The role of migration traps in the formation of binary black holes in AGN disks

TL;DR

The paper interrogates whether binary black holes forming in AGN disks preferentially arise at migration traps by explicitly integrating BH migration under self-consistent torques from SG disk models. Using a large Monte Carlo suite with 1D radial migration, Hill-stability pair-up criteria, and hierarchical seeding (Ng), it maps pair-up radii as functions of $M_\bullet$, $\alpha$, and $m$, comparing two torque prescriptions (Grishin 2024 and Bellovary 2016) and examining Type II gap-opening. It finds that for $M_\bullet\lesssim 10^{8} M_\odot$ the majority of pair-ups cluster near migration traps, with significant offsets due to differential migration and traffic-jam effects, while higher $M_\bullet$ reduce trap dominance and shift pair-ups inward; Ng BHs exhibit stronger trap associations. The results provide physically grounded pair-up radii and timescales that can be incorporated into population synthesis to improve BBH merger rate predictions and interpretation of GW data, while highlighting the limitations of assuming fixed trap sites. The work also quantifies how disk viscosity and migration prescriptions influence trap relevance and hierarchical merger clustering, offering a framework to refine AGN-channel BBH models.

Abstract

Binary black holes (BBHs) forming in the accretion disks of active galactic nuclei (AGNs) represent a promising channel for gravitational-wave production. BBHs are often assumed to form at migration traps, i.e. radial locations where the Type I migration of embedded stellar-mass black holes (BHs) transitions from outwards to inwards. In this work, we test this assumption by explicitly simulating the radial migration of BH pairs in AGN disks under different torque prescriptions, including thermal effects and the switch to Type II migration. We map where and when binaries form as a function of supermassive BH (SMBH) mass, disk viscosity, and migrating BH mass. We find that, for SMBH masses below $10^8 M_\odot$, the majority of pair-up events occur near migration traps ($\gtrsim 80\%$). In contrast, for higher SMBH masses, differential migration dominates and off-trap pair-ups can prevail. Certain disk configurations (e.g., $α= 0.01$, $M_\bullet < 10^6 M_\odot$) present a significant overdensity of pair-ups even in the absence of traps due to traffic-jam accumulations where the gamma profile changes slope sharply. We also investigate hierarchical BBH formation, showing that higher-generation pair-ups cluster more tightly around trap or traffic-jam radii. Our results provide realistic prescriptions for BBH pair-up locations and timescales, highlighting the limitations of assuming fixed BBH formation sites.

Figures (11)

• Figure 1: Examples of torque profiles as a function of radial distance (in Schwarzschild radii) for BHs embedded in a SG disk. Each plot corresponds to a different combination of torque prescription (top: Grishin_2024; bottom: Bellovary_2016), disk viscosity parameter $\alpha$ (left: $\alpha = 0.01$; right: $\alpha = 0.1$) and SMBH mass ($\log M_\bullet / \,\mathrm{M}_\odot = 5.0, 6.3, 7.7, 9.0$, represented in different colors). Solid and dashed lines indicate positive and negative net torques, respectively, while shaded regions denote uncertainty in the torque determined by computing it over a range of migrator masses between $5 \,\mathrm{M}_\odot$ and $50 \,\mathrm{M}_\odot$. Vertical dotted lines mark the locations of migration traps.
• Figure 2: Two-dimensional histograms showing the distribution of BBH pair-up locations in the radius–mass plane ($R$ vs $M_\bullet$), for different combinations of torque prescription (top: Grishin_2024; bottom: Bellovary_2016) and disk viscosity $\alpha$ (left: 0.01; right: 0.1) in a SG disk. The color map indicates the number of pair-ups in each bin $N_\mathrm{pair}$. Red crosses mark the locations of migration traps.
• Figure 3: Fraction of binary pair-ups occurring within migration traps as a function of the SMBH mass. The vertical axis shows the occurrence $f_\mathrm{trap}$ of pair-up events that take place in proximity to predefined migration trap locations, while the horizontal axis shows the logarithm of the central SMBH mass. Different marker fillings indicate the BH generation (filled: $1g$; hollow: $Ng$), while color encodes the viscosity parameter $\alpha$ (orange: 0.01; teal: 0.1; navy blue: 0.4). The two torque formalisms are distinguished by marker shape and line style (squares and solid lines: Grishin_2024; circles and dashed lines: Bellovary_2016). Trap proximity is defined using a logarithmic tolerance on radial separation (see \ref{['sec:traprelevance']} for details).
• Figure 4: Histograms of binary pair-up radii $R_\mathrm{pair}$ (in units of Schwarzschild radii) for first-generation ($1g$) and $N$th-generation ($Ng$) BHs, across a range of SMBH masses ($\log M_\bullet / \,\mathrm{M}_\odot = 6, 7, 8$ respectively in the three columns) and viscosity parameters (upper row: $\alpha=0.01$; lower row: $\alpha=0.1$). Panels show the pair-up radii probability density functions (PDFs), normalized separately in each panel. The $1g$ distributions are shown as step histograms, while $Ng$ distributions are overlaid either as filled or hatched histograms for visual distinction. Vertical dotted lines indicate the positions of migration traps identified from the torque profile. Color represents the migration model used (green: Grishin_2024; purple: Bellovary_2016).
• Figure 5: Pair-up efficiency as a function of the central SMBH mass. The vertical axis shows the fraction of BHs that successfully form a binary during the simulation, while the horizontal axis shows the logarithm of the SMBH mass. As in \ref{['fig:pairup_trap_fraction']}, different marker fillings indicate the BH generation (filled: $1g$; hollow: $Ng$), color encodes the viscosity parameter $\alpha$ (orange: 0.01; teal: 0.1; navy blue: 0.4), and the two torque prescriptions are distinguished by marker shape and line style (squares and solid lines: Grishin_2024; circles and dashed lines: Bellovary_2016).