SUPERHUMPS
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Comprehensive simulations of superhumps
Authors:Amanda J. Smith (1), Carole A. Haswell
(1), James R. Murray (2), Michael R. Truss (3),
Stephen B. Foulkes (1) ((1) The Open
University, (2) Swinburne University of
Technology, (3) Durham University
(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 semidetached 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.