Gravitational waves emitted by coalescing compact objects carry information about the spin of the individual bodies. However, with present detectors only the mass-weighted combination of the components of the spin along the orbital angular momentum can be measured accurately. This quantity, the effective spin ${\chi }_{\mathrm{eff}}$, is conserved up to at least the second post-Newtonian order. The measured distribution of ${\chi }_{\mathrm{eff}}$ values from a population of detected binaries, and in particular whether this distribution is symmetric about zero, encodes valuable information about the underlying compact-binary formation channels. In this paper we focus on two important complications of using the effective spin to study astrophysical population properties: (i) an astrophysical distribution for ${\chi }_{\mathrm{eff}}$ values which is symmetric does not necessarily lead to a symmetric distribution for the detected effective spin values, leading to a selection bias; and (ii) the posterior distribution of ${\chi }_{\mathrm{eff}}$ for individual events is asymmetric and it cannot usually be treated as a Gaussian. We find that the posterior distributions for ${\chi }_{\mathrm{eff}}$ systematically show fatter tails toward larger positive values, unless the total mass is large or the mass ratio $m_2/m_1$ is smaller than $\sim 1/2$. Finally we show that uncertainties in the measurement of ${\chi }_{\mathrm{eff}}$ are systematically larger when the true value is negative than when it is positive. All these factors can bias astrophysical inference about the population when we have more than $\sim 100$ events and should be taken into account when using gravitational-wave measurements to characterize astrophysical populations.

• Received 28 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.083007