Comparison of Binary Black Hole Initial Data Sets

We present improvements to construction of binary black hole initial data used in SpEC (Spectral Einstein Code). We introduce new boundary conditions for the elliptic equations that enforce the excision surfaces to be slightly inside rather than on the apparent horizons, thus avoiding extrapolation into the black holes at the last stage of initial data construction. We find that this improves initial data constraint violations near and inside the apparent horizons by about 3 orders of magnitude. We construct several initial data sets including initial data in the harmonic and damped harmonic gauges and compare them by evolving them. We show that the gravitational waveform extracted during the evolution of these different initial data sets agree very well, after excluding the spurious transients known as "junk radiation". Among the cases considered, harmonic initial data leads to significantly lower junk radiation, smaller temporal variation in black hole spins and masses during the junk radiation stage, smaller constraint violations, and better computational efficiency.