Inferences about Supernova Physics from Gravitational-Wave Measurements: GW151226 Spin Misalignment as an Indicator of Strong Black-Hole Natal Kicks

The inferred parameters of the binary black hole GW151226 are consistent with nonzero spin for the most massive black hole, misaligned from the binary’s orbital angular momentum. If the black holes formed through isolated binary evolution from an initially aligned binary star, this misalignment would then arise from a natal kick imparted to the first-born black hole at its birth during stellar collapse. We use simple kinematic arguments to constrain the characteristic magnitude of this kick, and find that a natal kick $v_k\gtrsim 50\mathrm{km}/\mathrm{s}$ must be imparted to the black hole at birth to produce misalignments consistent with GW151226. Such large natal kicks exceed those adopted by default in most of the current supernova and binary evolution models.

Figure 1

Comparing kick-induced misalignments with GW151226. Left: Contour plot of the cumulative probability distribution $P(\gamma <{\gamma }_{*})$ of the spin misalignment $\gamma$ produced by the first SN kick in a binary similar to the progenitor of GW151226. The natal kick is assumed to be drawn from a Maxwellian distribution characterized by $\sigma$, which enters our predictions only through its ratio with the binary orbital velocity $v$. For a sense of scale, horizontal dashed lines are drawn at $\gamma =25°$ and $\gamma =80°$ as found as upper and lower bounds for GW151226 [1]. Right: Fraction of surviving binaries with spin misalignment consistent with GW151226 as a function of the dimensionless kick magnitude $\sigma /v$. The lighter pink line shows $P(\gamma <80°)-P(\gamma <25°)$ from our Monte Carlo runs, while the darker red curve shows a polynomial fit. For context, the horizontal dashed line shows $(\cos 25°-\cos 80°)/2$, as expected from random spin-orbit misalignment, while the horizontal dotted line corresponds to $(80°-25°)/180°$, as expected in the limit of large $\sigma$. As natal kicks increase in magnitude, the fraction with misalignment consistent with GW151226 first increases substantially, as most surviving binaries have been modestly kicked relative to their orbital speed.

Figure 2

Kick velocities consistent with GW151226 misalignment: Left: Cumulative distribution $⟨P(\gamma <{\gamma }_{*})⟩$ averaged over masses and separations as a function of misalignment angle $\cos \gamma$ and physical natal kick strength $\sigma$. The top axis shows the correspondent three-dimensional root-mean-square velocity $\sqrt{⟨v_k^2⟩}=\sqrt{3}\sigma$. Right: Difference $⟨P(\gamma <80°)-P(\gamma <25°)⟩$ versus $\sigma$ and $\sqrt{⟨v_k^2⟩}$, illustrating how the expected fraction of binaries with misalignments consistent with GW15226 changes with the characteristic natal kick magnitude. The lighter pink line shows results of our Monte Carlo runs, while the darker red curve corresponds to a polynomial fit. Vertical green dotted lines are drawn at $\sigma \simeq 26,36$, and $92\mathrm{km}/\mathrm{s}$, corresponding to probabilities of 5%, 10%, and 30%; the dashed blue line at $\sigma =265\mathrm{km}/\mathrm{s}$ marks the typical natal kick magnitude imparted to neutron stars [14].