Gabriel Török

On the amplitudes of NS kHz quasiperiodic oscillations

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 the collaboration with

M.A. Abramowicz, D. Barret, P.Bakala, M. Bursa, J. Horák, W. Kluzniak, M. Urbanec, and Z. Stuchlík

Fig: nasa.gov

1. X-ray timing observations of NS X-ray binaries

Fig: nasa.gov

LMXBs short-term X-ray variability

• Low frequency QPOs (up to 100Hz)

• hecto-hertz QPOs (100-200Hz)

• kHz QPOs (~200-1500Hz): Lower and upper QPO mode forming twin peak QPOs

frequency

pow

er

Sco X-1

Lower QPO

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.

2. kHz QPO amplitude evolution in six atoll sourcesProfitting 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 rL, rU .

Example of 4U 1636:Upper QPO frequency U [Hz]

Lower QPO frequency L [Hz]

Weak lower QPO

Upper QPO amplitude rU

Lower QPO amplitude rL

equality at U ~ 1000Hz~ 1000Hz

4U 1636

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 U ~ 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.

Weak lower QPO

Upper QPO frequency U [Hz]

Lower QPO frequency L [Hz]

equality at U ~ 900Hz~ 900Hz

Example of 4U 1608:

4U 1608 Upper QPO amplitude rU

Lower QPO amplitude rL

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 ~ 900-1100Hz.

There is an additional equality at high frequencies in four sources.

2. kHz QPO amplitude evolution in six atoll sources

In case of the amplitude equality at low frequencies U ~ 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 = U / L the similarity is most obvious:

The interval U ~ 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.

2. kHz QPO amplitude evolution in six atoll sources

2.1 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.

Amplitude difference r = rL – rU as it behaves in terms of the frequency ratio R

Points:Cont. segmentsCurves:published datainterpolation

[Török 2008, A&A submitted]

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.

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).

1636, simulation of detections expectinguniform source distribution of QPO pairs (Török et al, Acta Astronomica 2008)

Simultaneousdetections

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.

frequencyfrequency

Upper QPO dominates Upper QPO dominates having high amplitude,having high amplitude,Weak lower QPOWeak lower QPO

Lower QPO dominates Lower QPO dominates With high amplitude and Q,With high amplitude and Q,Weak upper QPOWeak upper QPO

ratio higher than 3:2 ratio lower than 3:2Upper QPO

Lower QPO

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.

2.2 Possible relation to twin peak QPO ratio clustering

observedsimulated

4U 1636

Bar

ret

& B

ou

telie

r,

New

AR

200

8

Tö

rök

et a

l, A

cta

Ast

r. 2

008

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.

2.2 A possible relation to twin peak QPO ratio clustering

06141728

16081636

18201735

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).

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.

3.1 Bonus: implications for concrete QPO models

Lower QPOLower QPOBoth QPOsBoth QPOs Upper QPOUpper QPO

Difference betweenDifference betweenlower and upper QPOlower and upper QPOamplitude [rms,%]amplitude [rms,%]

Here we use an illustration based on the relativistic precession model of Stella Here we use an illustration based on the relativistic precession model of Stella and Vietri. and Vietri. Note however that its frequency identification coincides with those of Note however that its frequency identification coincides with those of radial m=-1 and vertical m=-2 disc oscillation modes. radial m=-1 and vertical m=-2 disc oscillation modes. It is qualitatively valid for It is qualitatively valid for several other modelsseveral other models, e.g., NS warp disc precession model of S. Kato (2008)., 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