1. Gabriel Török* 3:2 controversy …hope for underlying QPO physics ? *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. X-ray timing observations of low mass X-ray binaries Figs on this page: nasa.gov LMXBs short-term X-ray variability Low frequency QPOs (up to 100Hz) hecto-hertz QPOs (100-200Hz) kHz QPOs (~200-1500Hz) frequency power Sco X-1

3. 1.2. kHz Quasiperiodic oscillations: BH and NS Upper QPO frequency Lower QPO frequency Neutron stars Black holes (microquasars)

4. 1.3.Ratio clustering Upper QPO frequency Lower QPO frequency Neutron stars Abramowicz et al. (2003), A&A

5. 1.3.Ratio clustering Histograms of frequency ratio for observations displaying two significant kHz QPOs (Abramowicz et al 2005) in six atoll sources. Histograms peaks close to 3:2 3:23:25:4 3:2 5:4 4:3 4:3

6. 2. 3:2 controversy ?? Belloni et al. (2004,2005A&A) studied frequency distributions in several sources. They confirmed the clustering around 3:2 and other ratios, but put some doubts on its interpretation. Consequently, Belloni et al. (2007,MNRAS) examined lower QPO frequency distibution in the atoll source 4U 1636-53 and assuming a linear correlation between lower and upper kHz QPO frequency discussed the inferred ratio distribution. They concluded that there is no preferred ratio in the source. This result contradicts previous finding of ratio clustering in 1636-53.

7. 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. 2.2 Exploring 4U 1636-53 kHz QPO data

8. The part of data displaying significant twin peak QPOs is restricted to about 20 hours of observation. The detections of the single significant QPOs extend to about 10 times larger part of observations. It is possible to determine whether the single peaks belong to group of upper or lower QPOs safely using the Quality factor diagram (Barret 2005). We have therefore - - significant lower QPO detections (lower QPOs) - - significant upper QPO detections (upper QPOs) - - twin QPOs (overlap between lower and upper QPO observations) 2.2 Exploring 4U 1636-53 kHz QPO data

9. lower QPOs upper QPOs 2.3 Distributions twin QPOs - significant lower QPO detections (lower QPOs) - - significant upper QPO detections (upper QPOs) - - twin QPOs (overlap between lower and upper QPO observations) (Torok et al. (2008), AcA submitted)

10. 2.3 Ratio distribution (Torok et al. (2008), AcA submitted)

11. 2.4 Resolving the controversy correlation between lower and upper QPO frequency (used by Belloni at al. 2007) Distribution of the ratio inferred from the lower frequency distribution (FD) differs from those inferred from the upper FD and both differ from really observed distribution of ratio. There are the preferred frequency ratios.

12. 3. Implications for orbital kHz QPO models …hope for underlaying physics ? Figs on this page: nasa.gov

13. 3.Implications for orbital models lower QPOs twin QPOs upper QPOs => For models which identifies given QPO frequency to an orbital radius, one can look from where the oscillations come. Here we focus on the relativistic precession model of Stella and Vietri. Torok et al. (2008), AcA, accepted Ratio radius

14. 3.1 Bonus lower QPOs twin QPOs upper QPOs Difference between lower and upper QPO amplitude [rms,%] Torok (2008), A&A, submitted Here we focus on the relativistic precession model of Stella and Vietri. Note however that its frequency identification coincides with those of radial m=1 and vertical m=2 disc oscillation modes. Our conclusions are also qualitatively valid for several other models, e.g., NS warp disc precession model of S. Kato (2008).

15. 4. References Figs on this page: nasa.gov

16. 5. References Abramowicz et al., A&A L, 2003 Barret et al., 2005, MNRAS Belloni et al., 2005, A&A Mendez, 2006, MNRAS Belloni et al., 2007, MNRAS Torok, 2007, A&A L, submitted Presentation download: www.physics.cz/research in sect. news SLIDE UNDER THE CONSTRUCTION