correlated spectral and timing properties of neutron stars...

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


single source (4U 1636–53)12 sources (max values)

Barret et al. 2006Barret et al. 2006Mendez 2006Mendez 2006


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

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

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