Binary Stars

The SPH code has routines to create binaries with both irrotational and corotating velocity profiles. For the former case, there is no fixed reference frame in which the material is stationary, and we have not yet implemented a way to relax the matter configuration exactly. For ways of calculating these configurations, see, e.g., Gourgoulhon et al. (2001); Taniguchi et al. (2001); Taniguchi & Gourgoulhon (2002), and references therein.

On the other hand, binary stars in corotation, also known as synchronized binaries, can be relaxed, since they are static in a frame which rotates with the same angular frequency as the matter. For this case, called by setting the parameter NRELAX=2, the code adds in a false centrifugal force, to handle the rotation of the frame, yielding a force law for quantities in the corotating frame

$$\frac{d\vec{v}}{dt}=\vec{a}+\Omega^2 \vec{r}-\frac{\vec{v}}{t_{relax}},$$ (13)

where we calculate the corotating frame's angular velocity by taking the average of the net forces on each component of the binary divided by the distance from the origin to the center of mass of each component. Note that this routine works for a given binary separation, which is given by the input parameter SEP0. After each timestep, we shift the positions of both stars very slightly to keep the center of mass separation at the proper value, with the system center of mass at the origin. It is possible to edit the code to produce a relaxed sequence with a smoothly varying separation, by defining a new separation variable and replacing references to SEP0 in the relaxation subroutines. See the file sepscan.f for an example of this.

We have subroutines that can take either a relaxed single-star model and place it in a binary, or create both stars from scratch, with either equal-mass or equally-spaced particles, like before. The code can also handle binaries for which the stars have different masses. Note that in this case, if you wish to use models of relaxed single stars, you will have to calculate each separately.