Gravitational-wave astrophysics with effective-spin measurements: Asymmetries and selection biases

Abstract

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 χ_(eff), is conserved up to at least the second post-Newtonian order. The measured distribution of χ_(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 χ_(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 χ_(eff) for individual events is asymmetricand it cannot usually be treated as a Gaussian. We find that the posterior distributions for χ_(eff) systematically show fatter tails toward larger positive values, unless the total mass is large or the mass ratio m2/m1 is smaller than ∼1/2. Finally we show that uncertainties in the measurement of χ_(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 ∼100 events and should be taken into account when using gravitational-wave measurements to characterize astrophysical populations.