Anisotropies in the astrophysical gravitational-wave background: Predictions for the detection of compact binaries by LIGO and Virgo

We develop a detailed anisotropic model for the astrophysical gravitational-wave background, including binary mergers of two stellar-mass black holes, two neutron stars, or one of each, which are expected to be the strongest contributions in the LIGO-Virgo frequency band. The angular spectrum of the anisotropies, quantified by the ${C}_{\ensuremath{\ell}}$ components, is calculated using two complementary approaches: (i) a simple, closed-form analytical expression, and (ii) a detailed numerical study using an all-sky mock light cone galaxy catalogue from the Millennium simulation. The two approaches are in excellent agreement at large angular scales, and differ by a factor of order unity at smaller scales. These anisotropies are considerably larger in amplitude than e.g., those in the temperature of the cosmic microwave background, confirming that it is important to model these anisotropies, and indicating that this is a promising avenue for future theoretical and observational work.