Length dependence of waveform mismatch: a caveat on waveform accuracy

Understand

The Simulating eXtreme Spacetimes Collaboration's code SpEC can now routinely simulate binary black hole mergers undergoing $\sim25$ orbits, with the longest simulations undergoing nearly $\sim180$ orbits.

• While this sounds impressive, the mismatch between the highest resolutions for this long simulation is $\mathcal{O}(10^{-1})$.
• Meanwhile, the mismatch between resolutions for the more typical simulations tends to be $\mathcal{O}(10^{-4})$, despite the resolutions being similar to the long simulations'.
• In this note, we explain why mismatch alone gives an incomplete picture of code -- and waveform -- quality, especially in the context of providing waveform templates for LISA and 3G detectors, which require templates with $\mathcal{O}(10^{3}) - \mathcal{O}(10^{5})$ orbits.