On the precession of accretion discs in X-ray binaries

In this Letter, recent results on the nodal precession of accretion discs in close binaries are applied to the discs in some X-ray binary systems. The ratio between the tidally forced precession period and the binary orbital period is given, as well as the condition required for the rigid precession of gaseous Keplerian discs. Hence the minimum precessional period that may be supported by a fluid Keplerian disc is determined. It is concluded that near-rigid body precession of tilted accretion discs can occur and generally reproduce observationally inferred precession periods, for reasonable system parameters. In particular, long periods in SS 433, Her X-1, LMC X-4 and SMC X-1 can be fitted by the tidal model. It is also found that the precession period that has been tentatively put forward for Cyg X-2 cannot be accommodated by a tidally precessing disc model for any realistic choice of system parameters.     

Three-dimensional smoothed particle hydrodynamics simulations of radiation-driven warped accretion discs

We present three-dimensional smoothed particle hydrodynamics calculations of warped accretion discs in X-ray binary systems. Geometrically thin, optically thick accretion discs are illuminated by a central radiation source. This illumination exerts a non-axisymmetric radiation pressure on the surface of the disc, resulting in a torque that acts on the disc to induce a twist or warp. Initially planar discs are unstable to warping driven by the radiation torque and, in general, the warps also precess in a retrograde direction relative to the orbital flow. We simulate a number of X-ray binary systems which have different mass ratios, using a number of different luminosities for each. Radiation-driven warping occurs for all systems simulated. For mass ratios   q ∼ 0.1  a moderate warp occurs in the inner disc while the outer disc remains in the orbital plane (cf. X 1916−053). For less extreme mass ratios, the entire disc tilts out of the orbital plane (cf. Her X–1). For discs that are tilted out of the orbital plane in which the outer edge material of the disc is precessing in a prograde direction, we obtain both positive and negative superhumps simultaneously in the dissipation light curve (cf. V603 Aql).     

Warped accretion discs and the long periods in X-ray binaries

Precessing accretion discs have long been suggested as explanations for the long periods observed in a variety of X-ray binaries, most notably Her X-1/HZ Her. We show that an instability of the response of the disc to the radiation reaction force from the illumination by the central source can cause the disc to tilt out of the orbital plane and precess in something like the required manner. The rate of precession and disc tilt obtained for realistic values of system parameters compare favourably with the known body of data on X-ray binaries with long periods. We explore other possible types of behaviour than steadily precessing discs that might be observable in systems with somewhat different parameters. At high luminosities, the inner disc tilts through more than 90°, i.e., it rotates counter to the usual direction, which may explain the torque reversals in systems such as 4U 1626−67.     

Outbursts of irradiated accretion discs

I solve analytically the viscous evolution of an irradiated accretion disc, as seen during outbursts of soft X-ray transients. The solutions predict steep power-law X-ray decays L _X ∼ (1 + t/t_visc)⁻⁴, changing to L _X ∼ (1 − t/t'_visc)⁴ at late times, where t _visc, t '_visc are viscous time-scales. These forms closely resemble the approximate exponential and linear decays inferred by King and Ritter in these two regimes. The decays are much steeper than for unirradiated discs because the viscosity is a function of the central accretion rate rather than of local conditions in the disc.     

Impact of reverberation in flared accretion discs on temporal characteristics of X-ray binaries

Observations suggest that accretion discs in many X-ray binaries are likely flared. An outer edge of the disc intercepts radiation from the central X-ray source. Part of that radiation is absorbed and re-emitted in the optical/UV spectral ranges. However, a large fraction of that radiation is reflected and appears in the broad-band X-ray spectrum as a Compton reflection bump. This radiation is delayed and variability is somewhat smeared compared with the intrinsic X-ray radiation. We compute response functions for flat and flared accretion discs and for isotropic and anisotropic X-ray sources. A simple approximation for the response function which is valid in the broad range of the disc shapes and inclinations, inner and outer radii, and the plasma bulk velocity is proposed. We also study the impact of the X-ray reprocessing on temporal characteristics of X-ray binaries such as the power spectral density, auto- and cross-correlation functions, and time/phase lags. We propose a reprocessing model which explains the secondary peaks in the phase lag Fourier spectra observed in Cyg X-1 and other Galactic black hole sources. The position of the peaks could be used to determine the size of the accretion disc.     

The correlations between the twin kHz quasi-periodic oscillation frequencies of low-mass X-ray binaries

We analyzed the recently published kHz quasi-period oscillaiton (QPO) data in the neutron star low-mass X-ray binaries (LMXBs), in order to investigate the different correlations of the twin-peak kHz QPOs in bright Z sources and in the less luminous Atoll sources. We find a power-law relation  ν₁∼ν ^b ₂  between the upper and the lower kHz QPOs with different indices: b ≃ 1.5 for the Atoll source 4U 1728-34 and b ≃ 1.9 for the Z source Sco X-1. The implications of our results for the theoretical models for kHz QPOs are discussed.     

Two-temperature accretion flows in magnetic cataclysmic variables: structures of post-shock emission regions and X-ray spectroscopy

We use a two-temperature hydrodynamical formulation to determine the temperature and density structures of the post-shock accretion flows in magnetic cataclysmic variables (mCVs) and calculate the corresponding X-ray spectra. The effects of two-temperature flows are significant for systems with a massive white dwarf and a strong white-dwarf magnetic field. Our calculations show that two-temperature flows predict harder keV spectra than one-temperature flows for the same white-dwarf mass and magnetic field. This result is insensitive to whether the electrons and ions have equal temperature at the shock, but depends on the electron–ion exchange rate, relative to the rate of radiative loss along the flow. White-dwarf masses obtained by fitting the X-ray spectra of mCVs using hydrodynamic models including the two-temperature effects will be lower than those obtained using single-temperature models. The bias is more severe for systems with a massive white dwarf.     

Self-regulated gravitational accretion in protostellar discs

We present a numerical model for the evolution of a protostellar disc that has formed self-consistently from the collapse of a molecular cloud core. The global evolution of the disc is followed for several million years after its formation. The capture of a wide range of spatial and temporal scales is made possible by use of the thin-disc approximation. We focus on the role of gravitational torques in transporting mass inward and angular momentum outward during different evolutionary phases of a protostellar disc with disc-to-star mass ratio of order 0.1. In the early phase, when the infall of matter from the surrounding envelope is substantial, mass is transported inward by the gravitational torques from spiral arms that are a manifestation of the envelope-induced gravitational instability in the disc. In the late phase, when the gas reservoir of the envelope is depleted, the distinct spiral structure is replaced by ongoing irregular non-axisymmetric density perturbations. The amplitude of these density perturbations decreases with time, though this process is moderated by swing amplification aided by the existence of the disc's sharp outer edge. Our global modelling of the protostellar disc reveals that there is typically a residual non-zero gravitational torque from these density perturbations, i.e. their effects do not exactly cancel out in each region. In particular, the net gravitational torque in the inner disc tends to be negative during first several million years of the evolution, while the outer disc has a net positive gravitational torque. Our global model of a self-consistently formed disc shows that it is also self-regulated in the late phase, so that it is near the Toomre stability limit, with a near-uniform Toomre parameter Q ≈ 1.5–2.0. Since the disc also has near-Keplerian rotation, and comparatively weak temperature variation, it maintains a near-power-law surface density profile proportional to r ^−3/2.     

Concave accretion discs and X-ray reprocessing

Spectra of Seyfert 1s are commonly modelled as emission from an X-ray-illuminated flat accretion disc orbiting a central black hole. This provides both reprocessed and direct components of the X-ray emission, as required by observations of individual objects, and possibly a fraction of the cosmological X-ray background. There is some observational motivation for us to at least consider the role that an effectively concave disc surface might play: (1) a reprocessed fraction ≳1/2 in some Seyferts and possibly in the X-ray background, and (2) the commonality of a sharp iron line peak for Seyferts at 6.4 keV despite a dependence of peak location on inclination angle for flat disc models. Here it is shown that a concave disc may not only provide a larger total fraction of reprocessed photons, but can also reprocess a much larger fraction of photons in its outer regions compared with a flat disc. This reduces the sensitivity of the 6.4-keV peak location to the inner disc inclination angle because the outer regions are less affected by Doppler and gravitational effects. If the X-ray source is isotropic, the reprocessed fraction is directly determined by the concavity. If the X-ray source is anisotropic, the location of iron line peak can still be determined by concavity but the total reflected fraction need not be as large as for the isotropic emitter case. The geometric calculations herein are applicable to general accretion disc systems illuminated from the centre.     

Tilted accretion discs in cataclysmic variables: tidal instabilities and superhumps

We investigate the growth of tidal instabilities in accretion discs in a binary star potential, using three-dimensional numerical simulations. As expected from analytic work, the disc is prone to an eccentric instability provided that it is large enough to extend to the 3:1 resonance. The eccentric disc leads to positive superhumps in the light curve. It has been proposed that negative superhumps might arise from a tilted disc, but we find no evidence that the companion gravitational tilt instability can grow fast enough in a fluid disc to create a measurable inclination. The origin of negative superhumps in the light curves of cataclysmic variables remains a puzzle.