Comprehensive simulations of superhumps

Abstract

(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

Local and global dynamics of eccentric astrophysical discs

“…Numerical simulations of eccentric discs have mainly been carried out using smoothed particle hydrodynamics (SPH), which readily produces eccentric discs in circular binary stars with mass ratios typical of SU UMa stars (Whitehurst 1988;Lubow 1991b;Murray 1996Murray , 1998Murray , 2000Smith et al 2007). More recently, grid-based simulations have also found the development of eccentric discs in the presence of a planetary (Kley & Dirksen 2006) or stellar (Kley, Papaloizou, & Ogilvie 2008;Marzari et al 2009Marzari et al , 2012 companion.…”

Cycles in the cataclysmic variable V795 Herculis

“…The superhump profile in SU UMa systems is usually of a roughly triangular shape with sharp maxima and minima (e.g. Warner 1995; Kato et al 2009; see also model of Smith et al 2007) and the amplitude evolves gradually during stage B. In contrast, in V795 Her some profiles largely deviated from this scheme even during the neighboring nights within a given time segment.…”

“…Applying the model of Smith et al (2007), our analysis shows that the strength and optical luminosity of the spiral arms of the precessing disk largely vary at a given Φ sh for different epochs of the superhump cycle within a given time segment in V795 Her. A zone of quiescence at Φ sh ≈ 0.6−0.7 can be identified with the phase of the missing arms and the lowest disk eccentricity.…”

“…Later on, the time evolution of this flickering is divergent for the individual nights. As modeled by Smith et al (2007), the strongest spiral arms and the highest eccentricity of the particle motion occurs in the outer half of the superhumping disk. Strong spiral arms are formed during Φ sh of the peak intensity.…”

“…8). The outer about 40 percent of the disk radius are most influenced by the tidal forces producing the superhump light (see model of Smith et al 2007). The viscous timescale of the disk is much longer than P sh (see Sect.…”