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 $χ_{\mathrm{eff}}$, is conserved up to at least the second post-Newtonian order. The measured distribution of $χ_{\mathrm{eff}}$ 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 $χ_{\mathrm{eff}}$ values which is symmetric does not necessarily lead to a symmetric distribution for the detected effective spin values, leading to a \emph{selection bias}; and (ii) the posterior distribution of $χ_{\mathrm{eff}}$ for individual events is \emph{asymmetric} and it cannot usually be treated as a Gaussian. We find that the posterior distributions for $χ_{\mathrm{eff}}$ 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 $χ_{\mathrm{eff}}$ 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.
Biases from Astrophysical Environmental Effects in Standard-Siren Cosmology
Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Institute of Physics and Astronomy, University of Potsdam（波茨坦大学物理与天文研究所）；Deutsche Zentrum für Astrophysik DZA（德国天体物理学中心）；Gravitation Astroparticle Physics Amsterdam (GRAPPA), University of Amsterdam（阿姆斯特丹大学引力与粒子物理阿姆斯特丹研究组）；Center for Cosmology, Particle Physics and Phenomenology - CP3, Université Catholique de Louvain（天主教鲁汶大学宇宙学、粒子物理与现象学中心）；Royal Observatory of Belgium（比利时皇家天文台）；Nikhef（荷兰国家核与亚原子物理研究所）
Distinguishing cosmology, astrophysics and systematics: the Bayesian search for a primordial gravitational-wave background in next-generation observatories
Princeton University（普林斯顿大学）；University of Nevada, Las Vegas（内华达大学拉斯维加斯分校）
Nowhere left to hide: revealing realistic gravitational-wave populations in high dimensions and high resolution with PixelPop
LIGO Laboratory, Massachusetts Institute of Technology（麻省理工学院引力波实验室）；Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究研究所）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Nottingham Centre of Gravity & School of Mathematical Sciences, University of Nottingham（诺丁汉大学重力研究中心与数学科学学院）
Biases in Tests of General Relativity from Microlensed Gravitational-Wave Signals
Inter-University Centre for Astronomy and Astrophysics (IUCAA)（天文与天体物理大学间中心）；University of Birmingham（伯明翰大学）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）
