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Register a new userDisc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model
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Added by
Gabriel T\\\"or\\\"ok Jr.
Publication date
2010
fields
Physics
and research's language is
English
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The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among other ideas, it has been suggested that a non-linear resonance between two oscillation modes in an accretion disc orbiting either a black hole or a neutron star plays a role in exciting the observed modulation. Several possible resonances have been discussed. A particular model assumes resonances in which the disc-oscillation modes have the eigenfrequencies equal to the radial and vertical epicyclic frequencies of geodesic orbital motion. This model has been discussed for black hole microquasar sources as well as for a group of neutron star sources. Assuming several neutron (strange) star equations of state and Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies expected from the model to those observed. Our comparison implies that the inferred neutron star radius RNS is larger than the related radius of the marginally stable circular orbit rms for nuclear matter equations of state and spin frequencies up to 800Hz. For the same range of spin and a strange star (MIT) equation of state, the inferrred radius RNS is roughly equal to rms. The Paczynski modulation mechanism considered within the model requires that RNS < rms. However, we find this condition to be fulfilled only for the strange matter equation of state, masses below one solar mass, and spin frequencies above 800Hz. This result most likely falsifies the postulation of the neutron star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes could stay among the possible choices only if a fairly non-geodesic accretion flow is assumed, or if a different modulation mechanism operates.
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Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates. We find that for dimensionless black hole spin a<0.9, the resonant eigenfrequencies are very close to those calculated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation. The situation becomes different for a>0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a~0.7 to a~0.6. Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a<0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a~1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT).
We study non-geodesic corrections to the quasicircular motion of charged test particles in the field of magnetized slowly rotating neutron stars. The gravitational field is approximated by the Lense-Thirring geometry, the magnetic field is of the standard dipole character. Using a fully-relativistic approach we determine influence of the electromagnetic interaction (both attractive and repulsive) on the quasicircular motion. We focus on the behaviour of the orbital and epicyclic frequencies of the motion. Components of the four-velocity of the orbiting charged test particles are obtained by numerical solution of equations of motion, the epicyclic frequencies are obtained by using the standard perturbative method. The role of the combined effect of the neutron star magnetic field and its rotation in the character of the orbital and epicyclic frequencies is discussed.
Across black hole (BH) and neutron star (NS) low-mass X-ray binaries (LMXBs), there appears to be some correlation between certain high- and low-frequency quasi-periodic oscillations (QPOs). In a previous paper, we showed that for BH LMXBs, this could be explained by the simultaneous oscillation and precession of a hot, thick, torus-like corona. In the current work, we extend this idea to NS LMXBs by associating the horizontal branch oscillations (HBO) with precession and the upper-kiloHertz (ukHz) QPO with vertical epicyclic motion. For the Atoll source 4U 1608-52, the model can match many distinct, simultaneous observations of the HBO and ukHz QPO by varying the inner and outer radius of the torus, while maintaining fixed values for the mass (M_{NS}) and spin (a_*) of the neutron star. The best fit values are M_{NS} = 1.38 pm 0.03 M_odot and a_* = 0.325 pm 0.005. By combining these constraints with the measured spin frequency, we are able to obtain an estimate for the moment of inertia of I_{NS} = 1.40 pm 0.02 times 10^{45} g cm^2, which places constraints on the equation of state. The model is unable to fit the lower-kHz QPO, but evidence suggests that QPO may be associated with the boundary layer between the accretion flow and the neutron star surface, which is not treated in this work.
We explore some properties of twin kilohertz quasiperiodic oscillations (QPOs) in a simple toy-model consisting of two oscillation modes coupled by a general nonlinear force. We examine resonant effects by slowly varying the values of the tunable, and nearly commensurable, eigenfrequencies. The behavior of the actual oscillation frequencies and amplitudes during a slow transition through the 3:2 resonance is examined in detail and it is shown that both are significantly affected by the nonlinearities in the governing equations. In particular, the amplitudes of oscillations reflect a resonant exchange of energy between the modes, as a result the initially weaker mode may become dominant after the transition. We note that a qualitatively similar behavior has been recently reported in several neutron star sources by Torok (2008, arXiv:0812.4751), who found that the difference of amplitudes in neutron star twin peak QPOs changes sign as the observed frequency ratio of the QPOs passes through the value 3:2.
3D MHD simulation of accretion onto neutron stars have shown in the last few years that the footprint (hotspot) of the accretion flow changes with time. Two different kinds of accretion, namely the funnel flow and the equatorial accretion produced by instabilities at the inner disk, produce different kinds of motion of the hotspot. The funnel flow produces hotspots that move around the magnetic pole, while instabilities produce other hotspots that appear randomly and move along the equator or slightly above. The angular velocities of the two hotspots are different, the equatorial one being higher and both close to the Keplerian velocity in the inner region. Modeling of the lightcurves of these hotspots with Monte Carlo simulations show that the signatures produced in power specra by them, if observed, are QPOs plus low frequency components. Their frequencies, general behavior and features describe correctly most of the properties of kHz QPOs, if we assume the funnel flow hotspots as the origin of the lower kHz QPO and instabilities as the origin of the upper kHz QPO.
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