Eccentricity Reduction for Quasicircular Binary Evolutions

Abstract: Simulation of quasicircular compact binaries is a major goal in numerical relativity, as they are expected to constitute most gravitational wave observations. However, given that orbital eccentricity is not well-defined in general relativity, providing initial data for such binaries is a challenge for numerical simulations. Most numerical relativity codes obtain initial conditions for low-eccentricity binary simulations by iterating over a sequence of short simulations -- measuring eccentricity mid-evolution and correcting the initial data parameters accordingly. Eccentricity measurement depends on a numerically challenging nonlinear fit to an estimator model, and the resulting eccentricity estimate is extremely sensitive to small changes in how the fit is performed. We have developed an improved algorithm that produces more consistent measurements of eccentricity relative to the time window chosen for fitting. The primary innovations are the use of the nonlinear optimization algorithm, variable projection, in place of more conventional routines, an initial fit parameter guess taken from the trajectory frequency spectrum, and additional frequency processing of the trajectory data prior to fitting.