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.     

On the observability of spiral structures in cataclysmic variable accretion discs

We use the grid of hydrodynamic accretion disc calculations of Stehle to construct orbital phase‐dependent emission‐line profiles of thin discs carrying spiral density waves. The observational signatures of spiral waves are explored to establish the feasibility of detecting spiral waves in cataclysmic variable discs using prominent emission lines in the visible range of the spectrum. For high Mach number accretion discs ( M v _φ c _s≃ 15 – 30), we find that the spiral shock arms are so tightly wound that they leave few obvious fingerprints in the emission lines. Only a minor variation of the double peak separation in the line profile at a level of ∼8 per cent is produced. For accretion discs in outburst ( M ≃ 5 – 20) however, the lines are dominated by the emission from an m =2 spiral pattern in the disc. We show that reliable Doppler tomograms of spiral shock patterns can be reconstructed provided that a signal‐to‐noise ratio of at least 15, a wavelength resolution of ∼80 km s⁻¹ and a time resolution of ∼50 spectra per binary orbit are achieved. We confirm that the observed spiral pattern in the disc of IP Pegasi can be reproduced by tidal density waves in the accretion disc and demands the presence of a large, hot disc, at least in the early outburst stages.     

The effective temperature distribution of steady-state, mass-losing accretion discs

Mass loss appears to be a common phenomenon among astrophysical accretion disc systems. An outflow emanating from an accretion disc can act as a sink for mass, angular momentum and energy, and can therefore alter the dissipation rates and effective temperatures across the disc. Here, the radial distributions of dissipation rate and effective temperature across a Keplerian, steady-state, mass-losing accretion disc are derived, using a simple, parametric approach that is sufficiently general to be applicable to many types of dynamical disc–wind models.
Effective temperature distributions for mass-losing accretion discs in cataclysmic variables are shown explicitly, with parameters chosen to describe both radiation-driven and centrifugally driven outflows. For realistic wind mass-loss rates of a few per cent, only centrifugally driven outflows – particularly those in which mass loss is concentrated in the inner disc – are likely to alter the effective temperature distribution of the disc significantly. Accretion discs that drive such outflows could produce spectra and eclipse light curves that are noticeably different from those produced by standard, conservative discs.     

Atlas of tilted accretion discs and source to negative superhumps

Using smoothed particle hydrodynamics, we numerically simulate steady-state accretion discs for cataclysmic variable dwarf novae systems that have a secondary-to-primary mass ratio  0.35 ≤ q ≤ 0.55  . After these accretion discs have come to quasi-equilibrium, we rotate each disc out of the orbital plane by  δ= (1, 2, 3, 4, 5 or 20)°  to induce negative superhumps. For accretion discs tilted  5°  , we generate light curves and associated Fourier transforms for an atlas on negative superhumps and retrograde precession. Our simulation results suggest that accretion discs need to be tilted more than 3° for negative superhumps to be statistically significant. We also show that if the disc is tilted enough such that the gas stream strikes a disc face, then a dense cooling ring is generated near the radius of impact.
In addition to the atlas, we study these artificially tilted accretion discs to find the source to negative superhumps. Our results suggest that the source is additional light from innermost disc annuli, and this additional light waxes and wanes with the amount of gas stream overflow received as the secondary orbits. The nodes, where the gas stream transitions from flowing over to under the disc rim (and vice versa), precess in the retrograde direction.     

The standstill luminosity in Z Cam systems

We consider accretion discs in close binary systems. We show that the heating of a disc at the impact point of the accretion stream contributes significantly to the local energy budget at its outer edge. As a result, the thermal balance relation between local accretion rate and surface density (the 'S-curve') changes; the critical mass transfer rate above which no dwarf nova outbursts occur can be up to 40 per cent smaller than without impact heating. Standstills in Z Cam systems thus occur at smaller mass transfer rates than otherwise expected, and are fainter than the peak luminosity during the dwarf nova phase as a result.     

Accretion disc dynamics in extreme mass ratio compact binaries

An analysis is presented of a numerical investigation of the dynamics and geometry of accretion discs in binary systems with mass ratios   q = M ₂/ M ₁ < 0.1  , applicable to ultracompact X-ray binaries, AM CVn stars and very short period cataclysmic variables. The steady-state geometry of the disc in the binary reference frame is found to be quite different from that expected at higher mass ratios. For   q ∼ 0.1  , the disc takes on the usual elliptical shape, with the major axis aligned perpendicular to the line of centres of the two stars. However, at smaller mass ratios the elliptical gaseous orbits in the outer regions of the disc are rotated in the binary plane. The angle of rotation increases with gas temperature, but is found to vary inversely with q . At   q = 0.01  , the major axis of these orbits is aligned almost parallel to the line of centres of the two stars. These effects may be responsible for the similar disc structure inferred from Doppler tomography of the AM CVn star GP Com, which has   q = 0.02  . The steady-state geometry at low mass ratios is not predicted by an inviscid, restricted three-body model of gaseous orbits; it is related to the effects of tidal-viscous truncation of the disc near the Roche lobe boundary. Since the disc geometry can be inferred observationally for some systems, it is proposed that this may offer a useful diagnostic for the determination of mass ratios in ultracompact binaries.     

Eccentric discs in binaries with intermediate mass ratios: superhumps in the VY Sculptoris stars

We investigate the role of the eccentric disc resonance in systems with mass ratios q ≳1/4, and demonstrate the effects that changes in the mass flux from the secondary star have upon the disc radius and structure. The addition of material with low specific angular momentum to the outer edge of a disc restricts that disc radially. Should the mass flux from the secondary be reduced, it is possible for the disc in a system with mass ratio as large as 1/3 to expand to the 3:1 eccentric inner Lindblad resonance and for superhumps to be excited.     

Accretion disc outbursts: a new version of an old model

We have developed 1D time-dependent numerical models of accretion discs, using an adaptive grid technique and an implicit numerical scheme, in which the disc size is allowed to vary with time. The code fully resolves the cooling and heating fronts propagating in the disc. We show that models in which the radius of the outer edge of the disc is fixed produce incorrect results, from which probably incorrect conclusions about the viscosity law have been inferred. In particular we show that outside-in outbursts are possible when a standard bimodal behaviour of the Shakura–Sunyaev viscosity parameter α is used. We also discuss to what extent insufficient grid resolution has limited the predictive power of previous models. We find that the global properties (magnitudes, etc.) of transient discs can be addressed by codes using a high, but reasonable, number of fixed grid points. However, the study of the detailed physical properties of the transition fronts generally requires resolutions which are out of reach of fixed grid codes. It appears that most time-dependent models of accretion discs published in the literature have been limited by resolution effects, improper outer boundary conditions, or both.     

Precessing warped accretion discs in X-ray binaries

We study the radiation-driven warping of accretion discs in the context of X-ray binaries. The latest evolutionary equations are adopted, which extend the classical alpha theory to time-dependent thin discs with non-linear warps. We also develop accurate, analytical expressions for the tidal torque and the radiation torque, including self-shadowing.
We investigate the possible non-linear dynamics of the system within the framework of bifurcation theory. First, we re-examine the stability of an initially flat disc to the Pringle instability. Then we compute directly the branches of non-linear solutions representing steadily precessing discs. Finally, we determine the stability of the non-linear solutions. Each problem involves only ordinary differential equations, allowing a rapid, accurate and well-resolved solution.
We find that radiation-driven warping is probably not a common occurrence in low-mass X-ray binaries. We also find that stable, steadily precessing discs exist for a narrow range of parameters close to the stability limit. This could explain why so few systems show clear, repeatable 'superorbital' variations. The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close to the stability limit for a reasonable choice of parameters. Systems far from the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably experience quasi-periodic or chaotic variability as first noticed recently by Wijers and Pringle. We show that radiation-driven warping provides a coherent and persuasive framework but that it does not provide a generic explanation for the long-term variabilities in all X-ray binaries.     

Are superhumps good measures of the mass ratio for AM CVn systems?

We extend recent work that included the effect of pressure forces to derive the precession rate of eccentric accretion discs in cataclysmic variables to the case of double degenerate systems. We find that the logical scaling of the pressure force in such systems results in predictions of unrealistically high primary masses. Using the prototype AM CVn as a calibrator for the magnitude of the effect, we find that there is no scaling that applies consistently to all the systems in the class. We discuss the reasons for the lack of a superhump period to mass ratio relationship analogous to that known for SU UMa systems and suggest that this is because these secondaries do not have a single valued mass–radius relationship. We highlight the unreliability of mass ratios derived by applying the SU UMa expression to the AM CVn binaries.     

Post-common-envelope binaries from SDSS – I. 101 white dwarf main-sequence binaries with multiple Sloan Digital Sky Survey spectroscopy

We present a detailed analysis of 101 white dwarf main-sequence binaries (WDMS) from the Sloan Digital Sky Survey (SDSS) for which multiple SDSS spectra are available. We detect significant radial velocity variations in 18 WDMS, identifying them as post-common-envelope binaries (PCEBs) or strong PCEB candidates. Strict upper limits to the orbital periods are calculated, ranging from 0.43 to 7880 d. Given the sparse temporal sampling and relatively low spectral resolution of the SDSS spectra, our results imply a PCEB fraction of ≳15 per cent among the WDMS in the SDSS data base. Using a spectral decomposition/fitting technique we determined the white dwarf effective temperatures and surface gravities, masses and secondary star spectral types for all WDMS in our sample. Two independent distance estimates are obtained from the flux-scaling factors between the WDMS spectra, and the white dwarf models and main-sequence star templates, respectively. Approximately one-third of the systems in our sample show a significant discrepancy between the two distance estimates. In the majority of discrepant cases, the distance estimate based on the secondary star is too large. A possible explanation for this behaviour is that the secondary star spectral types that we determined from the SDSS spectra are systematically too early by one to two spectral classes. This behaviour could be explained by stellar activity, if covering a significant fraction of the star by cool dark spots will raise the temperature of the interspot regions. Finally, we discuss the selection effects of the WDMS sample provided by the SDSS project.