Hydrodynamic simulations of the accretion disk in U Geminorum

The occurrence of a two-armed spiral structure during outburst

Mathematisches Institut der Universität Tübingen, 72076 Tübingen, Germany e-mail: klingler@na.uni-tuebingen.de

Received: 25 June 2003
Accepted: 11 October 2005

Abstract

Aims.We use a new numerical hydrodynamic technique to simulate the evolution of the disk in 2D until the outburst is fully developed. The results are used to construct Doppler tomograms that closely agree with the time-resolved spectroscopic observations of U Geminorum during its 2000 March outburst when it showed two spiral arms.Methods.We use the Shakura-Sunyaev alpha viscosity prescription for the disk, where most of the angular momentum transport originates in internal stresses rather than in globally excited waves or shocks. Other effects, such as the Rossby-waves instability found in axisymmetric potentials, are often found discussed as a possible cause of angular momentum transport. These Rossby-waves also show a spiral pattern, but most of them may be damped out due to the viscous hydrodynamic assumption. Our simulations reproduce the spiral feature that was found in the observational data, which confirms the eligibility of the so-called α-disk model. Radiation transport in the vertical direction is taken into account by solving the energy equation, while the calculations consider dissipative heating and radiative cooling with adequate opacity laws.Results.We found that the outburst of U Geminorum can be described within the “disk-instability-model”, as the viscous stress lets the disk expand out to regions where tidal disturbances induce a two armed spiral pattern. Initially these arms first become optically thick and then they get hot. A heating wave propagates until the whole disk is optically thick. In this state the two-armed spiral pattern still exists, and its spatial location is strongly correlated with the location of the two stars. This is in excellent agreement with those observations showing two transient spirals during outburst. A high resolution calculation of the region surrounding the hot spot is given in this paper. We examine whether the physical conditions near the hot spot – or near the inner boundary layer – are suitable for inducing thermal instability.