The Effect of Thermal Torques on AGN Disc Migration Traps and Gravitational Wave Populations

Accretion discs in active galactic nuclei (AGN) foster black hole (BH) formation, growth, and mergers. Stellar mass BHs migrate inwards under the influence of hydrodynamical torques unless they encounter a region where the torque flips sign. At these migration traps, BHs accumulate and merge via dynamical or gas-assisted interactions, producing high-frequency LIGO/Virgo/KAGRA (LVK) gravitational wave (GW) sources and potentially cutting off the supply of extreme mass ratio inspirals that would otherwise make low-frequency, {\it LISA}-band GWs. In this paper, we study the interplay between different types of migration torques, focusing especially on the ``thermal torques’’ generated by the thermal response of the AGN to embedded stellar-mass BHs that accrete through their own mini-discs.In contrast to previous work, we find that Type I torques cannot produce migration traps on their own, but thermal torques often do, particularly in low-mass AGN. The migration traps produced by thermal torques exist at much larger radii ($\sim {10}^{3-5}$ gravitational radii) than do previously identified Type I traps, carrying implications for GW populations at multiple frequencies. Finally, we identify a bifurcation of AGN discs into two regimes: migration traps exist below a critical AGN luminosity, and do not at higher luminosities. This critical luminosity is fit as ${\log }_{10}{L}_{\mathrm{A}\mathrm{G}\mathrm{N}}^c=45-0.32{\log }_{10}(\alpha \mathrm{/}0.01)$ where $\alpha$ is the AGN alpha viscosity parameter, a range compatible with recent claims that LVK GWs are not preferentially associated with high-luminosity AGN.