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Optical Image Analysis to detect EM-Counterparts of GW-Transients
Marica Branchesi (Università di Urbino/INFN)&
Eric Chassande-Mottin (APC/CNRS)
Virgo Ego Scientific Forum School(Cascina 2-6 May 2011)
ASTRONOMICAL OBSERVATIONS
Electromagnetic Spectrum
Ground Based and Space Telescopes
Panoramic of ASTRONOMICAL IMAGES in different wavelength bands
X-ray and Radio ImagesOptical Images
Chandra-Observatory
VLA
HST
Keck Observatory
Silla Observatory
Electromagnetic Radiation from Astrophysical Objects
LUMINOSITY is the amount of energy an object radiates in unit time:
Intrinsic quantity for a given objects Not dependent on the observer’s distance or viewing angle
Units: erg/s (cgs) or watts (SI)
dtdE
L
SPECTRUM: distribution of luminosity as a function of wavelength or frequency
The shape of the spectrum depends on the radiation emission process(es)
Monochromatic L ,l Ln: relative to a given wavelength or frequency (erg s-1 Å-1 or erg s-1 Hz-1)
Bolometric L: integrated over all wavelengths or frequencies (ers s-1 )
dLdLL
00
What is observed and mesured of EM Radiation from Astrophysical Objects?
FLUX is the radiative energy per unit time passing through a unit area
dtdAdE
dAdL
f
dfdff
00
Monochromatic f ,l fn intensity in (ergs or photons) per unit area, time, ,l or n (erg cm-2 s-1 Å-1 or erg s-1 Hz-1)
Total Flux (units erg cm-2 s-1 )
Types of Astronomical Spectra
Real Detectors are sensitive over a finite range of l (or n)
In the “optical band” there are many bandpasses (photometric systems)
Some example of optical bandpass curves
(Fukugita et al. 1995)
FLUX - Inverse Square Law
The 1/d2 fall-off of flux with distance from the source
If d is the distance from the center of the source to the observer:
24 d
Lf
fddAfL 24
Optical Wavelengths: Magnitude
For historical reason fluxes in the optical band are measured in magnitudesThe scale was defined by Pogson in 1856 using a logarithmic scale as the “logarithmic response” of the human eye:
)/(log5.2 211021 ffmm an object 2.5 magnitudes brighter than another has a 10 times larger flux smaller magnitudes correspond to brighter objects
5log5 10 dmM
measure of intrinsic luminosity
Apparent Magnitude
Absolute Magnitude: magnitude that an object would have at a distance of 10 parsec
5log5 10 dMmDistance Modulus
d = source distance in parsec
d = source distance in parsec
Astronomical Image Processing
1 Step) IMAGE CALIBRATION: different steps to follow and software to use on the basis of observed wavelength band
2 Step) IMAGE ANALYSIS: different analysis to perform and software to use on the basis of the project goal
IMAGE CALIBRATION: process by which astronomers convert electronic signal from the telescope into meaningful astronomical data
Raw Data Calibrated Image
calibration
Optical Image Calibration Process
1) Dark Frame Subtraction to compensate for Thermal effects that add (taken preventing ligth entering the camera) unwanted intensity Readout Noise, electronics
produce noise when reading and transmitting data
2) Flat Field Correction to overcome image variations due to a (taken observing a source with uniform illumination) not uniform response/ sensitivity of the detector
3) Bad Pixel Masks to exclude “hot and cold pixels”, pixels that saturate prematurely or do not produce signal
4) Fringe correction to remove the fringe pattern due to atmospheric OH emission (in i- and z-band)
Are the images ready to be analyzed?
In order to make astrometry (evaluation of object position) and photometry (measure of the flux) two other steps are necessary:
• Astrometric Calibration
• Photometric Calibration
Astrometric Calibration to find mathematical transformation relating the positions of pixels in the image CCD to celestial coordinates on the sky
by using Reference Stars with well known celestial coordinate in the FOV
Star Catalogs suitable for astrometric use:
• GSC, HST Guide Star Catalog • USNO, US Naval Observatory Astrometric Catalog
Celestial Coordinates - Right Ascension and Declination
Celestial Sphere
Celestial Equator
Ecliptic
Celestial Equatorial Coordinate System
Dec measured from the celestial equator from 0° to +90° towards North Pole and from 0° to -90° towards South Pole.
RA measured east from the Vernal Equinox Point in hours, 0h to 24h or in degree 0° to 360°
Photometric Calibration – Standard Stars
General Formula for a object’s magnitude in a filter i:
ii ZPDNm exp)/(log5.2 10
where DN = net source counts,Exp = exposure time
ZPi (1 sec) = Zero-Point to determine or given as ZPi (exp) = ZPi (1 sec) + 2.5log10(exp) mi = -2.5log10(DN) + ZPi (exp)
For a standard star mi is known and tabulated for different filters.
ZPi is determined by evaluating DN for standard stars visible in the
image FOV or for standard stars observed during the same night
Standard Star Catalogs suitable for photometric use:
• BSC, Bright Star Catalog • Landolt (1992, AJ, 104, 336)• Tycho Catalog
Zero-point is dependent on airmass
Airmass = 1/cos(z) , z=zenith distance(ratio between the thickness of the Earth’s atmosphere at the observing altitude and at the zenith)
Due to Earth’s Atmospheric Extinction (absorption and scattering of light ) a source appears bigther observed at the zenith and fainter close to the horizon
Select STANDARD STARS whose airmass is the same as the target airmass
The conversion of “Clear filter observed flux (DN)” into “standard reference magnitude system” can be done
estimating the Zero-Point (ZP) by using a linear least squares fit between:
“not calibrated magnitude” xxxxxxxxxxxxxxxxxxxxxx )
and
“reference-catalog magnitude” for common stars in the FOV
There are telescopes , likeTAROT, that observe
with a “Clear filter”
))((log5.2 10 ADUcountsDN
Photometric Calibration – “Clear Filter” Wide Field Telescope
Reference Star Catalog USNO-A2.0 that lists magnitudes in a standard red filter: POSSI-R1
The POSSI red magnitude is chosen as reference
Example for TAROT images
1.0
0.8
0.6
0.4
0.2
0
Tra
sm
iss
ion
(%)
POSS-I 103aE
Wavelength (Angstroms)
6000 6400 6800
R1 magnitude USNOA-2-2.5
log
10 (
DN
(AD
U c
ou
nts
))+Z
P
Linear Least Squares Fit
musno = mimage+ ZPusing USNO stars brigther than mag=16
IMAGE ANALYSIS: DS9-Saoimage
DS9 - Astronomical imaging and data visualization application
Astronomical Image and Table Format FITS - Flexible Image Transport System
Celestial Coordinates (RA,Dec)Image Pixel Coordinates (X,Y)
File Name Pixel Count in ADU
Simple Aperture Photometry
Sum counts in all pixels aperture
Sky background counts in annulus or separate region
m = - 2.5 log (Source_counts) + ZP
Source_counts =Total_counts – Bkg_counts
Define the correct size of aperture Star Brightness Profile
Size comprimise between including all the light from the star and excluding excessive amount of noisy background
good choice 1.5 or 2.0 X FWHM
FWHM
Image Resolution
In the absence of aberrations and atmospheric turbulence, the Point-Spread Function (the response to a point-source) is the Airy pattern
Diffraction-Limited PSF
The IMAGE RESOLUTION: minimum angular separation at which two equally bright stars would just be distinguished
Airy DiskFirst Diffraction Ring
Dsen
22.1
D =aperture diameter
l = wavelength of light
Larger aperture telescope
Higher Resolution
The “seeing” is estimated by measuring the FWHM (full width at half maximum) of
the star brightness radial profile
The observation “seeing” gives the measure of IMAGE RESOLUTION
The FWHM is estimated by fitting with a Gaussian model the brightness profile of a sample of not saturated stars (e.g. IRAF)
Lens or mirror aberrations and atmospheric turbulence cause the width of the PSF to broaden and its shape to become distorted
Central maxima of PSF expanded by atmospheric turbulence is called “seeing”
The resolution of ground-based telescope is limited by the atmosphere
Signal To Noise Ratio
For a counting process (e.g photons) the error is the “Poisson noise”:
Since the source is seen over a background:
SSS
NS
SScountsource
S
S
2/
_
22
222
/
other
othersky
BskyT
BBST
BS
SSNS
where Bsky are the sky background counts
and Bother are readout and dark noise
in the same area occupied by the source.
SExtractor for large field photometry
SExtractor is an astronomical software to extract and build catalogs of objects from optical images
Steps:1) Estimate Background and its RMS noise
2) Detect objects (thresholding)
3) Deblend merged objects
4) Measure shapes and position
5) Perform Photometry
6) Classify objects: star-like/galaxy
7) Output catalog
Detection SExtractor consider a “minimum number” of adjacent pixel above a “certain threshold” an object detection
Deblending use a multiple pass thresholding to separate neighbour objects detected as single source
Photometry isophotal, isophotal-corrected, automatic, best-estimate and fixed circular aperture approaches
star
galaxy
ISOPHOTAL the user defines the threshold above which SExtractor does photometry: pixels above this threshold constitute an isophotal area
ISOPHOT-CORRECTED objects rarely have all their flux within neat boundaries, some of the flux is in the “wings” of the profile. Sextractor do a correction for that, assuming a symmetric Gaussian profile for the object
AUTOMATIC SExtractor uses an adaptive elliptical aperture around every detected object by analyzing the objet’s light ditribution and using the Kron (1980) approach: the ellipical sizes are defined in order to capture most (> 90%) of the objetc flux
BEST is usually equal to AUTO photometry, but if the contribution of other nearby sources exceeds 10%, it is ISOPHOT-CORRECTED
FIXED CIRCULAR APERTURES the user specified fixed circular aperture where the flux is estimated
Limiting Magnitude: point where Differential/Integral Source Counts distribution (vs magnitude) bends and moves away from the power law of the reference USNOA
Differential Source Counts Integral Source Counts
R magnitudeR magnitude
Co
un
ts(0
.5 m
ag b
in)/
sq d
egre
e
Co
un
ts(<
mag
)/sq
deg
ree+
x x+
Limiting magnitudeLimiting magnitude
USNOA countsUSNOA counts
TAROT image countsTAROT image counts
Image Sensitivity – Limiting Magnitude
For large FOV images the survey sensitivity can be estimated by comparing “image Source Counts” with a “Reference-Catalog Source Counts”
in the same region of the sky
Example for TAROT images
Analysis Procedure for Optical Images taken with Wide Field Telescopes
Searching for Electromagnetic Counterparts
of Gravitational-Wave Transients
A goal of LIGO and Virgo interferometers is the first direct detection of gravitational waves from ENERGETIC ASTROPHYSICAL events:
Mergers of NeutronStars and/or BlackHoles SHORT GRB
Kilonovas
Core Collapse of Massive Stars Supernovae
LONG GRB
Limit regions to observe to Globular Clusters and Galaxies within 50 Mpc
(GWGC catalog White et al. 2011)
GW Source Sky Localization: signals near threshold localized to regions of tens of square degrees possibly in several disconnected patches
Necessity of wide field of view telescopes
LIGO/Virgo horizon: a stellarmass BH/NS binary inspiral detected out to 50 Mpc distance that includes thousands of galaxies GW observable sources are likely to be extragalactic
The expected EM counterpart are transient objects whose brightness changes with time: Optical Afterglows
Metzger et al.(2010), MNRAS, 406..265
Kann et al. 2010, ApJ, 720.1513
Kann et arXiv:0804.1959
KILONOVASRadioactively Powered Object
LONG/SOFT GRBMassive star Progenitor
SHORT/HARD GRB Compact Object
mergers
R m
agn
itu
de
assu
min
g z
=1
R m
agn
itu
de
assu
min
g z
=1
Time (days after burst in the observer frame)Time (days after burst in the observer frame)Time (Days)
Lu
min
osi
ty (
erg
s s-1
)
Metzger et al.(2010), MNRAS, 406..265
The study of transient objects requires the analysis of images taken over several nights to sample flux variation as a function of time - light curve study
Analysis Procedure for Wide Field Optical Images
Limited Sky localization of GW interferometers
Wide field of view optical images
Requires to develop specific methods to detect the Optical Transient Counterpart of the GW trigger
Main steps for a EM-counterpart Detection Pipeline:
Find all “Transient Objects” visible in the images
Select the EM-counterpart from the “Contaminating Transients”
detect sources in each image
select“unknown objects”
(not in USNO2A)
Catalog-based Detection Pipeline
SExtractor to build catalog of all the objects visible in each image
Match Algorithm (Valdes et al 1995; Droege et al 2006) to identify “known stars” in USNO2A (catalog of 5 billion stars down to R ≈ 19 mag)
select centralpart of
the image
FOV restricted to region with radius = 0.8 deg for TAROT
avoid problemsat image edges
Magnitude consistency
to recover possible transients that
overlap with known galaxies/stars
Recover from the list of “known objects”: |USNO_mag – TAROT_mag| > 4σ
Octave Code
11
search for objects in common to
several images
Spatial cross-positional check with match-radius of 10 arcsec for TAROT chosen on the basis of position uncertainties
reject cosmic rays, noise, asteroids...
select objects in “on-source”
(nearby galaxies)
“On-source region” = regions occupied by Globular Clusters and Galaxies up to 50 Mpc (GWGC catalog, White et al 2011)
reject backgroundevents
“Light curve” analysis
reject “contaminatingobjects” (galaxy, variable stars, false transients..)
Possible Optical counterparts
…..Catalog-based Detection Pipeline
“Light curve” analysis - cut based on the expected luminosity dimming of the EM counterparts
recall magnitude α [-2.5 log10 (Luminosity)]
expect Luminosity α [time- β] magnitude α [2.5 β log10(time)]
slope index = measurement of (2.5 β)to discriminate expected light curve from “contaminating events”
The expected slope index for SHORT/LONG GRB is around 2.7 and kilonova is around 3
Optical counterparts the ones with slope index > 0.5
Coloured points = Optical LGRB TransientsBlack squares = contaminating objects
Contaminating objects that could pass the cut are only variable AGN or Cepheid stars
Dis
tan
ce in
Mp
c
Initial Red magnitude
Slo
pe
Ind
ex
Thank you for your attention!!
Ready to start the practical section....
You are provided with a set of 10 images taken by TAROT telescope observing the same region of the sky during three consecutive nights
after a fictitious GW trigger
Some optical transients have been injected in the images by using LONG and SHORT GRB and kilonova models
The transients were injected in nearby galaxies (within the LIGO/Virgo horizon of 50 Mpc) with an offset from the galaxy center
in the range of the observed ones for GRBs (within 100 Kpc)