Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

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.Comment: 7 pages, 4 figures (in colour), accepted for publication in Astronomy & Astrophysic

Oscillations of Thick Accretion Discs Around Black Holes

We present a numerical study of the response of a thick accretion disc to a localized, external perturbation with the aim of exciting internal modes of oscillation. We find that the perturbations efficiently excite global modes recently identified as acoustic p--modes, and closely related to the epicyclic oscillations of test particles. The two strongest modes occur at eigenfrequencies which are in a 3:2 ratio. We have assumed a constant specific angular momentum distribution within the disc. Our models are in principle scale--free and can be used to simulate accretion tori around stellar or super massive black holes.Comment: 4 pages, 4 figures, accepted for publication as a letter in the Monthly Notices of the Royal Astronomical Societ

Of NBOs and kHz QPOs: a low-frequency modulation in resonant oscillations of relativistic accretion disks

The origin of quasi periodic modulations of flux in the kilohertz range (kHz QPOs), observed in low-mass X-ray binaries, is usually assumed to be physically distinct from that of the ``normal branch oscillations'' (NBOs) in the Z-sources. We show that a low-frequency modulation of the kHz QPOs is a natural consequence of the non-linear relativistic resonance suggested previously to explain the properties of the high-frequency twin peaks. The theoretical results discussed here are reminiscent of the 6 Hz variations of frequency and amplitude of the kHz QPOs reported by Yu, van der Klis and Jonker (2001).Comment: Accepted for publication in PASJ; 4 pages, 1 figur

Leaving the ISCO: the inner edge of a black-hole accretion disk at various luminosities

The "radiation inner edge" of an accretion disk is defined as the inner boundary of the region from which most of the luminosity emerges. Similarly, the "reflection edge" is the smallest radius capable of producing a significant X-ray reflection of the fluorescent iron line. For black hole accretion disks with very sub-Eddington luminosities these and all other "inner edges" locate at ISCO. Thus, in this case, one may rightly consider ISCO as the unique inner edge of the black hole accretion disk. However, even for moderate luminosities, there is no such unique inner edge as differently defined edges locate at different places. Several of them are significantly closer to the black hole than ISCO. The differences grow with the increasing luminosity. For nearly Eddington luminosities, they are so huge that the notion of the inner edge losses all practical significance.Comment: 12 pages, 15 figures, submitted to A&

QPOs in Cataclysmic Variables and in X-ray Binaries

Recent observations, reported by Warner and Woudt, of Dwarf Nova Oscillations (DNOs) exhibiting frequency drift, period doubling, and 1:2:3 harmonic structure, can be understood as disc oscillations that are excited by perturbations at the spin frequency of the white dwarf or of its equatorial layers. Similar quasi-periodic disc oscillations in black hole low-mass X-ray binary (LMXB) transients in a 2:3 frequency ratio show no evidence of frequency drift and correspond to two separate modes of disc oscillation excited by an internal resonance. Just as no effects of general relativity play a role in white dwarf DNOs, no stellar surface or magnetic field effects need be invoked to explain the black hole QPOs.Comment: Revised version. Astronomy & Astrophysics (Letters), in pres

A non-linear resonance model for the black hole and neutron star QPOs: theory supported by observations

Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray binaries. It has been suggested that the highest QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two modes of accreting disk oscillation. This hypothesis implies certain very general predictions, several of which have been borne out by observations. Some of these follow from properties of non-linear oscillators, while the others are specific to oscillations of fluid in strong gravity. A 3:2 resonant ratio of frequencies can be clearly recognized in the black-hole as well as in the neutron-star QPO data.Comment: 8 pages, 8 figures, to appear in Proceedings of the Albert Einstein Century International Conferenc

QPOs in microquasars and Sgr A*: measuring the black hole spin

In all four microquasars which show double peak kHz QPOs, the ratio of the two frequencies is 3:2. This strongly supports the suggestion that twin peak kHz QPOs are due to a resonance between some modes of accretion disk oscillations. Here, we stress that fits to observations of the hypothetical resonances between vertical and radial epicyclic frequencies (particularly of the parametric resonance) give an accurate estimate of the spin for the three microquasars with known mass. Measurement of double peak QPOs frequencies in the Galaxy centre seems also to be consistent with the 3:2 ratio established by previous observations in microquasars, however the Sgr A* data are rather difficult for the same exact analysis. If confirmed, the 3:2 ratio of double peak QPOs in Sgr A* would be of a fundamental importance for the black hole accretion theory and the precise measurement could help to solve the question of QPOs nature.Comment: 5 pages, 5 figures, 3 table

The slimming effect of advection on black-hole accretion flows

At super-Eddington rates accretion flows onto black holes have been described as slim (aspect ratio $H/R \lesssim 1$) or thick (H/R >1) discs, also known as tori or (Polish) doughnuts. The relation between the two descriptions has never been established, but it was commonly believed that at sufficiently high accretion rates slim discs inflate, becoming thick. We wish to establish under what conditions slim accretion flows become thick. We use analytical equations, numerical 1+1 schemes, and numerical radiative MHD codes to describe and compare various accretion flow models at very high accretion rates.We find that the dominant effect of advection at high accretion rates precludes slim discs becoming thick. At super-Eddington rates accretion flows around black holes can always be considered slim rather than thick.Comment: 8 pages, 5 figures. Astronomy & Astrophysics, in pres