Sn

1
32 ratio in NS X-ray observations summary of
recent progress
Gabriel Török
Institute of Physics, Faculty of Philosophy and
Science, Silesian University in Opava, Bezrucovo
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
2
Outline

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

3
I. Basic introduction
Fig nasa.gov
4
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 gt)
• 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
• - gt90 of radiation in X-ray
• (unitstens
  of keV)

• Companion

• density comparable to the Sun
• mass in units of solar masses
• temperature roughly as the T Sun
• moreless optical wavelengths

5
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/rc2) and test extremal implications of
General relativity (or other theories).
6
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.

• Gamma ray

• X-ray

white dot of GRS 1915105
radio

• Disc

• Companion

• Jet

• Example of the Galactic microquasar GRS 1915105
  the concept and what is seen.

Fig nasa.gov., Hannikainen et al. 2003
7
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.

8
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 simulation of black hole long
term variability
time
Fig and movieUKAFF
9
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
movieUKAFF
10
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
11
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
r5 and Q5
NS QPOs frequencies up to 1500Hz often
amplitudes up to r20 and quality factors up to
Q200
12
3. kHz QPOs in BH and NS frequency correlations
(and differences)
Bursaplot
Neutron stars variable frequencies
Upper QPO frequency
Black holes fixed 32 ratio (microquasars)
Lower QPO frequency
13
II. 32 kHz QPO frequency ratio in NS systems


Fig nasa.gov
clustering
14
4. Ratio clustering
Neutron stars variable frequencies
Upper QPO frequency
Black holes fixed 32 ratio (microquasars)
Lower QPO frequency
15
4. Ratio clustering
Neutron stars variable frequencies
Abramowicz et al. (2003), AA
Upper QPO frequency
ratio peaks to 32
Lower QPO frequency
16
4. Ratio clustering 32 controversy ??
Belloni et al. (2004,2005AA) studied frequency
distributions in several sources. They confirmed
the clustering around 32 and other ratios, but
put some doubts on its interpretation. Consequent
ly, 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.
17
4.2 Exploring 4U 1636-53 kHz QPO data
The observational data we use here correspond to
all the RXTE observations of the atoll source 4U
163653 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.

18
4.2 Exploring 4U 1636-53 kHz QPO data

• The part of data displaying significant twin peak
  QPOs is restricted to about 20 hours of
  observation.

19
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)
20
4.3 Ratio distribution
(Torok et al. (2008a), AcA)
21
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.
22
III. 32 kHz QPO frequency ratio in NS systems
Fig nasa.gov
amplitude evolution
23
5. kHz QPO amplitude evolution in six atoll
sources
Sco X-1
height h
Upper QPO
width w at ½ h
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
24
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 rL, rU . Example of 4U 1636
Upper QPO frequency nU Hz
Upper QPO amplitude rU
4U 1636
Lower QPO amplitude rL
equality at nU 1000Hz
Weak lower QPO
Lower QPO frequency nL Hz
25
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.
Upper QPO frequency nU Hz
Example of 4U 1608
Upper QPO amplitude rU
4U 1608
Lower QPO amplitude rL
equality at nU 900Hz
Weak lower QPO
Lower QPO frequency nL Hz
26
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 data conclusively
  indicates that in all the six sources the both
  QPO amplitudes equal each other at nU
  900-1100Hz.
• There is an additional equality at high
  frequencies in four sources.

27
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.

28
5.1 kHz 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, AA submitted
29
5.1 relation 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 1.251.4 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
30
5.1 relation 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 1.251.4 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
31
5.1 relation 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 1.251.4 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
32
5.1 relation 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 1.251.4 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
33
5.1 relation 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 1.251.4 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
34
5.1 relation 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
35
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 32 value in that
  source (Török et al 2008a, Acta Astronomica).

36
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 32 value in that
  source (Török et al 2008a, Acta Astronomica).

Most likely, in 4U 1636 the simultaneous
detections of both modes cluster around the 32
value because there is a reverse of their
dominance.
ratio higher than 32 ratio lower than 32
Lower QPO dominates with high amplitude and
Q, Weak (often undetected) upper QPO
Upper QPO dominates having high amplitude, Weak
lower QPO
frequency
37
5.2 Possible relation to twin peak QPO ratio
clustering
Most likely, in 4U 1636 the simultaneous
detections of both modes cluster around the 32
value because there is a reverse of their
dominance.
ratio higher than 32 ratio lower than 32
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
• 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)

Upper QPO
Lower QPO
Simultaneous detections
38
5.2 Possible relation to twin peak QPO ratio
clustering
Most likely, in 4U 1636 the simultaneous
detections of both modes cluster around the 32
value because there is a reverse of their
dominance.

?
39
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
40
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
41
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 - impossible to
simulate (?)
Similar Q and r evolution distribution - possible
to simulate (?)
42
5.3 kHz QPO amplitude evolution other sources
Rgt1.5
R1.5
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.
43
5.3 kHz QPO amplitude evolution other sources
Rgt1.5
R1.5
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.
44
5.3 kHz QPO amplitude evolution other sources
frequency
Ratio R
Rgt1.5
R1.5
Rlt1.5
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).
45
5.3 kHz QPO amplitude evolution other sources
Interpolated data of three Z-sources. Data from
Méndez 2006 (AA).
46
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).
47
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.
48
5.3 kHz QPO amplitude evolution atoll-Z
relation ?
Six atolls
32 (canonical Bursa) line
32 line
plot adopted from Zhang et al 2006
49
6. Summary and discussion

• there arised several interesting findings on
  32 in NS sources during past few years
• in several sources the twin kHz QPO datapoints
  cluster close close to (black hole) 32 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 32 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..

50
6. Summary and discussion

• in several sources the twin kHz QPO datapoints
  cluster close close to (black hole) 32 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 32 ratio in at least 10 sources
• amplitudes of kHz QPO modes equal in given
  source close to 32 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 32
  orbit.

51
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).
52
7.1 Bonus II variable eigenfrequencies
Horák et al. 2008
53
7.1 Bonus III there is never enough of
confusion.