Equilibrium Configurations of Synchronous Binaries: Numerical Solutions and Application to Kuiper-Belt Binary 2001 QG298

Abstract

We present numerical computations of the equilibrium configurations of tidally-locked homogeneous binaries, rotating in circular orbits. Unlike the classical Roche approximations, we self-consistently account for the tidal and rotational deformations of both components, and relax the assumptions of ellipsoidal configurations and Keplerian rotation. We find numerical solutions for mass ratios q between 1e-3 and 1, starting at a small angular velocity for which tidal and rotational deformations are small, and following a sequence of increasing angular velocities. Each series terminates at an appropriate ``Roche limit'', above which no equilibrium solution can be found. Even though the Roche limit is crossed before the ``Roche lobe'' is filled, any further increase in the angular velocity will result in mass-loss. For close, comparable-mass binaries, we find that local deviations from ellipsoidal forms may be as large as 10-20%, and departures from Keplerian rotation are significant. We compute the light curves that arise from our equilibrium configurations, assuming their distance is >>1 AU (e.g. in the Kuiper Belt). We consider both backscatter (proportional to the projected area) and diffuse (Lambert) reflections. Backscatter reflection always yields two minima of equal depths. Diffuse reflection, which is sensitive to the surface curvature, generally gives rise to unequal minima. We find detectable intensity differences of up to 10% between our light curves and those arising from the Roche approximations. Finally, we apply our models to Kuiper Belt binary 2001 QG298, and find a nearly edge-on binary with a mass ratio q = 0.93 ^{+0.07}_{-0.03}, angular velocity Omega^2/G rho = 0.333+/-0.001 (statistical errors only), and pure diffuse reflection. For the observed period of 2001 QG298, these parameters imply a bulk density, rho = 0.72 +/- 0.04 g cm^-3.