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In relation to the mentioned models, both the kinematic of geodesic motion and the physics of disc oscillations depends strongly on the properties of epicyclic frequencies.

In relation to the mentioned models, both the kinematic of geodesic motion and the physics of disc oscillations depends strongly on the properties of epicyclic frequencies.

Onorbitalmodels of kHz QPOsin neutron star binaries

Gabriel Török*

*Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-74601 Opava, Czech Republic

The presentation draws mainly from a collaboration with

M.A. Abramowicz, D. Barret, P.Bakala, M. Bursa, J. Horák, W. Kluzniak, M. Urbanec, and Z. Stuchlík

- Introduction:
- Quasi-periodic oscillations (QPOs) in X-ray from the NS an BH systems

Figs on this page:nasa.gov

1.1.X-ray timing observations

Light curve:

I

t

Power density spectra (PDS):

Power

Frequency

Figs on this page:nasa.gov

1.3.kHz Quasiperiodic oscillations: BH and NS

2. Orbital models of kHz QPOs

General belief dominating in the astrophysical community links the kHz QPOs to the orbital motion near the inner edge of an accretion disc.

Figs on this page:nasa.gov

2.1.Geodesic motion models: orbital motion in a strong gravity

Several models have been outlined to explain the kHz QPO frequencies and and not all of them but a lot of them relate this QPOS to the orbital motion near the inner edge of an accretion disc.

2.1.Geodesic motion models: orbital motion in a strong gravity

Imply the existence of the periastron and nodal (Lense-Thirring) precession

Stella, L. \& Vietri, M. 1999, Phys. Rev. Lett., 82, 17

related the kHz QPOs to the Keplerian and periastron precession of the blobs close to the inner edge of an accretion disc.

- Relativistic precession model

2.2 Orbital resonance models

Relativistic precession model

(Stella, L. \& Vietri, M. 1999, Phys. Rev. Lett., 82, 17)

related the kHz QPOs to the frequencies of geodesic motion

(Keplerian and periastron precession of the blobs close to the inner edge of an accretion disc).

Resonance model

Kluzniak, W., Abramowicz, M. A., 2000, Phys. Rev. Lett. (submitted); Klu\'zniak, W., \& Abramowicz, M. A., 2001, Acta Physica Polonica B 32, 3605 [http://th-www.if.uj.edu.pl/acta/vol32/t11.htm]

related the kHz QPOs to a resonance between disc oscillation modes corresponding to the frequencies of geodesic motion.

2.3 Orbital models

- Relativistic precession model
- (Stella, L. \& Vietri, M. 1999, Phys. Rev. Lett., 82, 17)
- related the kHz QPOs to the frequencies of geodesic motion
- (Keplerian and periastron precession of the blobs close to the inner edge of an accretion disc).
- Resonance model
- Kluzniak, W., Abramowicz, M. A., 2000, Phys. Rev. Lett. (submitted); Klu\'zniak, W., \& Abramowicz, M. A., 2001, Acta Physica Polonica B 32, 3605 [http://th-www.if.uj.edu.pl/acta/vol32/t11.htm]
- related the kHz QPOs to a resonance between disc oscillation modes corresponding to the frequencies of geodesic motion.
- There are several other models among the two representative classes above.
- In next we present some rather strong observational restrictions which pose a challlenge to all of them and in particular to those which relates the QPO frequency directly to a radial position in the accretion disc
- = n(r).
(For such a models we discuss the relation betwee the observed QPO frequencies and the relevant radial position in the disc.)

3. Measuring the radial position in the disc

It is not a good idea to measure in kilometres at all, but the usual much more convenient mass independent radial coordinates also do not pose a best choice…

Figs on this page:nasa.gov

3.1 Importance of the epicyclic frequencies

In relation to the mentioned models, both the kinematic of geodesic motion and the physics of disc oscillations depends strongly on the properties of epicyclic frequencies.

3.1 Importance of the epicyclic frequencies

In relation to the mentioned models, both the kinematic of geodesic motion and the physics of disc oscillations depends strongly on the properties of epicyclic frequencies.

For a correct treatment of this properties in a case of particular rotating neutron star it neccesary to use such an “ugly” metric description like those derived by Hartle & Thorne (1968)

3.1 Importance of the epicyclic frequencies

In relation to the mentioned models, both the kinematic of geodesic motion and the physics of disc oscillations depends strongly on the properties of epicyclic frequencies.

For a correct treatment of this properties in a case of particular rotating neutron star it neccesary to use such an “ugly” metric description like those derived by Hartle & Thorne (1968).

The relevant therms for the frequencies derived by Abramowicz, Almergren, Kluzniak, Thampan then do not fit to the screen at all…

3.1 Measuring the radial position

3.1 Measuring the radial position

While the frequencies itself strongly depends on both the mass and angular momentum and meaning of usual dimensinless radial coordinate is confused by spin, the ratio of epicyclic frequencies or a similar function is in relation to the physics of the disc rather insensitive to the compact object properties.

Note: the ratio of epicyclic frequencies diverges at the ISCO so it is more convenient to use e.g. ratio of the Keplerian and periastron preccesion frequency.

3. Measuring the radial position from observation

Back to the Schwarzschild…

Figs on this page:nasa.gov

3.1 Measuring the radial position from observation

Many of orbital QPO models identify the QPO frequency directly to a radial position in the accretion disc

n = n(r).

In most of them the upper and lower observed QPO frequency is given by the functions

which can be expressed as a combination of the epicyclic frequencies.

Therefore for all these models there is a good mass and angular momentum independent measure of the radial position relevant to a given twin QPO detection given just by the ratio of the observed frequencies:

For a given model it is then not difficult to solve the functions f1, f2 for M=1, j=0, q=0 for the ratio R with respect to the Schwarzschild coordinate r

R => r,

and the measurement can be compared or collected with a very small unacurratness for the sources independently on properties of their central compact object.

3.2 Application to the relativistic preccesion model

3.2 Application to the relativistic preccesion model

4. Exploring the data

Figs on this page:nasa.gov

3. Exploring the data

The observational data we use here correspond to all the RXTE observations of the atoll source 4U 1636+53 proceeded by the shift-add technique through continuous segments of observation (the analysis of Barret et al. 2005).

The part of data displaying significant twin peak QPOs is restricted to about 20 hours of observation represented in our study by the averaged 23 datapoints corresponding to the individual continuous observations. It is needed for a further study to proceed this data by other methods in order to obtain more detailed view of the data distribution. However, in terms of the RP model the 23 significant datapoints we use represent (under the assumption of the hot spot lifetime being equal to few orbits) the statistics of ~10^7 individual hot spots.

3. Exploring the data

The observational data we use here correspond to all the RXTE observations of the atoll source 4U 1636+53 proceeded by the shift-add technique through continuous segments of observation (the analysis of Barret et al. 2005).

The part of data displaying significant twin peak QPOs is restricted to about 20 hours of observationrepresented in our study by the averaged 23 datapoints corresponding to the individual continuous observations. It is needed for a further study to proceed this data by other methods in order to obtain more detailed view of the data distribution. However, in terms of the RP model the 23 significant datapoints we use represent (under the assumption of the hot spot lifetime being equal to few orbits) the statistics of ~10^7 individual hot spots.

3. Exploring the data

The observational data we use here correspond to all the RXTE observations of the atoll source 4U 1636+53 proceeded by the shift-add technique through continuous segments of observation (the analysis of Barret et al. 2005).

The part of data displaying significant twin peak QPOs is restricted to about 20 hours of observationrepresented in our study by the averaged 23 datapoints corresponding to the individual continuous observations. It is needed for a further study to proceed this data by other methods in order to obtain more detailed view of the data distribution. However, in terms of the RP model the 23 significant datapoints we use represent (under the assumption of the hot spot lifetime being equal to few orbits) the statistics of ~10^7 individual hot spots.

The corresponding detections of the single QPOs extends to about 10 times larger part of observations.

3. Exploring the data

Twin peaks

3. Exploring the data

(The vertical axes scale is arbitrary.)

To be done instantenously…

4. Bonus I

4. Bonus I

5. Bonus II

5.Bonus II

Figs on this page:nasa.gov

- 6. References
- Abramowicz, Barret, Bursa, Horák, Kluzniak, Olive, Rebusco, Török,
- 2006, proc. Of RAGtime 2005,
- download: ADS or www.physics.cz/research

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