1. Gabriel Török* On orbital models of kHz QPOs in neutron star binaries *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

2. 1. 1.Introduction: Quasi-periodic oscillations (QPOs) in X-ray from the NS an BH systems Figs on this page: nasa.gov

3. t I Power Frequency 1.1. X-ray timing observations Light curve: Power density spectra (PDS): Figs on this page: nasa.gov

4. hi-frequency QPOs low-frequency QPOs frequency power 1.2. Quasiperiodic oscillations

5. 1.3. kHz Quasiperiodic oscillations: BH and NS

6. 2. Orbital models of kHz QPOs 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.

7. 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.

8. 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

9. 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. 2.2 Orbital resonance models

10. 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 =  r). (For such a models we discuss the relation betwee the observed QPO frequencies and the relevant radial position in the disc.) 2.3 Orbital models

11. 3. Measuring the radial position in the disc Figs on this page: nasa.gov 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…

12. 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.

13. 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

14. 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 Importance of the epicyclic frequencies

15. 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 Measuring the radial position

16. 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. 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 Measuring the radial position

17. 3. Measuring the radial position from observation Figs on this page: nasa.gov Back to the Schwarzschild…

18. 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. Many of orbital QPO models identify the QPO frequency directly to a radial position in the accretion disc = (r). 3.1 Measuring the radial position from observation

19. 3.2 Application to the relativistic preccesion model

21. Figs on this page: nasa.gov 4. Exploring the data

22. 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

23. 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

24. 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. The corresponding detections of the single QPOs extends to about 10 times larger part of observations. 3. Exploring the data

25. Twin peaks

26. 3. Exploring the data ? Twin peaks

27. 3. Exploring the data Twin peaks all upper peaks

28. 3. Exploring the data Twin peaks all upper peaksall lower peaks

29. 3. Exploring the data Twin peaks single upper peakssingle lower peaks

30. 3. Exploring the data Twin peaks single upper peakssingle lower peaks

31. 3. Exploring the data Twin peaks single lower peakssingle upper peaks

32. 3. Exploring the data (The vertical axes scale is arbitrary.)

33. 4. Conclusions To be done instantenously…

34. 4. Bonus I

36. 5. Bonus II

38. 6. References Figs on this page: nasa.gov

39. 6. References Abramowicz, Barret, Bursa, Horák, Kluzniak, Olive, Rebusco, Török, 2006, proc. Of RAGtime 2005, download: ADS or www.physics.cz/research Presentation download: www.physics.cz/research in sect. news SLIDE UNDER THE CONSTRUCTION