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Pavel Bakala ,Gabriel Török, Zdeněk Stuchlík and Eva Šrámková
Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-74601 Opava, Czech Republic
Supported by
On a multi-resonant origin of high frequency QPOs in the atoll source 4U 1636-53
Ragtime 9
Supported by
Ragtime 9
On the general--relativity predicted relations matching neutron star kHz QPOs
Pavel Bakala ,Gabriel Török, Zdeněk Stuchlík and Eva Šrámková
Or
On a multi-resonant origin of high frequency QPOs in the atoll source 4U 1636-53
Orbital motion in a strong gravity
Figs on this page: nasa.gov
General belief dominating in the astrophysical community links the kHz QPOs to the orbital motion near the inner edge of an accretion disc.
Orbital motion in a strong gravity
Geodesic motion models: orbital motion in a strong gravity
Imply the existence of the periastron and nodal (Lense-Thirring) precession
Periastron precession frequency
Nodal ( declination ) precession frequency
Total precession frequency
rk k
r
Testing frequency relations
Figs on this page: nasa.gov
Data of atoll source 4U-1636-53
Testing frequency relations:Stella, Bursa and Total precession
3.2 Fitting the data in the Hartle-Thorne metric
3.2 Fitting the data in the Hartle-Thorne metric
3.2 Fitting the data in the Hartle-Thorne metric
Fitting the data in the Hartle-Thorn
We consider the external rotating neutron spacetime description given by
„ugly“ HARTLE-THORN METRIC.
We use slightly modified relations for geodesic frequencies derived byAbramowicz, M.A., Almergren, G.J.E., Kluzniak, W., Thampan, A.V., 2003astro-ph/0312070.
Numbers
Figs on this page: nasa.gov
Data of atoll source 4U-1636-53
Numbers
The atoll source 4U 1636-53
(Rough “fit by eye”, in the Schwarzschild case,where the relations coincide.)
Numbers – fits and resulting parameters The atoll source 4U 1636-53
Orbital model Mass
(Msun)
Angular momentum
Quadrupole momentum
Stella 2.65 0.478 0.228
Bursa 2.36 0.495 0.245
Total precession
1.68 0.0 0.0
Extension – non geodesics correction
Figs on this page: nasa.gov
The discussed geodesic relations provide fits which are in good qualitative agreement with general trend observed in the neutron star kHz QPO data .No one of this relations provides really good fits (we checked for the other five atoll sources, that trends are same as for 4U 1636-53) with realistic values of mass and angular momentum with respect to the present knowledge of the neutron star equations of state
To check whether some non geodesic influence can resolve the problem above we consider the assumption that the effective frequency of radial oscillations maybe lowered, e.g., by the hotspots interaction with the accretion disk or with the neutron star magnetic field.
Then, in the possible lowest order approximation, the effective frequency of radial oscillations may be written as
)0.1(~ krr wherewhere k k is a small konstant is a small konstant..
Multiresonant orbital model with non geodesics correctionMultiresonant orbital model with non geodesics correction
Corrected radial epicyclic frequency correspondCorrected radial epicyclic frequency correspondss to more rea to more realisticlistic values of mass values of mass
CorrectCorrectééd d Total precesssion modelTotal precesssion model gives minimum of gives minimum of χχ22 with non zero angular momentumwith non zero angular momentum
Total precession Total precession model model with with non geodesics non geodesics correctioncorrection
Summary
Multiresonant orbital model of QPOs provide fits which are in good qualitative agreement with general trend observed in the neutron star kHz QPO data.
For realy satisfactory fit we have to consider non geodesics correction.
In zero aproximation we introduce corrected radial epicyclic frequency.
Stella and Total precession model with non geodesic correction provides better fits and more realistic values of mass and angular momentum.
Corrected orbital model
Mass (Msun)
Angular momentum Quadrupole momentum
Correction parameter k
Stella 1.79 0.08 0.0064 0.20
Bursa 2.25 0.5 0.25 0.13
Total precession
1.69 0.07 0.0049 0.20
Bonus : Epicyclic frequencies in dipole magnetic field on a pure Schwarzschild background
M=1.5 MM=1.5 Msunsun
B=10B=107 7 GaussGaussRRstarstar=4M=4M
Q=10Q=1010 10
Shift of marginally stable orbitShift of marginally stable orbit
Thank you for your atention
Figs on this page: nasa.gov
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