Distribution of Effective Spins and Masses of Binary Black Holes from the LIGO and Virgo O1-O3a Observing Runs

The distribution of effective spin $\chi_{\rm eff}$, a parameter that encodes the degree of spin-orbit alignment in a binary system, has been widely regarded as a robust discriminator between the isolated and dynamical formation pathways for merging binary black holes. Until the recent release of the GWTC-2 catalog, such tests have yielded inconclusive results due to the small number of events with measurable nonzero spins. In this work, we study the $\chi_{\rm eff}$ distribution of the binary black holes detected in the LIGO-Virgo O1-O3a observing runs. Our focus is on the degree to which the $\chi_{\rm eff}$ distribution is symmetric about $\chi_{\rm eff} = 0$ and whether the data provides support for a population of negative-$\chi_{\rm eff}$ systems. We find that the $\chi_{\rm eff}$ distribution is asymmetric at 95% credibility, with an excess of aligned-spin binary systems ($\chi_{\rm eff}>0$) over anti-aligned ones. Moreover, we find that there is no evidence for negative-$\chi_{\rm eff}$ systems in the current population of binary black holes. Thus, based solely on the $\chi_{\rm eff}$ distribution, dynamical formation is disfavored as being responsible for the entirety of the observed merging binary black holes, while isolated formation remains viable. We also study the mass distribution of the current binary black hole population, confirming that a single truncated power law distribution in the primary source-frame mass, $m_1^{\rm src}$, fails to describe the observations. Instead, we find that the preferred models have a steep feature at $m_1^{\rm src} \sim 40 \,\rm M_\odot$ consistent with a step and an extended, shallow tail to high masses.