Irrotational Binaries

For irrotational NS, i.e. those with no net vorticity in the inertial frame, there is no simple way to relax the matter configuration. Instead, we highly recommend that you first compute relaxed single-star models, and then place them in a binary. We allow you to deform the spherical stars into triaxial ellipsoids, by specifying the semi-major axes in each of the three principal directions. Values for these axis lengths can be found for a number of different EOS in series of papers by Lai et al. (1994b); Lai et al. (1994a); Lai et al. (1994c); Lai et al. (1993b); Lai et al. (1993c) and a paper by Lombardi et al. (1997). We recommend perusing them thoroughly before continuing onward. Please note that by our definition, ``irrotational'' does not necessarily mean that every point on the star has the same velocity in the inertial frame. Rather, it refers only to a lack of vorticity. From Lombardi et al. (1997), we determine that for a triaxial ellipsoidal star whose center of mass is at some distance $x_0$ from the origin, traveling initially in the y-direction with orbital velocity $\Omega x_0$, and with semi-major axes $a_1$ and $a_2$ in the x- and y-directions, a particle located at coordinates $(x,y)$ with respect to the center of mass of the star has a velocity in the inertial frame given by

$$v_x = \frac{2a_1^2}{a_1^2+a_2^2}\Omega y-\Omega y= \frac{a_1^2-a_2^2}{a_1^2+a_2^2}\Omega y,$$

$$v_y = -\frac{2a_2^2}{a_1^2+a_2^2}\Omega x+\Omega(x_0+x)= \frac{a_2^2-a_1^2}{a_1^2+a_2^2}\Omega x+\Omega x_0.$$ (33)

We note that for circular stars, this reduces to simple translationary motion. For elliptical stars, the surface shape rotates with the orbital velocity in such a way that the surface profile is invariant in the corotating frame. Since the code cannot perform a relaxation loop to solve for $\Omega$, we estimate the proper binary angular velocity by calculating the net inward force on both components of the binary, analogously to the corotating case.

As in the case of corotating systems, the initial binary separation is set with the parameter SEP0, and the mass ratio is given by QDAR.