Using Spin to Understand the Formation of LIGO and Virgo's Black Holes

With the growing number of binary black hole (BBH) mergers detected by the Advanced LIGO and Virgo detectors, it is becoming possible to constrain the properties of the underlying population and better understand the formation of these systems. Black hole (BH) spin orientations are one of the cleanest discriminators of formation history, with BHs in dynamically formed binaries in dense stellar environments expected to have spins distributed isotropically, in contrast to isolated populations where stellar evolution is expected to induce spins preferentially aligned with the orbital angular momentum. In this work, we propose a simple, model-agnostic approach to characterizing the spin properties of LIGO/Virgo's BBH population. Using measurements of the effective spin of the binaries, we introduce a simple parameter to quantify the fraction of the population that is isotropically distributed, regardless of the spin magnitude distribution of the population. Once the orientation characteristics of the population have been determined, we show how measurements of effective spin can be used to directly constrain the BH spin magnitude distribution. We find that most effective spin measurements are too small to be informative, with the first four events showing a slight preference for a population with alignment, with an odds ratio of 1.2. We argue that it will be possible to distinguish symmetric and anti-symmetric populations at high confidence with tens of additional detections, although mixed populations may take significantly longer to disentangle. We also derive BH spin magnitude distributions from LIGO's first four BBHs under the assumption of aligned or isotropic populations.