Institute of Physics, Silesian University in Opava

1. On NSMass-Spin Relations Implied by Models of Twin Peak QPOs Gabriel Török, Pavel Bakala, Eva Šrámková, Zdeněk Stuchlík, Martin Urbanec, Kateřina Goluchová Institute ofPhysics, Silesian University in Opava CZ.1.07/2.3.00/20.0071Synergy , GAČR 209/12/P740, 202/09/0772,SGS-01-2010, www.physics.cz

2. 1. Introduction • MOTIVATION Compact object: - black hole or neutron star(>10^10gcm^3) • LMXB Accretion disc LMXBs • T ~ 10^6K • >90% of radiation • in X-ray • Companion: • density comparable to the Sun • mass in units of solar masses • temperature ~ roughly as the T Sun • more or less optical wavelengths Observations: The X-ray radiation is absorbed by the Earth atmosphere and must be studied using detectors on orbiting satellites representing a 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). Figs:space-art,nasa.gov

3. 1. Introduction • MOTIVATION Individual peaks can be related to a set of oscillators, as well as to time evolution of a singleoscillator. LMXBsshort-term X-ray variability: peaked noise (Quasi-PeriodicOscillations) Sco X-1 power • LowfrequencyQPOs (up to 100Hz) • hecto-hertz QPOs (100-200Hz),... • HF QPOs (~200-1500Hz): • Lower and upper QPO feature • forming twin peak QPOs frequency The HF QPO origin remains questionable, it is most often expected that it is associated to orbital motion in the inner part of the accretion disc. Fig:nasa.gov

4. 2. Observed Twin Peak QPO Frequencies Upper frequency [Hz] Lower frequency [Hz]

5. 3. RelativisticPrecessionModel: Inferring NS Parameters One can solve the RP model definition equations (Kerr approximation) Obtaining the relation between the expected lower and upper QPO frequency which can be compared to the observation in order to estimate mass M and “spin” j … The two frequenciesscalewith 1/M andthey are also sensitive to j. For matching of the data it is an important question whether there exist identical or similar curves for different combinations of M and j.

6. 3. RelativisticPrecessionModel: Ambiguity in Mandj Orbital Radius Infinity ISCO

7. 3. RelativisticPrecessionModel: Ambiguity in Mandj Orbital Radius M = 2.5….4 MSUN Ms = 2.5 MSUN M~ Ms[1+0.75(j+j^2)] Infinity ISCO Torok et al.(2010), ApJ

8. 3. RelativisticPrecessionModel: Ambiguity in Mandj Orbital Radius Orbital Radius Infinity ISCO Infinity ISCO M = 2.5….4 MSUN Ms = 2.5 MSUN M~ Ms[1+0.75(j+j^2)] Torok et al.(2010), ApJ • Foreach pair ofparametersMand j,the RP model gives a differentcurve, butonecanfindclassesofcurvesthat are nearlyidentical. • boundedby therelationM ~Ms[1+0.7(j+j^2)]. The best fits of data of a given source should be therefore reached for thecombinations of M and j which can be predicted just from one parametric fit assuming j = 0.

9. 4. Results of Data Matching (Circinus X-1) Color-coded map of χ2 [M,j,10^6 points] well agrees with rough estimate given by simple one-parameter fit. M-j relation expected from Ms = 2.2M_sun Bestχ2numericaly Best χ2exactKerrsolution Best χ2linearizedKerrfrequencies Torok et al.(2010), ApJ

10. 5. Justification Torok et al.(2010),ApJ High-mass (i.e. compact) neutron star can be well approximated via simple and elegant terms associated to Kerr geometry. The non-rotating NS mass predicted by theRP model is high. Thus, theKerr geometryhas thepotential to provide rather precise spin-corrections.

11. 5. Justification Torok et al.2012, ApJ, accepted In theHartle-Thorne spacetime there is a degeneracy not only between the NS mass and angular momentum but also between these quantities and theNS quadrupole moment q [here j ∈ (0, 0.3) and q/j^2 ∈ (1, 8)].

12. 6. Conclusions • The twin peak QPO data matching by theRP model implies rather preferred mass-angular-momentum relations rather than single combinations of M and j. • Severalotherpointswillbediscussedin thepresentation of Kateřina Goluchová (Fridaymorning).

13. ADVERTISING

14. 7. Advertising • The twin peak QPO data matching by theRP model implies rather preferred mass-angular-momentum relations ratherthan single combinations of M and j. • More in thetalkof Kateřina Goluchová (FridayMorning): • Thesame conclusion holds for both high- and low- frequency sources. • (e.g. 4U~1636-53 and Circinus X-1) Torok et al.2012, ApJ, accepted

15. 7. Advertising • The twin peak QPO data matching by theRP model implies rather preferred mass-angular-momentum relations ratherthan single combinations of M and j. • More in thetalkof Kateřina Goluchová (FridayMorning): • Thesame conclusion holds for both high- and low- frequency sources. • (e.g. 4U~1636-53 and Circinus X-1) • The same conclusion is valid for several other twinpeak QPO models. Torok et al.2012, ApJ, accepted

16. 7. Advertising • The twin peak QPO data matching by theRP model implies rather preferred mass-angular-momentum relations ratherthan single combinations of M and j. • More in thetalkof Kateřina Goluchová (FridayMorning): • Thesame conclusion holds for both high- and low- frequency sources. • (e.g. 4U~1636-53 and Circinus X-1) • The same conclusion is valid for several other twinpeak QPO models. • The M − j degeneracies can in principle be eliminatedusing angular momentum estimates based on the X-rayburstobservations Torok et al.2012, ApJ, accepted

17. END Thankyouforyourattention…