Gabriel Török 3:2 ratio in NS X-ray observations: summary of recent progress The presentation draws mainly from the collaboration with M.A. Abramowicz, D. Barret, P.Bakala, M. Bursa, J. Horák, W. Kluzniak, and Z. Stuchlík Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ Opava, Czech Republic

Outline Basic introduction: 1. 1.Low-mass X-ray binaries (LMXBs), accretion discs 2. 2.kHz variability, its origin 3. 3.kHz QPOs in BH and NS sources 3:2 frequency ratio in NS systems: 4. Ratio clustering 5. Amplitude evolution 6. Summary and discussion Bonus: implications, queries and future prospects

I. Basic introduction Fig: nasa.gov

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability density comparable to the Sun mass in units of solar masses temperature ~ roughly as the T Sun moreless optical wavelengths Artists view of LMXBs “as seen from a hypothetical planet” Companion: Compact object: - black hole or neutron star Accretion disc: - - Keplerian ang. momentum distribution (or >) - - highest velocities in percents of light speed - - disipation and angular momentum transfer - - release of gravitational energy (up ~0.5M!) - - temperature of the disc inner part reaches milions of Kelvins - >90% of radiation in X-ray (units—tens of keV)

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability Artists view of LMXBs “as seen from a hypothetical planet” X-ray satellites “the real eyes” Observations: The X-ray radiation is absorbed by Earth atmosphere and must be studied using detectors on orbiting satellites representing rather expensive research tool. On the other hand, it provides a unique chance to probe effects in the strong-gravity-field region (GM/r~c^2) and test extremal implications of General relativity (or other theories).

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability Example of the Galactic microquasar GRS : the concept and what is seen. Gamma rayX-ray “white dot” of GRS Companion Disc Jet Fig: nasa.gov., Hannikainen et al Observations: Our connection to the accreting compact objects is quite subtle. Typically, the whole information coming to vicinity of Earth is carried by countrates of thousands (hundreds) photons detected per second. radio

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability Here we focus on the timing properties of X-ray detected from LMXBs. Observed systems shows rather complicated behaviour in - -Long-term variability (discussed in terms of lightcurves, from hours to days) - -Short-term variability (discussed in terms of PDS, mHz to kHz), corresponding to the “relativistic orbital” timescales. Although here we concentrate on the short term variability, it should be stressed that this variability is tightly connected to the long term variability and also to the source spectral properties. The next marginal slide is devoted to the long term variability just to illustrate the complexity of the problem.

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability Fig and movie:UKAFF Observations: Our connection to the accreting compact objects is quite subtle. Typically, the whole information coming to vicinity of Earth is carried by countrates of ~hundreds photons per second. Here we focus on timing properties of X-ray detected from LMXBs. Observed systems shows rather complicated behaviour in both - Long-term variability ( in terms of lightcurves, from hours to days) - Short-term variability (discussed in terms of PDS, mHz to kHz) time I densityemissivity UKAFF supercomputer simulation of black hole long term variability low high

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability movie:UKAFF Long-term variability ( in terms of lightcurves, from hours to days) time Brightness densityemissivity low high low high

2. Short term variability – kHz range Figs: from the collection of van der Klis, 2006 frequency power Sco X-1 LMXBs exhibit several peaked features (QPOs) in their PDS. Particular kind of QPOs belongs to the kHz range. Peaks in the kHz range of PDS arise across several different systems (BH microquasars, NS Z- and atoll sources, milisecond X-ray pulsars, NS microquasar). These kHz QPOs attract a lot of attention due their possible link to an orbital motion in vicinity of binary central compact object. The kHz QPOs often come in pairs.

3. kHz QPOs in BH and NS systems: properties (and differencies) Power Frequency height h width w at ½ h Quality factor Q indicates sharpness of the peak, Q ~ h/w Amplitude r indicates strength of peak variability (its energy) in terms of “rms amplitude” = percentual fraction (root mean square fraction) of the peak energy with the respect to the total countrate (r ~ area under peak) BH QPOs (Galactic microquasars): frequencies up to 500Hz low amplitude and Q : typically up to r~5% and Q~5 NS QPOs: frequencies up to 1500Hz often amplitudes up to r~20% and quality factors up to Q~200

3. kHz QPOs in BH and NS: frequency correlations (and differences) Upper QPO frequency Lower QPO frequency Neutron stars: variable frequencies Black holes: fixed 3:2 ratio (microquasars) Bursaplot

II. 3:2 kHz QPO frequency ratio in NS systems: Fig: nasa.gov clustering

4. Ratio clustering Upper QPO frequency Lower QPO frequency Black holes: fixed 3:2 ratio (microquasars) Neutron stars: variable frequencies

4. Ratio clustering Upper QPO frequency Lower QPO frequency Abramowicz et al. (2003), A&A Neutron stars: variable frequencies ratio peaks to 3:2

4. Ratio clustering: 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 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 our previous (unpublished) findings on ratio clustering in

The observational data we use here 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. 4.2 Exploring 4U kHz QPO data

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) 4.2 Exploring 4U kHz QPO data

lower QPOs upper QPOs 4.3 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., AcA, 2008a)

4.3 Ratio distribution (Torok et al. (2008a), AcA)

4.4 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.

III. 3:2 kHz QPO frequency ratio in NS systems: Fig: nasa.gov amplitude evolution

5. kHz QPO amplitude evolution in six atoll sources Fig: nasa.gov frequency power Sco X-1 Upper 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. For instance Q_L is never above 50 in the atoll sources… Lower QPO Power Frequency height h width w at ½ h Quality factor Q indicates sharpness of the peak, Q ~ h/w Amplitude r indicates strength of peak variability (its energy) in terms of “rms amplitude” = percentual fraction (root mean square fraction) of the peak energy with the respect to the total countrate (r ~ area under peak)

5. kHz QPO amplitude evolution in six atoll sources Profitting from the existing studies, we look at a large amount of the data published for the six atoll sources 4U 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 r L, r U. Example of 4U 1636: Upper QPO frequency U [Hz] Lower QPO frequency L [Hz] Weak lower QPO Upper QPO amplitude r U Lower QPO amplitude r L ~ 1000Hz equality at U ~ 1000Hz 4U 1636

5. 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 U ~ Hz, 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. Weak lower QPO Upper QPO frequency U [Hz] Lower QPO frequency L [Hz] ~ 900Hz equality at U ~ 900Hz Example of 4U 1608: 4U 1608 Upper QPO amplitude r U Lower QPO amplitude r L

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 data conclusively indicates that in all the six sources the both QPO amplitudes equal each other at U ~ Hz.   There is an additional equality at high frequencies in four sources. 5. kHz QPO amplitude evolution in six atoll sources

  In case of the amplitude equality at low frequencies U ~ Hz, 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 = U / L the similarity is most obvious: The interval U ~ Hz corresponds to R within a range , i.e, to 5% of the total range of ratio R =   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. 5. kHz QPO amplitude evolution in six atoll sources

Amplitude difference  r = r L – r U as it behaves in terms of the frequency ratio R Points (Dataset I): Continuos segments, one coherent analysis Curves: miscellaneous available published data interpolation [Török 2008, A&A submitted] 5.1 kHz 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. 5.1 relation between two QPOs as depends on frequency ratio R~1.25 R < 1.5R ~ 1.5R > 1.5 PDS:

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. 5.1 relation between two QPOs as depends on frequency ratio R~1.25 R < 1.5R ~ 1.5R > 1.5 PDS:

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. R~1.25 R < 1.5R ~ 1.5R > relation between two QPOs as depends on frequency ratio PDS:

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. R~1.25 R < 1.5R ~ 1.5R > relation between two QPOs as depends on frequency ratio PDS:

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. R~1.25 R < 1.5R ~ 1.5R > relation between two QPOs as depends on frequency ratio PDS:

Note: the lack of datapoints for high R can be caused by weakness of the lower QPO (datapoints in the plot are all above 2.5 sigma significancy, the extra insignificant “diamond” has less than 2 sigma, being typical for that part of data). 5.1 relation between two QPOs as depends on frequency ratio R~1.25 R < 1.5R ~ 1.5R > 1.5 PDS:

5.2 Possible relation to twin peak QPO ratio clustering   Results of Belloni et al (MNRAS) indicate that there is no preferred lower QPO frequency in 4U 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 2008a, Acta Astronomica).

5.2 Possible relation to twin peak QPO ratio clustering   Results of Belloni et al (MNRAS) indicate that there is no preferred lower QPO frequency in 4U 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 2008a, Acta Astronomica). Most likely, in 4U 1636 the simultaneous detections of both modes cluster around the 3:2 value because there is a reverse of their dominance. frequency Upper QPO dominates having high amplitude, Weak lower QPO Lower QPO dominates with high amplitude and Q, Weak (often undetected) upper QPO ratio higher than 3:2 ratio lower than 3:2

5.2 Possible relation to twin peak QPO ratio clustering Most likely, in 4U 1636 the simultaneous detections of both modes cluster around the 3:2 value because there is a reverse of their dominance. frequency Upper QPO dominates having high amplitude, Weak lower QPO Lower QPO dominates With high amplitude and Q, Weak upper QPO ratio higher than 3:2 ratio lower than 3:2 Simultaneous detections Upper QPO Lower QPO   uniform source distribution of pairs   random walk along freq. correlation   observed correlations of Q and r   approximative contrate-frequency relation The simulated distributions well agree wih observation. (Török et al, Acta Astronomica 2008b) simulation of detections expecting

5.2 Possible relation to twin peak QPO ratio clustering Most likely, in 4U 1636 the simultaneous detections of both modes cluster around the 3:2 value because there is a reverse of their dominance. [?]

  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.   The 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/ Possible relation to twin peak QPO ratio clustering observed simulated 4U 1636 Barret & Boutelier, NewAR 2008 Török et al, Acta Astr. 2008b

  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. 5.2 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 5.2 A possible relation to twin peak QPO ratio clustering Similar Q and r evolution distribution - possible to simulate (?) Similar Q and r Distribution - impossible to simulate (?)

5.3 kHz QPO amplitude evolution – other sources Two PDS of XTE J1807, from Homan et al. 2007(ApJ), correspond to 1.7 and 1.5 frequency ratio. R>1.5 ~750/450 ~1.7 ~600/900 ~1.5 R~1.5

5.3 kHz QPO amplitude evolution – other sources Two PDS of XTE J1807, from Homan et al. 2007(ApJ), correspond to 1.7 and 1.5 frequency ratio. Recently, Homan et al. 2007b (ATEL) reported in the same source an observation of a strong QPO above 800Hz, while the other QPO was not detected in that observation. R>1.5 ~ 820Hz R~1.5

5.3 kHz QPO amplitude evolution – other sources Two PDS of XTE J1807, from Homan et al. 2007(ApJ), correspond to 1.7 and 1.5 frequency ratio. Recently, Homan et al. 2007b (ATEL) reported in the same source an observation of a strong QPO above 800Hz, while the other QPO was not detected in that observation. Assuming (due to Q) that the detected is the lower QPO and assuming a frequency correlation, the right panel corresponds to the low ratio R. The behaviour of amplitudes in this Z-(atoll) source follows the same track we discussed previously. (We thank M. Méndez for pointing out the existence of this data). R>1.5R~1.5 frequency power frequency R<1.5 Ratio R

5.3 kHz QPO amplitude evolution – other sources Interpolated data of three Z-sources. Data from Méndez 2006 (A&A).

5.3 kHz QPO amplitude evolution – 10 sources A similar effect is at present known to be displayed by 10 NS sources (representing more than a half of the actual NS population with clear variable kHz QPO frequencies).

Very recently M. Méndez et al. pointed out that the two PDS on left are rather typical for Z sources while the PDS on right is typical for atoll sources. frequency power frequency XTE J1807 (“Z-atoll source”) 5.3 kHz QPO amplitude evolution – atoll-Z relation ?

Six atolls plot adopted from Zhang et al :2 (“canonical Bursa”) line 3:2 line

6. Summary and discussion   there arised several interesting findings on “3:2” in NS sources during past few years   in several sources the twin kHz QPO datapoints cluster close close to (“black hole”) 3:2 ratio (and/or less often other ratios)   slopes and intercepts of several (12) NS sources are anticorrelated   amplitudes of kHz QPO modes equal in given source close to 3:2 ratio in at least 10 sources   there is most likely a division between the atoll and Z sources in terms of the frequency ratio distribution as well as in terms of amplitudes   our understanding to these findings is yet very poor..

6. Summary and discussion   in several sources the twin kHz QPO datapoints cluster close close to (“black hole”) 3:2 ratio (and/or less often other ratios)   slopes and intercepts of several (12) NS sources are anticorrelated   amplitudes of kHz QPO modes equal in given source close to 3:2 ratio in at least 10 sources   All these findings seems to be related. The relation is however unclear… Implications for orbital QPO models:   The existence of above strong similarities 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…]   it is also suggestive of QPO resonant origin   For several of the QPO orbital models our findings imply existence of a prominent “3:2” orbit.

7.1 Bonus: implications for concrete QPO models Lower QPO Both QPOs Upper QPO Difference between lower and upper QPO amplitude [rms,%] 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). Combined data of 1636 and 1728 QPO clustering) Also a region of maximal lower QPO coherence 0.4 km from ISCO 10km from ISCO 0.4 km from ISCO 10km from ISCO

7.1 Bonus II: variable eigenfrequencies Horák et al. 2008

7.1 Bonus III: there is never enough of confusion….