
5×
10−5
GR
B090926A
(1.9±
0.0
5)×
10−4
20±
2-0
.75±
0.0
1-2
.59±
0.0
5314±
44.3
16×
10−5
GR
B091003
(4.1
6±
0.0
3)×
10−5
21±
0.5
-1.1
3±
0.0
1-2
.64±
0.2
486.2±
23.6
2.2
79×
10−5
Note
.—
Th
e7
LA
Tob
serv
edb
urs
tsth
at
have
bee
nob
serv
edbySwift
an
dd
etec
ted
by
the
XR
T.
Th
efi
rst
6co
lum
ns
giv
eth
eb
urs
tp
ara
met
ers
as
mea
sure
dby
theFermi
GB
M(G
his
ellin
iet
al.
2010),
incl
ud
ing
those
for
GR
B090510A
,w
hic
hw
as
als
olo
cali
zed
bySwift
BA
T.
Th
ela
stco
lum
ngiv
esth
ep
red
icte
dB
AT
flu
ence
sas
extr
ap
ola
ted
from
the
GB
Mp
ara
met
ers.
Th
ein
dic
esβ1GBM
an
dβ2GBM
are
the
low
an
dh
igh
Ban
dsp
ectr
al
para
met
ers,
resp
ecti
vel
y.W
eu
sea
Ban
d-f
un
ctio
nfo
rth
eG
BM
spec
tru
m,
wit
hth
eex
cep
tion
of
GR
B090323,
for
wh
ich
acu
toff
pow
er-l
aw
mod
elis
ad
op
ted
.a:
Act
ual
flu
ence
ob
serv
edby
BA
T.
19
certain amount of error will be introduced into the expected BAT fluence due to
differences that would exist in the observed T90 between the two instruments. In
the case of the long bursts, this error is negligible in comparison to the GBM
parameter errors. Because GRB 090510A is a short burst, a small difference in T90
results in a proportionally larger error than a difference in a few seconds for longer
bursts. However, our calculated value of the fluence for GRB 090510A differs by
less than a factor of two from the BAT observed value.
We compare the calculated fluences to a sample of 343 BAT-triggered bursts
from April, 2005 to June, 2009. The sample is comprised of both short and long
bursts, across a wide spread of energies. The percentile ranking as a function of
BAT fluence (or calculated fluence) is shown in Figure 2.3. All but one of the
LAT-detected bursts are brighter than 88% of the BAT sample of bursts. The
exception is the only LAT short burst, GRB 090510A.
Ukwatta et al. (2009) reported possible soft, extended γ-ray emission associated
with GRB 090510A as seen by the Konus-Wind. Because it was at a higher redshift
than most short GRBs, z=0.903 (Rau et al. 2009), BAT couldn’t confirm any
extended emission (De Pasquale et al. 2010). When we compare GRB 090510A to
the BAT-triggered extended emission short GRBs, we find that it is only brighter
than 18% of the sample. If extended emission is in fact present, GRB 090510A
would be one of the lowest fluence extended emission bursts triggered by the BAT.
If there was no extended emission associated with GRB 090510A, then it would
be brighter than ∼77% of all BAT-triggered non-extended emission short bursts,
making it a better corollary to the long LAT GRBs.
We have shown that the long LAT-detected GRBs are brighter than 88% of
BAT-triggered bursts and that the lone short burst is also brighter than ∼77%
of other short bursts. To test whether this trend continues to the X-ray and
20
Figure 2.3 Distribution curve for 343 BAT bursts from April, 2005 to June, 2009,and 7 LAT bursts as a function of fluence. The stars indicate the LAT-detectedGRBs, also observed by Swift, using the predicted BAT fluence. GRB 090510A isshown on both the short and extended emission curves, joined by an arrow.
21
Figure 2.4 X-ray and uv/optical distribution curves. X-ray curves using flux from284 XRT afterglows. Long bursts flux taken at 70 ks, short and extended emissionat 35 ks. Short burst curve is shifted to left by a factor of 2, for clarity. GRB090510A is shown on both the short and extended emission curves, joined by anarrow. Optical distribution curve is shown as magnitudes in UVOT v filter at 70ks. Observations resulting in upper limits are not included. Stars indicate LATbursts.
22
UV/optical wavelengths, we also compared the optical afterglows of the LAT sam-
ple to BAT-triggered bursts with XRT and UVOT afterglows. We compared the
X-ray flux of the LAT burst, in counts s−1, at ∼70 ks to a selection of 314 X-ray
light curves taken from the XRT light curve repository (Evans et al. 2007, 2009).
GRB 090510A was only detected by the XRT until ∼35 ks, so we used the flux at
35 ks for comparing the short and extended emission bursts. We find the X-ray
afterglows of long LAT-triggered bursts are brighter than those of 80% of the BAT-
triggered bursts, as shown in Figure 2.4. The X-ray afterglow of GRB 090510A is
brighter than 64% (69%) of the BAT extended emission (short) bursts.
We compared the optical flux in counts s−1 at 70 ks to 103 bursts with UVOT
afterglows included in The Second Swift Ultra-Violet/Optical Telescope GRB Af-
terglow Catalog (Roming et al. 2014). All light curves were normalized to the
v filter and extrapolated to 70 ks (if necessary) for our comparison. Our pre-
liminary results, shown in Figure 2.4, indicate that the optical afterglows of long
LAT bursts are brighter than 77% of BAT-triggered optical afterglows, with GRB
090926A falling in the top 3% of optical afterglow brightness. Additionally, GRB
090510A is one of only two extended emission GRBs, or one of five short GRBs,
still detected by the UVOT at 70 ks. Regardless of which category (short or
extended emission) GRB 090510A belongs to, it is brighter than ∼90% of other
short/extended emission optical afterglows.
2.2.2 Late time flares in GRB 090926A
X-ray flares at late times have been attributed to two different sources (Wu et al.
2007): central engine powered internal emission, or features of the external shock.
There is evidence suggesting that the GRB prompt emission and X-ray flares orig-
inate from similar physical processes (see Burrows et al. 2005b; Zhang et al. 2006;
23
Chincarini et al. 2007; Krimm et al. 2007), including a lower energy budget and
‘spiky’ flares more like those actually seen in X-ray light curves. If the central en-
gine is the source of GRB flares, the X-ray flare spectrum should be similar to that
of the prompt spectrum. In the case of GRB 090926A, the prompt emission was
seen to have a Band-function spectrum (Band et al. 1993). Assuming the optical
behaves similarly to the X-ray and that the flares are caused by central engine
activity, we would expect a Band-function spectrum during the flares. A Band-
function spectrum is not observed during the X-ray variability or optical flares.
The flares are both well fit by a power-law, with no indication of a break in the
spectrum or sign of spectral evolution in the X-ray. It should be stated, however,
that the statistics of the X-ray light curve are low enough that detecting a Band
spectrum may not be possible, even if it exists. Combining the poor statistics with
the dominate underlying continuum, it is not surprising that a power-law is the
best fit. We also find no evidence of change in the spectral shape after creating
a spectral energy distribution using uv/optical photometry before and during the
first flare.
A non Band-like spectrum for the flares does not expressly prohibit central
engine activity from being the source of the flares, but it does allow for alternate
explanations. Code for modeling X-ray flares in GRBs developed by Maxham &
Zhang (2009) can produce optical flares through the collision of low energy shells
or wide shells. If the two flares are indeed due to internal shocks, then this code
can put constraints on the time of ejection and maximum energy (Lorentz factor)
of the matter shells that could produce such flares. Since ejection time in the GRB
rest frame is highly correlated to the collision time of shells in the observer frame,
this means that the central engine is active around 70 ks and 197 ks.
Using the prompt emission fluence to constrain the total energy contained in
24
the blastwave, the internal shock model requires that Lorentz factors of the shells
causing flares must be less than the Lorentz factor of the blastwave when the
shells are ejected. Fast moving shells will simply collide onto the blastwave giving
small, undetectable glitches, whereas slow moving shells will be allowed to collide
internally, releasing the energy required to detect a flare. Specifically, we find
maximum Lorentz factors of 8.2 (E52.3
n)1/8 and 5.5 (E52.3
n)1/8 for the first and second
flare, respectively and in terms of the energy in the prompt emission in units of
1052.3 ergs and number density of the ambient medium.
Collisions between these relatively low energy shells are expected to be seen in
the lower energy UV/optical bands. In the synchrotron emission model, Epeak =
2Γγe2~eBmec∝ L1/2 for electrons moving with a bulk Lorentz factor Γ with typical
energy γemec2, since the comoving magnetic field B ∝ L1/2 (Zhang & Meszaros,
2002). This is consistent with the empirical Yonetoku relation Ep ∝ L1/2iso (Yonetoku
et al. 2004) for prompt GRB emission. Applying this relation to the two flares,
one predicts Ep of 0.8 and 0.5eV for each flare, respectively. This is consistent
with the observation that both flares are more prominent in the optical band than
in the X-ray band. Finding Ep using the Amati relation, Ep ∝ E1/2iso , (Amati et al.
2002) gives Ep values for both flares around 1 keV, which are inconsistent with
the observation. Unlike for individual burst pulses (whose durations do not vary
significantly), which seem to follow an Amati relation (Krimm et al. 2009), the
Yonetoku relation may be more relevant for flares because it is consistent with the
more generic synchrotron emission physics. Since the duration of a flare depends
on the epoch of the flare (the time it is seen), the Amati relation is not expected
to hold.
25
2.3 Astrophysical Interpretations
Our study of these two groups of GRB from the LAT and BAT has shown that the
LAT-detected bursts are generally brighter than their BAT-triggered counterparts.
We find that their fluence is consistently higher than the “average” BAT burst,
and that their X-ray and UV/optical afterglows are brighter than ∼80% of BAT
GRBs.
Although we are working with a small sample of LAT bursts, and therefore
suffer the consequences of small number statistics, our preliminary results indicate
that LAT bursts exhibit bright late time X-ray and UV/optical afterglows because
they are brighter at all wavelengths than the ‘average’ burst, assuming the higher
than average fluence can be extrapolated down to X-ray and UV/optical wave-
lengths. This seems to be the most likely explanation, given the known correlation
between prompt emission and afterglow emission brightness (Gehrels et al. 2008).
We cannot say definitively, however, that this is the reason for the bright afterglows
at late times, due to the presence of flares, which indicate possible late time central
engine activity that could cause a rebrightening. Without coverage of the early
afterglow, it is impossible to say how the afterglow arrived at the state in which we
observe it ∼70 ks after the trigger. If we simply extrapolate the optical light curve
of GRB 090926A backward, we find that they could have peaked as high as v =
10 mag within the first hundred seconds after the trigger. Extrapolating the LAT
spectrum of GRB 090926A to the v band yields a peak magnitude of v = 4, or if we
assume a cooling break at GeV energies, the spectral index changes to β ≈ −0.76,
yielding a magnitude of v = 15, consistent with our extrapolation backwards and
the idea that LAT bursts are uniquely bright at all wavelengths. However, if the
early afterglow was fainter than v ≈ 15 mag, then some sort of sustained energy
injection would be required to keep the flux elevated at a level where we could then
26
observe the bright afterglow at 70 ks after the trigger. Such an energy injection
would test our current theoretical understanding of GRB optical afterglows. Our
ability to determine the true nature of LAT-detected burst is contingent on our
ability to follow-up LAT-detected GRBs at earlier times than has been achieved
with the current sample.
Chapter 3
Ultraviolet/Optical Flares
3.1 Flare Finding Algorithm
For the purposes of this portion of the study we will be using the light curves
produced by Roming et al. (2014, in preparation). This Second Swift Ultravi-
olet/Optical Telescope GRB Afterglow Catalog provides a complete dataset of
fitted UVOT light curves for both long and short GRBs observed by Swift from
April 2005 through Dec 2010, and makes use of optimal co-addition (Morgan et al.
2008). Optimal co-addition is a process that optimally weights each exposure in
order to maximize the signal-to-noise-ratio (S/N), which decreases as the source
count rate becomes low and the background relatively high. The method takes
into account the decaying nature of the GRB light curve, predicting the expected
count rate over time and calculates the correct amount of image co-addition nec-
essary to produce the maximum (S/N). Optimal co-addition results in a greater
number of detections at late times and better sampled light curves, increasing the
probability of detecting flares. In addition to being optimally co-added, the Sec-
ond UVOT GRB Catalog also normalizes the GRB light curves to a single filter
from the 7 possible filters used during observations. This normalization further
28
increases the timing resolution of the overall light curve during those periods when
multiple filters were used during the same orbit. These two methods combined,
optimal co-addition and normalization, have resulted in a completely unique and
previously unavailable data set that is suited for use in searching for flares and
other small features (as opposed to the First UVOT GRB Catalog; Roming et al.
2009). This sample is also approximately twice as large as the sample provided
in Roming et al. (2009). Due to the normalization of the light curves, we will not
be performing any chromatic analysis on the light curves, and our experience in
fitting GRB light curves leads us to believe that our detected flares will not evolve
significantly with energy over the limited energy band observed by the UVOT. Our
analysis described below is performed on the residuals of the fitted UVOT light
curves that we calculate using the fitting parameters provided by Roming et al.
(2014, in preparation).
Even with the increased probability of detecting flares that comes with using
optimally co-added data, the flares that we hope to identify are below the signifi-
cance level of the previous X-ray studies previously mentioned (e.g., Falcone et al.
2007; Chincarini et al. 2007) and we require a statistically robust method to con-
firm that the flares are real and not part of the background noise. For this study
we have used the publicly available R (R Core Team 2013) package strucchange
(Zeileis et al. 2002) and the breakpoints analysis function contained within the
package (Zeileis et al. 2003). The breakpoints function specifically employs the
approach of dynamic programming to compute the optimal number of breakpoints1
in a time series of data. Because we are using the residuals to fitted light curves,
1The term “breakpoints” is possibly less familiar than the term “changepoint”, however thereis a distinct difference in the analysis used in their calculation. The desired outcome of thebreakpoints analysis being used is the same as when using change point analysis, to find changesin the mean of time series data. However, as opposed to change point analysis, cumulative sumsare not used by the breakpoints function. In order to avoid any confusion with change pointanalysis and changepoints, the terms breakpoint analysis and breakpoints are used instead.
29
our data is roughly fit by a line of slope 0 and scattered around some mean. A
breakpoint in this case is the last data point before a sudden change in that mean
due to an unfitted feature in the original light curve. The determination of break-
points involves computing a triangular residual sum of squares (RSS) matrix for
each possible combination of light curve segments, beginning with data point i
and ending at with i′
with i < i′. This process breaks the time series into smaller
pieces, by finding the optimal segmentation that minimizes the RSS. As one would
expect, the absolute minimal RSS would lead to fitting the light curve with n− 1
breakpoints (where n is the number of data points), with an individual segment
connecting each data point. To counter this effect, the breakpoints function also
computes the Bayesian Information Criterion (BIC; Schwarz 1978),
BIC = −2× L+ k ln(n), (3.1)
where k is the number of free parameters to be estimated, n is again the number
of data points in the light curve and L is the maximized value of the log-likelihood
function,
L = (log (p) (D|θj,Mj)− log (p) (D|θj+1,Mj+1)), (3.2)
which compares the probabilities of two possible fits to the data, functions Mj
and Mj+1, each with their respective set of parameters θj and θj+1, and returns the
more likely fit based on the observed data points, D. In our case these functions
will be piecewise constant and flares will be identified as changes in the constant
mean and are represented by the θj parameters. The BIC is penalized and be-
comes increasingly large when either the data is poorly fit or when the number
of free parameters increases and the data is overfit. The BIC is therefore mini-
mized using the simplest model that sufficiently fits the data. The breakpoints
30
function returns the optimal number of breakpoints by calculating the fit that
simultaneously minimizes the RSS and BIC values.
The BIC is unlike many of the more commonly used statistical measurements
used in astronomy (e.g. χ2, F-test, etc.). The BIC is a “summary of the evidence
provided by the data in favor of one scientific theory, represented by a statistical
model, as opposed to another” (Kass & Raftery 1995), but it does not provide a
definite strength or probability to a preferred statistical model. The calculated
BIC value for any individual model is nothing more than a number and cannot
be used to determine the goodness of fit for the model to the data. The BIC
is only meaningful when used as a comparative tool to determine which of two
models is the better fit to the data. When comparing two different models the
model with the smaller BIC value is a better representation of the data. However
if the difference in the BIC is only marginal, then the two models are effectively
equivalent and the simpler model with fewer free parameters would be the optimal
fit. Kass & Raftery (1995) provide a guideline for interpreting the difference in
BIC values for two models and the strength of evidence for the preferred fit:
BICi − BICmin Evidence Against Model i
0 to 2 Not worth more than a bare mention
2 to 6 Positive
6 to 10 Strong
>10 Very Strong
For our purposes we will require BICi − BICmin > 6, or ‘Strong’ evidence, to
determine the preferred fit. In the case of BICi − BICmin < 6, we will adopt the
simplest fit model (i.e. fewest breakpoints) that satisfies the criterion of BICi−1−
BICi > 6. This means that our fits are conservative, relative to the value of
BICmin which is the ‘best’ fitting model, but likely overfits the data and would
31
introduce noise to our flare sample.
The breakpoints function, like many purely statistical analysis methods, does
not take into account the systematic and random error present in all data. The
assumption made by the algorithm is that the variance of the observed data points
is much larger than the typical error associated with any given data point. Under
this assumption, the errors can be ignored because they do not impact the ability of
the algorithm to detect a breakpoint. For most astronomical data this assumption
is not true. In order to reintroduce the effects of these errors, we run a Monte Carlo
simulation, randomizing the values of the observed data points in line with the
measured errors. For each Monte Carlo iteration we calculate the optimal number
of breakpoints and their corresponding times. For the purposes of this study we
performed 10, 000 Monte Carlo simulations on each GRB light curve. For each
light curve we examine the BIC value for each potential number of breakpoints
(i.e. 1, 2, 3, 4...n − 1) over all 10, 000 iterations and do the same for the RSS
values. Applying the BICi − BICmin > 6 criteria allows us to determine the
statistically preferred fit to the data, that does not overfit the light curve. Each of
the breakpoints found in this optimal fit correspond to a specific data point where
the original fit to the GRB light curve no longer adequately describes the data
and is likely caused by a flare. Appendix A provides a more detailed explanation,
showing results of the breakpoints function running on simulated light curves and
flares.
Once the breakpoints associated with our potential flares have been identified,
we extract the properties of the flare from the light curve. A well defined flare
consists of three breakpoints: 1) Tstart, the time of the initial deviation from the
underlying light curve decay, 2) Tpeak, the time of the peak of the flare, where the
slope goes from positive to negative again, and 3) Tstop, the time when the decay
32
of the flare returns to the underlying decay slope. Where all three of these flare
components are detected, our algorithm automatically groups them together to
form nominal flares. We can not precisely identify the exact time of Tstart, Tpeak,
or Tstop, and in some cases may not be able to identify all three components for
each flare, due to insufficient sampling of the light curve and because of observing
constraints creating gaps in the light curve. In these cases the algorithm will
identify the parts of the flare that are detected and fill in the missing pieces using
the next closest data point, again to be inspected and verified later. Because
of these limitations we only calculate limits on the boundaries of Tstart and Tstop
based on the available data, and cannot precisely define Tpeak, but rather use the
observed data point exhibiting the highest flux during the period of flaring as
a lower limit. Our estimates of the peak flux ratio, relative to the flux of the
underlying light curve at the same time, will also be a lower limit due to the
limitations in calculating Tpeak. This approach will ensure that we do not bias
further studies with underestimated values of the peak flux. Our determination of
∆t/t is also limited by the uncertainty in determining Tpeak because the true peak
flux may occur any time between Tstart and Tstop and may not have been observed.
However, because most flares are relatively short the error in our estimate of ∆t/t
is only a few percent. In the few cases of flares with distinct features that could
be analytically fit (e.g. Tstart and Tpeak for the flare peaking near 80 kiloseconds in
GRB 090926A shown in Figure 3.1), these limits closely match the values derived
from fitting the flare itself. We therefore see no need to apply a different approach
to the those few exceptional flares, by explicitly fitting them, but rather use the
same limit approach as for the rest of the data set.
Figure 3.1 shows the results of running the flare finding algorithm on the light
curve of GRB 090926A. Because the flaring occurs at such late times, the flares
33
Figure 3.1 Breakpoints identified in the UV/optical light curve of GRB 090926A.
34
have much longer durations than if they had occurred early in the light curve and
the individual components become easy to see. The figure show the 9 identified
breakpoints as vertical lines. These 9 breakpoints were then combined to create 3
individual flares, each with a Tstart, Tpeak and Tstop. The observing gap after the
peak of the second flare means that we can only provide a lower limit on Tstop by
placing it at the first data point after the gap. Using the flare finding algorithm
we were able to successfully identify the two flares that we previously identified
in Figure 2.2 (Swenson et al. 2010), but also detected a third flare starting at the
beginning of the light curve that we were unsure of when attempting to identify
flares by eye.
It should be noted that the Monte Carlo simulations being employed adds
a further noise component in addition to the statistical error already present in
the data. The simulated light curves used for breakpoint detection are therefore
conservative relative to the observed light curve, and the breakpoints identified are
found to be significant in spite of the additional noise component, making them
robust. Additionally the calculated confidence measure should be viewed as a lower
limit as many of the weaker flares may suffer in their detection fraction due to the
noise introduced in the Monte Carlo simulations.
3.2 UV/Optical Flares Table
Here we present the results of our analysis of the 201 UVOT GRB light curves
from the Second UVOT GRB Catalog (Roming et al. 2014, in preparation). We
find the presence of at least 119 unique potential flaring periods, for which we can
distinguish start and stop times, detected in 68 different light curves. Some of these
identified flares may actually be multiple superimposed flares that we are unable to
individually resolve due to timing resolution, however we still refer to each unique
35
time period as being a ‘flare’. Table 3.1) provides the following information for
each potential flare: 1) GRB Name, 2) the GRB redshift (blank if unknown) 3)
the flare peak time, defined as the observed time since the initial burst of the
highest flux data point during the flaring period, as well as the limits on 4) Tstart
and 5) Tstop, set to the last and first data points, respectively, that are well fit by
the underlying light curve. 6) A limit on ∆t/t based on the calculated peak time,
Tstart and Tstop, and 7) a lower limit on the ratio of the peak flux during the flaring
period, relative to the flux of the underlying light curve at the same time, using
the actual observed flux at the flare peak time and an interpolation of the flux of
the underlying light curve at the same time. The flux ratio is normalized using
the flux of the underlying light curve to allow for direct comparison of each flare
across all light curves. Lastly, 8) the confidence measure of the detected flare as a
fraction of the number of times the flare was identified during the 10, 000 Monte
Carlo simulations.
36
Tab
le3.
1:F
lare
sar
elist
edin
chro
nol
ogic
alor
der
by
GR
Bdat
e,th
enso
rted
by
confiden
ce.
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
GR
B05
0319
3.24
333.
5827
2.87
428.
210.
470.
830.
5075
GR
B05
0319
1061
.79
927.
0612
08.4
10.
261.
190.
3259
GR
B05
0319
802.
8473
9.17
927.
060.
230.
310.
252
GR
B05
0505
4.27
3181
.79
3181
.79
8065
.87
1.54
2.11
0.94
08
GR
B05
0525
0.60
627
1.40
257.
7529
9.17
0.15
0.56
0.96
44G
RB
0505
2560
8.92
510.
8563
6.67
0.21
1.24
0.41
49G
RB
0505
2518
6.92
172.
6821
4.72
0.22
1.03
0.96
51
GR
B05
0712
7874
96.2
571
4478
.38
8440
68.3
80.
1626
.48
0.96
01
GR
B05
0721
494.
7442
3.97
508.
920.
170.
540.
4482
GR
B05
0801
398.
3538
3.12
439.
890.
141.
240.
885
GR
B05
0801
341.
2232
7.61
355.
350.
080.
720.
8037
GR
B05
0802
1.71
887.
9880
3.49
1104
.62
0.34
0.91
0.50
38G
RB
0508
0214
28.4
712
99.3
014
92.6
90.
140.
700.
4371
GR
B05
0815
131.
7899
.32
145.
330.
351.
640.
5691
GR
B05
0824
0.83
9423
6.29
8183
8.89
2034
83.4
81.
2911
.65
0.77
43
GR
B05
0908
3.35
368.
5821
4.89
435.
090.
601.
590.
9147
GR
B05
1117
A61
0.93
555.
9977
3.26
0.36
0.85
0.61
6
GR
B06
0206
4.05
129.
9093
.51
1444
.54
10.4
01.
670.
6495
Con
tinued
onN
ext
Pag
e...
37
Tab
le3.
1–
Con
tinued
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
GR
B06
0313
524.
1247
0.21
795.
270.
621.
390.
7843
GR
B06
0428
B14
5182
.38
1413
52.7
817
4712
.64
0.23
8.90
0.56
8
GR
B06
0512
0.44
2844
8.07
432.
0140
19.5
08.
012.
250.
817
GR
B06
0526
3.21
262.
7724
2.76
272.
780.
111.
080.
9724
GR
B06
0526
192.
7117
7.44
242.
760.
340.
750.
9178
GR
B06
0526
292.
7928
2.79
312.
810.
100.
040.
5578
GR
B06
0604
2.68
203.
7119
3.70
213.
570.
100.
440.
4402
GR
B06
0708
108.
6598
.65
128.
670.
280.
340.
6744
GR
B06
0729
0.54
1858
1.79
1256
8.86
3110
9.46
1.00
0.37
0.99
89
GR
B06
0904
B0.
725
6.86
234.
9428
4.31
0.19
2.13
0.84
75
GR
B06
0912
0.94
225.
1320
9.74
245.
140.
160.
410.
7158
GR
B06
0912
375.
2436
5.23
395.
250.
080.
700.
5805
GR
B06
0912
285.
1726
5.16
305.
190.
140.
240.
5041
GR
B06
1021
0.34
6322
2.52
192.
5023
2.53
0.18
0.54
0.74
12G
RB
0610
2142
74.5
345
2.69
4683
.61
0.99
0.31
0.58
13G
RB
0610
2152
95.8
046
83.6
152
98.2
40.
120.
270.
5805
GR
B07
0208
1.17
4336
59.0
942
7659
.38
4800
22.6
60.
121.
520.
673
GR
B07
0318
0.84
246.
4522
6.44
256.
460.
120.
160.
2538
GR
B07
0318
1914
58.1
914
2816
.11
2963
19.5
00.
802.
630.
3125
Con
tinued
onN
ext
Pag
e...
38
Tab
le3.
1–
Con
tinued
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
GR
B07
0420
1939
.71
1750
.87
5792
.08
2.08
2.03
0.62
16
GR
B07
0518
273.
7224
3.70
317.
920.
271.
630.
8283
GR
B07
0518
193.
6517
7.69
206.
810.
151.
240.
5656
GR
B07
0518
117.
8110
7.80
137.
830.
250.
240.
4614
GR
B07
0611
2.04
4733
.36
3347
.02
1049
2.06
1.51
0.78
0.94
38
GR
B07
0616
1011
.36
846.
2311
49.2
60.
300.
900.
9267
GR
B07
0616
787.
5246
8.17
816.
630.
440.
470.
8939
GR
B07
0721
B3.
626
275.
2625
5.24
285.
270.
111.
170.
9697
GR
B07
1031
2.69
1118
.38
1102
.01
1158
.87
0.05
1.18
0.76
47G
RB
0710
3157
6.25
546.
5684
2.05
0.51
1.32
0.74
GR
B07
1031
1166
6.85
7596
.43
1423
9.37
0.57
1.60
0.68
42
GR
B07
1112
C0.
8259
5.43
572.
5263
6.93
0.11
1.57
0.78
43G
RB
0711
12C
245.
4221
5.39
285.
450.
291.
380.
706
GR
B07
1112
C18
094.
0012
735.
3645
965.
981.
8455
.43
0.68
09
GR
B08
0212
156.
7912
6.10
178.
160.
331.
820.
7306
GR
B08
0212
266.
8822
3.14
295.
850.
270.
900.
535
GR
B08
0212
356.
9534
0.57
378.
720.
111.
090.
2891
GR
B08
0303
573.
7351
2.75
620.
900.
192.
070.
7797
GR
B08
0303
223.
4719
3.45
256.
430.
280.
760.
5921
GR
B08
0319
B0.
9425
2.59
232.
5826
2.60
0.12
0.10
0.65
66
Con
tinued
onN
ext
Pag
e...
39
Tab
le3.
1–
Con
tinued
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
GR
B08
0319
C1.
9512
89.5
911
94.1
413
94.4
50.
161.
920.
8361
GR
B08
0330
1.51
138.
3112
8.30
148.
320.
140.
460.
7335
GR
B08
0413
B1.
142
8.29
412.
4445
3.43
0.10
1.18
0.71
2
GR
B08
0520
1.55
192.
4517
0.56
332.
620.
840.
650.
4985
GR
B08
0703
146.
8413
6.83
166.
860.
200.
260.
8849
GR
B08
0721
2.6
123.
5412
3.54
133.
550.
080.
080.
6278
GR
B08
0721
300.
4629
0.45
330.
480.
130.
260.
6111
GR
B08
0804
2.2
482.
5141
2.46
532.
550.
250.
460.
8254
GR
B08
0810
3.35
113.
0610
3.06
133.
090.
270.
160.
9201
GR
B08
0810
229.
1219
9.09
289.
170.
390.
170.
7133
GR
B08
0905
B2.
374
286.
8527
6.84
306.
560.
101.
010.
5412
GR
B08
0905
B50
7.00
476.
9852
7.02
0.10
0.36
0.37
13
GR
B08
0906
256.
2624
1.19
284.
020.
174.
860.
6933
GR
B08
0913
6.7
1253
8.61
6082
.72
1458
9.25
0.68
2.49
0.75
57G
RB
0809
1355
1292
.31
5128
41.4
188
7145
.81
0.68
2.34
0.56
95
GR
B08
0916
A0.
689
470.
2146
0.21
490.
230.
061.
260.
7993
GR
B08
0916
A37
0.14
360.
1439
0.16
0.08
1.47
0.52
95
Con
tinued
onN
ext
Pag
e...
40
Tab
le3.
1–
Con
tinued
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
GR
B08
0928
1.69
4329
.05
2090
.70
4944
.90
0.66
1.18
0.89
33G
RB
0809
2824
7.11
217.
0925
7.12
0.16
1.88
0.78
26
GR
B08
1007
0.52
9525
3.00
206.
9827
3.03
0.26
0.89
0.69
11G
RB
0810
0743
3.15
413.
1351
3.20
0.23
0.60
0.55
28
GR
B08
1008
1.96
726
2.09
243.
0930
2.12
0.23
0.14
0.75
85G
RB
0810
0812
66.8
612
27.4
112
91.1
90.
051.
330.
7367
GR
B08
1029
3.84
715
712.
6686
59.6
322
090.
420.
850.
320.
8647
GR
B08
1126
153.
7714
3.76
173.
800.
200.
440.
7555
GR
B09
0123
1112
.77
950.
6711
22.6
60.
150.
530.
8807
GR
B09
0123
668.
0860
8.41
707.
520.
150.
550.
8018
GR
B09
0123
1408
.58
1368
.14
1467
.41
0.07
0.42
0.75
55
GR
B09
0401
B11
17.7
610
68.5
611
87.5
60.
116.
240.
8217
GR
B09
0510
0.90
314
7.51
132.
4715
7.52
0.17
1.29
0.79
21
GR
B09
0529
2.62
512
04.8
595
7.27
1688
.56
0.61
2.97
0.90
25
GR
B09
0530
1.26
613
3.67
123.
6614
3.68
0.15
0.19
0.87
36G
RB
0905
3017
3.71
153.
6918
3.71
0.17
0.15
0.81
89G
RB
0905
3063
4.84
595.
0775
6.78
0.25
1.72
0.68
9
Con
tinued
onN
ext
Pag
e...
41
Tab
le3.
1–
Con
tinued
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
GR
B09
0618
0.54
715.
4870
5.59
764.
510.
080.
540.
8776
GR
B09
0618
2089
.69
2079
.80
2104
.10
0.01
1.47
0.71
39G
RB
0906
1825
97.4
725
82.0
026
21.8
40.
020.
950.
6723
GR
B09
0618
666.
8564
1.01
691.
170.
080.
680.
6045
GR
B09
0618
1916
.21
1906
.32
1930
.64
0.01
1.27
0.55
GR
B09
0618
829.
0481
3.52
853.
390.
050.
440.
5474
GR
B09
0926
A2.
1062
8170
1.3
7013
6.27
1443
08.9
80.
971.
120.
9078
GR
B09
0926
A47
722.
5746
791.
3051
749.
930.
102.
510.
8781
GR
B09
0926
A23
2412
.66
1965
69.4
824
8216
.91
0.22
0.65
0.61
23
GR
B09
1018
0.97
134
1.45
331.
4537
1.48
0.12
0.26
0.72
97
GR
B09
1029
2.75
210
59.1
710
49.2
811
47.6
00.
090.
820.
6614
GR
B09
1029
543.
6652
3.65
553.
480.
050.
790.
5801
GR
B09
1127
0.49
6940
5.64
6896
1.88
7400
7.65
0.07
1.80
0.16
44
GR
B10
0425
A1.
755
2412
6.33
2364
0.73
3874
6.47
0.63
2.82
0.92
08G
RB
1004
25A
719.
7765
1.76
947.
330.
414.
120.
8502
GR
B10
0805
A15
1.24
141.
2317
1.25
0.20
0.35
0.32
25G
RB
1008
05A
409.
4339
2.57
423.
800.
081.
060.
3222
GR
B10
0805
A63
0.03
589.
5970
7.20
0.19
1.56
0.27
33G
RB
1008
05A
3938
7.52
2955
5.01
5684
0.63
0.69
1.97
0.25
61
Con
tinued
onN
ext
Pag
e...
42
Tab
le3.
1–
Con
tinued
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
GR
B10
0814
A1.
4422
4.40
214.
3924
4.42
0.13
0.35
0.36
92G
RB
1008
14A
284.
4627
4.45
294.
470.
070.
460.
3079
GR
B10
0901
A1.
408
416.
8739
6.86
436.
890.
101.
450.
8464
GR
B10
0901
A22
8.79
208.
7723
8.80
0.13
1.55
0.23
95G
RB
1009
01A
1767
9.91
1007
0.17
2163
4.66
0.65
0.27
0.22
95
GR
B10
0906
A1.
727
445.
6242
4.48
465.
410.
093.
220.
7149
GR
B10
1017
A18
0.65
144.
9021
5.47
0.39
1.78
0.79
94
GR
B10
1117
B16
4.51
154.
5017
4.52
0.12
0.47
0.51
2G
RB
1011
17B
307.
9923
4.39
328.
000.
300.
620.
3753
2O
ur
anal
ysi
sid
enti
fies
asp
ecifi
cd
ata
poi
nt
inth
eli
ght
curv
eas
bei
ng
ass
oci
ate
dw
ith
thes
equ
anti
ties
.T
he
larg
enu
mb
erof
dig
its
rep
orte
dfo
rTpeak,Tsta
rt
andTstop
are
not
refl
ecti
veof
ou
rco
nfi
den
cein
thei
rd
eter
min
ati
on
,b
ut
are
rath
erth
eti
mes
tam
pass
oci
ate
dw
ith
the
dat
ap
oint
iden
tifi
ed.
We
hav
ech
osen
not
toro
un
dth
ese
valu
esfo
rtw
ore
aso
ns:
1)
any
rou
nd
ing
dec
isio
nw
em
ake
wou
ldb
earb
itra
ry,
and
2)th
ere
lati
veeff
ect
ofth
ero
un
din
gon
each
valu
ew
ou
ldd
iffer
dep
end
ing
on
the
size
of
the
valu
e.T
his
als
op
reve
nts
the
intr
od
uct
ion
ofan
arbit
rary
bia
sto
the
dat
a.3A
llti
mes
are
rela
tive
toth
eti
me
ofth
ein
itia
lb
urs
ttr
igger
.∆t/t
isca
lcu
late
das
(Tstop−Tsta
rt)/Tpeak.Tsta
rt
an
dTstop
are
low
eran
du
pp
erli
mit
s,re
spec
tivel
y.F
lux
Rat
iois
calc
ula
ted
as
the
flu
xat
the
flare
pea
kti
me
div
ided
by
the
inte
rpol
ate
dfl
ux
of
the
un
der
lyin
gli
ght
curv
eat
the
sam
eti
me,
nor
mal
ized
usi
ng
the
flu
xof
the
un
der
lyin
gli
ght
curv
e,an
dis
alo
wer
lim
itof
the
act
ual
pea
kfl
ux
rati
o.
Th
eco
nfi
den
cem
easu
rere
pre
sents
the
frac
tion
ofti
mes
the
flare
was
iden
tifi
edd
uri
ng
the
10,0
00
Monte
Carl
osi
mu
lati
on
s.
43
3.3 Discussion
Our analysis shows that at least 33% of the light curves in the Second UVOT
GRB Catalog contain possible episodes of flaring. This number is very much in
line with analysis that has been performed on X-ray light curves (e.g.,Chincarini
et al. 2010). This result, however, does not correct for those light curves that were
so poorly sampled, or for which observations did not start until such late times as
to make the detection of any flares challenging. It is not unreasonable to assume
that an even larger fraction of the light curves in the Second UVOT GRB Catalog
contain flares that will simply never be detected due to these issues.
For the purposes of this analysis we have divided the detected flares into three
groups. First the ‘gold’ group, defined as those flares with a confidence measure
greater than 0.7 and a ∆t/t ≤ 0.5. This group provides a good detection rate and
satisfies the somewhat ‘classic’ definition of a flare. This group contains 46 flares.
Next is the ‘silver’ group, which expands the parameters to flares with either a
confidence measure greater than 0.6 or ∆t/t ≤ 1.0. This group has 24 flares after
excluding the overlap from the ‘gold’ group. The final group, the ‘bronze’ group,
contains the remaining 49 detected flares.
For those light curves with detected flares, the most common number of flares
for each group is 1 per GRB with the average number of flares for each group
being ∼2. Fig 3.2 shows the distribution of flares per GRB for the gold, silver, and
bronze groups, shown in black, blue and red, respectively. The flares in the gold
and silver groups come primarily GRBs with a single flare, while the bronze group
has a large fraction of its flares coming not only from single flare GRBs, but also
contains GRBs with two and three or more flares. No GRB had more than three
flares all belonging to the gold group. GRB 090618 displayed the most flaring
activity with 6 unique flaring episodes detected with flares being represented in all
44
1 2 3 4Number of Flares byDistribution
0
10
20
30
40NumberofGRBs
1 2 3 4 5 6 7Number of Flares per Burst
Figure 3.2 Histograms of the number of detected flares per GRB, shown as thenumber of flares per GRB by distribution (left panel), with the three distributionbeing the gold (black shading), silver (blue shading) and bronze (red shading)groups described in the text. Also shown is the overall distribution of flares perGRB (right panel).
three groups.
The earliest flare peak time occurs at 108 seconds after the trigger of GRB
060708, and the latest detected flare peaks at 787 kiloseconds after the trigger of
GRB 050712, with 85% of all detected flares peaking before 1000 seconds. Fig-
ure 3.3 shows the distribution of Tpeak for the three groups of flares. The gold
group has an average Tpeak of ∼500 seconds, while the introduction of later flares
in the silver and bronze groups push their average Tpeak to > 1000 seconds after the
GRB trigger. However, the most commonly observed Tpeak for both the silver and
bronze groups is also ∼500 seconds. It appears that all three groups are similarly
distributed, but with fewer late time detections in the gold group due to the strict
criteria for gold designation and the difficulties in detecting flares at late times
45
Time since Trigger (s)
NumberofGRBs
01
2
3
4
5
67
01
2
3
4
5
67
101 102 103 104 105 106 10701
2
3
4
5
67
Figure 3.3 Histogram of the distribution of Tpeak. The three distributions are thegold (top), silver (middle) and bronze (bottom) distributions described in the text.
when the flux is low and the errors larger.
The duration of the flares, taking into account the limited nature of our de-
termination of Tstart and Tstop, vary from ∆t/t of 0.01 to greater than 10, with at
least 80% of the bursts exhibiting a ∆t/t < 0.5. Figure 3.4 shows the distribution
of ∆t/t for the three groups of bursts. Both the gold and the bronze groups can
be fit by the same Gaussian function, with different maximums, centered at ∼0.14
and with a full width at half max varying between 0.17 for the gold group to 0.23
for the bronze group. We are unable to say how the silver group compares to the
gold and bronze due to the lack of detections, though the relative consistency in
distribution for all the groups for Tpeak and between the gold and bronze groups for
∆t/t shows that the detection algorithm is robust even at lower confidence levels.
It should be noted that for flares with ∆t/t > 0.5, particularly those observed in
the first few hundred seconds of the light curve, may actually be the onset of the
46
log(∆t/t)
NumberofGRBs
02
4
6
8
10
12
02
4
6
8
10
12
−2 −1 0 1 2
02
4
6
8
10
12
Figure 3.4 Distribution of ∆t/t, calculated as (Tstop−Tstart)/Tpeak, for the detectedflares. The three flares with ∆t/t > 2.0 are omitted for scaling purposes. The threedistributions are the gold (top), silver (middle) and bronze (bottom) distributionsdescribed in the text.
forward shock emission and may not be an entire class of their own (Oates et al.
2009).
The relative strengths of the flares varies from a minimum flux ratio of 0.04
to a maximum of 55.42. Figure 3.5 shows the distribution of the flare flux ratios
for the three groups. The bronze group is the only distribution with detections in
each bin. The gold group is noticeably missing detections at ∼0.3, ∼0.6 and ∼0.9.
While the silver group, which has fewer detections overall, is missing detections
at ∼0.5-0.6 and ∼0.8. This may indicate a preferred set of flare strengths in the
UV/optical, though, a single Gaussian fit to the gold group does provide a centered
value consistent with the bronze group, indicating that it may simply be a lack of
bursts with gold flare detections causing the poor fit and that all three groups are in
fact equally well fit by the same Gaussian. A larger sample of gold flares, meaning
47
continued GRB light curve observations in the UV/optical, will be required to
determine whether it is a lack of data or an actual physical phenomenon causing
the observed structure. More than 83% of the bursts have flux ratios between
0.04 and 2, with representatives in each of the three groups, while there are 19
relatively strong flares with flux ratios > 2. Interestingly, 14 of the 19 relatively
strong flares are among the 15% of flares that peak later than 1000 seconds. After
the first 1000 seconds, light curves have generally poor timing resolution due to
the decaying nature of the afterglow, so it may be a simple observational bias that
leads to a large fraction of those late-time flares having large flux ratios (i.e. larger
flares are easier to to detect than small flares at late times). Further analysis and
simulations will be required to determine whether an observational bias exists or
whether the high fraction of large late-time flares is indicative of a unique subset
of GRBs capable of producing these types of flares.
In addition to analyzing the burst parameters individually, we also performed
an analysis of the UV/optical flare parameters compared to the GRB prompt
parameters for each burst. Specifically we compared the reported T90, prompt
emission fluence, and the amount of structure present in the prompt emission (i.e.
single FRED (Fast Rise, Exponential Decay)-like peak versus multi-peak struc-
ture) to Tpeak, ∆t/t, the flux ratio and the number of flares per GRB and find no
correlation between any of the prompt emission parameters and flare parameters.
We interpret the lack of correlation to indicate that the emission source of the
UV/optical flares detected is not the same as that of the high energy prompt GRB
emission.
48
FluxRatio
NumberofGRBs
01
2
3
4
5
67
01
2
3
4
5
67
0 1 2 3 4 5
01
2
3
4
5
67
Figure 3.5 Distribution of flare flux ratio, relative to the underlying light curve. Theflares with flux ratios > 5 are omitted for scaling purposes. The three distributionsare the gold (top), silver (middle) and bronze (bottom) distributions described inthe text.
Chapter 4
X-ray Flares
4.1 Modifications to Flare Finding Algorithm for
X-ray Data
For this portion of the study we will use the publicly available XRT light curves
from the online Swift-XRT GRB Catalogue (Evans et al. 2007, 2009). We down-
loaded the light curves for the time period covering January 2005 through Decem-
ber 2012, inclusive, as well as the best fit parameters for each burst. We calculated
the light curve residuals using the best fit parameters and perform our flare find-
ing analysis on these residuals. Our flare finding analysis follows the same basic
methodology set forth in Chapter 3, however some modifications were necessary.
A few minor changes in the actual processing of the data were required, as
opposed to the UV/optical dataset. Due to the much higher density of data points
available in many of the X-ray light curves, as opposed to the relatively sparsely
sampled UV/optical light curves, were were forced to limit the number of potential
breakpoints identified to 75 per light curve. By default the analysis iteratively
adds additional breakpoints between ever data point in the light curve, beginning
50
with the strongest (i.e. most likely) breakpoint. This process is computationally
intensive and adding an arbitrarily large number of additional breakpoints increases
the processing time exponentially. By limiting the number of breakpoints to 75
we are allowing for a minimum of 25 individual flares per light curve. Our results
presented in this paper show that no burst had more than nine individual flares
identified, so the truncation of the analysis had no effect on the end results.
For the sake of consistency, we assume that the fits provided by the Swift-XRT
GRB Catalogue (Evans et al. 2007, 2009) are correct in fitting just the underlying
light curve and not the flares1. This assumption may result in the identification
of a ‘flare’ during the fast initial decay phase of the canonical light curve (Nousek
et al. 2006). Because there is no data prior to the start of the XRT observations
we can not conclusively differentiate between observations that start during the
canonical fast initial decay phase versus those that may start during the decay of
a flare. A large number of XRT observations begin during the fast initial decay
phase and the Swift-XRT GRB Catalogue does not always fit that initial steep
decay as part of the light curve, particularly if the observed portion of the phase
is extremely short. In these cases our flare analysis will identify the initial steep
decay as being part of a flare, which may or may not be the case.
Additionally, due to the number of data points contained in some of the bright-
est X-ray light curves, the process of iteratively fitting every data point requires a
large number of CPU cycles and completing the normal 10, 000 Monte Carlo iter-
ations would have required several years of computational time. In those cases we
limited the number of iterations to 1, 000 Monte Carlo simulations and report our
1We perform our analysis on the fitted light curve residuals to speed up the flare findingprocess. The accuracy of the initial light curve fit does not contribute significantly to the resultsof our analysis. Analysis performed on a subset of light curves, rather than on the residuals,showed that we recover a fit consistent with those provided by Evans et al. (2007, 2009), butwhich required approximately twice as many CPU cycles to recover both the general fit to thelight curve as well as any flares.
51
confidence measure as the fraction of times the flare was recovered for those 1, 000
simulations. The increased number of data points also generally corresponds to a
decrease in the duration of each data point which ultimately makes the calculation
Tstart, Tpeak and Tstop more precise. However, we will continue to refer to them as
“limits” because not all of the X-ray light curves benefit from having exceptionally
bright afterglows and there are still instances of poor timing resolution and gaps
in the data that prevent us from determining a more accurate breakpoint.
4.2 X-ray Flares Table
Here we present the results of our analysis of the 680 XRT GRB light curves taken
from the online Swift-XRT GRB Catalogue (Evans et al. 2007, 2009) spanning
January 2005 to December 2012, inclusive. We detect 498 unique potential flaring
periods, for which we can distinguish start and stop times, detected in 326 different
light curves. A number of these identified flares are actually multiple superimposed
flares contained within a shared ‘flaring period’. Because of the high density of
data points in the X-ray light curves, we are able to resolve periods of multiple
overlapping flares. Due to the overlapping, we can not uniquely identify the start
or stop of the individual flares within the larger ‘flaring period’. We are limited
to identifying only the start and stop times of the entire period containing the
overlapping flares. For the sake of simplicity and completeness we will include
these flaring periods in our analysis and simply refer to these flaring periods as
‘flares’. Table 4.1 provides the following information for each potential flare: (1)
Whether or not the flare is isolated or is part of a larger flaring period, (2) GRB
Name, (3) the GRB redshift (blank if unknown), (4) the flare peak time, defined
as the data point most often identified as the flare peak during the Monte Carlo
simulations, as well as limits on (5) Tstart and (6) Tstop, defined as the last and first
52
data points, respectively that are well fit by the underlying light curve. (7) a limit
on ∆t/t based on the peak time, Tstart and Tstop, and (8) the ratio of the peak flux
during the flaring period, relative to the flux of the underlying light curve at the
same time, using the observed flux at the flare peak time and an interpolation of
the flux of the underlying light curve. The flux ratio is normalized using the flux
of the underlying light curve to allow for direct comparison of each flare across all
light curves. Finally, (9) the confidence measure of the detected flare indicating
the fractional number of times the flare was recovered during the 10, 000 Monte
Carlo simulations.
We previously discussed the difficulty in identifying flares, particularly at late
times in the light curve due to the degradation of the underlying afterglow. We
present in Table 4.1 all potential flares found by our analysis, regardless of their
confidence, meaning that a small number may be related to statistical fluctuations
or non-flaring activity. This was done in an attempt to eliminate bias from our
conclusions, as well as those from subsequent studies that use this data.
53
Tab
le4.
1:F
lare
sar
elist
edin
chro
nol
ogic
alor
der
by
GR
Bdat
e,th
enso
rted
by
confiden
ce.
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0501
2872
0.13
686.
1578
4.77
0.14
0.43
0.51
63N
GR
B05
0128
293.
3027
8.18
305.
280.
090.
340.
4182
NG
RB
0502
19A
129.
1012
6.20
131.
460.
040.
660.
7269
NG
RB
0502
19A
262.
8524
5.68
295.
790.
190.
720.
6922
NG
RB
0502
19A
164.
0215
9.94
169.
350.
060.
460.
5689
NG
RB
0503
181.
4432
447.
3528
612.
7832
788.
650.
131.
750.
3661
NG
RB
0503
193.
2414
38.0
813
76.8
415
10.2
00.
090.
880.
7775
NG
RB
0504
012.
913
9.69
134.
3915
1.31
0.12
0.40
0.53
26N
GR
B05
0401
173.
4916
9.78
187.
330.
100.
390.
3651
NG
RB
0504
0621
0.50
112.
6535
4.36
1.15
20.4
20.
9250
NG
RB
0504
2211
7.30
117.
3024
3.46
1.08
14.7
50.
9557
NG
RB
0505
02B
749.
0113
6.66
1625
.30
1.99
278.
871.
0000
NG
RB
0505
02B
7703
0.88
2481
4.44
1486
57.1
61.
615.
061.
0000
NG
RB
0506
0731
0.98
278.
6068
6.64
1.31
43.2
11.
0000
NG
RB
0507
1226
2.74
194.
5641
4.77
0.84
3.21
1.00
00N
GR
B05
0712
478.
8945
7.87
546.
780.
194.
761.
0000
NG
RB
0507
14B
377.
5331
0.24
5616
.99
14.0
684
.09
1.00
00
Con
tinued
onN
ext
Pag
e...
54
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0507
1638
8.94
358.
6147
1.15
0.29
4.97
0.53
35N
GR
B05
0716
174.
4916
1.11
194.
710.
190.
290.
4958
NG
RB
0507
1798
.36
94.3
110
5.11
0.11
0.18
0.38
36
NG
RB
0507
2123
2.62
219.
5423
9.21
0.08
0.26
0.55
01
NG
RB
0507
2627
7.06
226.
6132
6.97
0.36
1.73
1.00
00N
GR
B05
0726
163.
5314
8.62
177.
980.
180.
420.
5163
NG
RB
0507
303.
9743
0.47
345.
5653
1.29
0.43
2.87
1.00
00N
GR
B05
0730
677.
4761
5.53
765.
810.
221.
231.
0000
NG
RB
0507
3022
4.30
209.
2427
2.92
0.28
0.95
1.00
00
NG
RB
0508
0372
6.03
577.
6490
8.04
0.46
0.55
0.84
39N
GR
B05
0803
1180
.30
1003
.83
1247
.73
0.21
0.72
0.79
23
NG
RB
0508
1422
39.7
410
77.3
812
353.
555.
032.
630.
7119
NG
RB
0508
1426
2.27
249.
6440
5.51
0.59
0.46
0.51
31
NG
RB
0508
1916
446.
4211
135.
2536
537.
511.
541.
880.
7895
NG
RB
0508
20A
2.61
224
8.09
215.
8046
81.5
318
.00
59.6
71.
0000
NG
RB
0508
2242
4.22
336.
2894
5.97
1.44
40.8
61.
0000
NG
RB
0508
2223
8.70
208.
4425
8.12
0.21
2.55
1.00
00N
GR
B05
0822
1110
75.7
893
374.
5215
0646
.78
0.52
2.06
0.46
05
Con
tinued
onN
ext
Pag
e...
55
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0509
083.
3539
9.39
294.
6978
4.93
1.23
14.2
31.
0000
NG
RB
0509
0814
3.35
129.
5019
1.89
0.44
1.99
0.92
11
NG
RB
0509
15A
105.
7394
.78
156.
230.
584.
911.
0000
NG
RB
0509
15A
533.
3244
4.90
658.
530.
401.
310.
7139
NG
RB
0509
1618
807.
5317
052.
5822
517.
670.
2939
.66
1.00
00
NG
RB
0509
22B
812.
9861
5.57
1486
.43
1.07
40.0
80.
9196
NG
RB
0509
22B
375.
9636
3.91
391.
720.
070.
230.
7037
NG
RB
0510
0613
0.83
122.
1314
4.20
0.17
1.09
0.83
49N
GR
B05
1008
5113
.48
4944
.48
5250
.01
0.06
0.69
0.72
56
NG
RB
0510
21B
158.
8912
6.44
209.
280.
520.
810.
6059
NG
RB
0511
17A
1324
.39
1257
.16
5021
.08
2.84
5.60
1.00
00N
GR
B05
1117
A10
72.2
981
9.59
1233
.96
0.39
2.33
0.77
84N
GR
B05
1117
A43
6.58
301.
9775
1.52
1.03
1.80
0.77
47
NG
RB
0512
1013
3.23
119.
8415
6.19
0.27
1.16
0.79
04N
GR
B05
1210
164.
0115
6.19
217.
250.
370.
730.
4352
NG
RB
0512
2711
4.33
103.
4816
5.68
0.54
0.81
1.00
00
NG
RB
0601
0552
190.
6440
674.
9498
642.
801.
112.
650.
3072
NG
RB
0601
0845
45.1
143
82.3
947
03.7
80.
071.
860.
9791
NG
RB
0601
0812
2.79
122.
7933
7.44
1.75
2.86
0.97
84
Con
tinued
onN
ext
Pag
e...
56
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0601
11A
91.2
082
.56
131.
180.
531.
551.
0000
NG
RB
0601
11A
168.
7614
9.80
204.
450.
322.
631.
0000
NG
RB
0601
11A
288.
1820
4.45
525.
471.
1123
.18
1.00
00N
GR
B06
0111
A15
916.
4215
514.
3116
275.
010.
051.
680.
4902
NG
RB
0601
11B
156.
3413
6.70
182.
760.
290.
480.
3835
NG
RB
0601
153.
5339
9.88
308.
4671
8.93
1.03
3.57
1.00
00
NG
RB
0601
1617
9.04
179.
0420
9.90
0.17
1.34
0.96
88N
GR
B06
0116
1201
.25
1089
.15
1356
.86
0.22
0.86
0.77
09
NG
RB
0601
242.
297
571.
2621
3.78
1144
1.52
19.6
578
9.65
1.00
00
NG
RB
0602
0270
0.75
360.
7810
40.5
50.
975.
250.
9011
NG
RB
0602
04B
121.
5410
8.08
139.
530.
262.
741.
0000
NG
RB
0602
04B
317.
4327
5.00
493.
000.
6952
.47
1.00
00N
GR
B06
0204
B21
0.99
198.
3431
0.00
0.53
2.01
0.55
19
NG
RB
0602
064.
0554
46.8
417
87.6
323
560.
914.
003.
001.
0000
NG
RB
0602
103.
9119
9.90
164.
6930
2.20
0.69
12.1
30.
8724
NG
RB
0602
1037
7.04
302.
2060
7.66
0.81
7.89
0.87
19N
GR
B06
0210
106.
8610
4.12
120.
230.
150.
860.
5564
NG
RB
0602
190.
0331
6473
.92
5879
.34
1066
2.93
0.74
1.30
0.53
41
Con
tinued
onN
ext
Pag
e...
57
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0602
23A
4.41
1319
.42
811.
2653
24.4
43.
4213
.66
1.00
00N
GR
B06
0223
A38
7.14
292.
6556
3.22
0.70
0.97
0.57
24
YG
RB
0603
1210
9.76
65.7
424
5.11
1.63
49.6
61.
0000
NG
RB
0603
1254
2.17
462.
8085
0.48
0.72
1.79
0.96
87
NG
RB
0603
1319
1.19
154.
8423
8.67
0.44
1.90
0.70
24N
GR
B06
0313
137.
1412
0.54
154.
840.
250.
790.
6440
NG
RB
0603
1928
0.38
261.
5530
9.05
0.17
0.77
0.97
71
NG
RB
0604
0373
.33
70.0
779
.57
0.13
0.94
0.54
77
NG
RB
0604
1364
2.87
547.
9493
0.63
0.60
3.37
1.00
00
NG
RB
0604
181.
4913
0.77
116.
6117
3.07
0.43
7.22
0.82
15
NG
RB
0604
2160
45.4
351
77.3
010
810.
050.
931.
280.
9931
NG
RB
0605
10A
775.
4274
8.18
807.
800.
080.
680.
2755
NG
RB
0605
10A
1201
.00
1171
.45
1229
.73
0.05
0.78
0.24
47
YG
RB
0605
10B
4.9
301.
2217
2.14
468.
310.
9813
.75
1.00
00N
GR
B06
0510
B10
05.7
175
1.94
5502
.63
4.72
27.5
20.
7393
NG
RB
0605
120.
4428
201.
9017
4.23
379.
871.
023.
531.
0000
YG
RB
0605
263.
2124
7.69
181.
7994
8.01
3.09
389.
561.
0000
NG
RB
0606
02B
195.
4117
4.52
246.
990.
371.
190.
7366
Con
tinued
onN
ext
Pag
e...
58
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
YG
RB
0606
042.
6813
6.86
124.
3022
8.00
0.76
4.86
1.00
00
NG
RB
0606
073.
082
98.6
193
.41
132.
300.
393.
151.
0000
NG
RB
0606
0726
4.86
216.
8538
9.35
0.65
10.7
51.
0000
NG
RB
0606
0718
0.79
169.
8920
5.33
0.20
0.86
0.43
65
NG
RB
0607
073.
4318
6.08
175.
4122
8.78
0.29
1.41
0.96
18
NG
RB
0607
1229
9.00
271.
4334
6.85
0.25
1.70
0.93
14
NG
RB
0607
142.
7113
7.70
123.
5815
8.50
0.25
3.76
0.82
46N
GR
B06
0714
175.
6715
8.50
225.
140.
387.
440.
8246
NG
RB
0607
1920
0.98
139.
2737
2.09
1.16
6.68
1.00
00
NG
RB
0608
011.
1310
9.74
96.1
114
9.52
0.49
0.64
0.92
23
NG
RB
0608
05A
4304
.05
579.
4119
615.
794.
424.
970.
6054
NG
RB
0608
1351
5.90
495.
8654
1.34
0.09
0.72
0.44
17N
GR
B06
0813
109.
1610
5.35
129.
530.
220.
420.
4068
NG
RB
0608
140.
8413
0.69
120.
7516
1.32
0.31
1.18
0.83
25
NG
RB
0609
04A
303.
9525
3.97
454.
430.
669.
921.
0000
NG
RB
0609
04A
675.
9663
4.19
1036
.13
0.59
6.89
1.00
00N
GR
B06
0904
A21
32.6
310
36.1
358
529.
1526
.96
8.77
0.94
32N
GR
B06
0904
A15
4.26
162.
8123
9.88
0.50
0.18
0.32
14
NG
RB
0609
04B
0.7
171.
7212
7.96
3760
.36
21.1
524
3.84
1.00
00
Con
tinued
onN
ext
Pag
e...
59
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0609
063.
6916
2.75
162.
7524
4.43
0.50
4.54
1.00
00
NG
RB
0609
081.
8836
136.
1113
1.28
145.
010.
101.
120.
9211
NG
RB
0609
1951
5.99
353.
9069
0.68
0.65
0.91
0.98
27
NG
RB
0609
263.
243
5.99
391.
9658
5.62
0.44
0.44
0.62
80
NG
RB
0609
2955
3.06
371.
6511
20.6
71.
3584
6.44
1.00
00
NG
RB
0610
0470
.54
70.5
412
0.35
0.71
1.15
0.91
87
NG
RB
0611
10A
0.75
713
5.58
111.
7520
9.17
0.72
1.31
1.00
00
NG
RB
0611
211.
314
80.5
367
.01
100.
570.
420.
890.
9752
NG
RB
0611
2111
9.28
106.
1112
8.79
0.19
0.81
0.41
26
NG
RB
0612
0214
0.58
125.
8418
4.32
0.42
3.74
1.00
00
NG
RB
0701
0368
7.45
355.
5290
7.00
0.80
0.72
0.67
08
NG
RB
0701
0735
7.16
291.
3639
9.01
0.30
9.64
1.00
00N
GR
B07
0107
8706
8.24
6978
4.94
1779
39.3
81.
293.
890.
7498
NG
RB
0701
102.
352
1070
7.35
4084
.37
2753
5.08
2.19
8.94
1.00
00
YG
RB
0701
2936
0.99
230.
1310
70.2
42.
3373
.58
1.00
00
NG
RB
0702
2010
7.97
104.
7111
7.67
0.12
0.68
0.43
55N
GR
B07
0220
523.
9450
0.25
580.
400.
150.
680.
3057
NG
RB
0703
061.
496
181.
7417
4.80
208.
040.
188.
010.
7592
Con
tinued
onN
ext
Pag
e...
60
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0703
180.
8427
0.70
235.
6442
3.34
0.69
3.06
1.00
00N
GR
B07
0318
193.
7718
6.64
216.
470.
150.
500.
8203
NG
RB
0703
3022
2.54
164.
5636
1.76
0.89
11.8
71.
0000
NG
RB
0704
19B
243.
7619
8.74
325.
850.
521.
290.
9989
NG
RB
0704
19B
100.
2386
.51
140.
860.
540.
310.
2634
NG
RB
0704
2022
932.
7618
762.
0323
152.
810.
198.
381.
0000
NG
RB
0705
1818
6.29
96.2
035
7.02
1.40
14.5
31.
0000
NG
RB
0705
20A
238.
8323
5.94
3975
.32
15.8
41.
180.
5075
NG
RB
0705
20B
187.
5614
6.20
375.
301.
226.
661.
0000
NG
RB
0705
210.
553
331.
5829
6.68
408.
250.
340.
740.
6976
NG
RB
0705
3142
7.93
371.
5055
8.68
0.44
0.99
0.75
98
NG
RB
0706
112.
0434
20.8
534
20.8
541
31.2
40.
211.
230.
9931
NG
RB
0706
1648
5.09
415.
1670
9.34
0.61
3.25
0.91
43N
GR
B07
0616
757.
2771
3.97
843.
160.
172.
030.
9012
NG
RB
0706
1619
8.94
191.
3320
3.66
0.06
0.90
0.81
82
NG
RB
0706
2114
5.12
135.
9915
4.04
0.12
0.96
0.55
78
NG
RB
0707
0430
3.20
258.
0152
09.4
116
.33
25.5
21.
0000
Con
tinued
onN
ext
Pag
e...
61
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0707
14A
310.
8823
4.46
484.
190.
801.
120.
7697
NG
RB
0707
14A
904.
8274
2.63
1369
.29
0.69
0.98
0.49
04
NG
RB
0707
14B
0.92
122.
8011
4.75
128.
570.
110.
850.
2043
NG
RB
0707
21B
3.62
631
1.06
238.
9839
4.60
0.50
11.7
91.
0000
NG
RB
0707
21B
623.
0057
4.66
748.
510.
280.
840.
7423
NG
RB
0707
24A
0.45
710
5.01
89.4
812
3.46
0.32
1.63
1.00
00
NG
RB
0708
022.
4516
2.48
162.
4824
7.07
0.52
2.47
0.95
24
NG
RB
0708
0812
6.53
121.
1114
4.19
0.18
0.65
0.59
54
NG
RB
0710
312.
6945
4.98
380.
9561
31.1
812
.64
5.78
1.00
00N
GR
B07
1031
150.
2814
1.28
173.
110.
210.
520.
8280
NG
RB
0710
3119
5.98
187.
9622
7.76
0.20
0.63
0.71
22N
GR
B07
1031
257.
3424
4.61
300.
070.
221.
410.
6853
NG
RB
0711
0432
810.
4832
444.
4833
294.
060.
031.
500.
5673
YG
RB
0711
1859
6.12
333.
1515
73.0
92.
0811
.63
0.74
22
NG
RB
0711
221.
1440
0.50
357.
4551
6.66
0.40
0.64
0.68
66
NG
RB
0712
270.
383
158.
6615
3.12
191.
640.
240.
410.
7518
YG
RB
0801
2316
6.07
155.
9837
3.14
1.31
1.26
0.86
81
NG
RB
0802
102.
6418
9.07
174.
6525
6.70
0.43
8.61
1.00
00
Con
tinued
onN
ext
Pag
e...
62
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
YG
RB
0802
1229
4.14
173.
4644
8.66
0.94
26.4
41.
0000
NG
RB
0802
29A
104.
4193
.74
173.
110.
760.
980.
9438
YG
RB
0803
102.
4320
5.60
126.
2011
31.5
64.
8941
.66
1.00
00N
GR
B08
0310
4858
.46
1442
.36
1754
0.08
3.31
3.18
0.53
55
NG
RB
0803
19B
0.94
7013
34.4
176
075.
3925
4460
7.50
3.52
12.2
80.
5956
NG
RB
0803
19D
295.
7523
8.44
490.
770.
856.
460.
9597
NG
RB
0803
2030
9.90
273.
9244
4.89
0.55
6.68
1.00
00N
GR
B08
0320
211.
2919
6.35
273.
920.
373.
210.
6243
NG
RB
0803
2069
9.37
759.
7897
2.75
0.36
2.02
0.61
98
NG
RB
0803
2522
0.02
198.
7137
9.57
0.82
2.01
1.00
00N
GR
B08
0325
175.
5916
3.52
175.
590.
070.
430.
8691
NG
RB
0804
0944
1.94
342.
7556
15.3
911
.93
0.92
0.77
22
NG
RB
0804
2665
3.06
572.
1173
6.85
0.25
0.72
0.93
87
YG
RB
0805
0648
0.47
366.
3356
52.4
011
.00
43.6
91.
0000
NG
RB
0805
0617
4.65
160.
3720
7.62
0.27
1.07
0.78
26
NG
RB
0805
1646
3.15
356.
7357
2.61
0.47
0.89
0.70
85
NG
RB
0805
1713
1.45
131.
4556
5.45
3.30
18.5
80.
9385
NG
RB
0806
0290
6.16
890.
4792
2.79
0.04
1.53
0.60
63
Con
tinued
onN
ext
Pag
e...
63
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0806
041.
4297
2.20
896.
4410
65.0
40.
170.
850.
3884
NG
RB
0806
073.
0412
3.97
117.
3520
9.98
0.75
5.45
1.00
00
NG
RB
0807
0338
0.77
306.
9542
0.32
0.30
0.66
0.61
19N
GR
B08
0703
217.
3418
9.30
306.
950.
540.
530.
4867
NG
RB
0807
100.
8534
67.7
433
14.7
347
16.9
90.
400.
580.
5107
NG
RB
0807
1416
5.06
143.
5317
0.17
0.16
1.30
0.45
06
NG
RB
0807
23A
160.
3013
3.13
193.
330.
380.
690.
9053
NG
RB
0807
27A
317.
8224
3.40
426.
370.
580.
930.
9880
NG
RB
0808
0294
.21
86.4
310
4.05
0.19
2.80
1.00
00
NG
RB
0808
042.
211
7.49
114.
2412
1.16
0.06
0.50
0.72
53N
GR
B08
0804
137.
4713
3.67
145.
290.
080.
330.
5335
YG
RB
0808
051.
5112
0.25
89.9
022
4.96
1.12
4.70
1.00
00
NG
RB
0808
103.
3510
3.46
88.2
913
2.09
0.42
4.54
1.00
00Y
GR
B08
0810
208.
0018
7.38
335.
210.
715.
381.
0000
NG
RB
0809
05A
0.12
1825
6.22
200.
9231
0.51
0.43
0.81
0.78
08
NG
RB
0809
0618
0.59
160.
8525
7.76
0.54
2.17
1.00
00N
GR
B08
0906
577.
7655
2.98
709.
400.
271.
070.
8932
Con
tinued
onN
ext
Pag
e...
64
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0809
136.
718
63.8
198
4.59
8580
.70
4.08
6.46
0.99
97N
GR
B08
0913
485.
1730
5.21
608.
290.
621.
240.
7351
NG
RB
0809
16A
0.68
992
.22
91.4
297
.82
0.07
0.74
0.79
20
NG
RB
0809
1928
5.07
206.
6371
1.80
1.77
5.82
0.99
84
NG
RB
0809
281.
6920
6.76
176.
2726
9.13
0.45
3.94
1.00
00N
GR
B08
0928
349.
6334
3.42
400.
610.
162.
071.
0000
NG
RB
0810
081.
967
301.
4428
4.17
403.
080.
395.
901.
0000
YG
RB
0810
0817
1.82
126.
2223
7.45
0.65
2.05
0.74
15
NG
RB
0810
1111
3.45
113.
4520
8.35
0.84
5.85
1.00
00N
GR
B08
1011
5270
4.36
4431
1.60
7294
9.15
0.54
1.03
0.68
49
NG
RB
0810
24A
168.
5212
9.46
254.
250.
7413
.52
0.93
30
NG
RB
0811
0295
4.84
876.
4657
96.5
25.
1530
.54
1.00
00
NG
RB
0811
2136
45.3
834
42.1
539
13.0
20.
130.
970.
5174
NG
RB
0811
2832
368.
0814
915.
6972
762.
531.
791.
800.
4221
YG
RB
0812
1014
1.11
111.
5424
9.65
0.98
8.48
1.00
00N
GR
B08
1210
316.
9528
2.45
471.
490.
601.
780.
8943
NG
RB
0901
1147
4.40
174.
3812
01.4
22.
1620
.85
1.00
00
Con
tinued
onN
ext
Pag
e...
65
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0901
2317
81.9
514
52.2
919
12.6
90.
261.
150.
7904
NG
RB
0901
2348
3.95
416.
2966
7.62
0.52
1.35
0.43
20
NG
RB
0903
0947
41.2
043
52.0
616
512.
022.
560.
890.
6757
NG
RB
0903
28A
0.73
693
405.
5563
169.
3898
447.
090.
381.
240.
5401
YG
RB
0904
0713
4.67
111.
1074
6.38
4.72
12.4
11.
0000
NG
RB
0904
17B
1507
.40
1244
.48
5401
.39
2.76
11.9
11.
0000
NG
RB
0904
18A
1.60
815
7.92
152.
7417
2.02
0.12
0.31
0.35
74
YG
RB
0904
1932
1.96
265.
9610
15.3
92.
334.
180.
9837
NG
RB
0904
2296
.73
73.8
512
0.62
0.48
0.82
0.98
81
NG
RB
0904
238.
217
4.42
136.
9027
3.99
0.79
13.2
21.
0000
NG
RB
0904
262.
609
296.
2020
0.23
417.
240.
730.
600.
6446
NG
RB
0904
29A
169.
0515
6.27
209.
160.
312.
770.
9287
NG
RB
0904
29A
101.
2488
.71
117.
800.
290.
840.
7504
NG
RB
0904
29A
130.
1712
0.73
138.
180.
130.
750.
6688
NG
RB
0904
29A
252.
3124
1.35
3766
9.76
148.
341.
230.
5717
NG
RB
0904
29B
626.
0429
0.50
1554
2.75
24.3
63.
860.
9746
NG
RB
0905
1515
9.26
79.5
128
8.97
1.32
16.0
01.
0000
Con
tinued
onN
ext
Pag
e...
66
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0905
164.
109
274.
0026
7.27
282.
370.
065.
951.
0000
NG
RB
0905
1620
4.58
201.
1620
7.78
0.03
1.33
0.24
87
NG
RB
0905
193.
8522
1.48
203.
8724
2.48
0.17
1.27
0.87
10
NG
RB
0905
292.
625
1378
5.24
2778
5.00
1489
37.1
18.
790.
210.
8682
NG
RB
0905
301.
266
263.
9719
2.74
303.
820.
420.
710.
8561
NG
RB
0906
0711
9.71
96.3
054
9.87
3.79
7.91
1.00
00
NG
RB
0906
21A
268.
1615
3.69
795.
782.
3955
2.54
1.00
00
NG
RB
0906
2814
599.
1335
22.2
842
257.
782.
654.
210.
7659
NG
RB
0907
09A
1.8
88.7
179
.38
105.
820.
303.
101.
0000
NG
RB
0907
09A
399.
7836
6.96
466.
430.
250.
910.
8495
NG
RB
0907
09A
281.
8324
8.49
307.
030.
210.
650.
6830
YG
RB
0907
15B
328
9.92
59.3
336
3.63
1.05
30.3
11.
0000
NG
RB
0907
2726
9.62
131.
6340
78.6
514
.64
109.
211.
0000
NG
RB
0907
2717
1920
.17
1136
99.9
328
5295
.30
1.00
1.43
0.62
79
NG
RB
0907
2822
7.44
194.
0631
5.61
0.53
0.80
0.49
78
NG
RB
0908
092.
737
178.
6117
0.45
3512
.68
18.7
115
.04
1.00
00N
GR
B09
0809
4702
.60
3628
.26
9240
.61
1.19
8.73
1.00
00N
GR
B09
0809
2279
9.20
1145
9.20
3100
7.17
0.86
1.05
0.68
37
Con
tinued
onN
ext
Pag
e...
67
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0908
122.
452
137.
7710
2.78
199.
200.
700.
660.
9197
NG
RB
0908
1225
7.63
246.
3831
8.82
0.28
1.78
0.89
79
NG
RB
0908
31C
182.
2815
5.56
296.
960.
787.
050.
9134
NG
RB
0908
31C
431.
8037
1.25
617.
500.
572.
380.
7988
NG
RB
0909
02B
1.82
243
6259
.21
3387
70.6
670
3452
.43
0.84
1.32
0.55
44
NG
RB
0909
04A
300.
0128
8.54
358.
190.
232.
760.
9685
NG
RB
0909
04A
6758
.74
6107
.89
1053
2.16
0.65
0.93
0.39
39
NG
RB
0909
04B
120.
5112
0.51
145.
200.
203.
380.
9745
NG
RB
0909
04B
903.
8080
3.70
967.
610.
181.
000.
5399
NG
RB
0909
1278
1.36
781.
3685
0.68
0.09
2.26
0.84
77
NG
RB
0909
26A
2.10
6246
846.
7346
677.
9851
695.
210.
110.
780.
5713
NG
RB
0909
26A
2030
29.1
119
3054
.42
2323
75.7
30.
190.
890.
3281
NG
RB
0909
26A
8611
6.04
8126
6.45
1444
10.2
40.
731.
710.
2109
NG
RB
0909
271.
3722
29.0
922
29.0
926
49.0
60.
190.
870.
9198
YG
RB
0909
29B
149.
5881
.59
3453
.39
22.5
413
.26
1.00
00
NG
RB
0910
241.
092
5145
.00
4606
.70
3201
9.65
5.33
1.63
0.92
04N
GR
B09
1024
3207
.78
3207
.78
3395
.99
0.06
1.92
0.78
46
Con
tinued
onN
ext
Pag
e...
68
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
0910
2634
1.14
288.
8954
5.75
0.75
6.52
0.99
32N
GR
B09
1026
877.
1161
8.25
5557
.31
5.63
3.06
0.72
91N
GR
B09
1026
173.
0415
8.18
222.
060.
371.
200.
5386
NG
RB
0910
292.
752
323.
6023
3.28
601.
561.
148.
670.
8354
NG
RB
0911
0420
3.85
191.
1125
0.03
0.29
1.52
0.87
65
NG
RB
0911
09A
3.07
624
8.34
227.
2727
8.06
0.20
0.71
0.60
50
NG
RB
0911
30B
99.9
283
.85
171.
670.
883.
150.
9167
NG
RB
0912
08B
1.06
310
1.40
101.
4014
4.38
0.42
0.93
0.84
09
NG
RB
0912
2110
6.33
87.6
419
6.18
1.02
10.9
10.
7838
NG
RB
0912
2162
.99
62.9
987
.64
0.39
5.96
0.77
21
NG
RB
1001
11A
951.
3281
7.28
4644
.77
4.02
0.80
0.93
11
NG
RB
1001
17A
0.92
181.
6015
0.75
470.
161.
762.
350.
7065
YG
RB
1002
12A
120.
4364
.70
459.
253.
2821
.32
1.00
00N
GR
B10
0212
A66
8.35
610.
3379
5.63
0.28
12.2
90.
7407
NG
RB
1002
19A
4.66
6717
800.
4413
234.
1218
999.
620.
320.
980.
7968
YG
RB
1003
02A
4.81
325
0.31
225.
1478
0.53
2.22
13.3
21.
0000
NG
RB
1003
02A
134.
4812
3.44
150.
190.
201.
510.
8935
NG
RB
1003
02A
188.
3117
4.49
201.
330.
141.
400.
7201
Con
tinued
onN
ext
Pag
e...
69
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1003
16B
1.18
1064
.41
395.
1637
185.
7134
.56
2.82
0.96
65
NG
RB
1003
16C
261.
0118
8.34
574.
541.
481.
140.
9899
NG
RB
1004
13A
149.
9113
8.19
160.
530.
150.
900.
7837
NG
RB
1004
13A
278.
4425
0.86
289.
210.
141.
050.
7793
NG
RB
1004
13A
222.
4819
2.98
234.
850.
190.
830.
5932
NG
RB
1004
25A
1.75
570
.97
69.8
585
.61
0.22
2.54
0.82
57N
GR
B10
0425
A48
2.86
347.
5761
0.09
0.54
0.95
0.51
49
NG
RB
1005
04A
52.9
652
.96
69.4
30.
3110
.39
1.00
00N
GR
B10
0504
A81
.58
74.9
511
7.28
0.52
1.02
0.86
52
NG
RB
1005
13A
4.77
221
3.64
163.
4369
8.32
2.50
5.83
0.90
78
NG
RB
1005
22A
2021
.97
1703
.73
5996
.03
2.12
0.46
0.47
85
NG
RB
1005
26A
183.
9516
8.61
259.
300.
491.
800.
9893
NG
RB
1006
14A
161.
9215
4.70
180.
640.
160.
630.
9164
NG
RB
1006
14A
957.
8289
8.59
1163
.40
0.28
0.76
0.58
11
NG
RB
1006
19A
941.
5386
2.01
5001
.70
4.40
71.4
11.
0000
NG
RB
1006
19A
88.3
772
.86
123.
360.
576.
760.
9822
NG
RB
1006
21A
0.54
265
.92
65.9
269
.85
0.06
3.53
0.98
05
NG
RB
1006
25A
191.
4813
4.47
326.
501.
000.
690.
5371
Con
tinued
onN
ext
Pag
e...
70
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1007
02A
361.
0523
7.42
442.
050.
571.
190.
3849
YG
RB
1007
04A
173.
5414
5.30
348.
811.
1716
.89
0.97
34
NG
RB
1007
25A
69.1
869
.18
73.5
50.
062.
040.
7670
YG
RB
1007
25B
217.
5411
4.22
369.
851.
1856
.43
0.78
92
NG
RB
1007
27A
243.
3716
3.06
669.
582.
0863
.09
1.00
00
NG
RB
1007
28A
1.56
757
4.10
512.
6465
4.75
0.25
6.75
0.88
12N
GR
B10
0728
A31
7.33
298.
0338
0.33
0.26
4.43
0.81
21N
GR
B10
0728
A70
1.40
673.
3188
6.50
0.30
2.50
0.77
56N
GR
B10
0728
A12
3.41
109.
4013
7.56
0.23
0.93
0.71
11N
GR
B10
0728
A39
2.83
380.
3341
5.01
0.09
3.55
0.51
52N
GR
B10
0728
A22
1.84
197.
9824
7.34
0.22
1.01
0.50
01N
GR
B10
0728
A88
.39
82.8
910
0.06
0.19
0.48
0.36
98N
GR
B10
0728
A46
2.31
448.
4449
8.57
0.11
1.14
0.27
46N
GR
B10
0728
A26
9.42
251.
7729
2.42
0.15
0.88
0.21
22
NG
RB
1007
28B
2.10
610
4.13
88.3
714
4.33
0.54
0.65
0.63
30
NG
RB
1008
02A
478.
0227
4.48
4633
.13
9.12
47.2
91.
0000
NG
RB
1008
02A
3339
2.37
2913
2.41
4037
3.93
0.34
1.55
0.44
87
NG
RB
1008
05A
636.
2942
3.70
4348
.88
6.17
23.0
61.
0000
NG
RB
1008
07A
88.3
577
.18
262.
372.
1027
.40
1.00
00
Con
tinued
onN
ext
Pag
e...
71
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1008
14A
1.44
147.
0011
9.46
357.
381.
622.
180.
9918
NG
RB
1008
14A
1393
11.6
069
791.
0737
4420
.00
2.19
1.81
0.65
27
NG
RB
1008
16A
0.80
4973
.82
73.8
291
.72
0.24
1.05
0.86
00N
GR
B10
0816
A13
9.65
125.
0921
1.06
0.62
1.24
0.85
62
NG
RB
1008
23A
4748
.51
4398
.85
5317
.38
0.19
2.07
0.47
37
YG
RB
1009
01A
1.40
839
9.18
132.
5238
51.9
99.
3242
.59
1.00
00N
GR
B10
0901
A28
505.
8112
080.
0867
586.
831.
951.
680.
8896
NG
RB
1009
02A
411.
0235
5.83
634.
690.
6813
1.92
1.00
00N
GR
B10
0902
A20
15.8
318
46.2
221
94.7
80.
171.
090.
5733
YG
RB
1009
05A
319.
4616
1.44
563.
721.
2647
.64
1.00
00N
GR
B10
0905
A54
12.1
618
50.2
772
00.8
10.
991.
130.
5858
NG
RB
1009
05A
1683
.70
1535
.22
1850
.70
0.19
0.95
0.42
21
NG
RB
1009
06A
1.72
711
7.90
86.1
519
9.41
0.96
23.1
61.
0000
NG
RB
1009
15A
157.
8415
3.95
166.
300.
080.
340.
6480
NG
RB
1009
15A
191.
0117
9.20
194.
340.
080.
780.
3489
NG
RB
1010
11A
120.
1010
8.08
143.
440.
290.
650.
6533
NG
RB
1010
11A
241.
3721
5.77
296.
950.
340.
980.
4961
NG
RB
1010
17A
849.
8567
9.06
1058
.20
0.45
0.60
0.54
88N
GR
B10
1017
A18
1.22
173.
9319
3.02
0.11
0.71
0.33
20
Con
tinued
onN
ext
Pag
e...
72
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1010
23A
75.2
575
.25
77.6
30.
038.
140.
9456
NG
RB
1010
24A
513.
9048
2.84
576.
600.
180.
330.
3508
NG
RB
1010
30A
86.6
884
.33
89.9
60.
060.
260.
4242
NG
RB
1011
17B
184.
2216
1.53
244.
900.
450.
440.
6498
NG
RB
1011
17B
266.
0624
4.90
312.
120.
250.
800.
5989
NG
RB
1012
04A
3161
64.0
329
0600
.72
3347
43.3
40.
140.
880.
3346
NG
RB
1012
13A
95.3
495
.34
98.2
70.
030.
450.
5303
NG
RB
1012
13A
6334
3.55
3488
3.14
8022
9.22
0.72
1.36
0.52
22
NG
RB
1012
19A
0.71
817
0.16
84.2
527
0.53
1.09
7.92
0.95
01
NG
RB
1012
19B
327.
6630
0.05
554.
060.
780.
940.
6871
NG
RB
1012
25A
2259
0.84
1074
0.74
5660
8.60
2.03
34.2
80.
8784
NG
RB
1012
25A
6108
.55
4988
.46
7477
.77
0.41
5.03
0.77
67
YG
RB
1101
02A
263.
1819
3.02
443.
520.
9538
.17
1.00
00N
GR
B11
0102
A13
9.57
139.
5717
8.35
0.28
16.6
41.
0000
NG
RB
1101
06B
829.
5958
3.60
1111
.41
0.64
0.62
0.75
93
NG
RB
1101
12A
752.
3460
1.82
4917
.12
5.74
0.89
0.99
22N
GR
B11
0112
A26
8.00
186.
6544
7.82
0.97
0.65
0.81
04
Con
tinued
onN
ext
Pag
e...
73
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1101
19A
197.
0916
4.64
305.
240.
710.
110.
9121
NG
RB
1101
19A
48.5
348
.53
68.5
60.
411.
690.
8997
NG
RB
1101
19A
127.
4299
.59
147.
520.
382.
030.
8311
NG
RB
1101
19A
657.
9153
3.00
4942
.73
6.70
6.81
0.79
89N
GR
B11
0119
A38
5.41
364.
5444
1.68
0.20
2.36
0.56
54
NG
RB
1101
28A
2.33
912
9.73
129.
7331
5.19
1.43
2.02
0.99
91N
GR
B11
0128
A17
1625
.12
8337
7.92
2174
45.3
30.
781.
120.
5554
NG
RB
1102
01A
148.
3411
0.01
308.
081.
342.
190.
7542
NG
RB
1102
05A
2.22
615.
5659
5.33
716.
930.
201.
990.
8407
NG
RB
1102
05A
8284
0.56
7612
4.31
1187
78.5
40.
510.
810.
2399
NG
RB
1102
08A
68.6
268
.62
143.
901.
102.
960.
9999
NG
RB
1102
08A
844.
8161
7.34
5677
.35
5.99
0.71
0.71
11
NG
RB
1102
13A
1.46
98.7
887
.04
103.
590.
170.
750.
4149
NG
RB
1102
23A
275.
0618
8.23
353.
460.
600.
800.
7730
NG
RB
1102
23B
65.1
558
.32
77.6
30.
301.
720.
8741
NG
RB
1102
23B
1173
.23
1075
.00
1235
.58
0.14
1.18
0.64
55
NG
RB
1103
05A
358.
9725
3.95
638.
551.
071.
050.
5774
Con
tinued
onN
ext
Pag
e...
74
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1103
12A
154.
0014
8.94
168.
460.
131.
130.
9126
NG
RB
1103
12A
423.
5632
2.33
529.
200.
490.
770.
7002
NG
RB
1103
12A
737.
8864
6.25
808.
110.
220.
530.
3664
NG
RB
1103
12A
2167
73.8
614
1370
.86
3633
58.2
71.
020.
920.
2426
NG
RB
1103
15A
514.
7541
1.47
3796
.30
6.58
8.86
0.99
69
NG
RB
1103
18B
140.
0511
0.67
275.
631.
181.
980.
9708
NG
RB
1103
19A
65.9
662
.89
67.8
50.
080.
370.
3692
NG
RB
1104
07A
436.
3440
1.55
802.
430.
923.
281.
0000
NG
RB
1104
07A
4967
.67
4448
.41
5294
.80
0.17
1.33
0.44
89
NG
RB
1104
14A
385.
1027
5.54
648.
810.
977.
050.
8878
NG
RB
1104
14A
155.
6913
9.68
172.
830.
210.
800.
6283
NG
RB
1105
20A
258.
1614
6.39
494.
651.
356.
610.
9241
NG
RB
1105
20A
625.
8849
4.65
737.
500.
390.
960.
7595
NG
RB
1105
21A
184.
2321
5.74
524.
901.
680.
430.
7281
NG
RB
1105
30A
7344
.57
2560
.24
1354
2.38
1.50
0.57
0.75
48N
GR
B11
0530
A13
41.8
110
09.0
417
18.7
70.
531.
250.
6712
NG
RB
1106
10A
217.
9817
9.12
291.
110.
511.
110.
7112
NG
RB
1106
10A
653.
1461
4.80
811.
510.
301.
830.
6782
NG
RB
1106
10A
1999
25.9
911
9058
.16
2987
60.9
50.
901.
340.
6189
Con
tinued
onN
ext
Pag
e...
75
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1106
25A
726.
7768
5.98
829.
530.
200.
770.
4342
NG
RB
1107
09A
56.1
256
.12
75.1
60.
341.
661.
0000
NG
RB
1107
09A
91.5
587
.76
109.
090.
230.
960.
6242
YG
RB
1107
09B
650.
1541
7.88
1522
.12
1.70
37.9
11.
0000
NG
RB
1107
09B
70.7
270
.72
112.
030.
584.
060.
7481
NG
RB
1107
09B
157.
6713
3.39
256.
110.
780.
760.
7203
NG
RB
1107
15A
0.82
5016
5.92
3504
9.31
2572
77.3
64.
432.
920.
5119
NG
RB
1107
26A
398.
0935
4.92
492.
300.
351.
160.
9631
NG
RB
1107
26A
52.7
448
.97
117.
521.
300.
420.
9532
NG
RB
1108
01A
1.85
838
2.04
322.
0177
4.21
1.18
77.0
41.
0000
NG
RB
1108
01A
213.
1817
6.15
261.
790.
402.
210.
6649
NG
RB
1108
20A
269.
3014
2.11
558.
351.
5510
72.5
51.
0000
NG
RB
1109
15A
161.
6714
8.71
216.
960.
421.
410.
7723
NG
RB
1109
21A
224.
2015
5.43
403.
301.
113.
710.
7655
NG
RB
1109
21A
526.
1540
3.30
830.
050.
815.
920.
6207
NG
RB
1109
21A
1285
.70
1182
.23
1346
.57
0.13
0.93
0.37
62
YG
RB
1110
16A
610.
6238
7.58
4950
.64
7.47
119.
781.
0000
NG
RB
1110
18A
118.
3011
8.30
191.
880.
627.
100.
9997
Con
tinued
onN
ext
Pag
e...
76
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1110
20A
904.
7455
7.83
1204
.88
0.72
1.05
0.67
95N
GR
B11
1020
A34
831.
6125
977.
8052
426.
190.
761.
220.
5243
NG
RB
1110
22B
455.
8041
0.88
521.
260.
240.
630.
5284
YG
RB
1111
03B
115.
8811
0.88
4672
.68
39.3
730
.10
1.00
00
NG
RB
1111
07A
2.89
333
2.37
91.6
758
7.32
1.49
6.95
0.69
13
NG
RB
1111
17A
150.
1610
7.95
247.
290.
930.
590.
7561
NG
RB
1111
23A
487.
9046
6.14
656.
270.
391.
910.
9799
NG
RB
1111
23A
285.
3726
7.58
300.
850.
120.
500.
5189
NG
RB
1111
23A
146.
2113
9.44
157.
620.
120.
340.
4287
NG
RB
1111
29A
254.
0319
4.19
357.
280.
640.
560.
6207
NG
RB
1201
02A
1074
.69
937.
1310
435.
958.
8413
.79
0.96
22
NG
RB
1201
21A
108.
0310
8.03
154.
600.
434.
910.
9966
NG
RB
1201
21A
1451
.90
928.
7264
99.6
53.
840.
960.
5121
NG
RB
1202
13A
5511
.00
957.
6211
236.
181.
872.
520.
8825
NG
RB
1202
24A
99.1
499
.14
194.
320.
9630
.91
0.99
96N
GR
B12
0224
A11
16.5
458
2.13
5248
.08
4.18
1.94
0.89
22
NG
RB
1203
05A
117.
9686
.36
310.
191.
902.
150.
9957
Con
tinued
onN
ext
Pag
e...
77
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
YG
RB
1203
08A
123.
6811
1.40
316.
021.
656.
911.
0000
NG
RB
1203
08A
2386
.69
1932
.85
5891
.78
1.66
0.63
0.49
88
NG
RB
1203
11A
6671
6.90
3309
2.84
1047
85.2
61.
070.
890.
9656
NG
RB
1203
12A
90.9
190
.91
132.
310.
462.
010.
9973
NG
RB
1203
20A
161.
2216
1.22
312.
330.
9452
.97
0.99
95N
GR
B12
0320
A41
696.
1116
636.
8113
9911
.52
2.96
3.10
0.57
23
NG
RB
1203
24A
102.
8499
.97
120.
890.
201.
090.
8069
NG
RB
1203
26A
1.79
840
264.
8917
496.
2368
368.
091.
262.
540.
7154
NG
RB
1203
27A
2.81
931.
1685
6.83
963.
570.
110.
790.
3666
NG
RB
1203
28A
63.4
563
.45
88.0
40.
393.
620.
9258
NG
RB
1203
28A
123.
1988
.04
232.
501.
179.
990.
9121
NG
RB
1203
28A
551.
9936
6.34
783.
080.
751.
670.
6212
NG
RB
1204
01A
239.
1619
6.14
350.
840.
650.
820.
6788
NG
RB
1204
01A
105.
5510
5.55
107.
950.
020.
780.
4007
NG
RB
1205
14A
142.
8012
6.64
471.
162.
4113
.47
0.99
98N
GR
B12
0514
A64
3.81
471.
1644
97.9
46.
257.
070.
6668
NG
RB
1205
21A
216.
6498
.67
325.
921.
051.
770.
9789
NG
RB
1205
21B
6380
.21
5604
.57
7181
.97
0.25
1.81
0.33
65
Con
tinued
onN
ext
Pag
e...
78
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1206
12A
4956
.31
1337
.61
1730
1.26
3.22
8.38
0.92
24N
GR
B12
0612
A18
1.49
171.
1719
3.16
0.12
1.57
0.51
48
NG
RB
1207
01A
305.
1627
3.31
459.
200.
611.
210.
8231
NG
RB
1207
01A
634.
4853
8.54
6076
.92
8.73
0.83
0.58
57
NG
RB
1207
03A
72.5
472
.54
92.4
60.
271.
700.
9290
NG
RB
1207
03A
177.
4915
9.99
193.
410.
190.
840.
6880
NG
RB
1207
03A
232.
2421
4.10
252.
480.
170.
840.
3913
NG
RB
1207
11B
805.
1544
3.94
892.
780.
562.
780.
9424
NG
RB
1207
11B
357.
8034
1.53
417.
470.
210.
930.
6084
NG
RB
1207
12A
4.17
4512
6970
.53
6763
3.74
4625
12.4
43.
112.
600.
7872
NG
RB
1207
14A
2983
2.97
2193
8.09
4277
7.41
0.70
0.59
0.35
89
NG
RB
1207
22A
300.
5821
7.42
558.
651.
143.
590.
8054
NG
RB
1207
22A
141.
6014
1.60
217.
420.
546.
660.
7907
NG
RB
1207
24A
1.48
119.
9511
7.16
129.
340.
100.
430.
5839
NG
RB
1207
28A
136.
6213
6.62
236.
800.
7315
.00
0.99
62N
GR
B12
0728
A54
8.01
357.
7310
61.7
31.
2818
.40
0.80
91
NG
RB
1207
29A
513.
2244
2.45
565.
390.
240.
520.
5557
NG
RB
1207
29A
95.5
890
.39
97.6
00.
080.
680.
5227
NG
RB
1208
04A
82.8
282
.82
104.
290.
261.
130.
9142
NG
RB
1208
04A
289.
8226
0.75
418.
230.
540.
860.
6700
Con
tinued
onN
ext
Pag
e...
79
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1208
07A
115.
4710
1.13
221.
151.
046.
930.
9920
NG
RB
1208
16A
210.
7217
2.29
257.
860.
410.
890.
6112
NG
RB
1208
16A
497.
4738
3.06
580.
380.
400.
870.
3832
NG
RB
1209
07A
0.97
175.
1912
1.88
311.
061.
080.
480.
6776
NG
RB
1209
11A
4752
.70
4548
.38
5063
.46
0.11
1.10
0.79
67
NG
RB
1209
22A
324.
6630
5.30
349.
920.
141.
560.
5833
NG
RB
1209
22A
411.
6736
1.28
490.
650.
313.
350.
2708
NG
RB
1210
01A
373.
9533
5.69
421.
890.
230.
810.
4449
NG
RB
1210
11A
4044
.76
3792
.69
4241
.53
0.11
1.42
0.33
71N
GR
B12
1011
A45
05.0
242
41.5
347
47.3
70.
111.
480.
3131
NG
RB
1210
24A
2.29
820
5.13
182.
8724
7.53
0.32
0.31
0.93
36N
GR
B12
1024
A27
7.11
247.
5335
2.16
0.38
2.08
0.69
50
NG
RB
1210
27A
1.77
360
74.9
011
50.7
235
420.
685.
6444
2.82
0.98
53N
GR
B12
1027
A24
7.49
221.
0752
1.32
1.21
3.40
0.81
34
NG
RB
1210
28A
765.
2362
0.09
1257
.88
0.83
9.71
0.82
83
NG
RB
1211
02A
56.9
654
.23
61.3
20.
120.
510.
7088
NG
RB
1211
08A
139.
6610
4.34
503.
562.
8611
3.53
1.00
00N
GR
B12
1108
A62
3.81
751.
6282
3.91
0.27
0.38
0.43
41
Con
tinued
onN
ext
Pag
e...
80
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1211
17A
83.1
776
.32
104.
760.
340.
400.
5248
NG
RB
1211
23A
244.
2219
0.70
917.
742.
9818
.76
1.00
00
NG
RB
1211
25A
91.8
988
.06
122.
540.
381.
600.
9352
NG
RB
1211
28A
2.2
91.3
588
.11
127.
720.
430.
670.
8100
NG
RB
1212
09A
80.2
980
.29
133.
720.
678.
880.
9983
NG
RB
1212
11A
1.02
317
5.84
124.
5129
4.51
0.97
9.78
1.00
00N
GR
B12
1211
A96
.63
85.8
810
5.46
0.20
1.25
0.56
86
NG
RB
1212
12A
221.
0913
1.29
494.
361.
6416
.57
0.99
99N
GR
B12
1212
A57
7.29
494.
3693
9.07
0.77
17.1
40.
8500
NG
RB
1212
12A
58.4
858
.48
131.
291.
253.
960.
6032
NG
RB
1212
17A
736.
1622
2.19
1625
.91
1.91
165.
871.
0000
NG
RB
1212
26A
197.
7414
0.95
275.
390.
681.
300.
8769
Con
tinued
onN
ext
Pag
e...
81
Tab
le4.
1–
Con
tinued
Fla
ring
Peri
od
Sourc
eN
am
ez
Tpeak
2,3
Tsta
rt
l.l.
2,3
Tsto
pu.l
.2,3
∆t/
tF
lux
Rati
oC
on
fid
en
ce
(s)
(s)
(s)
low
er
lim
it
NG
RB
1212
29A
2.70
745
8.62
344.
7651
73.3
910
.53
35.2
71.
0000
NG
RB
1212
29A
232.
4821
6.72
261.
150.
190.
510.
4989
2O
ur
anal
ysi
sid
enti
fies
asp
ecifi
cd
ata
poi
nt
inth
eli
ght
curv
eas
bei
ng
ass
oci
ate
dw
ith
thes
equ
anti
ties
.T
he
larg
enu
mb
erof
dig
its
rep
orte
dfo
rTpeak,Tsta
rt
andTstop
are
not
refl
ecti
veof
ou
rco
nfi
den
cein
thei
rd
eter
min
ati
on
,b
ut
are
rath
erth
eti
mes
tam
pass
oci
ate
dw
ith
the
dat
ap
oint
iden
tifi
ed.
We
hav
ech
osen
not
toro
un
dth
ese
valu
esfo
rtw
ore
aso
ns:
1)
any
rou
nd
ing
dec
isio
nw
em
ake
wou
ldb
earb
itra
ry,
and
2)th
ere
lati
veeff
ect
ofth
ero
un
din
gon
each
valu
ew
ou
ldd
iffer
dep
end
ing
on
the
size
of
the
valu
e.T
his
als
op
reve
nts
the
intr
od
uct
ion
ofan
arbit
rary
bia
sto
the
dat
a.3A
llti
mes
are
rela
tive
toth
eti
me
ofth
ein
itia
lb
urs
ttr
igger
.∆t/t
isca
lcu
late
das
(Tstop−Tsta
rt)/Tpeak.Tsta
rt
an
dTstop
are
low
eran
du
pp
erli
mit
s,re
spec
tive
ly.
Flu
xR
atio
isca
lcu
late
das
the
flu
xat
the
flare
pea
kti
me
div
ided
by
the
extr
ap
olate
dfl
ux
of
the
un
der
lyin
gli
ght
curv
eat
the
sam
eti
me,
nor
mal
ized
usi
ng
the
flu
xof
the
un
der
lyin
gli
ght
curv
e,an
dis
alo
wer
lim
itof
the
act
ual
pea
kfl
ux
rati
o.
Th
eco
nfi
den
cem
easu
rere
pre
sents
the
frac
tion
ofti
mes
the
flare
was
iden
tifi
edd
uri
ng
the
10,0
00
Monte
Carl
osi
mu
lati
on
s.T
he
firs
tco
lum
nid
enti
fies
whet
her
the
iden
tifi
edfe
atu
reco
mes
from
an
over
lap
pin
g‘fl
ari
ng
per
iod
’.
82
4.3 Discussion
Our analysis shows that at least 47% of the analyzed XRT light curves contain
possible flaring episodes. This percentage is very similar to previous studies (e.g.,
O’Brien et al. 2006; Chincarini et al. 2010), in spite of our detection of a signifi-
cantly larger number of total flares and specifically a larger number of small, weak
flares. This may indicate that X-ray GRB afterglows comes in two varieties: those
with flares and those without.
In our analysis of the bulk properties of the detected X-ray flares we have
followed the same method used in Swenson et al. (2013) and divided the flares
into three groups: “gold”, “silver” and “bronze”. Our comparisons to UV/optical
flares will also come from our analysis found in Swenson et al. (2013).
The gold group is defined as those flares with confidence measure greater than
0.7 and ∆t/t ≤ 0.5. This group constitutes those flares which satisfy the somewhat
“classical” definition of a flare in terms of duration and have a good recoverability
rate. This group contains 127 flares. The silver group allows for longer flares and
lower confidence, expanding the parameters to confidence measure greater than 0.6
and ∆t/t ≤ 1.0. This group contains 115 flares after excluding overlap from the
gold group. The remaining flares that do not qualify for either the gold or silver
are grouped together in the bronze, which contains 256 flares.
Of the 326 X-ray light curves with flares, the average number of flares per GRB
is ∼1.5. Figure 4.1 shows the distribution of flares per GRB for the gold, silver and
bronze groups, shown in black, blue, and red, respectively. GRB 100728A had the
most resolved flares of the analyzed bursts, with nine, and five other GRB light
curves had five or more flares.
The flare peak times range from between 48 s after the trigger of GRB 110119A
to over 400 ks for GRB 090902B. 82% of all detected flares peaked before 1000 s,
83
1 2 3 4Number of Flares byDistribution
0
50
100
150
200
NumberofGRBs
1 2 3 4 5 6 7 8 9Number of Flares per Burst
Figure 4.1 Histograms of the number of detected flares per GRB, shown as thenumber of flares per GRB by distribution (left panel), with the three distributionsbeing the gold (black shading), silver (blue shading) and bronze (red shading)groups described in the text. Also shown is the overall distribution of flares perGRB (right panel).
84
Time since Trigger (s)
NumberofGRBs
05
10
15
20
25
05
10
15
20
25
101 102 103 104 105 106 10705
10
15
20
25
Figure 4.2 Histogram of the distribution of Tpeak. The three distributions are thegold (top), silver (middle) and bronze (bottom) distributions described in the text.
nearly matching the percentage seen in the UV/optical light curves. We suspect
that this similarity to the UV/optical flares is not coincidental and that many of
these flares may be correlated, or at the very least caused by a similar mechanism
that is active during the early stages of the GRB. This issue will be looked at in
depth in our next paper correlating the UV/optical and X-ray flares. Figure 4.2
shows the distribution of Tpeak for the three groups of flares. The grouping of
Tpeak ≤ 1000 s is immediately obvious in all three groups, and all three groups
appear to originate from a similar parent distribution peaking between 300 s and
500 s after the trigger.
The duration of the flares, recognizing that a number of the Tstart and Tstop
values are only limits, vary from ∆t/t of 0.02 to over 100 (though the extremely
large values are due to observing gaps in the data). Only ∼50% of the flares
exhibited ∆t/t ≤ 0.5, whereas this number was at least 80% for the UV/optical
85
flares. This difference between the duration of the X-ray and UV/optical flares
may be due to the UV/optical flares being generally fainter than those seen in the
X-ray. If we only see the peak of the flare in the UV/optical, then our measured
duration for the flare will be biased relative to the X-ray where we see more of
the flare rise and decay. Figure 4.3 shows the distribution of ∆t/t for the three
groups of flares. Ioka et al. (2005) showed that it is difficult to achieve rapid
variability, defined as ∆t/t ≤ 1, in the external shock and so an internal shock
model has been favored to explain the ∆t/t � 1 seen in most flares. However,
Figure 4.3 shows a significant number of possible flares that exhibit ∆t/t > 1.
For this work we are reporting all potential features detected by our flare finding
algorithm, and we treat them as potential flares. It is possible, however, that
a portion of our detected features, in particular those with ∆t/t ≥ 1, are due to
other processes, such as the emergence of the reverse shock, and are not flares. It is
also possible that these are flares caused by processes other than internal shocks.
An interesting relationship between the gold, silver and bronze groups needs to
be pointed out when interpreting Figure 4.3. There is a continuous distribution
of potential flares that spreads across all three groups, which we believe provides
evidence to the likelihood of the bronze group containing a high percentage of
reals flares, despite their ∆t/t value. The decision to split the detected flares
into three groups was based on our prior understanding of flare properties from
the previous studies mentioned earlier, namely that the majority of flares exhibit
∆t/t � 1. The groups were created so as to reflect this understanding, to reflect
the recoverability rate for each flare, and also to allow for direct comparison with
the UV/optical flares presented in Swenson et al. (2013). Because the flares do
not meet the criteria for the gold group they spill over into the silver and bronze
groups. This can be seen by the abrupt cut-off, based on our group criterion, in
86
log(∆t/t)
NumberofGRBs
051015202530
051015202530
−2 −1 0 1 2 3
051015202530
Figure 4.3 Distribution of logarithmic ∆t/t, calculated as (Tstop−Tstart)/Tpeak, forthe detected flares. The three distributions are the gold (top), silver (middle) andbronze (bottom) distributions described in the text.
the gold group at ∆t/t = 0.5 and the subsequent continuation of the distribution
in the silver group between 0.5 < ∆t/t ≤ 1.0 and the excess tail extending into the
bronze group at ∆t/t > 1.0. These large flares comprise the majority of the silver
group, with the remaining flares being distributed at ∆t/t < 0.5. The primary
distribution of the bronze flares, removing the extended tail from the gold and
silver groups, can be see at ∆t/t < 1.0 and peaking at ∆t/t ∼ 0.1 This work is
now challenging the understanding of what constitutes an X-ray flare by finding a
significant number of large potential flares exhibiting ∆t/t > 0.5 and, as Figure 4.3
shows, a significant tale in the distribution with ∆t/t > 1.0.
The relative strengths of the flares ranges from a minimum flux ratio of 0.1 to
a maximum of several thousand. Figure 4.4 shows the distribution of flare flux
ratios for the three groups. All three groups of flux ratios have long tails that
87
log(∆F/F)
NumberofGRBs
0
10
20
30
0
10
20
30
−1 0 1 2 3 4
0
10
20
30
Figure 4.4 Distribution of the logarithmic flare flux ratio, relative to the underlyinglight curve. The three distributions are the gold (top), silver (middle) and bronze(bottom) distributions described in the text.
extend into the tens, hundreds, and thousands for the gold, silver, and bronze
groups, respectively. The flux ratios shown in Figure 4.4 show the distributions
for those smaller, weaker flares that have previously been less studied. Unlike the
UV/optical flares, which had noticeable gaps in the distributions of flux ratios,
the X-ray flares show a much more continuous distribution in each group. Only a
small number (17%) of UV/optical flares were considered to be strong flares with
flux ratios > 2. By that same criteria 33% of X-ray flares are considered large,
showing the relative strength of X-ray flares compared to the UV/optical flares.
With the calculated ∆F/F and ∆t/t for each of our flares, we can compare
our flares to the kinematically allowed regions of afterglow variability calculated
by Ioka et al. (2005). Figure 4.5 shows the limits taken from Ioka et al. (2005) for
(a) dips due to the nonuniformity of the emitting surface, (b) bumps due to den-
88
sity fluxuations, (c) bumps the arise from patchy shells, which are constrained to
∆t/t > t, and (d) bumps arising from refreshed shocks, constrained to ∆t/t > t/4.
This same analysis was performed by Chincarini et al. (2007) for their collection
of 69 flares. They found that a large fraction of their flares could not be related
to external shocks. Only a single flare from their analysis exhibited ∆t/t > 1,
with 3 additional flares occupying the region explained by density fluctuations. In
contrast, a significant fraction of our flares lie either at ∆t/t > 1 or in the region
explained by density fluctuations. The only portion that we did not add signif-
icantly to, compared to Chincarini et al. (2007), is that region that can only be
explained by internal shocks.
We also categorized each flare, grouping them according to which phase of the
canonical X-ray light curve (Nousek et al. 2006) it peaked during. We used the
light curve classification provided in the XRT GRB Catalogue (Evans et al. 2007,
2009) to determine whether the light curve was canonical in shape. Figure 1.4
shows Tpeak vs ∆t for flares occurring during the initial fast decay phase (green
triangles), the shallow/plateau phase (red squares), and final decay phase (black
diamonds) of the light curve. The majority of light curves do not follow the
canonical classification, but for comparison we have included flares coming from
these light curves (gray circles). As Figure 4.6 shows, all the flares appear to
follow the same evolution in ∆t as the light curve progresses. This same result
was seen in our analysis of the remaining flare parameters. This means that either
the physical process creating the flares is the same for all phases of the light
curve, or multiple flare creation mechanisms are able to produce flares that behave
and evolve similarly. Additionally, we analyzed the full XRT GRB Catalogue
spanning January 2005 to December 2012 by separating the flaring and non-flaring
GRBs into two groups. We then categorized each light curve based on the light
89
−3 −2 −1 0 1 2 3
−3
−2
−1
0
1
2
3
4
−3 −2 −1 0 1 2 3log(∆t/t)
−3
−2
−1
0
1
2
3
4
log(∆
F/F
)
(b) Bumps (density) (a) Dips
(d) Bumps (refresh)
(c) Bumps (patchy)
Figure 4.5 Reconstruction of Figure 1 from Ioka et al. (2005), overplotted with theflares presented in this work. Flares are color-coded to reflect the distribution theybelong to: gold (gray points), silver (blue points), bronze (red points). The plottedlimits are also taken from Ioka et al. (2005) and show kinematically allowed regionsfor potential flare progenitors: (a) dips for on-axis (solid line) and off-axis (dashedline), (b) bumps due to density fluctuations for on-axis (solid line) and off-axis(dashed line), (c) bumps due to patchy shells, and (d) bumps due to refreshedshocks.
90
curve classification given in the XRT GRB Catalogue (‘No break’, ‘One-break’,
‘Canonical’, and ‘Oddball’). Analyzing the two distributions of light curve types
with a K-sample Anderson-Darling test (Scholz & Stephens 1987) yields a p-value
of > 0.95 indicating that the flaring and non-flaring GRBs are highly consistent
with belonging to the same parent population. This provides further evidence
that the mechanism powering the X-ray afterglow, which defines the eventual light
curve classification, is independent from the mechanism causing the X-ray flaring.
91
1 2 3 4 5 6
0
1
2
3
4
5
6
1 2 3 4 5 6log(Tpeak)
0
1
2
3
4
5
6
log(∆t)
Figure 4.6 Tpeak versus ∆t for flares occurring during the initial decay phase (greentriangles), the shallow/plateau phase (red squares), and final decay phase (blackdiamonds) of the canonical light curve (Nousek et al. 2006). Also shown are theremaining flares (gray circles) that belong to light curves exhibiting a non-canonicalshape. The gap from 3 . ∆t . 3.8 is due to the 96 minute orbit of Swift and ourmethodology for determining Tstop when the end of the flare is not observed dueto a break in the data.
Chapter 5
UV/Optical and X-ray Flare
Correlation
In the previous two chapters we presented the flares identified by our flare finding
algorithm in UVOT and XRT GRB light curves. In this chapter we will explore
what correlation exists between the UV/optical and X-ray flaring. During the
period spanning 2005 January through 2010 December (the period of time used for
the UV/optical flares in Chapter 3) we detected flaring in 263 individual GRB light
curves. Of those GRBs with observed flares, 68 had flares observed in UV/optical
and 235 exhibited X-ray flaring. There are only 40 (15.2%) GRB light curves
that exhibited flaring in both the UV/optical and X-ray. This means that ∼
59% (40/68) of the GRBs with observed UV/optical flares have potential X-ray
counterpart. The remaining ∼ 41% (28/60) of GRBs with UV/optical flares have
no detected in the X-ray light curve. In terms of GRBs with observed X-ray flares,
∼ 17% (40/235) also have UV/optical flares and therefore potential counterparts,
and ∼ 83% of the corresponding UV/optical light curves either exhibit no flaring
or were not detected by UVOT.
The remainder of this chapter will look at both the potential correlations be-
93
tween the flares observed in these 40 GRB light curves with flares observed in both
the UV/optical and X-ray. We will also examine how these potentially correlated
flares differ from those flares without observed counterparts.
5.1 Flares with potential counterparts
The simple presence of both X-ray and UV/optical flares in the same light curve
does not mean that they are necessarily correlated. We can, however, eliminate
those flares which we are highly confident are not associated with one another.
There is evidence that GRB flares follow a lag-luminosity relationship similar to
that seen in the GRB prompt emission (Norris et al. 2000; Margutti et al. 2010),
meaning that for a given pair of correlated X-ray and UV/optical flares we would
not expect to observe a UV/optical peak no earlier than the X-ray peak. Of the 40
GRB light curves with both UV/optical and X-ray flaring, there were 42 individual
flaring periods. Taking into account errors associated with the determination of
Tstart, Tpeak and Tstop, we do not find any strong evidence of a UV/optical flar-
ing peaking before the presumed X-ray counterpart, confirming our expectation.
There are eight potential flares for which the UV/optical Tstart occurs after Tstop of
the potential X-ray flare counterpart. Because these flares are temporally disjoint
from one another, we are not confident that they are correlated with one another,
leaving us with 34 sets of flares remaining. There are a further five UV/optical
flares with limited overlap, where the UV/optical flare Tpeak occurs after the po-
tentially corresponding X-ray flare Tstop. This leaves 29 flares for which we have
high confidence that the X-ray and UV/optical are associated with one another,
the five flares with only moderate confidence that the X-ray and UV/optical are
associated, and eight flares that are potentially uncorrelated. Table 5.1 shows the
parameters used for these 42 pairs of X-ray and UV/optical flares. Figures 5.1-
94
5.5 show correlation plots for various flare parameters for these 42 sets of flares,
with the five flares with minimal overlap being plotted in green, and the eight
potentially uncorrelated flares being plotted in red.
95
Tab
le5.1
:P
ote
nti
ally
corr
elate
dU
V/op
tica
lan
dX
-ray
flare
para
met
ers
SourceNam
eX-ray
X-ray
X-ray
X-ray
X-ray
UV/optical
UV/optical
UV/optical
UV/optical
UV/optical
Tpeak
Tsta
rt
Tsto
p∆t/t
∆F/F
Tpeak
Tsta
rt
Tsto
p∆t/t
∆F/F
(s)
(s)
(s)
(s)
(s)
(s)
GR
B050319
1438.0
81376.8
41510.2
00.0
90.8
81061.7
9927.0
61208.4
10.2
61.1
9G
RB
050721
232.6
2219.5
4239.2
10.0
80.2
6494.7
4423.9
7508.9
20.1
70.5
4G
RB
050908
399.3
9294.6
9784.9
31.2
314.2
3368.5
8214.8
9435.0
90.6
01.5
9G
RB
051117A
436.5
8301.9
7751.5
21.0
31.8
0610.9
3555.9
9773.2
60.3
60.8
5G
RB
060313
191.1
9154.8
4238.6
70.4
41.9
0524.1
2470.2
1795.2
70.6
21.3
9G
RB
060512
201.9
0174.2
3379.8
71.0
23.5
3448.0
7432.0
14019.5
08.0
12.2
5G
RB
060526
247.6
9181.7
9948.0
13.0
9389.5
6262.7
7242.7
6272.7
80.1
11.0
8G
RB
060604
136.8
6124.3
0228.0
00.7
64.8
6203.7
1193.7
0213.5
70.1
00.4
4G
RB
060904B
171.7
2127.9
63760.3
621.1
5243.8
4256.8
6234.9
4284.3
10.1
92.1
3G
RB
070318
270.7
0235.6
4423.3
40.6
93.0
6246.4
5226.4
4256.4
60.1
20.1
6G
RB
070518
186.2
996.2
0357.0
21.4
014.5
3273.7
2243.7
0317.9
20.2
71.6
3G
RB
070611
3420.8
53420.8
54131.2
40.2
11.2
34733.3
63347.0
210492.0
61.5
10.7
8G
RB
070616
485.0
9415.1
6709.3
40.6
13.2
5787.5
2468.1
7816.6
30.4
40.4
7G
RB
070616
757.2
7713.9
7843.1
60.1
72.0
31011.3
6846.2
31149.2
60.3
00.9
0G
RB
070721B
311.0
6238.9
8394.6
00.5
011.7
9275.2
6255.2
4285.2
70.1
11.1
7G
RB
071031
454.9
8380.9
56131.1
812.6
45.7
8576.2
5546.5
6842.0
50.5
11.3
2G
RB
080212
294.1
4173.4
6448.6
60.9
426.4
4266.8
8223.1
4295.8
50.2
70.9
0G
RB
080703
217.3
4189.3
0306.9
50.5
40.5
3146.8
4136.8
3166.8
60.2
00.2
6G
RB
080804
137.4
7133.6
7145.2
90.0
80.3
3482.5
1412.4
6532.5
50.2
50.4
6G
RB
080810
103.4
688.2
9132.0
90.4
24.5
4113.0
6103.0
6133.0
90.2
70.1
6G
RB
080810
208.0
0187.3
8335.2
10.7
15.3
8229.1
2199.0
9289.1
70.3
90.1
7G
RB
080906
180.5
9160.8
5257.7
60.5
42.1
7256.2
6241.1
9284.0
20.1
74.8
6G
RB
080913
1863.8
1984.5
98580.7
04.0
86.4
612538.6
16082.7
214589.2
50.6
82.4
9G
RB
080916A
92.2
291.4
297.8
20.0
70.7
4370.1
4360.1
4390.1
60.0
81.4
7G
RB
080928
206.7
6176.2
7269.1
30.4
53.9
4247.1
1217.0
9257.1
20.1
61.8
8G
RB
081008
301.4
4284.1
7403.0
80.3
95.9
0262.0
9243.0
9302.1
20.2
30.1
4G
RB
090123
1781.9
51452.2
91912.6
90.2
61.1
51408.5
81368.1
41467.4
10.0
70.4
2G
RB
090123
483.9
5416.2
9667.6
20.5
21.3
5668.0
8608.4
1707.5
20.1
50.5
5G
RB
090530
263.9
7192.7
4303.8
20.4
20.7
1173.7
1153.6
9183.7
10.1
70.1
5G
RB
090926A
46846.7
346677.9
851695.2
10.1
10.7
847722.5
746791.3
051749.9
30.1
02.5
1G
RB
090926A
203029.1
1193054.4
2232375.7
30.1
90.8
9232412.6
6196569.4
8248216.9
10.2
20.6
5G
RB
090926A
86116.0
481266.4
5144410.2
40.7
31.7
181701.3
070136.2
7144308.9
80.9
71.1
2G
RB
091029
323.6
0233.2
8601.5
61.1
48.6
7543.6
6523.6
5553.4
80.0
50.7
9G
RB
100425A
482.8
6347.5
7610.0
90.5
40.9
5719.7
7651.7
6947.3
30.4
14.1
2G
RB
100805A
636.2
9423.7
04348.8
86.1
723.0
6630.0
3589.5
9707.2
00.1
91.5
6G
RB
100814A
147.0
0119.4
6357.3
81.6
22.1
8224.4
0214.3
9244.4
20.1
30.3
5G
RB
100901A
399.1
8132.5
23851.9
99.3
242.5
9416.8
7396.8
6436.8
90.1
01.4
5C
onti
nu
edon
Nex
tP
age.
..
96
Tab
le5.1
–C
onti
nu
ed
SourceNam
eX-ray
X-ray
X-ray
X-ray
X-ray
UV/optical
UV/optical
UV/optical
UV/optical
UV/optical
Tpeak
Tsta
rt
Tsto
p∆t/t
∆F/F
Tpeak
Tsta
rt
Tsto
p∆t/t
∆F/F
(s)
(s)
(s)
(s)
(s)
(s)
GR
B100901A
28505.8
112080.0
867586.8
31.9
51.6
817679.9
110070.1
721634.6
60.6
50.2
7G
RB
100906A
117.9
086.1
5199.4
10.9
623.1
6445.6
2424.4
8465.4
10.0
93.2
2G
RB
101017A
181.2
2173.9
3193.0
20.1
10.7
1180.6
5144.9
0215.4
70.3
91.7
8G
RB
101117B
184.2
2161.5
3244.9
00.4
50.4
4164.5
1154.5
0174.5
20.1
20.4
7G
RB
101117B
266.0
6244.9
0312.1
20.2
50.8
0307.9
9234.3
9328.0
00.3
00.6
2
97
Figures 5.1, 5.2, and 5.3 show the correlation plots between the UV/optical
and X-ray for the flare parameters Tstart, Tpeak and Tstop, respectively. For each
plot, the dashed red line shows the 1:1 relationship. For both Tstart and Tpeak, the
correlations follow closely the 1:1 relationship, with the exception of one of the
loosely associated flares (green) and most of the potentially uncorrelated (red).
There is more deviation from the 1:1 correlation present in Figure 5.3, with four
X-ray flares having Tstop nearly an order of magnitude later in time than measured
in the UV/optical. However, each of these four outliers are due to our method
of defining the flare parameters in the case of an observing gap. Each of these 4
X-ray flares had not yet returned to the level of the underlying afterglow when
they were interrupted by an observing gap, and our methodology placed Tstop at
the time of the first observation after the gap. The associated UV/optical flares,
which had a smaller flux ratio, had already returned to the level of the underlying
light curve before the observing gap. Understanding the four outliers in Figure 5.3,
it is clear that there is a high degree of correlation between the overall duration
of these flares between the X-ray and UV/optical, which is expected if they are in
fact correlated with one another and originating from the same emission region.
The timing resolution of the light curves, in particular the UV/optical light
curves, is not high enough and the error bars remain large enough that we are
unable to determine whether there is any degree of lag between the X-ray and
UV/optical flares. We do, however, see no unexplainable outliers that lead us to
believe that the overall evolution of hard to soft seen in X-ray flares by Margutti
et al. (2010) does not also apply for X-ray and UV/optical flare pairs.
Figure 5.4 shows X-ray ∆t/t plotted against ∆t/t for the associated UV/optical
flares. In this figure, as well as Figure 5.5, we have also separated the flares
into “early” and “late” flares, based on whether Tpeak of the X-ray flare occurs
98
2 3 4 5 6
2
3
4
5
6
2 3 4 5 6UV/Opt log(Tstart)
2
3
4
5
6
X−Raylog(T
start)
Figure 5.1 X-ray Tstart versus UV/optical Tstart for potentially associated flares.Black point indicate high confidence of association, while green points exhibitedUV/optical Tpeak > X-ray Tstop and red points exhibit UV/optical Tstart > X-rayTstop.
99
2 3 4 5 6
2
3
4
5
6
2 3 4 5 6UV/Opt log(Tpeak)
2
3
4
5
6
X−Raylog(T
peak)
Figure 5.2 X-ray Tpeak versus UV/optical Tpeak for potentially associated flares.Black point indicate high confidence of association, while green points exhibitedUV/optical Tpeak > X-ray Tstop and red points exhibit UV/optical Tstart > X-rayTstop.
100
2 3 4 5 6
2
3
4
5
6
2 3 4 5 6UV/Opt log(Tstop)
2
3
4
5
6
X−Raylog(T
stop)
Figure 5.3 X-ray Tstop versus UV/optical Tstop for potentially associated flares.Black point indicate high confidence of association, while green points exhibitedUV/optical Tpeak > X-ray Tstop and red points exhibit UV/optical Tstart > X-rayTstop.
101
before or after T0 + 1000 seconds. The early flares are plotted as crosses, while
the late flares are represented by triangles, with the green points signifying the 5
potentially uncorrelated flares and the 1:1 relationship shown as the red dashed
line. Immediately obvious is that there are only three sets of flares which lie well
below the 1:1 relationship. Individual investigation shows that for two of the three,
the black triangle and black cross (belonging to GRB 050319 and GRB 101017A,
respectively), the flares in question occurred during a period when there were
multiple small X-ray flares, each resolved due to how bright the X-ray light curves
were, but only a single UV/optical light curve was identified due to the summing
of the UV/optical data. It is reasonable to assume there may also be multiple
UV/optical flares during the same period which are simply washed out due to the
lack of timing resolution. If this is the case, those points would no longer be outliers
and would move closer to the rest of the distribution. The third set of flares, the
green triangle, is associated with GRB 070611 and occurred late in the light curve
and the lack of timing resolution due to the faintness of the UV/optical light curve
results in a larger ∆t/t in the UV/optical than in the X-ray. Understanding these
outliers we can say that the duration of the X-ray light curve is consistently longer
than that of the UV/optical light curve.
Similar to the conclusions drawn from Figure 5.4, Figure 5.5 shows that the
X-ray flares are consistently brighter, relative to the underlying light curve, than
the UV/optical flares. There is a potential bias that may be evident in both Fig-
ures 5.4 and 5.5, that must be addressed however. In many cases the UV/optical
light curve is brighter than its corresponding X-ray light curve (in terms of pho-
tons detected/second), with the UV/optical additionally suffering from a much
higher background level, which means that a flare of equal size in both bands will
be observed with a larger ∆t/t and larger ∆F/F in the X-ray than it will in the
102
UV/optical. The flare can be thought of as an iceberg, where we see a larger
portion of the “tip” in the X-ray than we do in the UV/optical. In some ways
this places the X-ray and UV/optical on unequal footing, and makes direct com-
parisons of parameters difficult. For example, if a flare of equal flux is observed
simultaneously in both the UV/optical and the X-ray (same Tpeak), the relatively
brighter underlying light curve in the UV/optical will result in a later measurement
of Tstart relative to the X-ray and an earlier measurement of Tstop relative to the
X-ray. These measurement differences then result in a larger ∆t/t measurement
for the X-ray than the UV/optical for the same flare. A more useful measurement
would be to perform the ∆t/t calculation using points other than Tstart and Tstop.
One could imagine defining ∆t/t as FWHMflare/Tpeak, where FWHMflare is the
Full-Width at Half Maximum of the portion of the flare observed in excess of the
underlying light curve. Unfortunately, the majority of the UV/optical flares, and a
number of the smaller X-ray flares, do not permit us to make such a measurement.
It is possible that some of the relationship we see in Figures 5.4 and 5.5 is due
to this bias. However, there are many points in both figures that are more than an
order of magnitude larger in the X-ray than in the UV/optical, which leads us to
believe that there is still a trend for X-ray flares to be both longer in duration and
brighter than their UV/optical counterparts. Additionally, in both the ∆t/t and
∆F/F comparisons, the data points associated with late-time flares (Tpeak > 1000
seconds), all remain close to the 1:1 correlation line. If there is some amount of bias
present in these figures, any correction would move these late-time flares closer to
or below the 1:1 correlation line. This would again confirm the findings of softer
flare emission as time increases Margutti et al. (2010), evidenced as a relative
brightening of the UV/optical flare compared to the X-ray counterpart (either by
an increase in the UV/optical flux or decrease in the X-ray flux), leading to ∆t/t
103
−1 0 1
−1
0
1
−1 0 1UV/Opt log(∆t/t)
−1
0
1
X−Raylog(∆t/t)
Figure 5.4 X-ray ∆t/t versus UV/optical ∆t/t for potentially associated flares.Black point indicate high confidence of association, while green points exhibitedUV/optical Tpeak > X-ray Tstop and red points exhibit UV/optical Tstart > X-rayTstop. Crosses indicate flares with Tpeak < 1000 seconds, while triangles representflares with Tpeak > 1000 seconds.
104
−1 0 1 2 3
−1
0
1
2
3
−1 0 1 2 3UV/Opt log(∆F/F)
−1
0
1
2
3
X−raylog(∆F/F)
Figure 5.5 X-ray ∆F/F versus UV/optical ∆F/F for potentially associated flares.Black point indicate high confidence of association, while green points exhibitedUV/optical Tpeak > X-ray Tstop and red points exhibit UV/optical Tstart > X-rayTstop. Crosses indicate flares with Tpeak < 1000 seconds, while triangles representflares with Tpeak > 1000 seconds.
105
and ∆F/F measurements that would lie at or below the red dashed line.
5.2 Comparison to Flares with no potential coun-
terpart
Though there clearly seems to be a certain number of correlated X-ray and UV/optical
flares, the clear preference is for UV/optical flares to appear without an associated
X-ray flare. This potentially points to a different emission mechanism between
these two sets of UV/optical flares (those with and without X-ray counterparts),
as was already mentioned in the case of GRB 060313 (Roming et al. 2006b) where
the presence of UV/optical flares and lack of X-ray flares was consistent with
an emission mechanism involving density fluctuations in the circumburst medium
provided the cooling frequency, νc, lay between the X-ray and UV/optical bands.
We can further investigate this by comparing the parameters of the UV/optical
flares with X-ray counterparts to those without. Figure 5.6 shows the histogram of
∆F/F for the UV/optical flares with X-ray counterparts (blue) and those without
X-ray counterparts (red). The two distributions do not appear to deviate signifi-
cantly from one another (Anderson-Darling tests performed on each of the pairs of
distributions shown in Figures 5.6 – 5.13 reveal no significant difference between
flares with and without counterparts). Because flares become broader and exhibit
smaller ∆F/F as they occur later in the light curve, we normalized the distribution
using Tpeak for each flare and show the results in Figure 5.7. Again, both distri-
butions do not indicate a difference between the properties of these two groups of
UV/optical flares. The plot of (∆F/F )/Tpeak does show that the distribution is
skewed toward the right, which indicates a large number of bright flares or a pref-
erence towards flares at early-times (small Tpeak). We know from Figure 5.6 that
106
− −1 0 1 2
0.0
0.2
0.4
0.6
0.8
1.0
−2 −1 0 1 2UV/Opt log( F/F)
0.0
0.2
0.4
0.6
0.8
1.0
Perc
entile
No X ray Counterpart
Observed X ray Counterpart
Figure 5.6 Comparison of ∆F/F for UV/optical flares with (blue) and without(red) X-ray counterparts.
there is not an overabundance of bright flares, so the shape of the (∆F/F )/Tpeak
distribution is a confirmation of our finding in Chapter 3 that most flares occur
at early times. Both the ∆F/F and (∆F/F )/Tpeak distributions may be biased,
however, by the continuum level of the underlying light curve which effects the
value of ∆F . The plot of ∆F/F shows a sudden drop off to the right of the peak,
which can either be caused by a real lack of bright flares, or due to a bright under-
lying light curve that causes the distribution to be redistributed in favor of smaller
∆F/F .
In Figures 5.8 and 5.9 we attempt to correct for this potential bias and examine
the distributions of Fpeak and Fpeak/Tpeak, respectively. Figure 5.8 shows that
the sudden drop off seen in Figure 5.6 does not appear when looking only at
Fpeak, indicating that the drop off is likely due to bright underlying afterglows.
Additionally, the UV/optical flares with X-ray counterparts distribution continues
to closely match the distribution of UV/optical flares without X-ray counterparts,
107
− −5 −4 −3 −2 −1
0.0
0.2
0.4
0.6
0.8
1.0
−6 −5 −4 −3 −2 −1UV/Opt log(( F/F)/Tpeak)
0.0
0.2
0.4
0.6
0.8
1.0
Perc
entile
No X ray Counterpart
Observed X ray Counterpart
Figure 5.7 Comparison of (∆F/F )/Tpeak for UV/optical flares with (blue) andwithout (red) X-ray counterparts.
while correcting for the previously mentioned bias. This indicates that whatever
mechanism creates these two groups of flares, it does so in a way that produces
flares that exhibit very similar properties. As has previously been stated, internal
shocks are often identified as the preferred method for producing X-ray flares,
which also means that our 42 UV/optical flares identified as being associated with
X-ray flares likely also originate from these same internal shocks. The remaining
85 UV/optical flares without X-ray associations must also be caused by internal
shocks that do not produce simultaneous X-ray flares, or by an entirely different
mechanism that produces UV/optical flares with the same general properties as
those caused by internal shocks.
It is not unsurprising, due to the many reasons previously given as to why
UV/optical flares are difficult to detect, that a majority of X-ray flares do not
associated flares in the UV/optical. However, it is still useful to look at the dis-
tributions of X-ray flares with UV/optical counterparts and those without. We
108
−18 −17 −16 −15 −14 −13 −12
0.0
0.2
0.4
0.6
0.8
1.0
−18 −17 −16 −15 −14 −13 −12UV/Opt log(Fpeak)
0.0
0.2
0.4
0.6
0.8
1.0P
erc
entile
No X−ray Counterpart
Observed X−ray Counterpart
Figure 5.8 Comparison of Fpeak for UV/optical flares with (blue) and without (red)X-ray counterparts.
−24 −22 −20 −18 −16 −14
0.0
0.2
0.4
0.6
0.8
1.0
−24 −22 −20 −18 −16 −14UV/Opt log(Fpeak/Tpeak)
0.0
0.2
0.4
0.6
0.8
1.0
Perc
entile
No X−ray Counterpart
Observed X−ray Counterpart
Figure 5.9 Comparison of Fpeak/Tpeak for UV/optical flares with (blue) and without(red) X-ray counterparts.
109
− 0 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
−1 0 1 2 3 4X−ray log( F/F)
0.0
0.2
0.4
0.6
0.8
1.0
Perc
entile
No UV/Optical Counterpart
Observed UV/Optical Counterpart
Figure 5.10 Comparison of ∆F/F for X-ray flares with (blue) and without (red)UV/optical counterparts.
examine the same four distributions used for the UV/optical flares. Starting in
Figure 5.10, we see that despite the significantly larger number of X-ray flares with-
out UV/optical counterparts, the two distributions do not appear to be dissimilar.
As opposed to Figure 5.6 where the distribution dropped off on the high end of
∆F/F , the X-ray fall off on the low end. This represents our detection limit for X-
ray flares, due to the way in which the X-ray data is binned in the Swift XRT GRB
Catalogue (Evans et al. 2007, 2009). The uniform method for binning the X-ray
data causes the errors associated with each bin to be nearly constant, relative to
the flux level of the light curve. This results in the harsh cutoff in our detection of
the smallest X-ray flares. As mentioned in Chapter 4, we chose to use the binning
and fits provided by Swift XRT GRB Catlogue because our own calculated fits on
a subset of light curves did not differ greatly from those previously calculated, and
it significantly reduced the CPU cycles required to perform our analysis.
Figure 5.11 shows the distribution of (∆F/F )/Tpeak, which again shows the
110
− −4 −2 0 2
0.0
0.2
0.4
0.6
0.8
1.0
−6 −4 −2 0 2X−ray log(( F/F)/Tpeak)
0.0
0.2
0.4
0.6
0.8
1.0
Perc
entile
No X ray Counterpart
Observed X ray Counterpart
Figure 5.11 Comparison of (∆F/F )/Tpeak for X-ray flares with (blue) and without(red) UV/optical counterparts.
skewed distribution favoring early-time flares, though this distribution is much
more symmetric than the UV/optical distribution largely due to the number of
exceptionally bright X-ray flares which contribute to the right of the peak.
These distributions are suspect to the same bias mentioned for the UV/optical,
though to a lesser degree, so we again corrected for the bias by examining the dis-
tributions of Fpeak and (Fpeak/Tpeak). Figure 5.12 shows the distribution of Fpeak
and reveals a very smooth distribution for the X-ray flares without UV/optical
counterparts. The distribution of X-ray flares with UV/optical counterparts is
understandable sparse, but is again not inconsistent with the larger distribution.
Figure 5.13 shows the same distribution, normalized by Tpeak, and looks remark-
ablly similar to Figure 5.12. This is likely caused by the large percentage of X-ray
flares that occur within the first 1000 seconds after the GRB trigger, meaning
that the normalizing factor Tpeak for more than 80% of the flares is of order ∼ 2,
resulting in a simple relatively uniform shifting of the Fpeak distribution. As with
111
−16 −14 −12 −10 −8 −6
0.0
0.2
0.4
0.6
0.8
1.0
−16 −14 −12 −10 −8 −6X−ray log(Fpeak)
0.0
0.2
0.4
0.6
0.8
1.0
Perc
entile
No UV/Optical Counterpart
Observed UV/Optical Counterpart
Figure 5.12 Comparison of Fpeak for X-ray flares with (blue) and without (red)UV/optical counterparts.
the other three distributions, the X-ray flares with UV/optical counterparts does
not differ significantly from the X-ray flares without UV/optical counterparts.
One potential reason that the distributions of flares with associations and those
without is that all flares have counterparts, but they may not be detected. We
investigate this possibility by analyzing the light curves of each GRB with evidence
for flaring in either the X-ray or UV/optical and calculating an upper limit for the
flux of an unseen flare in the other bandpass. To form a proper upper limit, one
must deconvolve the light curve and simultaneously fit both the afterglow and flare
portions. We are unable to perform this proper fitting because we do not have a
standard functional form to use as a template for our flares, therefore we calculate
our upper limit using only the measured flux value of the data point closest to
the time of Tpeak of the corresponding observed flare and the error associated with
that data point. Assuming an unseen flare exists, its parameters must be consistent
with the observed light curve, meaning that its maximum Fpeak is only Fobs+Err+,
112
−20 −18 −16 −14 −12 −10 −8
0.0
0.2
0.4
0.6
0.8
1.0
−20 −18 −16 −14 −12 −10 −8X−ray log(Fpeak/Tpeak)
0.0
0.2
0.4
0.6
0.8
1.0
Perc
entile
No UV/Optical Counterpart
Observed UV/Optical Counterpart
Figure 5.13 Comparison of Fpeak/Tpeak for X-ray flares with (blue) and without(red) UV/optical counterparts.
where Fobs is the observed flux value and Err+ is the positive error on that flux
measurement. We can then calculate ∆F/F as,
∆F
F=Fpeak − Fobs
Fpeak=
(Fobs + Err+)− FobsFobs + Err+
=Err+
Fobs + Err+
(5.1)
Figure 5.14 shows the same X-ray ∆F/F versus UV/optical ∆F/F distribution
as Figure 5.5, but also includes our calculations for upper limits on unseen associ-
ated flares. The red crosses represent the associated flares plotted previously. The
blue crosses are the limits on ∆F/F for unseen X-ray flares where a UV/optical
flare was detected, and green crosses are the same limits for the case of an X-ray
flare detection with no corresponding UV/optical detection. In order to account
for the potential bias in ∆F/F previously mentioned, Figure 5.15 is the same dis-
tributions as Figure 5.14 only normalized by Tpeak. In both cases the dashed line
represents the 1:1 correlation.
There is little difference, other than scaling, between Figures 5.14 and 5.15
113
−2 −1 0 1 2
−2
−1
0
1
2
−2 −1 0 1 2UV/Opt log(∆F/F)
−2
−1
0
1
2
X−raylog(∆F/F)
UV/Optand X−ray both observed
UV/Optwith no X−rayCounterpart
X−raywith no UV/OptCounterpart
Figure 5.14 X-ray ∆F/F versus UV/optical ∆F/F for potentially associated flares(red), X-ray upper limits (blue) versus UV/optical ∆F/F , and X-ray ∆F/F ver-sus UV/optical upper limits (green). Upper limits are calculated as described inequation 5.1.
114
−1.0 −0.5 0.0 0.5
−1.0
−0.5
0.0
0.5
1.0
−1.0 −0.5 0.0 0.5UV/Opt log(∆F/F)/log(Tpeak)
−1.0
−0.5
0.0
0.5
1.0
X−
ray
log
(∆F
/F)/
log
(Tp
ea
k)
UV/Opt and X−ray both observed
UV/Opt with no X−ray Counterpart
X−ray with no UV/Opt Counterpart
Figure 5.15 X-ray (∆F/F )/Tpeak versus UV/optical (∆F/F )/Tpeak for potentiallyassociated flares (red), X-ray upper limita (blue) versus UV/optical (∆F/F )/Tpeak,and X-ray (∆F/F )/Tpeak versus UV/optical upper limits (green). Upper limitsare calculated as described in equation 5.1 and Tpeak for upper limits is the timeassociated with Fobs.
115
meaning they do not appear to be susceptible to the bias caused by brighter late-
time afterglows. Immediately noticeable in both figures is the clear separation
between the observed associated X-ray and UV/optical flare pairs (red) and the
UV/optical flare detections with X-ray upper limits (blue). We believe the clear
separation is a real detection limit imposed by our data, with the uniformity of the
cut-off in X-ray flux ratio being caused by the uniformity in the errors of the X-ray
data previously described. Below a level of log(∆F/F ) ≈ −0.5 in X-ray flux, flares
are no longer detectable because they do not contribute enough photons relative
to the level of the underlying light curve to be detected. Rebinning of the X-ray
data could potentially lower that limit and allow for detection of smaller flares,
but doing so would also decrease the timing resolution of the data, likely canceling
out any potential gains in sensitivity to ∆F/F .
Although there is overlap between the associated X-ray and UV/optical flares
(red) and the X-ray flare detections with UV/optical upper limits (green), there
is still a definite line at log(∆F/F ) ≈ −0.3 in UV/optical flux. At log flux ratio
levels larger than ∼-0.3, we always detect both the UV/optical and X-ray flare,
while below that level we see primarily upper limits, but still a significant fraction
of UV/optical detections. There are a number of possible explanations for the
observed overlap. The upper limit we calculate could be seen as a “worst case
scenario” limit, due to our not formally fitting a combined flare and afterglow
profile. Combined with the non-uniform nature of the errors associated with the
UV/optical data (as opposed to the X-ray data as previously mentioned), this may
elevate the calculated detection threshold causing the observed overlap. Alterna-
tively, this could be a real effect due to suppressed UV/optical flux from absorption
in the circumburst medium, or spectrally hard flares with the spectral peak in or
above the X-ray band with little to no flux in the UV/optical.
Chapter 6
Conclusions and Future Work
The study of X-ray flares has led to the conclusion that they are likely formed
through internal shocks due to activity originating from the central engine. If this
is true, then observing GRB flares provides us a glimpse into the heart of the
GRB that is otherwise limited to the γ-rays during the prompt emission phase.
The precise nature of the GRB central engine is still not fully understood and
being able to probe its properties across multiple energy bands will prove crucial
to solving the mystery.
The focus of previousl flare studies have been primarily on those flares observed
in the X-ray, and not without good reason. The availability of large numbers of
GRB light curves in other wavelengths has been sorely lacking. Even with Swift
UVOT observing nearly all GRB fields with up to seven ultraviolet and optical fil-
ters, the data have not been available in a format where a significant study of GRB
flares could be performed. This has now changed with the forthcoming “Second
Swift UVOT GRB Catalog” (Roming et al. 2014) which presents the UVOT GRB
data in a format that has been optimally co-added and normalized, producing the
best large collection of UV/optical GRB light curves currently available. One of
the primary goals of this dissertation was to utilize this new data set to identify the
117
UV/optical flares that have previously been overlooked. To this end we developed
a method analyzing and identifying flares in GRB light curves that would be as
unbiased as possible and limited on by the data itself.
In Chapter 2 we presented a case study of the flares in GRB 090926A, showing
that an internal shock source can be invoked to describe the properties of the flares
observed in both the UV/optical and in the X-ray. Additionally, we showed that
the presence of large late-time flares in the light curve of GRB 090926A were very
likely caused by the overall bright light curve of this exceptional GRB, and that
LAT triggered GRBs are generally brighter than their BAT triggered counterparts.
Subsequent studies of individual LAT triggered GRBs (e.g. Abdo et al. (2009))
show that these GRBs may belong to their subclass of GRBs.
In Chapter 3 we presented the results of our complete analysis of the UVOT
GRB Catalog, presenting 119 flaring periods in 68 UVOT GRB light curves. We
additionally analyzed the Swift XRT GRB Calalogue (Evans et al. 2007, 2009) to
push lower the detection threshold for GRB flares in the X-ray, and detected 498
flaring periods in 326 XRT GRB light curves, which we presented in Chapter 4.
Our analysis of the UV/optical and X-ray flares showed that while flaring is
generally restricted to the early-time light curve, flares can be seen to beyond 105
seconds. If in fact the central engine is driving these flares, as appears to be the
case for the very late-time flares in GRB 090926A, this means that the central
engine is regularly active well after the prompt emission phase is over. Further
reinforcing the idea that flares are, at the very least, caused by an emission source
completely independent of the external shock driving the afterglow is our analysis
shown in Figure 4.6, which showed that there appears to be no correlation between
the canonical phase of the light curve and the presence of flares. The distribution
of flare Tpeak versus ∆t/t was not only the same for each of the canonical phases
118
of the X-ray light curve, but was self consistent among all GRB flares, regardless
of the shape of the light curve.
As opposed to the X-ray flares, our analysis of the UV/optical flares in Chap-
ter 3 showed no correlation to the prompt γ-ray parameters. We examined poten-
tial correlations between T90, prompt emission fluence, and the amount of structure
in the prompt emission to the UV/optical flare parameters Tpeak, ∆t/t, ∆F/F and
the number of UV/optical flares per GRB. This lack of correlation is interpreted as
indicating a different emission source for the UV/optical flares than the one which
produces the high energy GRB prompt emission.
Chapter 4 showed that the X-ray flares presented appear to belong to a con-
tinuous distribution extending well beyond ∆t/t = 1. This is more easily shown
by combining the three confidence groups of Figure 4.3 into a single distribution,
as shown in Figure 6.1. This distribution shows a large number of flares in di-
rect opposition to the ‘classical’ definition of a GRB X-ray flare, ∆t/t << 1, that
seems to be used by the astronomical community at large. The previous studies
of X-ray flares discussed in Chapter 1 derived their conclusions, including the pre-
ferred internal shock emission mechanism, studying flares that generally obeyed
the ∆t/t << 1 criterion.
Our results bring into question whether the internal shock method remains the
preferred emission mechanism for ALL GRB X-ray flares. Figure 6.2 shows again
the recreation of Figure 1 from Ioka et al. (2005) with the kinematically allowed re-
gions for potential flare progenitors. All flares at values of log(∆t/t > 0), while still
explainable via internal shocks, reside in a parameter space where external shocks
can be produce the observed flare properties. However, the relatively smooth dis-
tribution of ∆t/t in Figure 6.1 argues for either a single flare emission mechanism,
or multiple emission mechanisms with significant overlap in the duration of flares
119
−2 −1 0 1 2 3log(∆t/t)
0
10
20
30
40NumberofFlares
Figure 6.1 Combined histogram of ∆t/t of X-ray flares in Figure 4.3, showing theapparent continuous distribution of X-ray flares discovered.
each mechanism produces.
The number of potentially associated X-ray and UV/optical flares was low
given the number of flares detected. Our analysis comparing the two groups of
flares, those with and without counterparts (Chapter 5), shows that the properties
of the two groups are remarkably similar, and it is difficult to tell whether the
lack of a detected flare in either X-ray or UV/optical is indicative of a separate
emission mechanism or simply due to the circumburst environment or differences in
parameters we have not yet explored. One way in which we could address this issue
is by examining the spectral properties of the X-ray flares. If the peak spectral
frequency lies at or above the X-ray band, then the contribution in the UV/optical
may be minimal or non-existent. An analysis of the X-ray flares, comparing the
hardness of those with and without UV/optical counterparts, could resolve this
issue. Unfortunately, many of our X-ray flares are small and care must be taken
120
−3 −2 −1 0 1 2 3
−3
−2
−1
0
1
2
3
4
−3 −2 −1 0 1 2 3log(∆t/t)
−3
−2
−1
0
1
2
3
4
log(∆F/F)
(b) Bumps(density) (a) Dips
(d) Bumps(refresh)
(c) Bumps(patchy)
Figure 6.2 Recreation of Figure 4.5 without separating flares into confidence groups.The plotted limits are taken from Ioka et al. (2005) and show kinematically allowedregions for potential flare progenitors: (a) dips for on-axis (solid line) and off-axis(dashed line), (b) bumps due to density fluctuations for on-axis (solid line) and off-axis (dashed line), (c) bumps due to patchy shells, and (d) bumps due to refreshedshocks.
121
to ensure that our flare hardness measurement is not contaminated by the softer
emission from the underlying afterglow. We are currently investigating how to best
address this issue.
It is possible that a number of the non-associated flares do come from a different
emission mechanism, however. As previously mentioned, Figure 6.2 shows that in
the case of the X-ray flares a large portion of the flares detected by our analysis
populate the parameter space of log(∆t/t) > 0, a region previously not considered
to be “flare”-like. It is reasonable to assume that a fraction of the UV/optical
flares detected may also lie in this region, and that a number of the unassociated
UV/optical flares may be originating in the external shock as was suggested for
GRB 060313. It is possible that certain mechanisms, such as the external shock, are
only produce flares observed in one of the two energy bands, X-ray or UV/optical,
depending on the properties of the external shock and circumburst medium.
In order to fully understand GRB flares and better constrain their emission
source, we need access to more GRB flares, particularly at softer energies. Data
with a higher timing resolution and a better constraint on the flux ratios in bands
other than the X-ray are crucial for us to better examine the relationship between
flares of all energies and how the relate to one another.
The study of GRB flares, and particularly the multi-wavelength study of GRB
flares, is a relatively new field of research and this dissertation shows that there
are many unanswered question about the source of GRB flaring, how they relate
to the central engine, and whether or not all GRB flares are produced by the same
physical mechanism.
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Appendix A:
Flare Finding Algorithm with
Examples
To verify the effectiveness of the breakpoints function, we performed a series of
tests on simulated UVOT data. Starting with a simple power-law light curve,
we induced a number of flares on the light curve and attempted to detect those
flares using the method previously described. In order to test the ability of the
breakpoints function to detect a wide variety of flares we varied the Tstart time, the
amplitude, the duration of the induced flares, as well as the slope of the underlying
light curve. All of our analysis is done on the residuals of the best fit to the light
curve.
We use the criterion of BICi − BICmin > 6, or ‘Strong’ evidence from Kass
& Raftery (1995), to determine the appropriate number of breakpoints to assign
to a specific light curve. We then attempt to group breakpoints together to form
individual flares based on the relative position of the potential breakpoints relative
to each other and relative to the underlying light curve. Our measure of confidence
is determined by the number of times a specific breakpoint was identified in the
course of the 10,000 Monte Carlo simulations, and also satisfied the criterion of
135
BICi −BICmin > 6.
As previously mentioned, the ideal case is when the amplitude and duration of
the flare are both large enough, and the sampling of the data high enough, to make
Tstart, Tpeak, and Tstop easily identifiable. In practice this is almost never the case,
but is useful when illustrating how the algorithm functions. Figure A.1 shows an
example of simulated UVOT data with an induced flare that meets this criterion,
and shows the potential breakpoints found by the code as vertical lines on top of
the data. Analysis of the potential breakpoints in relation to each other and to
the underlying light curve shows that they collectively form a single flare with the
three potential breakpoints marking the approximate times of Tstart, Tpeak, and
Tstop. As with all the identified flares, the values assigned to Tstart and Tstop are
lower and upper limits of the actual values, with the last data point before the flare
that is still well fit by the underlying light curve assigned to Tstart and the first
data point after the flare well fit by the underlying light curve assigned to Tstop.
In the case of a well sampled light curve and flare, like that shown in Figure A.1,
the limits given by Tstart and Tstop do not differ significantly from calculated values
derived from fitting the flare. The difference is less than the size of the exposure
bin for data points we identify as Tstart and Tstop. We therefore see no need to
alter our methodology and to fit those few flares that can be fit using a function,
particularly when the choice of the functional form of the flare will itself result in
different determinations for the values of Tstart, Tpeak, and Tstop. For this flare, the
measure of confidence for each individual breakpoint is very high. Specifically, the
breakpoint associated with Tpeak was identified in all 10,000 iterations. In this case
we are therefore 100% confident in the presence of a flare despite not detecting all
three components at 100% confidence. We assign the overall confidence of the flare
to be 1.0, reflecting this certainty. This example is truly the exceptional case, as
136
Figure A.1 Simulated UVOT data showing an optimal flare. All three componentsof the flare, Tstart, Tpeak and Tstop, are detected and identified.
UV/optical flares are rarely observed with such strength.
A more typical size flare is shown in Figure A.2. In this case, the vertical lines
again show the positions of potential breakpoints found by the flare finding code.
Further analysis shows that these two breakpoints again form a single flare, how-
ever, only the approximate Tpeak and Tstop times have been identified. A potential
Tstart breakpoint was never identified during the 10,000 Monte Carlo simulations.
This does not mean that the code failed to properly identify the flare, but rather
shows that even at low significance the code is able to detect flares, however all the
individual components of the flare may not be detected. In the case of the flare
137
in Figure A.2, the rise to the observed peak of the flare is short enough, due to a
combination of a shorter flare duration and a small peak amplitude, that there are
no observed data points during the rise of the flare. The first data point found by
the flare finding code that deviates from the underlying light curve is the observed
peak of the flare. In cases such as these the code picks the nearest observed data
point before the observed flare peak as being the lower limit for the Tstart. In this
case, the assigned time for Tstart is once again very close to the actual start of the
flare. This flare is given a confidence measure of 0.7434, which is the confidence
measure associated with the observed flare peak.
In both of the previous examples, the sample of the light curves was continuous
and uninterrupted. However, this is never the case with actual data. Our data
from the Second UVOT GRB Catalog (Roming et al. 2014, in preparation) are
influenced, at the very least, by the fact that the Swift satellite has a 96 minute
orbit and that any target on the sky will be unobservable for >50% of the orbit.
Additionally any number of other factors including the observing of higher priority
targets and conflicts with spacecraft observing constraints, have produced light
curves with uneven sampling and occasional large gaps. These gaps are the reason
that we have decided to provide limits on the values of Tstart and Tstop and to
use the observed time of peak flux when reporting Tpeak. Figure A.3 shows a
light curve much more reminiscent of the actual data we had to work with when
identifying flares. The vertical lines again show the results from running the flare
finding code on the same basic light curve and induced flares as in Figure A.1,
but with an observing gap overlapping the beginning of the flare. The code once
again identifies three distinct data points that are potential breakpoints. Analysis
of the data points shows that we are unable to determine whether they are all
associated with a single flaring event due to gaps in the light curve. Not only are
138
Figure A.2 Simulated UVOT data showing a flare with a small amplitude andduration. Due to the abrupt rise to the peak of the flare, the code does not identifya unique point as being associated with the start of the flare. We assign the firstpoint prior to Tpeak to be Tstart. The data point assigned as Tstart is identified bythe red line.
139
we uncertain whether the first and last potential breakpoints correspond to a Tstart
and Tstop of a given flare or multiple flares, we are also no longer confident that
the point identified as the peak observed flux is an accurate approximation of the
actual Tpeak or the peak flux level reached during the flare(s). Again we assign the
last data point before the flaring period that was well fit by the underlying light
curve as Tstart (in this case the last observed data point before the observing gap),
and do the same for Tstop by assigning the first data point after the flaring period
well fit by the underlying light curve (in this case the first data point after the
second observing gap). Because we did not observe the majority of the flare and
are uncertain in the actual peak flux achieved, the flux ratio we report becomes a
lower limit, based on the peak observed flux and the flux of the underlying light
curve at the time of the observed peak. This flare is given a confidence measure of
0.9784, which is again the confidence measure associated with the observed peak.
In each of these examples we have only shown cases where there are no addi-
tional potential breakpoints other than those associated with either Tstart, Tpeak
or Tstop. Occasionally the code does find more than three breakpoints for a single
flare, specifically in situations where there is poor data sampling during the peak
of the flare. In these cases, if no single data point stands out as a peak, the code
will identify points to either side of the peak as being potential peak candidates,
resulting in four breakpoints for a single flare. In these cases we assign the data
point with the larger flux to be the peak flux time used in our calculations of ∆t/t
and the flux ratio. It should be noted, that this same series of four breakpoints
could be the result of two individual flares occurring in quick succession. If the
timing resolution is larger than the ∆t/t of the flares, the code will not be able
to correctly identify two individual flares, but will rather identify a single broad
flaring period.
140
Figure A.3 Simulated UVOT data showing the influence of observing gaps on theflare finding code. An elevated flux level is identified as a potential Tpeak, howeverthe beginning and ending of the flare are not observed. The first data point priorto the observing gap is designated as Tstart and the first data point after the secondobserving gap is designated as Tstop.
Appendix B:
Step-by-Step Example of Flare
Finding Algorithm on the X-ray
Light Curve of GRB 090926A
In Chapter 3 we showed the results of our flare finding algorithm for the UVOT
light curve of GRB 090926A (Figure 3.1). Here we will show the step-by-step
analysis taken to identify flares in the X-ray light curve for GRB 090926A, shown
in Figure B.1
We use the residuals to the fitted light curve when searching for unfit features
(i.e. flares). The residuals are determined by first calculating the expected flux rate
based on a power-law fit to the light curve, using the parameters from Evans et al.
(2007, 2009) for the X-ray light curves and Roming et al. (2014) for the UV/optical,
and the appropriate power-law function. The functional forms of these power-laws
are shown in Equations B.1-B.4, with higher order broken power-laws following
a similar expansion. These values are then subtracted from the flux values cal-
culated in our Monte Carlo simulations, giving us 10,000 realizations of the light
curve residuals with which to identify flares. Figure B.2 shows one realization
142
105 10610−14
10−13
10−12
105 106
Time Since Trigger (s)
10−14
10−13
10−12
Flux(0.3−10keV)ergcm
−2s−1
Figure B.1 X-ray light curve for GRB 090926A. Single power-law fit from Evanset al. (2007, 2009) shown in red.
143
of the residuals used for GRB 090926A. Each set of residuals is run through our
flare finding algorithm, which calls the strucchange (Zeileis et al. 2002) program
to iteratively fit the residuals with increasingly complex functions and calculate
the BIC for the fit of each function. Table B.1 shows the BIC calculation for a
single Monte Carlo iteration of GRB 090926A. The value of the individual BIC
determinations for each additional breakpoint fit is not important. As explained
in Chapter 3, only the difference between the BIC values is important in deter-
mining how to optimally fit the data. In the case of this single iteration, BICmin
occurs with the addition of 6 breakpoints to the residuals of GRB 090926A. The
number of breakpoints that satisfies our criteria of BICi − BICmin > 6 is 4 addi-
tional breakpoints. For this iteration the optimal fit is realized with 4 additional
breakpoints.
single power-law:
F (t) = Nt−α1 (B.1)
broken power-law:
F (t) = N
t−α1 t < tb1
t(α2−α1) t > tb1
(B.2)
doubly broken power-law;
F (t) = N
t−α1 t < tb1
t(α2−α1)b1
t−α2 tb1 < t < tb2
t(α2−α1)b1
t(α3−α2)b2
t−α3 t > tb2
(B.3)
144
105 106−2
−1
0
1
2
3
4
105 106
Time Since Trigger (s)
−2
−1
0
1
2
3
4
ScaledResiduals
Figure B.2 Scaled residuals for X-ray light curve of GRB 090926A.
triple broken power-law:
F (t) = N
t−α1 t < tb1
t(α2−α1)b1
t−α2 tb1 < t < tb2
t(α2−α1)b1
t(α3−α2)b2
t−α3 tb2 < t < tb3
t(α2−α1)b1
t(α3−α2)b2
t(α4−α3)b3
t−α4 t > tb3
(B.4)
Each Monte Carlo iteration causes the values of the residuals to change, and
therefore the number of breakpoints required for the optimal fit also changes. For
each Monte Carlo iteration we determine the optimal fit as shown in Table B.1
and previously described. At the completion of the 10,000 iterations, a histogram
can be constructed to show the calculated optimal number of breakpoints for each
145
Table B.1. GRB 090926A, determination of optimal number ofbreakpoints
# of Breakpoints BICi − BICmin
1 91.382 56.473 21.104 6.685 4.186 07 1.898 3.13
Note. — BICmin for this Monte Carlo iteration of GRB 090926A re-quires an additional 6 breakpoints added to the fitted residuals. Fouradditional breakpoints, with BIC4 − BIC4 = 6.68, is the optimal fit forthis single iteration.
iteration. Figure B.3 shows the optimal number of breakpoints distribution for
the X-ray light curve of GRB 090926A. The optimal number of breakpoints varied
between 2 and 9, with 8 additional breakpoints being the number most frequently
required. We therefore conclude that 8 additional breakpoints are required to best
fit the X-ray residuals of GRB 090926A. Examining the results of the 10,000 Monte
Carlo simulations, we identify the 8 most frequently identified breakpoints, shown
in Table B.2.
Further examination of these 8 individual breakpoints shows that they identify
the times of Tstart, Tpeak and Tstop of three separate flares. Figures B.4 – B.6
show these three flares with the individual breakpoints identified. Figure B.4
shows a zoomed in portion of the residuals highlighting the first flare in the light
curve. The black vertical dashed lines are associated with the breakpoints at
146
2 4 6 8 10Optimal number of Breakpoints
0
1000
2000
3000HistogramDensity
Figure B.3 Histogram of the optimal number of breakpoints found in the X-rayresiduals of GRB 090926A for each of the 10,000 Monte Carlo simulations.
Table B.2. Breakpoints detected in X-ray residuals of GRB 090926A
Time of breakpoint (s) # of times identified
51695.21 5713203029.11 3281232375.73 318746846.73 3038
193054.42 2319144410.24 210986116.04 200281266.45 1187
Note. — 8 most frequently detected breakpoints in the X-ray residualsof GRB 090926A, ordered in decreasing number of detections.
147
4•104 5•104 6•104
−2
0
2
4
4•104 5•104 6•104
Time Since Trigger (s)
−2
0
2
4ScaledResiduals
Figure B.4 First observed flare in GRB 090926A. Dashed black vertical lines showtimes of detected breakpoints. The dashed red vertical line shows the time assignedas the beginning of the flare by the flare finding algorithm.
T = 51695.21, with a confidence of 5713/10, 000 = 0.5713, and T = 46846.73,
with a confidence of 3038/10, 000 = 0.3038. These two breakpoints constitute
Tstop and Tpeak, respectively. Examining Figure B.4, we see that the residuals are
elevated from the beginning of the observation, meaning that the flare began prior
to the start of the Swift observations and our algorithm was not able to identify
a breakpoint for Tstart of the flare. Our algorithm automatically assigns Tstart,
following the method prescribed in Appendix A, and that value is indicated by
the red vertical dashed line in Figure B.4 at T = 46677.98 The overall confidence
assigned to the flare is 0.5713, the highest confidence of any individual component
of the flare.
148
Figure B.5 and Figure B.5 show the remaining two flares with their associated
breakpoints identified by vertical dashed lines. The breakpoints in Figure B.5 are
associated with Tstart at T = 81266.45, with confidence of 1187/10, 000 = 0.1187,
Tpeak at T = 86116.04, with confidence of 2002/10, 000 = 0.2002, and Tstop at
T = 144410.24, with confidence of 2109/10, 000 = 0.2109. The overall confidence
assigned to the flare is 0.2109. The breakpoints in Figure B.6 are associated with
Tstart at T = 193054.42, with confidence of 2319/10, 000 = 0.2319, Tpeak at T =
203029.11, with confidence of 3281/10, 000 = 0.3281, and Tstop at T = 232375.73,
with confidence of 3187/10, 000 = 0.3187. The overall confidence assigned the flare
is 0.3281.
The parameter of ∆t/t is now calculated using the calculated values of Tstart,
Tpeak and Tstop. Equation B.5 shows the calculation of ∆t/t for the first X-ray flare
in GRB 090926A. The flux ratio, ∆F/F is calculated using Equation B.6, where
Fpeak is the measured flux value associated with Tpeak, and Flc is the extrapolated
flux value of the underlying light curve fit at Tpeak using the same fit parameters
for the light curve and equation as used to calculate the residuals.
∆t/t =Tstop − Tstart
Tpeak=
51695.21− 46677.98
46846.73= 0.11 (B.5)
∆F/F =Fpeak − Flc
Flc=
5.305113× 10−12 − 2.98040× 10−12
2.98040× 10−12= 0.78 (B.6)
149
7•104 1•105 2•105−2
−1
0
1
2
3
4
7•104 1•105 2•105
Time Since Trigger (s)
−2
−1
0
1
2
3
4
ScaledResiduals
Figure B.5 Second observed flare in GRB 090926A. Dashed black vertical linesshow times of detected breakpoints.
150
2•105 3•105−1.0
−0.5
0.0
0.5
1.0
2•105 3•105
Time Since Trigger (s)
−1.0
−0.5
0.0
0.5
1.0
ScaledResiduals
Figure B.6 Third observed flare in GRB 090926A. Dashed black vertical lines showtimes of detected breakpoints.
Vita
Craig Arnel Swenson
Education2014 Ph.D. in Astronomy & Astrophysics, Penn State University, University
ParkThesis: “X-ray, Ultraviolet, and Optical Flares In Gamma-Ray Burst LightCurves”Advisor: Pete Roming
2008 B.S. in Physics and Astronomy, Brigham Young University, ProvoThesis: “Automated IRAF Reduction Scripts for Astronomy Group atBrigham Young University”Advisor: Michael Joner
Professional Experience
Project Experience
2009 - 2014 NASA Swift Science Operations Team Member2008 - 2014 NASA Swift UVOT Science Team Member2008 - 2014 Research Assistant, Penn State University2009 - 2012 Science Planner for NASA Swift SatelliteSummer 2008 Telescope Operator, Brigham Young University2007 - 2008 Research Assistant, Brigham Young University
Teaching Experience
Teaching Assistant, Introductory Astronomy, PSU 2010Instructor, Elementary Astronomy Laboratory, PSU 2010Lab Instructor, Physics 328 (Observational Astronomy), BYU 2008Teaching Assistant, Physics 427 & 428 (Junior level astrophysics), BYU 2008Teaching Assistant, Introductory Astronomy, BYU 2007-2008Teaching Assistant in Introductory Physics Courses, BYU 2005-2006
AwardsPenn State Astronomy & Astrophysics Zaccheus Daniel Fellowship 2013Penn State Astronomy & Astrophysics Braddock/Roberts Fellowship foroutstanding academic and research record
2008
Brigham Young outstanding Physics Teaching Assistant 2006
