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Correlated spectral and timing properties of neutron stars
Correlated spectral and timing properties of neutron stars
Mariano MéndezMariano Méndez
Kapteyn Astronomical Institute, University of Groningen, The NetherlandsKapteyn Astronomical Institute, University of Groningen, The Netherlands
Marginally Stable Orbit (MSO)Marginally Stable Orbit (MSO)Marginally Stable Orbit (MSO)
2
2
1
1
1
E
≥
0
3
2
2
1
321
E
< 0
Radius of the marginally stable orbit (MSO)
2
2
1
1
321
Marginally Stable Orbit (MSO)Marginally Stable Orbit (MSO)Marginally Stable Orbit (MSO)
Kilohertz quasi-periodic oscillations (QPOs)Kilohertz quasiKilohertz quasi--periodic oscillations (QPOs)periodic oscillations (QPOs)va
n de
rKlis
et a
l. 19
97va
n de
rKlis
et a
l. 19
97
νuνl
kHz QPOskHz QPOs
νKepler (r=15 km) ≈
1180 Hz for a 1.4 M
¯
starνKepler (r=15 km) ≈
1180 Hz for a 1.4 M¯
star
l u
The frequencies of the two QPOs change with time.The frequencies of the two QPOs change with time.
Sco X–1Sco X–1
Men
dez &
van
der
Klis
200
1M
ende
z & v
an d
erK
lis 2
001
Freq
uenc
y→
Freq
uenc
y→
Time →Time →P
ower
sca
leP
ower
sca
le
Systematic frequency variations Systematic frequency variations
Stro
hmay
er e
t al.
1996
; For
d et
al.
1996
Stro
hmay
er e
t al.
1996
; For
d et
al.
1996
4U 0614+09
Initial observations suggested the frequencies of the QPOs, νl
and νu , were well correlated with the intensity of the source.
Initial observations suggested the frequencies of the QPOs, νl
and νu , were well correlated with the intensity of the source.
As the radius of the inner edge of the accretion disc decreases, probably driven by the rate of mass accretion through the disc, the orbital frequency at that radius increases.
But this frequency cannot be higher than the Keplerian frequency at the MSO.
As the radius of the inner edge of the accretion disc decreases, probably driven by the rate of mass accretion through the disc, the orbital frequency at that radius increases.
But this frequency cannot be higher than the Keplerian frequency at the MSO.
Marginally Stable OrbitMarginally Stable OrbitMarginally Stable Orbit
Zhan
g e t
al .
1998
Zhan
g e t
al .
1998
4U 1820–304U 1820–30
21 M
arch
199
7
10 S
ept 1
997
9 Fe
b 19
97
28 O
ct 1
996
1400
1200
1000
800
600
4001600 2000 2400 2800 3200
2-60 keV Rate (c/s)
Freq
(Hz)
νMSOνMSO
MSO: Observational evidence?MSO: Observational evidence?MSO: Observational evidence?
Detailed viewDetailed viewDetailed view
Men
dez 2
000
Men
dez 2
000
4U 1820–304U 1820–30
“Parallel Tracks”““Parallel TracksParallel Tracks””
Men
dez e
t al .
1998
; Men
dez &
van
de r
Kl is
199
9M
ende
z et a
l . 19
98; M
ende
z & v
an d
e rK
l is 1
999
MSO: Upper frequency bound?MSO: Upper frequency bound?MSO: Upper frequency bound?
Bar r
et e
t al .
2005
, 200
6Ba
r ret
et a
l . 20
05, 2
006
width
νamplitude
The other properties of the (kHz) QPOsThe other properties of the (kHz) QPOsThe other properties of the (kHz) QPOs
•
Either width (≡
FWHM) or coherence (Q = ν / FWHM; a.k.a. Quality Factor)
•
Amplitude (% rms ≡
r )
••
Either width (Either width (≡≡
FWHM) orFWHM) or coherence (coherence (QQ = = νν / FWHM;/ FWHM; a.k.a. Quality Factor)a.k.a. Quality Factor)
••
Amplitude (% Amplitude (% rmsrms ≡≡
r r ))
Drop of Q and rms at high frequencies: MSO?Drop of Drop of QQ and and rmsrms at high frequencies: MSO?at high frequencies: MSO?
Bar r
et e
t al .
2005
, 200
6Ba
r ret
et a
l . 20
05, 2
006
also Di Salvo et al. 2001, 2003; Mendez et al 2001; van Straaten et al. 2002, 2003 also Di Salvo et al. 2001, 2003; Mendez et al 2001; van Straaten et al. 2002, 2003
4U 1636–534U 1636–53
Coherence of the kHz QPOs across sourcesCoherence of the kHz QPOs across sourcesCoherence of the kHz QPOs across sources
v an
derK
l is e
t al .
1997
; Jon
k ere
t al.
2000
;M
ende
z et a
l . 20
01; D
i Sal
v o e
t al .
2003
v an
derK
l is e
t al .
1997
; Jon
k ere
t al.
2000
;M
ende
z et a
l . 20
01; D
i Sal
v o e
t al .
2003
Amplitude of the kHz QPOs across sourcesAmplitude of the kHz QPOs across sourcesAmplitude of the kHz QPOs across sources
J onk
ere t
al.
2000
; Men
dez e
t al .
2001
J onk
ere t
al.
2000
; Men
dez e
t al .
2001
Max. Q and rms of the kHz QPOs across sourcesMax. Max. QQ and and rmsrms of the kHz QPOs across sourcesof the kHz QPOs across sources
Mendez 2006Mendez 2006
Q and rms of the kHz QPOs across sourcesQQ and and rmsrms of the kHz QPOs across sourcesof the kHz QPOs across sources
Mendez 2006Mendez 2006 Barret et al. 2006Barret et al. 2006
Q and rms of the kHz QPOs across sourcesQQ and and rmsrms of the kHz QPOs across sourcesof the kHz QPOs across sources
single source (4U 1636–53)12 sources (max values)
Barret et al. 2006Barret et al. 2006Mendez 2006Mendez 2006
Q and rms of the kHz QPOs across sourcesQQ and and rmsrms of the kHz QPOs across sourcesof the kHz QPOs across sources
single source (4U 1636–53)12 sources (max values)
Barret et al. 2006Barret et al. 2006Mendez 2006Mendez 2006
Q and rms of the kHz QPOs across sourcesQQ and and rmsrms of the kHz QPOs across sourcesof the kHz QPOs across sources
I40–80 keV / I13–25 keV
Mendez 2006Mendez 2006
About Z’s and AtollsAbout ZAbout Z’’s and Atollss and Atolls
Has
i nge
r& v
an d
e rK
l is 1
989
Has
i nge
r& v
an d
e rK
l is 1
989
EIS
Individual sources:
•
QPO coherence and amplitude drop at high QPO frequencies.−
Higher frequencies generally imply source is brighter
−
Sources become softer as they become brighter.
→ QPO coherence and amplitude drop when the source becomes brighter and softer.
The population of sources:
•
Maximum QPO coherence and amplitude drop in brighter sources.−
Brighter sources (Z) are softer than weaker sources (Atoll).
→ Maximum QPO coherence and amplitude drop for bright and soft sources.
Individual sources:
•
QPO coherence and amplitude drop at high QPO frequencies.−
Higher frequencies generally imply source is brighter
−
Sources become softer as they become brighter.
→ QPO coherence and amplitude drop when the source becomes brighter and softer.
The population of sources:
•
Maximum QPO coherence and amplitude drop in brighter sources.−
Brighter sources (Z) are softer than weaker sources (Atoll).
→ Maximum QPO coherence and amplitude drop for bright and soft sources.
Individual sources vs. the population: Similar mechanism?
Individual sources vs. the population: Individual sources vs. the population: Similar mechanism?Similar mechanism?
The transient XTE J1701–462: The first Z source to convert into an Atoll source
The transient XTE J1701The transient XTE J1701––462:462: The first Z source to convert into an Atoll sourceThe first Z source to convert into an Atoll source
Hom
an e
t al.
2007
Hom
an e
t al.
2007
The transient XTE J1701–462: The first Z source to convert into an Atoll source
The transient XTE J1701The transient XTE J1701––462:462: The first Z source to convert into an Atoll sourceThe first Z source to convert into an Atoll source
Hom
an e
t al.
2007
Hom
an e
t al.
2007
The transient XTE J1701–462: The first Z source to convert into an Atoll source
The transient XTE J1701The transient XTE J1701––462:462: The first Z source to convert into an Atoll sourceThe first Z source to convert into an Atoll source
EIS
IS
LB
UB
The transient XTE J1701–462: The Z and Atoll type of kHz QPOs The transient XTE J1701The transient XTE J1701––462:462: The Z and Atoll type of kHz QPOsThe Z and Atoll type of kHz QPOs
νl ~ 600 Hz νu ~ 900 HzQl ~ 8 Qu ~ 10Rl ~ 3% ru ~ 3%
νl ~ 600 Hz νu ~ 900 HzQl ~ 8 Qu ~ 10Rl ~ 3% ru ~ 3%
νl ~ 800 HzQl ~ 100rl ~ 10%
νl ~ 800 HzQl ~ 100rl ~ 10%
Sann
ae t
al.
2009
Sann
ae t
al.
2009
The transient XTE J1701–462: Amplitude vs. frequency
The transient XTE J1701The transient XTE J1701––462:462: Amplitude vs. frequencyAmplitude vs. frequency
Sann
ae t
al.
2009
Sann
ae t
al.
2009
Upper limit for Q=20,50Atoll phase, in 256sUpper limit for Q=20,50Atoll phase, in 256s
Upper limit for Q=100Z phase, in 128s, 256s and 512s
Upper limit for Q=100Z phase, in 128s, 256s and 512s
ZZ
AtollAtoll
The transient XTE J1701–462: Coherence vs. frequency
The transient XTE J1701The transient XTE J1701––462:462: Coherence vs. frequencyCoherence vs. frequency
ZZ
AtollAtoll
Minimum Q for a 3-sigma detection of a 5% QPO in 128s, Z phase, 4 PCUs
Minimum Q for a 3-sigma detection of a 5% QPO in 128s, Z phase, 4 PCUs
Minimum Q for a 3-sigma detection of a 5% QPO in 256s, Atoll phase, 3PCUs
Minimum Q for a 3-sigma detection of a 5% QPO in 256s, Atoll phase, 3PCUs
Sann
ae t
al.
2009
Sann
ae t
al.
2009
Oscillation vs. ModulationOscillation vs. ModulationOscillation vs. Modulation- Oscillator: Probably in the disc; e.g.:
- Orbital, radial or vertical epicyclic frequencies,- Resonances.
- Modulator: Probably in a Comptonizing corona or boundary layer:
- QPO amplitudes larger than disc contribution to total flux.- QPO rms spectrum increases steeply with energy.- High amplitude at energies where disc contribution is negligible.
– Coherence of the QPO: Either lifetime of the oscillator, or time dependent efficiency of the modulator.
– Amplitude of the QPO: Energy-dependent efficiency of the modulator.
- Oscillator: Probably in the disc; e.g.:
- Orbital, radial or vertical epicyclic frequencies,- Resonances.
- Modulator: Probably in a Comptonizing corona or boundary layer:
- QPO amplitudes larger than disc contribution to total flux.- QPO rms spectrum increases steeply with energy.- High amplitude at energies where disc contribution is negligible.
– Coherence of the QPO: Either lifetime of the oscillator, or time dependent efficiency of the modulator.
– Amplitude of the QPO: Energy-dependent efficiency of the modulator.
Modulation mechanismModulation mechanismModulation mechanism
– Using a time-dependent Comptonization model, Lee & Miller (1998) find that the ability of a Comptonizing corona to modulate the oscillations decreases as the corona becomes cooler and more optically thick; this is also the regime at which the high-energy part of the emission becomes softer (e.g. Gierlinski & Done 2002).
– Gilfanov et al. (2003) find that the rms spectrum of the QPOs in 2 sources can be explained as variability in the flux of the boundary layer. They also find that the relative contribution of the boundary layer to the total flux decreases as inferred mass accretion rate increases (i.e., when sources become brighter).
– Using a time-dependent Comptonization model, Lee & Miller (1998) find that the ability of a Comptonizing corona to modulate the oscillations decreases as the corona becomes cooler and more optically thick; this is also the regime at which the high-energy part of the emission becomes softer (e.g. Gierlinski & Done 2002).
– Gilfanov et al. (2003) find that the rms spectrum of the QPOs in 2 sources can be explained as variability in the flux of the boundary layer. They also find that the relative contribution of the boundary layer to the total flux decreases as inferred mass accretion rate increases (i.e., when sources become brighter).
ConclusionsConclusionsConclusions1. Similar behavior of Q and r in individual sources and in
the population of sources suggests that these QPO parameters are most likely determined by the same mechanism in both cases.
2. 4U 1701-462 converted from a bright and soft Z source into a hard and weak Atoll source; the amplitude and coherence of the kHz QPOs changed accordingly, in line with what was known for other Z and Atoll sources.
The MSO cannot be the (only) cause of the drop of r and Q at high QPO frequencies in individual sources
1. Similar behavior of Q and r in individual sources and in the population of sources suggests that these QPO parameters are most likely determined by the same mechanism in both cases.
2. 4U 1701-462 converted from a bright and soft Z source into a hard and weak Atoll source; the amplitude and coherence of the kHz QPOs changed accordingly, in line with what was known for other Z and Atoll sources.
The MSO cannot be the (only) cause of the drop of r and Q at high QPO frequencies in individual sources