Recovering dark-matter effects in gravitational waveforms using parametrized post-Einsteinian templates

As a massive black hole (BH) grows in a dark matter (DM) halo, an over-density may form near the BH, called a DM spike. A binary formed from the massive BH with the DM spike and a compact secondary produces gravitational waves that dephase from vacuum binaries without DM. The planned LISA detector will be sensitive enough to detect this dephasing and characterize the DM spike surrounding the massive BH. We show that using gravitational waveforms without the DM effect to analyze this non-vacuum merger biases the measured parameters. However, these biases can be significantly reduced, and the DM effects determined, by using a waveform that includes the parameterized post-Einsteinian model that was originally developed for capturing non-GR effects.