An analytical joint prior for effective spins for inference on the spin distribution of binary black holes

Understand

We derive an analytical form of the joint prior of effective spin parameters, $\chi_\mathrm{eff}$ and $\chi_\mathrm{p}$, assuming an isotropic and uniform-in-magnitude spin distribution.

• This is a vital factor in performing hierarchical Bayesian inference for studying the population properties of merging compact binaries observed with gravitational waves.
• In previous analyses, this was evaluated numerically using kernel density estimation (KDE).
• However, we find that this numerical approach is inaccurate in certain parameter regions, where both $|\chi_\mathrm{eff}|$ and $\chi_\mathrm{p}$ are small.