Snmek 1

1
On the unity of black hole and neutron star kHz
QPOs
Gabriel Török, Pavel Bakala, Zdenek Stuchlík,Eva
rámková, Jirí Horák
Institute of Physics, Faculty of Philosophy and
Science, Silesian University in Opava, Bezrucovo
nám. 13, CZ-74601 Opava, Czech Republic
Astronomical Institute, Academy of Sciences,
Bocní II 1401, CZ-14131, Praha 4, Czech Republic
Supported byMSM 4781305903 and LC06014
Black Holes in Kraków,17th May 2007
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On the unity of black hole and neutron star kHz
QPOs
Gabriel Török, Pavel Bakala, Zdenek Stuchlík,Eva
rámková, Jirí Horák
Or
On the general--relativity predicted relations
matching neutron star kHz QPOs
Total precession
"Stella"
"Bursa"
Supported byMSM 4781305903 and LC06014
Black Holes in Kraków,17th May 2007
3
Outline
Presentation download www.physics.cz/research
in sect. news

• 1. Introduction Quasi-periodic oscillations
  (QPOs) in X-ray from the NS an BH systems
• - Black-hole and neutron star binaries,
  accretion disks and QPOs, BH and NS QPOs
• 2. Neutron star QPOs and some orbital models
• 2.1. Geodesic motion models (blobs)
• 2.2. Resonance models
• - 2.2.1. One eigenfrequency pair
  hypothesis
• - 2.2.2. More eigenfrequency pairs
  hypothesis
• 3. Testing frequency relations
• 3.0. Epicyclic resonances
• 3.1. Stella, Bursa, total precession and
  disc-oscillation relation
• 3.2. Fitting the data in the Hartle-Thorne metric
• 4. Numbers six atolls, Circinus X-1
• 5. Summary, blobs and disc-oscillations
• 6. Bonus (just to go back to the original title)

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• Introduction
• Quasi-periodic oscillations (QPOs) in X-ray
  from the NS an BH systems

Figs on this page nasa.gov
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1.1. Black hole binaries and accretion disks
radio
X-ray
and visible
Figs on this page nasa.gov
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1.2. X-ray observations
Light curve
I
t
Power density spectra (PDS)
Power
Frequency
Figs on this page nasa.gov
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1.3. Quasiperiodic oscillations
power
hi-frequency QPOs
low-frequency
QPOs
frequency
8
1.3. kHz Quasiperiodic oscillations BH and NS
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2. Neutron star QPOs and some orbital models
General belief dominating in the astrophysical
community links the kHz QPOs to the orbital
motion near the inner edge of an accretion disc.
Figs on this page nasa.gov
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2.1. Orbital motion in a strong gravity
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2.1. Geodesic motion models orbital motion in a
strong gravity
Imply the existence of the periastron and nodal
(Lense-Thirring) precession
Stella, L. \ Vietri, M. 1999, Phys. Rev. Lett.,
82, 17 related the kHz QPOs to the Keplerian and
periastron precession of the blobs close to the
inner edge of an accretion disc. - Relativistic
precession model
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2.2 Orbital resonance models
Relativistic precession model (Stella, L. \
Vietri, M. 1999, Phys. Rev. Lett., 82,
17) related the kHz QPOs to the frequencies of
geodesic motion (Keplerian and periastron
precession of the blobs close to the inner edge
of an accretion disc). Resonance model Kluzniak,
W., Abramowicz, M. A., 2000, Phys. Rev. Lett.
(submitted) Klu\'zniak, W., \ Abramowicz, M.
A., 2001, Acta Physica Polonica B 32, 3605
http//th-www.if.uj.edu.pl/acta/vol32/t11.htm r
elated the kHz QPOs to disc oscillation modes
corresponding to the frequencies of geodesic
motion.
13
2.2 Orbital resonance models

• Phenomenologically, there are two possibilities
  in the resonance models for NS QPOs
• one eigenfrequency pair hypothesis
• more eigenfrequency pairs hypothesis

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2.2.1. One eigenfrequency pair hypothesis
In this approach, the whole range of the observed
frequencies comes from one (most likely 32)
eigenfrequency pair, so called resonant point.
Abramowicz, Karas, Kluzniak, Lee, Rebusco,
Paola, 2003, PASJ...55..467A, see also M.A.
Abramowicz, D.Barret, M.Bursa, J.Hor\'ak,
W.Klu\'zniak, P.Rebusco, G.T\"or\"ok, in
Proceedings of RAGtime 6/7, Opava, 2005
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2.2.1. One eigenfrequency pair hypothesis
In this approach, the whole range of the observed
frequencies comes from one (32) eigenfrequency
pair, so called resonant point
The model knows how to unify
16
2.2.1. One eigenfrequency pair hypothesis
There are several good arguments supporting the
approach (see, e.g., Török, Abramowicz, Kluzniak,
Stuchlík 2006, proc. of Albert Einstein Conf.
Paris 2005, astro-ph/0603847). Especially the
existence of slope-shift anticorrelation. On the
other hand, this approach has some
difficulties,especially extremely large extension
from eigenfrequencies. Therefore, it may be
plausible to look for some other but close
alternatives
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2.2.2. More eigenfrequency pairs hypothesis
motivation
double peak distribution and amplitude behaviour
18
2.2.2. More eigenfrequency pairs hypothesis
motivation
From the double peak distribution and amplitude
behaviour it appears that for a given source
the upper and lower QPO frequency can be traced
through the whole observed range of frequencies
but the probability to detect both QPOs
simultaneously increases when the frequency ratio
is close to the ratio of small natural numbers.
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2.2.2. More eigenfrequency pairs hypothesis
From the double peak distribution and amplitude
behaviour it appears that for a given source
the upper and lower QPO frequency can be traced
through the whole observed range of frequencies
but the probability to detect both QPOs
simultaneously increases when the frequency ratio
is close to the ratio of small natural
numbers. Therefore, the whole effect may be
connected to the resonance between two modes with
floating eigenfrequencies, i.e., in this
approach, the range of the frequencies observed
in the source comes from several individual
eigen-frequency pairs correponding to the
different frequeny ratios and the observed
frequencies do not much differ from the resonant
eigenfrequencies. We have investigated a bit the
question Which modes can be in the game ?
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3. Testing frequency relations
Figs on this page nasa.gov
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3.0 Testing frequency relations Epicyclic
oscillations
There is no chance to fit the observed QPO
relationships by direct identifiation with
epicyclic frequencies.
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3.1 Testing frequency relations Stella, Bursa,
total precession and disc-oscillation relation
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3.2 Fitting the data in the Hartle-Thorn
We consider the external rotating neutron
spacetime description given by ugly
HARTLE-THORN METRIC.
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3.2 Fitting the data in the Hartle-Thorn
We consider the external rotating neutron
spacetime description given by ugly
HARTLE-THORN METRIC. We use slightly modified
relations for geodesic frequencies derived
by Abramowicz, M.A., Almergren, G.J.E.,
Kluzniak, W., Thampan, A.V., 2003 astro-ph/0312070
.
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4. Numbers
Figs on this page nasa.gov
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4. Numbers
The atoll source 4U 1636-53
(Rough fit by eye, in the Schwarzschild
case, where the relations coincide.)
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4. Numbers
The atoll source 4U 1636-53
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4. Numbers
The atoll source 4U 1636-53
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4. Numbers
The atoll source 4U 1636-53
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4. Numbers

• 51 Six atoll sources
• (namely
• 4U 1636-53, 4U 1608-52, 4U 1820-30, 4U 1735-44,
  4U 1728-34 , 4U 061409)
• Results for the five others are very similar to
  4U 1636-53 as their data are similar

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4. Numbers

• Results for the five others are very similar to
  4U 1636-53 as their data are similar
• What about the completely different source ??

Six atolls
Circinus X-1
32
4. Numbers

• Results for the five others are very similar to
  4U 1636-53 as their data are similar
• What about the completely different source -
  Circinus X-1

Stella M/M_sun j q
chi_squared

close to 3 0.5 0.25
14.25/8 BURSA M/M_sun j
q chi_squared

2.8 0.5
0.25 14.67/8 Total
precession M/M_sun j
q chi_squared

1.99 0.01 0.0001
12.38/8
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4. Numbers
Summary of fits by the total precesion relation
for six atolls and Circinus X-1
Source M j q \chi2/d.o.f.
0
614 1.71 0.06 0.004 2.7 1728 1.56 0.07
0.005 2.9 1735 1.67 0.07 0.005 1.4 1820
1.85 0.10 0.011 9.6 1636 1.77 0.05 0.003
3.0 Cir X-1 1.99 0.01 0.0001 1.5
At the moment, we are calculating data with
the last (disc-oscillation) relation -
preliminary, it fits with similar or slightly
better \chi2 to the total precession and gives
masses even 5--15 lower
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5. Summary, blobs vs. disc-oscillations
Figs on this page nasa.gov
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5. Summary, blobs and disc-oscillations
The two relations, one corresponding to the hot
spot QPO interpretation and so called total
precession, the other one corresponding to the
disc-oscillation QPO interpretation, fits the
high frequency QPOs in the discussed X-ray
sources with much lower chi-square than the
relation given by the relativistic precession
model and also imlies lower neutron star angular
momentum and mass
36
6. Bonus (just to go back to the original title)
Figs on this page nasa.gov
37
6. Bonus (just to go back to the original title)
The investigated total precession and
disc-oscillation frequency relation gives the
spin a 0.40.7 when applied to the microquasar
data and may in principle fit the spectral
continuum spin estimates (but the numbers do
not much fully)
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7. References
Figs on this page nasa.gov
39

• 7. References
• Török, Abramowicz, Kluzniak, Stuchlík
• 2005, AA, 436, p. 1, www.physics.cz/research
• Török, Abramowicz, Stuchlík, rámková,
• 2006, proc. of IAU meeting, astro-ph/0610497
• Török, Abramowicz, Kluzniak, Stuchlík
• 2006, proc. of Albert Einstein Conf. Paris 2005,
  astro-ph/0603847
• Horák, 2004, proc. of RAGtime 5, download ADS
• Abramowicz, Barret, Bursa, Horák, Kluzniak,
  Olive, Rebusco, Török,
• 2006, proc. Of RAGtime 2005, download ADS or
  www.physics.cz/research
• Abramowicz, Barret, Bursa, Horák, Kluzniak,
  Olive, Rebusco, Török
• 2006, submitted to MNRAS

Presentation download www.physics.cz/research in
sect. news
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