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MEASUREMENT OF BRANY BLACK HOLE PARAMETERSMEASUREMENT OF BRANY BLACK HOLE PARAMETERSIN THE FRAMEWORKIN THE FRAMEWORK
OFOF THE ORBITAL RESONANCE MODEL OF THE ORBITAL RESONANCE MODEL OF QPOQPOss
Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, CZ-74601 Opava, CZECH REPUBLIC
supported byCzech grant
MSM 4781305903
Presentation download:www.physics.cz/researchin section news
Zdeněk Stuchlík and Andrea Kotrlová
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Outline
1. Braneworld, black holes & the 5th dimension1.1. Rotating braneworld black holes
2. Quasiperiodic oscillations (QPOs)2.1. Black hole high-frequency QPOs in X-ray2.2. Orbital motion in a strong gravity2.3. Keplerian and epicyclic frequencies2.4. Digest of orbital resonance models2.5. Resonance conditions2.6. Strong resonant phenomena - "magic" spin
3. Applications to microquasars3.1. Microquasars data: 3:2 ratio3.2. Results for GRO J1655-403.3. Results for GRS 1915+1053.4. Conclusions
4. References
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1. Braneworld, black holes & the 5th dimension
Braneworld model - Randall & Sundrum (1999):
- our observable universe is a slice, a "3-brane" in 5-dimensional bulk spacetime
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1.1. Rotating braneworld black holes
The metric form on the 3-brane
– assuming a Kerr-Schild ansatz for the metric on the brane the solution in the standard Boyer-Lindquist coordinates takes the form
Aliev & Gümrükçüoglu (2005):
– exact stationary and axisymmetric solutions describing rotating BH localized on a 3-brane in the Randall-Sundrum braneworld
where
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1.1. Rotating braneworld black holes
The metric form on the 3-brane
– assuming a Kerr-Schild ansatz for the metric on the brane the solution in the standard Boyer-Lindquist coordinates takes the form
Aliev & Gümrükçüoglu (2005):
– exact stationary and axisymmetric solutions describing rotating BH localized on a 3-brane in the Randall-Sundrum braneworld
where
– looks exactly like the Kerr-Newman solution in general relativity, in which the square of the electric charge Q2 is replaced by a tidal charge parameter .
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1.1. Rotating braneworld black holes
The tidal charge
– means an imprint of nonlocal gravitational effects from the bulk space,
– may take on both positive and negative values !
The event horizon:
– the horizon structure depends on the sign of the tidal charge
condition:
for
for extreme horizon and
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1.1. Rotating braneworld black holes
The tidal charge
– means an imprint of nonlocal gravitational effects from the bulk space,
– may take on both positive and negative values !
The event horizon:
– the horizon structure depends on the sign of the tidal charge
condition:
for
for extreme horizon and
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1.1. Rotating braneworld black holes
The tidal charge
– means an imprint of nonlocal gravitational effects from the bulk space,
– may take on both positive and negative values !
The event horizon:
– the horizon structure depends on the sign of the tidal charge
condition:
forThis is not allowedin the framework
of general relativity !!
for extreme horizon and
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1.1. Rotating braneworld black holes
The tidal charge
– means an imprint of nonlocal gravitational effects from the bulk space,
– may take on both positive and negative values !
The effects of negative tidal charge
– tend to increase the horizon radius rh, the radii of the limiting photon orbit (rph), the innermost bound (rmb) and the innermost stable circular orbits (rms) for both direct and retrograde motions of the particles,
– mechanism for spinning up the black hole so that its rotation parameter exceeds its mass. Such a mechanism is impossible in general relativity !
The event horizon:
– the horizon structure depends on the sign of the tidal charge
condition:
forThis is not allowedin the framework
of general relativity !!
for extreme horizon and
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2. Quasiperiodic oscillations (QPOs)
Fig. on this page: nasa.gov
Black hole hi-frequency QPOs in X-ray
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hi-frequencyQPOs
low-frequencyQPOs
(McClintock & Remillard 2003)
2.1. Quasiperiodic oscillations
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2.1. Quasiperiodic oscillations
(McClintock & Remillard 2003)
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2.2. Orbital motion in a strong gravity
– the Keplerian orbital frequency– and the related epicyclic frequencies (radial , vertical ):
ν ~ 1/M
Rotating braneworld BH with mass M, dimensionless spin a, and the tidal charge :the formulae for
has a local maximum for all values of spin a- only for rapidly rotating BHs
xms – radius of the marginally stable orbit
Stable circular geodesics exist for
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2.3. Keplerian and epicyclic frequencies
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- can have a maximum at x = xex !!
Notice, that reality condition must be satisfied
2.3. Keplerian and epicyclic frequencies
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Can it be located above• the outher BH horizon xh
• the marginally stable orbit xms?
- can have a maximum at x = xex !!
Notice, that reality condition must be satisfied
2.3. Keplerian and epicyclic frequencies
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Can it be located above• the outher BH horizon xh
• the marginally stable orbit xms?
- can have a maximum at x = xex !!
Extreme BHs:
Notice, that reality condition must be satisfied
2.3. Keplerian and epicyclic frequencies
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2.3. Keplerian and epicyclic frequencies
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2.3. Keplerian and epicyclic frequencies
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2.3. Keplerian and epicyclic frequencies
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2.4. Digest of orbital resonance models
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2.4. Digest of orbital resonance models
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2.5. Resonance conditions
– determine implicitly the resonant radius
– must be related to the radius of the innermost stable circular geodesic
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2.5. Resonance conditions
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2.5. Resonance conditions
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2.5. Resonance conditions
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2.5. Resonance conditions
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2.5. Resonance conditions
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2.5. Resonance conditions
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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2.6. Strong resonant phenomena - "magic" spin
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3. Applications to microquasars
GRO GRO JJ1655-41655-400
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3. Applications to microquasars
GRS 1915+105GRS 1915+105
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3.1. Microquasars data: 3:2 ratio
Törö
k, A
bra
mow
icz,
Klu
znia
k,
Stu
chlík
20
05
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3.1. Microquasars data: 3:2 ratio
Törö
k, A
bra
mow
icz,
Klu
znia
k,
Stu
chlík
20
05
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3.1. Microquasars data: 3:2 ratio
Using known frequencies of the twin peak QPOs and the known mass M of the central BH, the dimensionless spin a and the tidal charge can be related assuming a concrete version of the resonance model.
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3.1. Microquasars data: 3:2 ratio
Using known frequencies of the twin peak QPOs and the known mass M of the central BH, the dimensionless spin a and the tidal charge can be related assuming a concrete version of the resonance model.
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3.1. Microquasars data: 3:2 ratio
Using known frequencies of the twin peak QPOs and the known mass M of the central BH, the dimensionless spin a and the tidal charge can be related assuming a concrete version of the resonance model.
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3.1. Microquasars data: 3:2 ratio
Using known frequencies of the twin peak QPOs and the known mass M of the central BH, the dimensionless spin a and the tidal charge can be related assuming a concrete version of the resonance model.
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3.1. Microquasars data: 3:2 ratio
Using known frequencies of the twin peak QPOs and the known mass M of the central BH, the dimensionless spin a and the tidal charge can be related assuming a concrete version of the resonance model.
The most recent angular momentumestimates from fits of spectral continua:
GRO J1655-40: a ~ (0.65 - 0.75)GRS 1915+105: a > 0.98
a ~ 0.7
- Shafee et al. 2006
- McClintock et al. 2006
- Middleton et al. 2006
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3.2. Results for GRO J1655-40
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3.2. Results for GRO J1655-40
Shafee et al. 2006
McC
linto
ck &
Rem
illard
20
04
Possible combinations of mass and spin predicted by individual resonance models for the high-frequency QPOs. Shaded regions indicate the likely ranges for the mass (inferred from optical measurements of radial curves) and the dimensionless spin (inferred from the X-ray spectral data fitting) of GRO J1655-40.
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3.2. Results for GRO J1655-40
Possible combinations of mass and spin predicted by individual resonance models for the high-frequency QPOs. Shaded regions indicate the likely ranges for the mass (inferred from optical measurements of radial curves) and the dimensionless spin (inferred from the X-ray spectral data fitting) of GRO J1655-40.
Shafee et al. 2006
McC
linto
ck &
Rem
illard
20
04
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3.2. Results for GRO J1655-40
The only model which matches the observational constraintsis the vertical-precession resonance (Bursa 2005)
Possible combinations of mass and spin predicted by individual resonance models for the high-frequency QPOs. Shaded regions indicate the likely ranges for the mass (inferred from optical measurements of radial curves) and the dimensionless spin (inferred from the X-ray spectral data fitting) of GRO J1655-40.
Shafee et al. 2006
McC
linto
ck &
Rem
illard
20
04
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3.2. Results for GRO J1655-40
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3.3. Results for GRS 1915+105
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3.3. Results for GRS 1915+105
McC
linto
ck &
Rem
illard
20
04
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3.3. Results for GRS 1915+105
estimate 1
1 - Middleton et al. 2006
McC
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Rem
illard
20
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3.3. Results for GRS 1915+105
estimate 1
estimate 2
2 - McClintock et al. 2006
1 - Middleton et al. 2006
McC
linto
ck &
Rem
illard
20
04
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3.3. Results for GRS 1915+105
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3.4. Conclusions
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3.4. Conclusions
β = 0
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3.4. Conclusions
-1 < β < 0.51 (βmax for a = 0.7)
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3.4. Conclusions
-1 < β < 0.51
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3.4. Conclusions
-1 < β < 0.51
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3.4. Conclusions
-1 < β < 0.51
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3.4. Conclusions
-1 < β < 0.51
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3.4. Conclusions
-1 < β < 0.51
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3.4. Conclusions
there is no specific type of resonance model that could work for both sources simultaneously
-1 < β < 0.51
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THANK YOUTHANK YOUFOR YOUR ATTENTIONFOR YOUR ATTENTION
4. References
• Abramowicz, M. A. & Kluzniak, W. 2004, in X-ray Timing 2003: Rossi and Beyond., ed. P. Karet, F. K. Lamb, & J. H. Swank, Vol. 714 (Melville: NY: American Institute of Physics), 21-28
• Abramowicz, M. A., Kluzniak, W., McClintock, J. E., & Remillard, R. A. 2004, Astrophys. J. Lett., 609, L63
• Abramowicz, M. A., Kluzniak, W., Stuchlík, Z., & Török, G. 2004, in Proceedings of RAGtime 4/5: Workshops on black holes and neutron stars, Opava, 14-16/13-15 October 2002/2003, ed. S. Hledík & Z. Stuchlík (Opava: Silesian University in Opava), 1-23
• Aliev, A. N., & Gümrükçüoglu, A. E. 2005, Phys. Rev. D 71, 104027
• Aliev, A. N., & Galtsov, D. V. 1981, General Relativity and Gravitation, 13, 899
• Bursa, M. 2005, in Proceedings of RAGtime 6/7: Workshops on black holes and neutron stars, Opava, 16-18/18-20 September 2004/2005, ed. S. Hledík & Z. Stuchlík (Opava: Silesian University in Opava), 39-45
• McClintock, J. E. & Remillard, R. A. 2004, in Compact Stellar X-Ray Sources, ed. W. H. G. Lewin & M. van der Klis (Cambridge: Cambridge University Press)
• McClintock, J. E., Shafee, R., Narayan, R., et al. 2006, Astrophys. J., 652, 518
• Middleton, M., Done, C., Gierlinski, M., & Davis, S. W. 2006, Monthly Notices Roy. Astronom. Soc., 373, 1004
• Randall, L., & Sundrum, R. 1999, Phys. Rev. Lett. 83, 4690
• Shafee, R., McClintock, J. E., Narayan, R., et al. 2006, Astrophys. J., 636, L113
• Stuchlík, Z. & Török, G. 2005, in Proceedings of RAGtime 6/7: Workshops on black holes and neutron stars, Opava, 16-18/18-20 September 2004/2005, ed. S. Hledík & Z. Stuchlík (Opava: Silesian University in Opava), 253-263
• Stuchlík, Z., Kotrlová, A., & Török, G. 2007: Black holes admitting strong resonant phenomena, submitted
• Stuchlík, Z., Kotrlová, A., & Török, G. 2007: Multi-resonance model of QPOs: possible high precision determination of black hole spin, in prep.
• Török, G., Abramowicz, M. A., Kluzniak,W. & Stuchlík, Z. 2005, Astronomy and Astrophysics, 436, 1
• Török, G. 2005, Astronom. Nachr., 326, 856