Gabriel Török* On orbital models of kHz QPOs *Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ 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

Gabriel Török* Outline 1. Orbital QPO models and frequency ratio The meaning - not of live but of the frequency ratio 2. 4U Ratio distribution in 4U Amplitude behaviour other atoll + 3 Z = set of 9 systematically investigated sources 4. Summary and conclusions 5. References

1. Orbital kHz QPO models and frequency ratio 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.

In several of them the upper and lower observed QPO frequency can be expressed as a combination of the epicyclic frequencies. When the spin and quadrupole momentum are fixed, for all these models there is a good mass independent measure of the radial position relevant to a twin QPO detection given just by the ratio of the observed frequencies: (and it has potentially different, but also a good, meaning for any resonant models). The two observed kHz QPO frequencies are well correlated. Many of QPO models identify the kHz QPO frequency directly to a radial position in the accretion disc  = (r). 1. Orbital models and frequency ratio

In addition, the frequency combination above provide in a less direct way the measure independent also on the angular momentum. For instance, when the spin is changing in the interval a=0..1, the ratio K / (   r ) equals 1 at the rms and its relative change at the position of maximum of the radial epicyclic frequency is 10x lower than the relative change of the dimensionless radial coordinate. FIG. by.MAA,, c FIG. by.MAA,, c Orbital models and frequency ratio

Therefore for the discussed models one can use for some purposes only the frequency ratio R instead of the frequency, eliminating the uncertanities given by properties of central compact object. It is easy to solve the expressions for the lower and upper QPO frequency for the ratio R with respect to the Schwarzschild coordinate r having the good intuitive, but physical, meaning of the position in the above dimensionless Figure. Measurements can be this way collected and compared for several sources (with a very small unacuratness). FIG. by.MAA, c FIG. by.MAA, c Orbital QPO models and frequency ratio

2. 4U Figs on this page: nasa.gov We use here the all data available from the RXTE observations of the atoll source 4U 1636 till 2005 coming from the study of Barret et al. (2005).

The observational data we use correspond to all the RXTE observations of the atoll source 4U 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. For instance in terms of the RP model, the 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 significant QPOs extend to about 10 times larger part of observations. It is possible to determine the single peaks safely using the Quality factor diagram (Barret 2005). 2.1 Exploring a bit the 4U kHz QPO data

2.2 4U : distributions Lower frequency distribution Upper frequency distribution The two frequency distributions obviously differ and both differ from twin peak frequency distribution implying the twin peak ratio distribution.

2.2 4U : distributions The ratio distribution R

Our rough analysis of the three distributions is in good agreement with the data from systematic 18 months campaign of Belloni et al [who, however, suppose existence of a generic equivalence of the three discussed distributions although (or as) they examin the data set having overlap between lower and upper QPO detections given by three continuous observations, being ~1/40 of the total of detected peaks] U : distributions

2.3 Implications (not only) for model of Stella & Vietri => One can look from where the three different distribution come Neutron star Relativistic precession model: rms =>

Neutron star Relativistic precession model: Area responsible for significant single UPPER PEAKS Area responsible for significant TWIN PEAKS Area responsible for significant single LOWER PEAKS 2.3 Implications (not only) for model of Stella & Vietri

Relativistic precession model: Note: The exactly same figure would appear also for the relevant discoseismology modes. Area responsible for significant single UPPER PEAKS Area responsible for significant TWIN PEAKS 2.3 Implications (not only) for model of Stella & Vietri Area responsible for significant single LOWER PEAKS Figure is mass and nearly angular momentum Independent Independent

Our rough analysis is in agreement with the data of Belloni et al with the (“old”) statement that the 3:2 ratio pops up in the NS observational data, i.e., The answer to the question whether a 3:2 ratio appears in NS sources is OBVIOUSLY YES (at least in the case of 4U ): The upper / lower QPO is much less / more often detected when the frequency ratio is higher / lower than 3:2. In terms of discussed orbital models one may say this about radius instead of frequency ratio. The other important question* is the question whether the above effect is because of undected QPOs are not produced, or whether they are only too weak (difficult) to be detected. In the second case it should be possible to obtain the transformation between frequency distributions from the correlation of QPO amplitude and quality factor. * Which we can not answer today ratio - summary

2.5 Amplitude difference Plot of the difference between rms amplitudes as a function of the frequency ratio Area responsible for significant TWIN PEAKS for instance, for relativistic precession model one can draw

3. 6x atoll + 3xZ Figs on this page: nasa.gov Being motivated by case of , we looked to several other sources.

3.1 Three more atoll sources, amplitude difference !!! Plot of the difference between rms amplitudes as a function of frequency ratio:

Set I: Analysis of continuoussegments (data and software provided by Didier Barret) Set II: Comes from interpolation of various data accumulated by Mendez (2006) 3.2 six atolls !!!

3.3 Three Z-sources, amplitude difference

3.4 Amplitude difference - summary GX pm > pm>0.0 GX pm ?? GX pm ?? 2.5 pm ?? atoll Z clustering 3/2 3/2 3/2, ? 3/2, ? 3/2, 5/4 3/2, 5/4 3/2 3/2 4/3 4/3 Notice that 1.5 = 3/2 = (2+1) / = 4/3 = (3+1) / = 4/3 = (3+1) / = 5/4 = (4+1) / = 5/4 = (4+1) / 4 *Errors are given by chi square + 1. *

4. Conclusions Figs on this page: nasa.gov

For existing observations, the actually observed ratio of QPO frequencies rathertends to cluster around ratios of small natural numbers. We do not know (yet) whether this effect can be fully understand in therms of Fourier signal decomposition and measurements conditions. Resolving this may require large observational campaign (few years of systematic observation of one source). It seems to be common property of several sources, that one QPO becomes weaker than the other one when the source pass 3/2 ratio. 4. Conclusions

In all 9 sources we discussed the amplitudes of observed oscillations equals when the source pass 3/2 ratio, more specifically, the roots of relevant interpolations are for all 9 sources most likely inside of the narrow 3% interval around R=1.5. This represents a serious challenge - any model should explain the amplitude difference behaviour. 4. Conclusions 10km ( =1.44 ) 500m e.g., Stella & vietri: e.g., Stella & vietri:

In all 9 sources we discussed the amplitudes of observed oscillations equals when the source pass 3/2 ratio, more specifically, the roots of relevant interpolations are for all 9 sources most likely inside of the narrow 3% interval around R=1.5. This represents a serious challenge - any model should explain the amplitude difference behaviour. 4. Conclusions There is qualitatively similar implication for several models including those of S. Kato. There is qualitatively similar implication for several models including those of S. Kato. The amplitude behaviour puts in addition strong restrictions to the choice of modes in case of disc oscillation model if the Pazcynski- or Lensing- modulation mechanisms are considered. The amplitude behaviour puts in addition strong restrictions to the choice of modes in case of disc oscillation model if the Pazcynski- or Lensing- modulation mechanisms are considered. e.g., S. Kato: e.g., S. Kato: 30km ( =1.44 ) 1km

5. References Figs on this page: nasa.gov

6. 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: in sect. news SLIDE UNDER THE CONSTRUCTION