Institute of Physics, Silesian University in Opava Gabriel Török GAČR 209/12/P740, CZ.1.07/2.3.00/20.0071 Synergy, GAČR 14-37086G, SGS- 11-2013, www.physics.cz Determination of compact object parameters from CO-AUTHORS: Eva Šrámková, Martin Urbanec, Kateřina Goluchová, Andrea Kotrlová, Karel Adámek, Jiří Horák, Pavel Bakala, Marek Abramowicz, Zdeněk Stuchlík, Wlodek Kluzniak, Gabriela Urbancová, Tomáš Pecháček observations of high frequency quasiperiodic oscillations
Transcript
Institute of Physics, Silesian University in OpavaGabriel Török
CO-AUTHORS:Eva Šrámková, Martin Urbanec, Kateřina Goluchová, Andrea Kotrlová, Karel Adámek, Jiří Horák, Pavel Bakala, Marek Abramowicz, Zdeněk Stuchlík, Wlodek Kluzniak, Gabriela Urbancová, Tomáš Pecháček
observations of high frequency quasiperiodic oscillations
Outline of our progress report1. Introduction: neutron star rapid X-ray variability, quasiperiodic
oscillations, twin peaks
2. Measuring BH spin from HF QPOs• 2.1 BH spin from geodesic models
(summary of some older results by Torok et al, 2011, A&A)• 2.2 Consideration of a>1 (Kotrlová et al 2014, A&A)• 2.3 Nongeodesic effects (Šrámková et al 2014, to be submitted)
3. Measuring NS spin from HF QPOs• 3.1 Mass-angular-momentum relations, EoS consideration
(summary of Torok et al, ApJ, 2010, 2012, Urbanec et al 2010, A&A)• 3.2 Detailed consideration of EoS and spin (Torok et al 2014, in prep.)• 3.3 Torus model (Torok et al 2014, in prep.)• 3.4 General constraints (Torok et al 2014, A&A)
Tento projekt je spolufinancován Evropským sociálním fondem a státním rozpočtem České republiky
• density comparable to the Sun• mass in units of solar masses• temperature ~ roughly as the T Sun• more or less optical wavelengths
Artists view of LMXBs“as seen from a hypothetical planet”
Companion:
Compact object:- black hole or neutron star (>10^10gcm^3)
>90% of radiation in X-ray
LMXB Accretion disc
Observations: The X-ray radiation is absorbed by the Earth atmosphere and must be studied using detectors on orbiting satellites representing rather expensive research tool. On the other hand, it provides a unique chance to probe effects in the strong-gravity-field region (GM/r~c^2) and test extremal implications of General relativity (or other theories).
Figure (“Bursa-plot”): after M. Bursa & MAA 2003, updated data
3:2
Figures -Left: after Abramowicz&Kluzniak (2001), McClintock&Remillard (2003); Right: Torok (2009)
1.1 Black hole and neutron star HF QPOs
• BH HF QPOs: (perhaps) constant frequencies, exhibit the 3:2 ratio
• NS HF QPOs: 3:2 clustering, - two correlated modes which exchange the dominance when passing the 3:2 ratio
It is unclear whether the HF QPOs in BH and NS sources have the same origin.
Ampl
itude
diff
eren
ce
Frequency ratio
Upp
er fr
eque
ncy
[Hz]
Lower frequency [Hz]
3:2
3:2
Figures -Left: after Abramowicz&Kluzniak (2001), McClintock&Remillard (2003); Right: Torok (2009)
1.1 Black hole and neutron star HF QPOs
• BH HF QPOs: (perhaps) constant frequencies, exhibit the 3:2 ratio
• NS HF QPOs: 3:2 clustering, - two correlated modes which exchange the dominance when passing the 3:2 ratio
It is unclear whether the HF QPOs in BH and NS sources have the same origin.
Ampl
itude
diff
eren
ce
Frequency ratio
Upp
er fr
eque
ncy
[Hz]
Lower frequency [Hz]
3:2
3:2
There is a large variety of ideas proposed to explain the QPO phenomenon [For instance, Alpar & Shaham (1985); Lamb et al. (1985); Stella et al. (1999); Morsink & Stella (1999); Stella & Vietri (2002); Abramowicz & Kluzniak (2001); Kluzniak & Abramowicz (2001); Abramowicz et al. (2003a,b); Wagoner et al. (2001); Titarchuk & Kent (2002); Titarchuk (2002); Kato (1998, 2001, 2007, 2008, 2009a,b); Meheut & Tagger (2009); Miller at al. (1998a); Psaltis et al. (1999); Lamb & Coleman (2001, 2003); Kluzniak et al. (2004); Abramowicz et al. (2005a,b), Petri (2005a,b,c); Miller (2006); Stuchlík et al. (2007); Kluzniak (2008); Stuchlík et al. (2008); Mukhopadhyay (2009); Aschenbach 2004, Zhang (2005); Zhang et al. (2007a,b); Rezzolla et al. (2003); Rezzolla (2004); Schnittman & Rezzolla (2006); Blaes et al. (2007); Horak (2008); Horak et al. (2009); Cadez et al. (2008); Kostic et al. (2009); Chakrabarti et al. (2009), Bachetti et al. (2010)…]
- in some cases the models are applied to both BHs and NSs, in some not- some models accommodate resonances, some do notThe ambition /common to several of the authors/ is to relate HF QPOs to orbital motion in strong gravity and infer the compact object properties using the QPO measurements…
1.2. The ambition
1.3 Models and frequency relations considered here
Several models imply observable frequencies that can be expressed in therms of combinations of frequencies of the Keplerian, radial and vertical epicyclic oscillations. In the simple case of geodesic approximation and Kerr metric these are
Here we only focus on the choice of few hot-spot and disc-oscillation models:
RP2
1.3 Models and frequency relations considered here
Here we only focus on the choice of few hot-spot and disc-oscillation models:
1.3 Models and frequency relations considered here
Here we only focus on the choice of few hot-spot and disc-oscillation models:
RPTDWDERKRRP1RP2
MODEL : Characteristic Frequencies
Cˇ adež et al. (2008), Kostic´ et al. (2009), and Germana et al.(2009)
Tidal DisruptionČadež et al. (2008), Kostič et al. (2009), Germana et al. (2009)
1.3 Models and frequency relations considered here
Here we only focus on the choice of few hot-spot and disc-oscillation models:
RPTD
ERKRRP1RP2
MODEL : Characteristic Frequencies
Cˇ adež et al. (2008), Kostic´ et al. (2009), and Germana et al.(2009)
Warped Disc Resonancea representative of models proposed by Kato (2000, 2001, 2004, 2005, 2008)
WD
(or torus)1.3 Models and frequency relations considered here
Here we only focus on the choice of few hot-spot and disc-oscillation models:
RPTD
ERKRRP1RP2
MODEL : Characteristic Frequencies
Cˇ adež et al. (2008), Kostic´ et al. (2009), and Germana et al.(2009)
Epicyclic Resonance, Keplerian Resonancetwo representatives of models proposed by Abramowicz, Kluzniak et al. (2000, 2001, 2004, 2005,…)
WD
(or torus)1.3 Models and frequency relations considered here
RPTD
ERKRRP1RP2
MODEL : Characteristic Frequencies
Cˇ adež et al. (2008), Kostic´ et al. (2009), and Germana et al.(2009)
Resonances between non-axisymmetric oscillation modes of a toroidal structure two representatives by Bursa (2005), Torok et al (2010) predicting frequencies close to RP model
2. 1 Models relating both of the 3:2 BH QPOs to a single radius
WD
Here we only focus on the choice of few hot-spot and disc-oscillation models:
(or torus)
Here we only focus on the choice of few hot-spot and disc-oscillation models:
RPTD
ERKRRP1RP2
MODEL : Characteristic Frequencies
WD
1.3 Models and frequency relations considered here
• the (advantage of) BH HF QPOs: (perhaps) constant frequencies, exhibit the mysterious 3:2 ratio
Upp
er fr
eque
ncy
[Hz]
Lower frequency [Hz]
• The BH 3:2 QPO frequencies are rather stable which imply that they depend mainly on the geometry and not so much on the dirty physics of the accreted plasma.
2.1 BH spin from the geodesic QPO models
RP
ERWD, TD
Different models associate QPOs to different radii…
2.1 BH spin from the geodesic QPO models
One can easily calculate the frequency.mass functions for each of the models.
Spin a
2.1 BH spin from the geodesic QPO models
Toro
k et
al.,
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&A
And compare the frequency.mass functions to the observation.For instance in the case of GRS 1915+105 (which here well represents all 3:2 microquasars).
Spin a
2.1 BH spin from the geodesic QPO models
Toro
k et
al.,
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&A
And compare the frequency.mass functions to the observation.For instance in the case of GRS 1915+105 (which here well represents all 3:2 microquasars).
Spin a
2.1 BH spin from the geodesic QPO models
Clearly, different models imply very different spins…
Toro
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When the dimensionless spin reads a>1, the behaviour of the epicyclic frequencies of orbital motion qualitatively changes. The situation is thus more complicated .
2.2 Consideration of a>1 (naked sigularities or superspinars - NaS)
Kotr
lová
et a
l., (2
014)
A&
A
When the dimensionless spin reads a>1, the behaviour of the epicyclic frequencies of orbital motion qualitatively changes. The situation is thus more complicated. Nevertheless, some models still imply smooth frequency.mass functions of the spin.
2.2 Consideration of a>1 (naked sigularities or superspinars - NaS)
BH NaS
Kotr
lová
et a
l., (2
014)
A&
A
When the dimensionless spin reads a>1, the behaviour of the epicyclic frequencies of orbital motion qualitatively changes. The situation is thus more complicated. Nevertheless, some models still imply smooth frequency.mass functions of the spin. Some of them not (discontinuities and dichotomies appear…)
2.2 Consideration of a>1 (naked sigularities or superspinars - NaS)
Kotrlová et al., (2014) A&A
When the dimensionless spin reads a>1, the behaviour of the epicyclic frequencies of orbital motion qualitatively changes. The situation is thus more complicated. Nevertheless, some models still imply smooth frequency.mass functions of the spin. Some of them not (discontinuities and dichotomies appear…)
2.2 Consideration of a>1 (naked sigularities or superspinars - NaS)
The case of epicyclic resonance model
Kotrlová et al., (2014) A&A
When the dimensionless spin reads a>1, the behaviour of the epicyclic frequencies of orbital motion qualitatively changes. The situation is thus more complicated. Nevertheless, some models still imply smooth frequency.mass functions of the spin. Some of them not (discontinuities and dichotomies appear…)
2.2 Consideration of a>1 (naked sigularities or superspinars - NaS)
The case of epicyclic resonance model
ZOOM
Kotrlová et al., (2014) A&A
2.2.1 Summary of BH spin estimates
• For black holes, different models imply very different spin values.
• Except one model, there is always an alternative compatible with existence of a superspinning compact object. Nevertheless, only epicyclic resonance model then implies spin close to unity, while others imply values that are several times higher.
Kotrlová et al., (2014) A&A
2.3. Non-geodesic effects consideration within ER model
Pressure supported fluid tori
Šrámková et al., (2014), in prep.
2.3. Non-geodesic effects consideration within ER model
Pressure supported fluid tori – impact of pressure on the resonant frequency
Šrámková et al., (2014), in prep.
For low spins the results agree with pseudonewtonian case investigated by Blaes et al 2008. For high spins, the situation is different. Resonant frequencies are decreasing instead of increasing as the torus thickness rises.
2.3. Non-geodesic effects consideration within ER model
For low spins the results agree with pseudonewtonian case investigated by Blaes et al 2008. For high spins, the situation is different. Resonant frequencies are decreasing instead of increasing as the torus thickness rises.
Pressure supported fluid tori – impact of pressure on the resonant frequency
Šrámková et al., (2014), in prep.
3.1 NS mass-angular momentum relations from HF QPO data
3.1 NS mass-angular momentum relations from HF QPO data
• We have considered the relativistic precession (RP) twin peak QPO model to estimate the mass of central NS in Circinus X-1 from the HF QPO data. We have shown that such an estimate results in a specific mass–angular-momentum (M–j) relation rather than a single preferred combination of M and j.
• Later we confronted our previous results with another binary, the atoll source 4U 1636–53 that displays the twin peak QPOs at very high frequencies, and extend the consideration to various twin peak QPO models. In analogy to the RP model, we find that these imply their own specific M–j relations.
Torok et al., (2010) ApJ
Torok et al., (2012) ApJ
RP MODEL (4U 1636-53): Color-coded map of chi^2 [M,j,10^6 points] well agrees with rough estimate given by simple one-parameter fit.
M= Ms[1+0.75(j+j^2)], Ms = 1.78M_sun
Best chi^2
Toro
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pJ.
3.1 NS mass-angular momentum relations from HF QPO data
3.1 NS mass-angular momentum relations from HF QPO dataSeveral other models and sources
Toro
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(201
2) A
pJ.
3.1 NS mass-angular momentum relations from HF QPO data
• One can calculate M-j relations from EoS and spin frequency and compare these to the results based on QPOs.
3.2 Detailed consideration of EoS and NS spin
Toro
k et
al.,
(201
4) in
pre
p.
• One can calculate M-j relations from EoS and spin frequency and compare these to the results based on QPOs.
3.2 Detailed consideration of EoS and NS spin
Toro
k et
al.,
(201
4) in
pre
p.
3.2 Detailed consideration of EoS and NS spin
• Another possibility is to INFER the spin from the QPO model. When EoS are considered directly for QPO modelling, the M-J degeneracy is broken and QPO models provide chi-square minima.
RP MODEL
Toro
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pre
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3.2 Detailed consideration of EoS and NS spin
• Another possibility is to INFER the spin from the QPO model. When EoS are considered directly for QPO modelling, the M-J degeneracy is broken and QPO models provide chi-square minima.
RP MODEL
X-ray burstVERY GOOD AGREEMENT !
Toro
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al.,
(201
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pre
p.
3.3 Torus Model
• The models which we have considered so far always require tuning of parameters in order to provide good fits of the high-frequency sources data.
• Here we attempt to fit the data with “modified RP model” which does not contain any new free parameters.
3.3 Torus ModelWe assume an inner pressure supported fluid torus with the CUSP CONFIGURATION. The torus moves in radial direction. The upper QPO frequency is given as the Keplerian frequency at the torus centre. The lower QPO frequency is the frequency of the m=1 radial epicyclic oscillations of the torus.
3.3 Torus ModelWe assume an inner pressure supported fluid torus with the CUSP CONFIGURATION. The torus moves in radial direction. The upper QPO frequency is given as the Keplerian frequency at the torus centre. The lower QPO frequency is the frequency of the m=1 radial epicyclic oscillations of the torus.
RP MODEL
BEST FITS
TORUS MODEL
Torok et al., (2014) in prep.
3.3 Torus ModelWe assume an inner pressure supported fluid torus with the CUSP CONFIGURATION. The torus moves in radial direction. The upper QPO frequency is given as the Keplerian frequency at the torus centre. The lower QPO frequency is the frequency of the m=1 radial epicyclic oscillations of the torus.
RP MODEL
BEST FITS
TORUS MODEL
CUSP
TOR
US
Torok et al., (2014) in prep.
3.4 General constraints
SPIN [Hz]
Num
ber o
f ISC
O-N
S [r
elati
ve u
nits
]
The ISCO-NS distribution has the peaks at the values of the spin which can be very different from the peak in the distribution of all NS.• High M -> peak at the original value of spin• Low M -> peak at the high value of spin• Inter. M -> two peaks – POSSIBLE DISTRIBUTION OF QPO SOURCES !
Toro
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&A
Lett
ers
3.5 Summary of NS spin estimates
• When only Kerr or Hartle-Thorne spacetime is assumed, the HF QPO data and their individual models imply mass-spin relations instead of the preferred combinations of these quantities.
• The degeneracy is broken when the EoS are considered.
• The relativistic precession model implies NS spin frequency in a perfect agreement with the observation (4U 1636-53).
• The modified RP model (torus model) provides good fits of the data without any tuning of parameters.
• Strong constrainst are possible even from very general assumptions.
