(Abridged) We use 3D SPH calculations with higher resolution, as well as with more realistic viscosity and sound-speed prescriptions than previous work to examine the eccentric instability which underlies the superhump phenomenon in semi-detached binaries. We illustrate the importance of the two-armed spiral mode in the generation of superhumps. Differential motions in the fluid disc cause converging flows which lead to strong spiral shocks once each superhump cycle. The dissipation associated with these shocks powers the superhump. We compare 2D and 3D results, and conclude that 3D simulations are necessary to faithfully simulate the disc dynamics. We ran our simulations for unprecedented durations, so that an eccentric equilibrium is established except at high mass ratios where the growth rate of the instability is very low. Our improved simulations give a closer match to the observed relationship between superhump period excess and binary mass ratio than previous numerical work. The observed black hole X-ray transient superhumpers appear to have systematically lower disc precession rates than the cataclysmic variables. This could be due to higher disc temperatures and thicknesses. The modulation in total viscous dissipation on the superhump period is overwhelmingly from the region of the disc within the 3:1 resonance radius. As the eccentric instability develops, the viscous torques are enhanced, and the disc consequently adjusts to a new equilibrium state, as suggested in the thermal-tidal instability model. We quantify this enhancement in the viscosity, which is ~10 per cent for q=0.08. We characterise the eccentricity distributions in our accretion discs, and show that the entire body of the disc partakes in the eccentricity.Comment: 18 pages (mn2e LaTeX), 14 figures, 5 tables, Accepted for publication in MNRA

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).

We present three‐dimensional smoothed particle hydrodynamics calculations of irradiation‐driven warping of accretion discs. Initially unwarped planar discs are unstable to the radiation reaction when the disc is illuminated by a central radiation source. The disc warps and tilts and precesses slowly in a retrograde direction; its shape continuously flexes in response to the changing orientation of the Roche potential. We simulate 10 systems: eight X‐ray binaries, one cataclysmic variable (CV) and a ‘generic’ low‐mass X‐ray binary (LMXB). We adopt system parameters from observations and tune a single parameter: our model X‐ray luminosity (L*), to reproduce the observed or inferred superorbital periods. Without exception, across a wide range of parameter space, we find an astonishingly good match between the observed LX and the model L*. We conclude irradiation‐driven warping is the mechanism underlying the long periods in X‐ray binaries. Our Her X‐1 simulation simultaneously reproduces the observed LX, the ‘main‐’ and ‘short‐high’ X‐ray states and the orbital inclination. Our simulations of SS 433 give a maximum warp angle of , a good match to the cone traced by the jets, but this angle is reached only in the outer disc. In all cases, the overall disc tilt is less than 13° and the maximum disc warp is less than and or equal to 21°. In particular, the disc warp in 4U 1626−67 cannot explain the observed torque reversals. Taking our results at face value, ignoring the finite opening angle of the disc, we deduce orbital inclinations of approximately 77° for 4U 1916−053 and approximately 69° for 4U 1626−67. We also simulate Cyg X‐2, SMC X‐1, Cyg X‐1 and LMC X‐3. For high‐mass X‐ray binary parameters, the discs' maximum angular elevation is invariably at the outer edge. For LMXBs with extreme mass ratios a strong inner disc warp develops, completely shadowing parts of the outer disc. This inner warped disc executes retrograde precession while the outer disc executes prograde apsidal precession. The remaining LMXBs develop a less extreme warp in the inner disc, with the entire disc tilting and precessing in a retrograde direction. For our CV, KR Aur, we matched the inferred disc precession period by adopting LX= 1037 erg s−1, which would require steady nuclear burning on the white dwarf surface.

Two‐dimensional smoothed particle hydrodynamics (SPH) simulations of a precessing accretion disc in a q= 0.1 binary system (such as XTE J1118+480) reveal complex and continuously varying shape, kinematics and dissipation. The stream–disc impact region and disc spiral density waves are prominent sources of energy dissipation. The dissipated energy is modulated on the period Psh= (P−1orb−P−1prec)−1 with which the orientation of the disc relative to the mass donor repeats. This superhump modulation in dissipation energy has a variation in amplitude of ∼10 per cent relative to the total dissipation energy and evolves, repeating exactly only after a full disc precession cycle. A sharp component in the light curve is associated with centrifugally expelled material falling back and impacting the disc. Synthetic trailed spectrograms reveal two distinct ‘S‐wave’ features, produced respectively by the stream gas and the disc gas at the stream–disc impact shock. These S‐waves are non‐sinusoidal, and evolve with disc precession phase. We identify the spiral density wave emission in the trailed spectrogram. Instantaneous Doppler maps show how the stream impact moves in velocity space during an orbit. In our maximum entropy Doppler tomogram, the stream impact region emission is distorted, and the spiral density wave emission is suppressed. A significant radial velocity modulation of the whole line profile occurs on the disc precession period. We compare our SPH simulation with a simple three‐dimensional model; the former is appropriate for comparison with emission lines, while the latter is preferable for skewed absorption lines from precessing discs.

We present results from three XMM-Newton observations of the M31 low mass X-ray binary (LMXB) XMMU J004314.4+410726.3 (Bo 158), spaced over 3 d in 2004 July. Bo 158 was the first dipping LMXB to be discovered in M31. Periodic intensity dips were previously seen to occur on a 2.78-h period, due to absorption in material that is raised out of the plane of the accretion disc. The report of these observations stated that the dip depth was anticorrelated with source intensity. In light of the 2004 XMM-Newton observations of Bo 158, we suggest that the dip variation is due to precession of the accretion disc. This is to be expected in LMXBs with a mass ratio 0.3 (period 4 h), as the disc reaches the 3:1 resonance with the binary companion, causing elongation and precession of the disc. A smoothed particle hydrodynamics simulation of the disc in this system shows retrograde rotation of a disc warp on a period of ∼11P orb , and prograde disc precession on a period of 29 ± 1P orb . This is consistent with the observed variation in the depth of the dips. We find that the dipping behaviour is most likely to be modified by the disc precession, hence we predict that the dipping behaviour repeats on an 81 ± 3 h cycle.