Transcript 2.3 Orbital resonance models

Multi-resonant models of quasi-periodic oscillations
Zdeněk Stuchlík, Gabriel Török, Petr Slaný
Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava,
Bezručovo nám. 13, CZ-74601 Opava, Czech Republic
• Introduction:
Quasi-periodic oscillations (QPOs) in X-ray from the NS an BH systems
and their resonant models
Figs on this page: nasa.gov
power
1.1 Quasiperiodic oscillations
hi-frequency
(kHz) QPOs
low-frequency
QPOs
frequency
1.1 Quasiperiodic oscillations
of the microquasar GRO 1655-40 from two different observations
hi-frequency
(kHz) QPOs
1.2 kHz quasiperiodic oscillations: BH and NS
2. Orbital and orbital resonance models of QPOs
General belief dominating in the astrophysical community links the kHz
QPOs to the orbital motion near the inner edge of an accretion disc.
Class of models relates kHz QPOs to orbital resonances….
Figs on this page: nasa.gov
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
2.2 Orbital resonance models
Relativistic precession model
(Stella, L. \& Vietri, M. 1999, Phys. Rev. Lett., 82, 17)
relates 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://thwww.if.uj.edu.pl/acta/vol32/t11.htm]
Orbital resonance model relates the kHz QPOs to disc oscillation modes
corresponding to the frequencies of geodesic motion.
2.2 Orbital resonance models
2.2 Orbital resonance models
2.2 Orbital resonance models
2.2 Resonance frequency scatter
2.2 Resonance in non-linear oscillations
2.3 Orbital resonance models – possible gravitational excitation
Investigated hypothesis: The gravitatational perturbations caused either by the
surface features or by the binary companion may be relevant as an excitation
mechanism which may also “feed“ the resonance.
Talk - Hledík, Stuchlík, Konar, Miller
2.3 Orbital resonance models – possible gravitational excitation
Investigated hypothesis: The gravitatational perturbations caused either by the
surface features or by the binary companion may be relevant as an excitation
mechanism which may also “feed“ the resonance.
2.3 Orbital resonance models – possible gravitational excitation
Investigated hypothesis: The gravitatational perturbations caused either by the
surface features or by the binary companion may be relevant as an excitation
mechanism which may also “feed“ the resonance.
2.3 Orbital resonance models – possible gravitational excitation
Investigated hypothesis: The gravitatational perturbations caused either by the
surface features or by the binary companion may be relevant as an excitation
mechanism which may also “feed“ the resonance.
2.3 Orbital resonance models – possible gravitational excitation
The gravitatational perturbations caused either by the surface features or by the
binary companion may be relevant as an excitation mechanism which may also
“feed“ the resonance. The analysis presented for the binary companion can be
applied also to black hole systems.
3. Multi-resonance models
Phenomenologically, there are two possibilities in the resonance models:
one eigenfrequency pair hypothesis or,
more eigenfrequency pairs hypothesis…
Figs on this page: nasa.gov
3. Multi-resonance models
• orbital resonance models involving Keplerian and epicyclic oscillations:
– a single resonance connected to one specific radius
– more instances of one resonance occuring (excited) at (or close to) more
specific radii
– more resonances sharing one specific radius
strong resonant phenomena – black holes with a specific spin
– more resonances occuring (excited) at (or close to) more specific radii
(the “ugly” case)
• extended resonance model with hump-induced oscillations
3.1 One resonance occuring (excited) at (or close to) more radii
Investigated hypothesis: the NS twin peak QPOs originate in a resonance
between two modes having time-dependent eigenfrequencies determined by the
frequencies of geodesic motion.
Talks
- Bakala,Torok, Stuchlík, Urbanec
- Urbanec, Stuchlík, Torok, Bakala, Čermák
3.1 One resonance occuring (excited) at (or close to) more radii
Investigated hypothesis: the NS twin peak QPOs originate in a resonance
between two modes having time-dependent eigenfrequencies determined by the
frequencies of geodesic motion.
4U 1636-53
} ~0.3M
For group of sources some of possible frequency relations considered in the
Hartle-Thorne metric implies the neutron star mass
M ~ 1.5-2M_sun and j ~ 0-0.2.
3.1 One resonance occuring (excited) at (or close to) more radii
For group of sources some of possible models (frequency relations) considered
in the Hartle-Thorne metric implies the neutron star mass M ~ 1.5-2M_sun and j ~
0-0.2. Concrete models give concrete restrictions to the neutron star structure.
Genetic Algorithm
3.2 More resonances sharing one specific radius
Investigated hypothesis: For a special values of black hole spin more resonances
can occur at the same radius. Strong resonance phenomena may arise when the
Keplerian and epicyclic frequencies are in the lowest possible ratio.
Talk – Kotrlová, Stuchlík, Torok
3.2 More resonances sharing one specific radius
Investigated hypothesis: For a special values of black hole spin more resonances
can occur at the same radius. Strong resonance phenomena may arise when the
Keplerian and epicyclic frequencies are in the lowest possible ratio.
3.2 More resonances sharing one specific radius
For a special values of black hole spin more resonances may occur at the same orbit.
Strong resonance phenomena may occur in the situation arising for the so called
"magic" spin a = 0.983 when the Keplerian and epicyclic frequencies are in the
lowest possible ratio 3:2:1 at the common radius.
3.3 Extended resonance model
Investigated hypothesis:excitation of the epicyclic oscillations by the processes
related to the LNRF orbital velocity hump arising in the case of near-extreme Kerr
black holes.
Talk – Slaný, Stuchlík, Torok
3.3 Extended resonance model
Investigated hypothesis: excitation of the epicyclic oscillations by the processes
related to the LNRF orbital velocity hump arising in the case of near-extreme Kerr
black holes:
3.3 Extended resonance model
In the relevant regions, for increasing rotational parameter the ratios of the
epicyclic frequencies to the humpy frequency tend to the ratios of small integers.
The regions are close to the 3:1 and 4:1 epicyclic resonant orbits.
4. Conclusions
Present:
Measured eigenfrequencies of QPOs
+ properly chosen orbital resonance
 black hole (neutron star) parameters
Future:
Mathematical theory of resonances
+ physical theory of accretion disks
 connection of resonance parameters & physical properties of disks
Observed details of QPOs (scatter of resonant frequencies, details of Török´s
energy switch effect, etc.) imply restrictions on physical properties of accretion disk
(or internal structure of neutron stars)