Corotating Binaries

Since we can relax corotating binary configurations, it is not necessary to compute a relaxed single star model first. In some cases, however, such as a system near the point of Roche lobe overflow, it is not always a bad idea. To allow for maximum flexibility, we have built-in routines which create binary systems from scratch with initially equally spaced particles in each star of variable mass, from scratch with equal-mass particles in each star laid down Monte Carlo style, and from previously calculated single star models. In all cases, please consult the notes on single-star configurations for more information on these techniques.

The initial binary separation is set by the user through the parameter ``SEP0''. It is possible during relaxation to have the binary separation be a function of time, with best results found by keeping the distance fixed for some amount of time until a relaxed configuration is achieved, then scanning slowly inwards in a quasi-equilibrium way. If you wish to employ a method like this, please look at the file named ``sepscan.f'', set the parameters as you wish, and use it to replace the ``CMADJ'' subroutine in advance.f.

In addition to equal mass binaries, i.e. those with mass ratio $q\equiv M_2/M_1=1.0$, the code can create from scratch unequal mass binaries with $q<1.0$. For such systems, the user is free to set the mass ratio of the system using the parameter ``QDAR''. The code will calculate the radius of the secondary star assuming the same equation of state (pressure-density relation) holds exactly for both stars. The power-law mass-radius relation is given by

$$\frac{R_2}{R_1}=\left(\frac{M_2}{M_1}\right)^{\frac{\Gamma-2}{3\Gamma-4}}= q^{\frac{\Gamma-2}{3\Gamma-4}}.$$ (32)

It is no problem for the code to calculate binary configurations which have the same adiabatic index $\Gamma$, but different values for the entropic variable $A_i$, but you will need to create each star in turn as a single star model, and run the routine ``setup2qr'', which creates a binary from previous models.