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 10 ^ { -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 \gg 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 QG _ { 298 } , 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 \pm 0.001 ( statistical errors only ) , and pure diffuse reflection .
For the observed period of 2001 QG _ { 298 } , these parameters imply a bulk density , \rho = 0.72 \pm 0.04 g cm ^ { -3 } .