The spin of the second-born black hole in coalescing binary black holes

Abstract

Context. Various binary black hole formation channels have been proposed since the first gravitational event GW150914 was discovered by the Advanced Laser Interferometer Gravitational-Wave Observatory (AdLIGO). For all evolutionary channels based on the evolution of isolated binaries, the immediate progenitor of the binary black hole is a close binary system composed of a black hole and a helium star. Aims. We study the spin angular momentum evolution of the helium star in order to constrain the spin of the second-born black hole. Methods. We perform detailed stellar structure and binary evolution calculations that take into account, mass-loss, internal differential rotation, and tidal interactions between the helium star and the black hole companion, where we also calculate the strength of the tidal interactions from first principles based on the structure of the helium stars. We systematically explore the parameter space of initial binary properties, including initial black hole and helium star masses, initial rotation of the helium star as well as metallicity.Results. We argue that the spin of the first-born black hole at its birth is negligible ( 0.1), hence the second-born black hole's spin dominates the measured effective spin, χ eff , from gravitational wave events of double black hole mergers. We find that tides can be important only when orbital periods are shorter than 2 days. Upon core collapse, the helium star produces a black hole (the secondborn black hole in the system) with a spin that can span the entire range from zero to maximally spinning. We show that the bimodal distribution of the spin of the second-born black hole obtained in recent papers is mainly due to oversimplifying assumptions. We find an anti-correlation between the merging timescale of the two black holes, T merger , and the effective spin χ eff . Finally, we provide new prescriptions for the tidal coefficient E 2 for both H-rich and the helium-rich stars. Conclusions. To understand the spin of the second-born black hole, careful treatments of both tides and stellar winds are needed. We predict that, with future improvements to AdLIGO's sensitivity, the sample of merging binary black hole systems will show an overdensity of sources with positive but small χ eff originating from lower mass black hole mergers born at low redshift.

Most Black Holes Are Born Very Slowly Rotating

“…Hence, we predict that most of the LIGO BH population will be consistent with zero spin even with significantly smaller uncertainties in χ eff . Two evolutionary scenarios leading to moderate/high BH spin are tidal torques that spin up a helium star in a short-period orbit after a common envelope event (Kushnir et al 2016;Qin et al 2018a), or rapid rotation (likely enforced by tidal spin-up) and low-metallicity that allows for homogeneous evolution (Maeder 1987;Woosley & Heger 2006;Yoon et al 2006). Both scenarios can produce moderate (a ∼ 0.1−0.5) BH spins, but only homogeneous evolution can produce very large spins with a ∼ 1, though it should only occur for high chirp mass (M chirp 25 M ) mergers.…”

“…In addition to the single-star models listed in Table 1, we have run several binary models involving a 40 M primary. In each of these models, tidal spin-up and mass transfer is included via the prescriptions of Qin et al (2018a). In the "Case A" scenario, the primary begins in a 3-day orbit with a companion of 20 M , such that mass transfer (which is assumed to be fully conservative) begins on the main sequence.…”

“…Most prior predictions of internal stellar rotation rates and natal NS/BH spins are therefore unreliable and could be overestimated. Models based on the Tayler-Spruit dynamo (Spruit 2002), such as Heger et al (2005) and Qin et al (2018a), predicted fairly slow rotation (a 0.1) for BHs born from single stars, thus many BHs are likely to rotate even slower than those estimates.…”

Unmodelled clustering methods for gravitational wave populations of compact binary mergers

“…The fourth sub-population (BBH2) has the same mass distribution as BBH1 but allows for the secondary companion to have aligned spin: a 1 is zero, and the secondary black hole spin a 2 is uniformly distributed between 0.7 and 0.95. For binary black holes formed through common envelope evolution, the first born black hole is likely to have negligible spin (Qin et al 2018;Bavera et al 2019). This is because most of its angular momentum is stored in the envelope during the giant stage, and is removed during mass transfer or common envelope evolution.…”

“…This is because most of its angular momentum is stored in the envelope during the giant stage, and is removed during mass transfer or common envelope evolution. The spin of the second born black hole is determined by the effects of wind mass loss and tides on its progenitor, a helium star (Kushnir et al 2016b;Zaldarriaga et al 2018;Gerosa et al 2018;Qin et al 2018;Bavera et al 2019). If the binary has a sufficiently short orbital period, the helium star may be spun up through tides and form a rapidly spinning black hole.…”