Measuring the effective spin of binary black holes

Gravitational waves emitted by coalescing compact objects carry information about the spin of the individual bodies. However, what can be measured best is the projection of the total spin along the orbital angular momentum, known as effective spin $\chi_{eff}$. This quantity, is also conserved up the the 2nd post-newtonian order. Various authors have proposed methods to use the measured $\chi_{eff}$ distribution to infer the underlying formation channels. However, care need to be exercised when drawing conclusions. In this talk we will show that a) the bayesian priors used can significantly affect the measurements of $\chi_{eff}$ b) even if the true astrophysical distribution of $\chi_{eff}$ were to be perfectly symmetric, the distribution of detectable $\chi_{eff}$ need not be; and c) the posterior distribution of $\chi_{eff}$ for individual events should not be treated as a gaussian. In particular, we find that the posterior distributions for $\chi_{eff}$ systematically show fatter tails toward larger positive values. Finally, we show that the uncertainties of the measured effective spins are as much as ~8 times larger when the spin is negative than when it is positive, where the amount of additional uncertainty depends on the mass and magnitude of $\chi_{eff}$.