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Gabriel Török

On the amplitudes of NS kHz quasiperiodic oscillations. Gabriel Török. Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-74601 Opava, Czech Republic. Fig: nasa.gov. The p resentation draws mainly from the collaboration with

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Gabriel Török

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  1. On the amplitudes of NS kHz quasiperiodic oscillations Gabriel Török Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-74601 Opava, Czech Republic Fig:nasa.gov The presentation draws mainly from the collaboration with M.A. Abramowicz, D. Barret, P.Bakala, M. Bursa, J. Horák, W. Kluzniak, M. Urbanec, and Z. Stuchlík

  2. 1. X-ray timing observations of NS X-ray binaries Sco X-1 LMXBs short-term X-ray variability power frequency • Low frequency QPOs (up to 100Hz) • hecto-hertz QPOs (100-200Hz) • kHz QPOs (~200-1500Hz): • Lower and upper QPO mode • forming twin peak QPOs Upper QPO Lower QPO Note: when only one kHz peak is weakly, but significantly, detected, it is still possible to estimate which of the two modes it is. Fig:nasa.gov

  3. 2.kHz QPO amplitude evolution in six atoll sources Profitting from the existing studies, we lookat a large amount of the data published for the six atoll sources4U 1728, 4U 1608, 4U 1636, 4U 0614, 4U 1820 and 4U 1735 [from Mendez et al. 2001; Barret et al. 2005,6;van Straaten et al. 2002; not all listed]. Taking into account the correlations between lower and upper QPO frequency we focus on evolution of the rms QPO amplitudes rL, rU . Example of 4U 1636: UpperQPO frequency nU [Hz] Upper QPO amplitude rU 4U 1636 Lower QPO amplitude rL equality atnU~ 1000Hz Weak lowerQPO LowerQPO frequency nL[Hz]

  4. 2. kHz QPO amplitude evolution in six atoll sources The behaviour is similar across six sources: Upper QPO amplitude is steadily decreasing with frequency. Lower QPO is first weak, increasing with frequency, reaching the same amplitude as the upper QPO at nU ~ 900-1100Hz, then it reaches a maximum and starts to decrease. There is possibly an equality of amplitudes again at high frequencies when both the QPOs start to disappear. Example of 4U 1608: UpperQPO frequency nU [Hz] Upper QPO amplitude rU 4U 1608 Lower QPO amplitude rL equality atnU~ 900Hz Weak lowerQPO LowerQPO frequency nL[Hz]

  5. 2.kHz QPO amplitude evolution in six atoll sources • To explore the findings of the amplitude equality we use the data and software of D. Barret and investigate the available segments of continuous observations (all public RXTE till 2004). • The analysis of these dataconclusively indicates that in all the six sources the both QPOamplitudesequal each other at nU ~ 900-1100Hz. • There is an additional equality at high frequencies in four sources.

  6. 2. kHz QPO amplitude evolution in six atoll sources • In case of the amplitude equality at low frequencies nU ~ 900-1100Hz, the relevant upper QPO frequency is within about 25% subinterval of total range covered by the six sources [15% if considered in terms of lower QPO frequency]. • In terms of the frequency ratio R = nU / nL the similarity is most obvious: The interval nU ~ 900-1100Hz corresponds to R within a range 1.45 -- 1.55, i.e, to 5% of the total range of ratio R =1.2 -- 3. • Such a strong similarity in ratio eventually supports the hypothesis of the orbital origin of QPOs under the assumption that the mass is the main difference across the sources.Frequencies of geodesic orbital motion close to neutron stars (nearly) scale with mass. Their ratio is therefore unaffected by the neutron star mass.

  7. 2.1kHz QPO amplitude evolution in terms of frequency ratio Note: Frequencies of sharp maxima of the high lower QPO coherence (Barret et al 2004,5) correspond to ratio 1.25—1.4 where are also maxima of amplitude difference. In that region therefore lower QPO fully dominates, while in the rest of data it is weak. Amplitude difference Dr = rL – rU as it behaves in terms of the frequency ratio R Points: Cont. segments Curves: published data interpolation [Török 2008, A&A submitted]

  8. 2.2 Possible relation to twin peak QPO ratio clustering • As reported several times (first in Abramowicz etal 2003 arguing for evidence of a resonance in QPO data), in many NS sources the ratio between the upper and lower QPO frequency cluster, most often close to the 3:2 value observed in BHs. • Recently, a large study of Belloni et al. 2007 (MNRAS) examined in detail the QPOs in 4U 1636-53 and pointed out that there is no preferred lower QPO frequency.

  9. 2.2 Possible relation to twin peak QPO ratio clustering • Recently Belloni et al. 2007 (MNRAS) pointed out that there is no preferred lower QPO frequency in 4U 1636-53. • the ratio of simultaneous significant detections of the lower and upper QPO however cluster close to the 3:2 value in that source (Török et al 2008, Acta Astronomica). Most likely, in 4U 1636 the simultaneous detections of both modes cluster around the 3:2value because there is a reverse of their dominance. 1636, simulation of detections expecting uniform source distribution of QPO pairs (Török et al, Acta Astronomica 2008) Upper QPO ratio higher than 3:2ratio lower than 3:2 Lower QPO dominates With high amplitude and Q, Weak upper QPO Upper QPO dominates having high amplitude, Weak lower QPO Lower QPO Simultaneous detections frequency

  10. 2.2 Possible relation to twin peak QPO ratio clustering • As found by Barret & Boutelier, 2008 (NewAR), the problem is more complicated and the observed clustering is in general not following from QPO properties and a uniform source distribution • Contrary to 1636, in 1820 the ratio clustering cannot be simulated from the uniform source distribution of the QPO pairs. • There roots of amplitude difference in 1820 are close to 3/2 and 4/3 frequency ratio. However, there is a lack of simultaneous detections close to 3/2. 4U 1636 observed simulated Török et al, Acta Astr. 2008 Barret & Boutelier, NewAR 2008

  11. 2.2 A possible relation to twin peak QPO ratio clustering • Contrary to 1636, in 1820 the ratio clustering cannot be simulated from the uniform source distribution of the QPO pairs [Barret & Boutelier,NewAR 2008]. • The problem of the ratio clustering remains a puzzle which can however bring some light onto the question of the QPO origin. • Histograms of frequency ratio based on twin detections • In the six atolls (at least one of) the roots of the amplitude difference coincides with the observed clustering. 0614 1728 1608 1636 1820 1735

  12. 3.Summary and conclusions • In the six atoll sources 4U 1728−34, 4U 1608−52, 4U 1636−53, 4U 0614+09, 4U 1820−30 and 4U 1735−44, • the lower and upper QPO amplitude equal each other within the interval of frequency ratio R=1.45-1.55 (i.e., R=3/2 \pm 3%). • There is again such an equality for four sources, namely in 4U 1820-30 and 4U 1735-44 at R~1.33; In 4U 1636-53 and 1608-52 at R~1.25. • There is a possible relation to the twin peak ratio clustering. A detailed investigation is needed also to determine the roots more precisely, especially in case of 1820 and 1735 (see, however, Barret & Boutelier 2008).

  13. 3.Summary and conclusions • In the six atoll sources 4U 1728−34, 4U 1608−52, 4U 1636−53, 4U 0614+09, 4U 1820−30 and 4U 1735−44, • the lower and upper QPO amplitude equal each other within the interval of frequency ratio R=1.45-1.55 (i.e., R=3/2 \pm 3%). • There is again such an equality for four sources, namely in 4U 1820-30 and 4U 1735-44 at R~1.33; In 4U 1636-53 and 1608-52 at R~1.25. • There is a possible relation to the twin peak ratio clustering. A detailed investigation is needed also to determine the roots more precisely, especially in case of 1820 and 1735 (see, however, Barret & Boutelier 2008). • Implications for orbital QPO models • The existence of such a strong similarity in terms of the frequency ratio challenges concrete QPO models. It possibly supports a general hypothesis of the orbital origin of QPOs.[The frequencies of geodesic orbital motion close to neutron stars (nearly) scale with mass. Their ratio is therefore unaffected by the neutron star mass…] • 3:2 ratio which appears in this similarity is suggestive in case of resonant model • For several of the QPO orbital models our findings imply existence of a prominent orbit (narrow orbital region) with balanced amplitudes of oscillations.

  14. 3.1 Bonus: implications for concrete QPO models QPO clustering) Lower QPO Both QPOs Upper QPO Combined data of 1636 and 1728 Difference between lower and upper QPO amplitude [rms,%] Also a region of maximal lower QPO coherence 0.4 km from ISCO 10km from ISCO Here we use an illustration based 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. It is qualitatively valid for several other models, e.g., NS warp disc precession model of S. Kato (2008).

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