3:2 ratio in NS X-ray observations:
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3:2 ratio in NS X-ray observations: summary of recent progress. Gabriel Török. Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-74601 Opava, Czech Republic. The p resentation draws mainly from the collaboration with

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Gabriel t r k

3:2 ratio in NS X-ray observations:

summary of recent progress

Gabriel Török

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, and Z. Stuchlík


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Outline

  • Basic introduction:

  • Low-mass X-ray binaries (LMXBs), accretion discs

  • kHz variability, its origin

  • 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


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I. Basic introduction

Fig:nasa.gov


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1. Low-mass X-ray binaries (LMXBs), accretion discs, variability

  • Artists view of LMXBs

  • “as seen from a hypothetical planet”

  • 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)

  • Companion:

  • density comparable to the Sun

  • mass in units of solar masses

  • temperature ~ roughly as the T Sun

  • moreless optical wavelengths


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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).


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1. Low-mass X-ray binaries (LMXBs), accretion discs, variability

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.

  • X-ray

  • Gamma ray

“white dot” of GRS 1915+105

radio

  • Disc

  • Companion

  • Jet

  • Example of the Galactic microquasar GRS 1915+105: the concept and what is seen.

Fig:nasa.gov., Hannikainen et al. 2003


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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-termvariability (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.


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low

high

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability

  • 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)

density

emissivity

I

UKAFF supercomputer simulationof black holelong term variability

time

Fig and movie:UKAFF


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low

high

1. Low-mass X-ray binaries (LMXBs), accretion discs, variability

Long-term variability ( in terms of lightcurves, from hours to days)

density

emissivity

low

high

Brightness

time

movie:UKAFF


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2. Short term variability – kHz range

Sco X-1

power

frequency

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.

Figs: from the collection of van der Klis, 2006


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height h

width w at ½ h

Power

Frequency

3.kHz QPOs in BH and NS systems: properties (and differencies)

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


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3.kHz QPOs in BH and NS: frequency correlations (and differences)

Bursaplot

Neutron stars:

variable frequencies

Upper QPO frequency

Black holes: fixed 3:2 ratio

(microquasars)

Lower QPO frequency


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II. 3:2 kHz QPO frequency ratio in NS systems:

Fig:nasa.gov

clustering


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4. Ratio clustering

Neutron stars:

variable frequencies

Upper QPO frequency

Black holes: fixed 3:2 ratio

(microquasars)

Lower QPO frequency


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4. Ratio clustering

Neutron stars:

variable frequencies

Abramowicz et al. (2003), A&A

Upper QPO frequency

ratio

peaks to 3:2

Lower QPO frequency


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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 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 our previous (unpublished) findings on ratio clustering in 1636-53.


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4.2Exploring 4U 1636-53 kHz QPO data

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.


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4.2Exploring 4U 1636-53 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)


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4.3 Distributions

  • - significant lower QPO detections (lower QPOs)

  • significant upper QPO detections (upper QPOs)

  • twin QPOs (overlap between lower and upper QPO observations)

lower QPOs upper QPOs

twin QPOs

(Torok et al. , AcA, 2008a)


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4.3 Ratio distribution

(Torok et al. (2008a), AcA)


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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.


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III. 3:2 kHz QPO frequency ratio in NS systems:

Fig:nasa.gov

amplitude evolution


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5. kHz QPO amplitude evolution in six atoll sources

Sco X-1

height h

width w at ½ h

UpperQPO

power

Power

Lower QPO

Frequency

frequency

Quality factor Q indicates sharpness of the peak, Q ~ h/w

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…

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)

Fig:nasa.gov


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5.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]


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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 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]


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5.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.


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5. 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.


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5.1kHz QPO amplitude evolution in terms of frequency ratio

Amplitude difference Dr = rL – rU 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]


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R < 1.5

R ~ 1.5

R > 1.5

R~1.25

5.1relation between two QPOs as depends on 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.

PDS:


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R < 1.5

R ~ 1.5

R > 1.5

R~1.25

5.1relation between two QPOs as depends on 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.

PDS:


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R < 1.5

R ~ 1.5

R > 1.5

R~1.25

5.1relation between two QPOs as depends on 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.

PDS:


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R < 1.5

R ~ 1.5

R > 1.5

R~1.25

5.1relation between two QPOs as depends on 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.

PDS:


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R < 1.5

R ~ 1.5

R > 1.5

R~1.25

5.1relation between two QPOs as depends on 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.

PDS:


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R < 1.5

R ~ 1.5

R > 1.5

R~1.25

5.1relation between two QPOs as depends on frequency ratio

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).

PDS:


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5.2 Possible relation to twin peak QPO ratio clustering

  • Results of Belloni et al. 2007 (MNRAS) indicate 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 2008a, Acta Astronomica).


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5.2 Possible relation to twin peak QPO ratio clustering

  • Results of Belloni et al. 2007 (MNRAS) indicate 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 2008a, 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.

ratio higher than 3:2ratio lower than 3:2

Lower QPO dominates

with high amplitude and Q,

Weak (often undetected)

upper QPO

Upper QPO dominates having

high amplitude,

Weak lower QPO

frequency


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5.2 Possible relation to twin peak QPO ratio clustering

Most likely, in 4U 1636 the simultaneous detections of both modes cluster around the 3:2value because there is a reverse of their dominance.

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

frequency

simulation of detections expecting

  • uniform source distribution of pairs

  • randomwalk along freq. correlation

  • observed correlations of Q and r

  • approximative contrate-frequency relation

  • Thesimulated distributions well agree wih observation.

  • (Török et al, Acta Astronomica 2008b)

Upper QPO

Lower QPO

Simultaneous

detections


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5.2 Possible relation to twin peak QPO ratio clustering

Most likely, in 4U 1636 the simultaneous detections of both modes cluster around the 3:2value because there is a reverse of their dominance.

[?]


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5.2 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.

  • 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 3/2.

4U 1636

observed

simulated

Török et al,

Acta Astr. 2008b

Barret & Boutelier,

NewAR 2008


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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

  • 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


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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

0614

1728

1608

1636

1820

1735

Similar Q and r

Distribution - impossibleto simulate (?)

Similar Q and r evolution

distribution - possible to simulate (?)


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5.3 kHz QPO amplitude evolution – other sources

R>1.5

R~1.5

~750/450

~1.7

~600/900

~1.5

Two PDS of XTE J1807, from Homan et al. 2007(ApJ), correspond to 1.7 and 1.5 frequency ratio.


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5.3 kHz QPO amplitude evolution – other sources

R>1.5

R~1.5

~ 820Hz

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.


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5.3 kHz QPO amplitude evolution – other sources

frequency

Ratio R

R>1.5

R~1.5

R<1.5

power

power

frequency

frequency

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).


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5.3 kHz QPO amplitude evolution – other sources

Interpolated data of three Z-sources. Data from Méndez 2006(A&A).


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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).


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5.3 kHz QPO amplitude evolution – atoll-Z relation ?

XTE J1807 (“Z-atoll source”)

power

power

frequency

frequency

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.


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5.3 kHz QPO amplitude evolution – atoll-Z relation ?

Six atolls

3:2 (“canonical Bursa”) line

3:2 line

plot adopted from

Zhang et al 2006


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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..


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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

  • 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.


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7.1 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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7.1 Bonus II: variable eigenfrequencies

Horák et al. 2008


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


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