Efficient computation of the gravitational wave spectrum emitted by eccentric massive black hole binaries in stellar environments

Understand

We present a fast and versatile method to calculate the characteristic spectrum $h_c$ of the gravitational wave background (GWB) emitted by a population of eccentric massive black hole binaries (MBHBs).

• We fit the spectrum of a reference MBHB with a simple analytic function and show that the spectrum of any other MBHB can be derived from this reference spectrum via simple scalings of mass, redshift and frequency.
• We then apply our calculation to a realistic population of MBHBs evolving via 3-body scattering of stars in galactic nuclei.
• We demonstrate that our analytic prescription satisfactorily describes the signal in the frequency band relevant to pulsar timing array (PTA) observations.