[Paper Review] Stellar/BH Population in AGN Disks: Direct Binary Formation from Capture Objects in Nuclei Clusters

Yihan Wang, Zhaohuan Zhu+1 more|arXiv (Cornell University)|Aug 17, 2023

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper proposes that stellar and black hole (BH) populations in active galactic nucleus (AGN) disks can directly form binaries through capture from nuclear star clusters, bypassing the need for migration traps. Using analytical and numerical models, it identifies new conserved integrals of motion governing capture dynamics, showing that captured object radial profiles follow dN/dr ∝ r^{-1/4} due to angular density and eccentricity distributions—enabling immediate binary formation in dense disk environments.

ABSTRACT

The Active Galatic Nuclei(AGN) disk has been proposed as a potential channel for the merger of binary black holes. The population of massive stars and black holes in AGN disks captured from the nuclei cluster plays a crucial role in determining the efficiency of binary formation and final merger rate within the AGN disks. In this paper, we investigate the capture process using analytical and numerical approaches. We discover a new constant integral of motion for one object's capture process. Applying this result to the whole population of the nuclei cluster captured by the AGN disk, we find that the population of captured objects depends on the angular density and eccentricity distribution of the nuclei clusters and is effectively independent of the radial density profile of the nuclei cluster and disk models. An isotropic nuclei cluster with thermal eccentricity distribution predicts a captured profile $d N/d r \propto r^{-1/4}$. The captured objects are found to be dynamically crowded within the disk. Direct binary formation right after the capture would be promising, especially for stars. The conventional migration traps that help pile up single objects in AGN disks for black hole mergers might not be required.

Motivation & Objective

• To investigate the capture of stars and black holes from nuclear star clusters (NSCs) into AGN accretion disks.
• To determine the radial distribution of captured objects and its dependence on NSC properties and disk dynamics.
• To assess whether migration traps are necessary for binary formation in AGN disks.
• To identify conserved quantities in the capture process that govern orbital evolution and final distribution.
• To evaluate the potential for direct binary formation immediately after capture, bypassing long migration phases.

Proposed method

• Derive timescale expressions for semi-major axis, eccentricity, and inclination evolution due to aerodynamic drag and gas dynamical friction.
• Identify new conserved integrals of motion: L cos²(I/2) cot^{γ−1}(I/2) for stars and L cos²(I/2) cot^{ζ−1}(I/2) for BHs, independent of disk or object mass.
• Model the radial distribution of captured objects using angular density and eccentricity distribution of the NSC, independent of radial density profiles.
• Apply self-gravitating disk models with surface density Σ ∝ r^{-3/2} to derive mass filling functions for captured stars and BHs.
• Simulate capture dynamics under varying initial inclinations, eccentricities, and arguments of periapsis to assess evolution timescales.
• Use numerical integration and analytical approximations to validate the conservation laws and predict final orbital distributions.

Experimental results

Research questions

• RQ1 What are the dominant timescales for semi-major axis, eccentricity, and inclination evolution during star/BH capture into AGN disks?
• RQ2 Can conserved integrals of motion be identified that govern the final orbital distribution of captured objects?
• RQ3 How does the radial distribution of captured stars and BHs depend on the properties of the nuclear star cluster and disk?
• RQ4 Is the formation of binary systems in AGN disks possible immediately after capture, eliminating the need for migration traps?
• RQ5 How do initial orbital parameters (inclination, eccentricity, argument of periapsis) influence the capture dynamics and final distribution?

Key findings

• The capture process is governed by two new conserved integrals of motion: L cos²(I/2) cot^{γ−1}(I/2) for stars and L cos²(I/2) cot^{ζ−1}(I/2) for BHs, independent of disk model or object mass.
• The radial number profile of captured objects follows dN/dr ∝ r^{-1/4} when the nuclei cluster is isotropic with a thermal eccentricity distribution.
• The radial distribution of captured objects depends solely on the angular density and eccentricity distribution of the nuclei cluster, not on its radial density profile or disk model.
• For self-gravitating AGN disks with Σ ∝ r^{-3/2}, the total mass of captured stars is described by a mass filling function 𝒪_M*(t) ∝ t^{1−γ_NS/3}, with objects distributed between r_g and r_m (Σ_m/Σ_*)^{1/3} t^{1/3}.
• Captured stars and BHs become dynamically crowded in the disk, enabling direct binary formation immediately after capture, reducing reliance on migration traps.
• High-inclination and high-eccentricity orbits exhibit faster semi-major axis shrinkage and inclination damping, and eccentricity evolution is sensitive to the argument of periapsis, with retrograde orbits showing eccentricity excitation followed by damping.