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Numerical simulations of binary black holes are accompanied by an initialspurious burst of gravitational radiation (called `junk radiation') caused by afailure of the initial data to describe a snapshot of an inspiral that startedat an infinite time in the past. A previous study showed that the superposedharmonic (SH) initial data gives rise to significantly smaller junk radiation.However, it is difficult to construct SH initial data for black holes withdimensionless spin $\chi\gtrsim0.7$. We here provide a class of spatialcoordinate transformations that extend SH to higher spin. The new spatialcoordinate system, which we refer to as superposed modified harmonic (SMH), ischaracterized by a continuous parameter -- Kerr-Schild and harmonic spatialcoordinates are only two special cases of this new gauge. We compare SMH withthe superposed Kerr-Schild (SKS) initial data by evolving several binary blackhole systems with $\chi=0.8$ and $0.9$. We find that the new initial data stillleads to less junk radiation and only small changes of black hole parameters(e.g. mass and spin). We also find that the volume-weighted constraintviolations for the new initial data converge with resolution during the junkstage $(t\lesssim700M)$, which means there are fewer high-frequency componentsin waveforms at outer regions.

Extending superposed harmonic initial data to higher spin