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Vznik této prezentace byl podpořen projektem CZ.1.07/2.3.00/09.0138 Tato prezentace slouží jako vzdělávací materiál. ON MASS CONSTRAINTS IMPLIED BY THE RELATIVISTIC PRECESSION MODEL OF TWIN-PEAK QPOs IN CIRCINUS X-1. P avel Bakala , Gabriel Török, E va Šrámková,
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Vznik této prezentace byl podpořen projektem CZ.1.07/2.3.00/09.0138Tato prezentace slouží jako vzdělávací materiál.
ON MASS CONSTRAINTS IMPLIED BY THE RELATIVISTIC PRECESSION MODEL OF TWIN-PEAKQPOsIN CIRCINUS X-1 Pavel Bakala, Gabriel Török, Eva Šrámková, Petr Celestian Čech, Zdeněk Stuchlík&Martin Urbanec Institute ofPhysics, Faculty of Philosophy and Science, Silesian University in Opava,Bezručovo n.13, CZ-74601, Opava Supported by grants OPVK CZ.1.07/2.3.00/09.0138, MSM 4781305903, LC 06014, GAČR202/09/0772, SGS/01/2010 and SGS/02/2010.
Introduction: accretion, quasiperiodicoscillations, twinpeaks Individual peaks can be related to a set of oscillators as well as to a time evolution of an oscillator. LMXBsshort-term X-ray variability: peaked noise (Quasi-PeriodicOscillations) Sco X-1 power • LowfrequencyQPOs (up to 100Hz) • hecto-hertz QPOs (100-200Hz) • kHz QPOs (~200-1500Hz): • Lower and upper QPO mode • forming twin peak QPOs frequency kHz QPO origin remains questionable, it is often expected that they are associated to the orbital motion in the inner part of the disc. Fig:nasa.gov
Circinus X-1and4U 1636-53 We focuse on the two representative neutron star sources. Upper vs. lower QPO frequencies in 1636-53 and Circinus X-1: Clustersofdetections : Circinus X1: 3:1 4U 1636 : 3:2 , 5:4
FittingtheLMXBs kHz QPO data by relativisticprecessionmodel frequency relations Therelativisticprecesion model (in next RP model) introduced by Stella andVietri, (1998, ApJ) indetifiestheupper QPO frequency as orbital (keplerian) frequencyandthelower QPO frequency as theperiastronprecesionfrequency. Thegeodesicfrequencies are the functionsoftheparametersofspacetime geometry (M, j, q) andtheappropriateradialcoordinate. (From : T. Belloni, M. Mendez, J. Homan, 2007, MNRAS)
Circinus X-1massestimationbased on RP model andSchwarzschild geometry
Orbital QPO models under high mass approximation through Kerrmetric NS spacetimes require three parametric description (M,j,Q), e.g., Hartle&Thorne (1968). However, high mass (i.e. compact) NS can be well approximated via simple and elegant terms associated to Kerr metric. This fact is well manifested on ISCO frequencies: Torok et al., (2010),ApJ Orbital QPO models predicts rather high NS masses when the non-rotating approximation is applied. For these models Kerr metric has a potential to provide rather precise spin-corrections which we utilize in next.
Relativistic precession model One can solve the RP model definition equations 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.
Ambiguity in M and j Foreach pair ofparametersM, j therelativisticprecesion model gives a differentcurve in thefrequency – frequencyplane. On the other hand, onecanfindclassesofvery similarcurveswithparametres M,j bounded by therelation:M= Ms[1+0.7(j+j^2)] M = 2.5….4 MSUN Ms = 2.5 MSUN M~ Ms[1+0.75(j+j^2)] Torok et al., (2010), ApJ For a mass Msof the non-rotating neutron star there is always a set of similar curves implying a certain mass-spin relation M (Ms, j) (implicitly given by the above plot). 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.
Relativistic precession model vs. data of 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= Ms[1+0.55(j+j^2)], Ms = 2.2M_sun Bestχ2numericaly Best χ2exactKerrsolution Best χ2linearizedKerrfrequencies
Relativistic precession model vs. data of 4U 1636-53 Color-coded map of χ2 [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 Bestχ2 chi^2 ~ 300/20dof chi^2 ~ 400/20dof Torok et al., (2010) in prep.
3.1. Nongeodesic corrections - It is often believed that, e.g., RP model fits well low-frequency sources but not high-frequency sources. The same non-geodesic corrections can be involved in both classes of sources. The above naive correction improves the RP model fits for both classes of sources.
Nongeodesic corrections - It is often believed that, e.g., RP model fits well low-frequency sources but not high-frequency sources. The same non-geodesic corrections can be involved in both classes of sources. The above naive correction improves the RP model fits for both classes of sources.
Conclusions • The estimate of mass calculatedin theSchwarzschild geometry representsthelowest limit of mass estimate implied by the RP model. • The RP modelis not able to provide independent mass and spin estimates based on thetwin-peak kHz QPOs data.. • Behavior of thetwin-peak QPOs data fits by the RP model frequency relations indicatesthe existence of non-geodesic influence on the orbital frequencies.
