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

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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

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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

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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

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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

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