Relaxation

A common problem with SPH codes is the fact that the initial configuration of particles you lay down will be to some extent out of equilibrium. In some case, the resulting oscillations of the matter can lead to spurious results. As a result, we recommend that whenever it is possible, you use our routines to relax a material configuration before computing a dynamical run. We currently have two such routines, for both single-stars and corotating binaries. We discuss each in turn, but the idea behind each is essentially the same. For equilibrium situations where the matter is fixed in a given reference frame, you calculate forces by the standard techniques, but add a drag term to the accelerations, such that

$$\frac{d\vec{v}}{dt}=\vec{a}-\frac{\vec{v}}{t_{relax}}.$$ (12)

The relaxation time, $t_{relax}$ is input to the code as a parameter TRELAX, and should correspond roughly with the dynamical timescale of the system, given by $t_d\equiv 1/\sqrt{G\rho}\approx\sqrt{R^3/GM}$, in order to ensure nearly critical damping.

In all cases, we turn off the dissipative effects of both artificial viscosity (Sec. 3.5) and radiation reaction (Sec. 3.6) during relaxation.