Inference of recoil kicks from binary black hole mergers up to GWTC--4 and their astrophysical implications

Abstract

We infer recoil (kick) velocities for all binary black hole merger events reported up to the GWTC--4 catalog, together with candidate intermediate-mass black hole events. We obtain informative kick constraints for GW231028\_153006 ($839^{+1018}_{-681}\,\mathrm{km\,s^{-1}}$) and GW231123\_135430 ($974^{+944}_{-760}\,\mathrm{km\,s^{-1}}$). Additionally, we compute recoil velocities for recently reported events from the ongoing fourth observing run: GW241011\_233834, GW241110\_124123, and GW250114\_082203, obtaining $v_{\rm kick} = 974^{+555}_{-466}\,\mathrm{km\,s^{-1}}$, $394^{+582}_{-207}\,\mathrm{km\,s^{-1}}$, and $115^{+301}_{-95}\,\mathrm{km\,s^{-1}}$, respectively. The remnant of GW241011\_233834 is therefore inferred to have one of the largest recoil velocities among currently known events. We find that present recoil kick constraints are driven primarily by measurements of the mass ratio and spin magnitudes, while the contribution from spin orientation angles remains subdominant in most cases. We estimate typical retention probabilities of the remnant black holes in GWTC catalogs to be $\sim 1$--$5\%$ for globular clusters, $\sim 15$--$30\%$ for nuclear star clusters, $\sim 5$--$40\%$ for dwarf galaxies, and $\sim 70$--$100\%$ for elliptical galaxies. We further show that, even for remnants retained in globular clusters, recoil-induced spatial displacements from the cluster core are often significant, which can substantially suppress the chances of hierarchical mergers. We find that the probability for a GWTC merger remnant to participate in hierarchical mergers is $\sim 0.1$--$1\%$ in globular clusters and $\sim 1$--$15\%$ in nuclear star clusters.

Figures (9)

• Figure 1: Inferred recoil kicks for all events. We show the posterior distributions of recoil kick velocities inferred from publicly available samples for events in GWTC--4 (blue), GWTC--3 (orange-red), GWTC--2.1 (green), and LVK candidate IMBH mergers (yellow). For comparison, we show the median and 90% credible interval of the prior as a horizontal dashed line and a gray shaded region, respectively. The events are ordered by their median inferred recoil kick velocities. More details are in Section \ref{['sec:kick']}.
• Figure 2: Example of events with large kick inference. Upper panel: We show recoil kick velocity posteriors (shaded blue histograms) inferred from the publicly available GWTC--4 posterior samples for the eight events whose Jensen--Shannon divergence (JSD) between the inferred posterior and the corresponding prior (shaded gray histograms) exceeds $0.07$ bits. For comparison, we also show kick posteriors obtained by propagating only the mass ratio $q$ and spin magnitudes $|\chi_{1,2}|$ posteriors through the recoil prescription, while drawing the spin orientation angles isotropically (maroon histograms). The corresponding kick posteriors obtained using the gwModel recoil prescription (for isotropic spin angles) are shown as black histograms. The JSD values between the default kick posterior and the prior are indicated in gray text, while the JSD values between the default posterior and the isotropic-angle case are indicated in maroon text. Lower panel: Same for the select events in GWTC--2.1 and GWTC--3 that have not already been analyzed in Ref. Islam:2023zzjMahapatra:2021hme. More details are in Section \ref{['sec:kick']}.
• Figure 3: Understanding the effect of spin angles on kick inference. We show the 5th and 95th percentiles of the inferred recoil kick velocity for the default precessing-spin recoil fits $v_{\rm kick}$ (blue circles) and aligned-spin recoil fits $v_{\rm kick}^{\rm as}$ (green diamonds) . For comparison, we also show the corresponding percentiles obtained by propagating only the mass ratio $q$ and spin magnitudes $|\chi_{1,2}|$ posteriors through the recoil prescription, while drawing the spin orientation angles isotropically (maroon plus symbols). In addition, the corresponding percentiles of the prior distribution are shown as gray squares. More details are in Section \ref{['sec:kick']}.
• Figure 4: Quantifying the effect of spin angles on kick inference. We show the Jensen--Shannon divergence (JSD) between the kick posterior $v_{\rm kick}$ and the distribution obtained under isotropic spin orientations, $v_{\rm kick}^{\rm iso}$, as a function of the JSD between the kick posterior $v_{\rm kick}$ and the prior distribution, $v_{\rm kick}^{\rm prior}$. For reference, we indicate a fiducial JSD threshold value of $0.02$ (red dashed line), which marks the onset of statistically non-negligible differences between two probability distributions. More details are in Section \ref{['sec:kick']}.
• Figure 5: Inference of kick for O4b GW events. We show the inferred recoil kick velocity posteriors for three recently announced GW events from the ongoing O4b observing run: GW241011_233834 (blue), GW241110_124123 (orange) and GW250114_082203 (green). For reference, we also show the corresponding kick prior distributions (gray). More details are in Section \ref{['sec:O4b']}.