On the applicability of QPO models
Gabriel Török, Pavel Bakala, Eva Šrámková, Zdeněk Stuchlík, Martin Urbanec,
& Kateřina Goluchová
Institute of Physics, Silesian University in Opava
CZ.1.07/2.3.00/20.0071 Synergy , GAČR 209/12/P740, 202/09/0772, SGS-01-2010, www.physics.cz
1. Introduction
MOTIVATION
LMXBs
Compact object:
- black hole or neutron star (>10^10gcm^3)
LMXB Accretion disc
T ~ 10^6K
>90% of radiation
in X-ray
Companion:
• density comparable to the Sun
• mass in units of solar masses
• temperature ~ roughly as the T Sun
• more or less optical wavelengths
Observations: The X-ray radiation is absorbed by the 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).
Figs: space-art, nasa.gov
1. Introduction
MOTIVATION
Sco X-1
power
LMXBs short-term X-ray variability:
peaked noise (Quasi-Periodic Oscillations)
Individual peaks can be related to a
set of oscillators, as well as to time
evolution of a single oscillator.
• Low frequency QPOs (up to 100Hz)
frequency
• hecto-hertz QPOs (100-200Hz),...
• HF QPOs (~200-1500Hz):
Lower and upper QPO feature
forming twin peak QPOs
Fig: nasa.gov
The
HF QPO origin remains
questionable,
it is most often
expected that it is associated to
orbital motion in the inner part of the
accretion disc.
Upper frequency [Hz]
2. Observed Frequencies
Lower frequency [Hz]
3. RP Model (NS parameters)
Definition equations (Kerr approximation)
Lead to the following relation between the expected lower and upper QPO frequency
which can be compared to the observation in order to estimate mass M and “spin” j …
3. RP Model (NS parameters)
Boutloukos et al. 2006, ApJ
• For historical reasons, there is a commonly used fitting of the frequency
difference.
• It is often quoted that some sources can be matched well but some not
(high frequency sources vs. low frequency sources).
4. Predictive Power
4. Predictive Power
Infinity
Orbital Radius
ISCO
4. Predictive Power
Infinity
Orbital Radius
ISCO
LEAST SQUARES ?
Relativistic frequencies scale with 1/M,
Because of that the predictive power depends on the frequency ratio R...
4. Predictive Power
Infinity
Orbital Radius
ISCO
Relativistic frequencies scale with 1/M,
Because of that the predictive power depends on the frequency ratio R...
Circinus X-1: R~3
4U 1636-53: R~1.5
5. Conclusions
• In general, the low-frequency sources data are matched by the models
better than the high-frequency sources. Based on the RP model, we
demonstrate that this dichotomy is related to strong variability of the model
predictive power across the frequency plane implied by the GR radial
dependence of the characteristic frequencies of orbital motion.
• As a consequence, restrictions on the models resulting from observations
of the low-frequency sources are weaker than those in the case of the highfrequency sources (and a need of correction to model can be common…).
END
Thank you for your attention…