Extreme-Mass-Ratio Inspirals in Gaseous Disks

Abstract

Gravitational waves from extreme mass ratio inspirals (EMRIs) are precise probes of the environment of the supermassive black holes (SMBHs) they orbit. If an SMBH is actively accreting, the surrounding gaseous disk can impart hydrodynamic torques on and assist the formation of EMRIs within it. Such disk-EMRI interactions could leave measurable imprints on future observations by the Laser Interferometer Space Antenna (LISA), and potentially provide a route to constrain disk properties using gravitational wave observations. We present herein a detailed relativistic analysis of these hydrodynamic interactions using linear theory. We first derive a Lagrangian governing the evolution of spiral density waves in the disk and use it to formulate a balance law for the transfer of angular momentum between the EMRI and disk. We then develop a stable numerical scheme which can be used to treat corotation resonances and find modal solutions in thin disks up to very large azimuthal numbers. Using this numerical scheme, we explore how SMBH spins, EMRI semi-major axes, disk scale heights, sound speed gradients, and surface density gradients affect the interaction between accretion disks and circular EMRIs. Our results show that relativistic effects substantially alter disk-EMRI interactions once the secondary orbit is within $\mathcal{O}(25)$ Schwarzschild radii from the SMBH. Comparing our numerical results with recent analytical models suggests that the impact of pressure gradients and softening of the gravitational potential is important for disks with finite thickness and cannot be captured by tuning the torque cutoff parameters in the analytical models. The framework provided here will help analyze the formation scenarios of EMRIs and build relativistically accurate waveform models of disk-EMRI interactions.