Tracking the Evolution of Supermassive Black Hole Binaries with Pulsar Terms

Abstract

Pulsar timing arrays will soon be able to resolve the loudest supermassive black hole binaries contributing to the stochastic gravitational wave background at nanohertz frequencies. While the few decades of observations are typically not enough to see these binaries evolve in frequency, the so-called pulsar terms offer a glimpse into the past and can help us map out the frequency evolution of these binaries over tens of thousands of years. Measuring this long-term frequency evolution can allow us to look for deviations from a vacuum binary evolution due to various environmental effects. We develop a Fisher-matrix approach to calculate how precisely the frequency can be tracked over time in this manner, and demonstrate its use on a realistic near-future pulsar timing array with a 30-year baseline. We find that the environmental effects predicted by 2-dimensional hydrodynamic simulations of circumbinary disks are unlikely to be detectable in the circular binaries we considered, however, in some cases they might result in biased chirp mass recovery if ignored. We also demonstrate how this approach allows one to test the orbital evolution predicted by general relativity in a purely gravitational-wave driven inspiral, and to put upper limits on additional generic environmental effects described by a power-law hardening model.