Improving Eccentricity Reduction for Black Hole Binaries in SpEC

Quasi-circular compact binaries are expected to make up the majority of binaries observed by LIGO. However, given that orbital eccentricity is not well-defined in general relativity, providing initial data for such binaries is a challenge for numerical simulations. SpEC obtains initial conditions for low-eccentricity binary simulations by iterating a sequence of short simulations with decreasing eccentricity. However, the current algorithm can be very sensitive to small changes in parameters, particularly as the eccentricity gets smaller. We have developed an improved algorithm that is more robust, consistent and accurate; the primary innovation is the use of variable projection in place of conventional nonlinear optimization routines.