Spin-Orbit Misalignments of Eccentric Black Hole Mergers in AGN Disks

TL;DR

The paper investigates how gas in AGN disks can realign spin orientations of dynamically formed BBHs before merger, producing distinct $χ_{ m eff}$ distributions. By combining PN N-body three-body scatterings with a gas-driven alignment prescription, it maps when alignment can outpace GW inspiral across disk radii and eccentricities. A key result is a robust eccentricity–$χ_{ m eff}$ correlation: quasi-circular mergers align efficiently and yield $χ_{ m eff}>0$, while highly eccentric mergers can retain misalignment unless alignment is exceptionally strong, potentially explaining events like GW190521 and GW231123. This framework provides observable signatures to identify the AGN channel in LVK data and guides future hydrodynamical modeling and population studies.

Abstract

The disks of active galactic nuclei (AGNs) provide a natural environment where stellar-mass black holes (BHs) can dynamically pair, undergo repeated interactions, and eventually merge. It is commonly assumed that gas accretion will both efficiently spin up disk-embedded black holes and align the orbits of embedded binaries with the disk plane, leading to mergers with preferentially positive effective spin parameters ($χ_{\mathrm{eff}}$). Such predictions have motivated the use of $χ_{\mathrm{eff}}$ as a diagnostic for identifying candidate AGN-embedded mergers in the LIGO-Virgo-KAGRA gravitational-wave catalog. In this work, we perform post-Newtonian $N$-body simulations of nearly planar binary-single encounters and apply an empirically motivated, gas-driven alignment prescription to characterize the expected $χ_{\mathrm{eff}}$-eccentricity correlations of AGN-embedded mergers. By comparing the alignment and gravitational-wave inspiral timescales, we identify the regions of parameter space, across both disk location and binary properties, where full disk-spin-orbit alignment is effective and where it is not. We find that quasi-circular binaries typically align by the time they merge, supporting the standard picture of spin-orbit aligned orientations. By contrast, eccentric binaries (with in-band eccentricity $e_{10\mathrm{Hz}}\gtrsim 0.1$) typically inspiral too quickly for gas torques to act, preserving the post-encounter spin-orbit misalignments and yielding more isotropic $χ_{\mathrm{eff}}$ distributions when disk densities and torque efficiencies are modest. This interplay naturally establishes a correlation between binary eccentricity and $χ_{\mathrm{eff}}$ in AGN disks, highlighting a new key observable of the AGN channel and a potential explanation for massive events such as GW190521 and GW231123.

Figures (7)

• Figure 1: Sketch of out-of plane of a typical BH binary-single interaction in an accretion disk. The small black arrows represent the black hole individual spins, which due to prior disk interaction, are aligned with the angular momentum of the disk $\hat{J}_{\rm AGN}$ and remain aligned throughout the process. Left panel: configuration of the three-body system before the encounter. The single approaches at some angle $\varphi$ the binary with its orbital angular momentum $\vec{J}_B$ aligned with the one of the disk $\hat{J}_{\rm AGN}$. Middle panel: the interaction with the single causes a kick tilting $\vec{J}_B$ at an angle $\theta_B$. Right panel: while the binary is merging due to GW radiation, it experiences gas accretion adding momentum $\Delta \vec{J}_{\rm gas}$ onto $\vec{J}_B$, thus realigning the binary with the disk. The figure is re-adapted from Samsing22.
• Figure 2: Alignment timescale maps for the Sirko03 disk model, shown as a function of SMBH mass and distance from the SMBH in units of $R_{\rm s}$. We consider a binary with initial semi-major axis $a_0=1$ AU, shown for different eccentricities at 10 Hz ($e_{\rm 10Hz}=0.01, 0.1, 0.9$) and two initial inclinations ($\theta_B=10^\circ, 110^\circ$). The dark shaded region marks where $a_0$ exceeds half of the Hill radius; these cases are excluded as we only consider binaries well embedded within their Hill sphere. Black curves indicate $t_{\rm align}=t_{\rm gw}$, with line style showing alignment efficiency: $f_{\rm rot}=0.1$ (solid), 1 (dashed), and 10 (dot-dashed). The dotted shaded area highlights regions where $t_{\rm align}>t_{\rm gw}$ for the fiducial $f_{\rm rot}=0.1$. Increasing $f_{\rm rot}$ enlarges the parameter space where alignment occurs before merger. According to Eqs. \ref{['eq:ratioad']}-\ref{['eq:ratiotl']}, higher eccentricities shrink the region where $t_{\rm align}>t_{\rm gw}$, particularly at larger inclinations, implying that more binaries merge misaligned.
• Figure 3: Distribution of binary inclinations $\theta_B$ for different merger populations. Top: results without gas. Quasi-circular mergers ($e<0.01$ at 10 Hz, yellow) show sharp peaks at $0^\circ$ and $180^\circ$, while eccentric mergers ($e>0.1$, blue) are more isotropic with a flatter distribution. Solid curves indicate the smoothed probability density estimates. Bottom: results including gas alignment for a $10^8 M_\odot$ SMBH and disk density $\rho_{\rm g}=10^{-12} \, \rm g \, cm^{-3}$ (representative of the Sirko03 model), with alignment efficiencies $f_{\rm rot}$ = 0 (blue), 0.1 (pink), 1 (green), and 10 (black). Increasing $f_{\rm rot}$ reduces the fraction of retrograde binaries, and at high efficiency ($f_{\rm rot} = 10$) the distribution departs significantly from the gas-free case. The evolution of $\theta_B$ is quantified using the expression given in Eq. \ref{['eq:efold']}. Histograms are based on PN N-body simulations of equal-mass $15 \, \rm M_\odot$ BHs with $a_0 = 1$ AU, where the single approaches the binary at an initial inclination of $0.1^\circ$.
• Figure 4: Ratio of negative to positive effective spin orientations, $N_{(\chi_{\rm eff}<0)}/N_{(\chi_{\rm eff}>0)}$, as a function of eccentricity at 10 Hz ($e_{\rm 10Hz}$). Results are shown for different alignment efficiencies: $f_{\rm rot}=0$ (no alignment, blue), $f_{\rm rot}=0.1$ (pink), and $f_{\rm rot}=1$ (green). For small eccentricities and high $f_{\rm rot}$, alignment is efficient and the ratio remains well below unity, reflecting the expected positive skewness of $\chi_{\rm eff}$ in AGN disks. For $f_{\rm rot}=0.1$ and at larger $e_{\rm 10Hz}$, the ratio grows and saturates near unity, indicating that alignment becomes less efficient than the GW inspiral. Without the effect of alignment, the excess of retrograde binaries reflects the outcome of three-body dynamics, while larger encounter angles ($\varphi$) suppress their production.
• Figure 5: Initial (blue stars) and final (red stars) inclination distributions $\theta_B$ as a function of $e_{\rm 10Hz}$, shown for $f_{\rm rot}=$ 1 (black), 10 (red). The black and red curves represent the maximum final inclination available for a binary starting at $\theta_{B,0}=180^\circ$, and the shaded region illustrates the available combinations of $\theta_{B,\, {\rm merge}} - e_{\rm 10Hz}$ at $f_{\rm rot}=10$. For the higher efficiency case, binaries with $e_{\rm 10Hz} \lesssim 0.2$ are fully realigned, while higher eccentricities lead to progressively larger residual tilts. The most eccentric mergers, with GW peak frequencies already above 10 Hz at formation, retain significant retrograde orientations due to their extremely short merger timescales.