In the grip of the disk: dragging the companion through an AGN

Abstract

Active galactic nuclei (AGN) have been proposed as environments that can facilitate the capture of extreme-mass-ratio binaries and accelerate their inspiral beyond the rate expected from gravitational wave emission alone. In this work, we explore binaries shortly after capture, focusing on the evolution of the binary parameters when the system is still far from merger. We find that repeated interactions with the AGN disk typically reduce both the inclination and semi-major axis of the orbit. The evolution of the eccentricity is more intricate, exhibiting phases of growth and decay. Nevertheless, as the binary gradually aligns with the disk plane, the system tends to circularize. Interestingly, we also identify scenarios where initially highly eccentric, nearly counter-rotating orbits can undergo a rapid transition to co-rotation while maintaining a constant eccentricity. These dynamical effects could have significant implications for the modeling and interpretation of LISA sources.

Figures (10)

• Figure 1: Aspect ratio (top panel) and density (bottom panel) for the Sirko-Goodman and Thompson et al. AGN models with $M = 10^7 M_{\odot}$, as obtained from Gangardt:2024bic. Benchmark parameters for the Sirko-Goodman model are listed in Table \ref{['tab:benchmark']}. The Thompson et al. model includes additional parameters: (i) supernova radiative fraction $\chi = 1$; (ii) angular momentum efficiency $m = 2$; and (iii) star formation radiative efficiency $\eta_{\rm star} = 0.001$.
• Figure 2: Schematic illustration of our setup. The system features an accretion disk in the equatorial plane, while the orbital plane (shown in blue) is inclined by an angle $\iota$ and follows an eccentric trajectory with semi-major axis $a$. The angle between the ascending node of the secondary (with mass $m_{\rm p}$) and its periapsis is the argument of periapsis $\omega$. The primary (with mass $M$) resides at one of the focal points of the ellipse. The axes are oriented such that the secondary interacts with the disk---thereby accreting matter or experiencing a drag---at the designated scattering points, located at $\vec{r} = (0, y, 0)$, and marked by green dots.
• Figure 3: The impact of dynamical friction from repeated scatterings on the evolution of the inclination, eccentricity and semi-major axis, for various initial inclinations. We use the benchmark parameters from Table \ref{['tab:benchmark']}, setting $e_0 = 0.5$, $a_0 = 10^6 M$ ($\sim 0.5\,\mathrm{pc}$) and $\omega_0 = \pi/3$. Increasing either the primary mass $M$ or the semi-major axis enhances the magnitude of the effect. The red-shaded region indicates where the assumptions underlying our algorithm break down \ref{['eq:min_incl']}.
• Figure 4: Similar configuration as in Fig. \ref{['fig:General_SG_varyIncl_M1e7']}, but now varying the initial eccentricity. We take $\iota_0 = \pi/3$ (solid) and $\iota_0 = 2\pi/3$ (dotted). The thin black lines denote the initially circular case $e_0 = 0$.
• Figure 5: Fractional change in inclination and eccentricity after $1000$ orbits, for $\iota_0 = 5\pi/6$ and either $e_0 = 0.8$ (solid) or $e_0 = 0.4$ (dashed). The benchmark parameters used are listed in Table \ref{['tab:benchmark']}.