Abstract
Massive black holes can grow in the presence of dark-matter environments and form dark-matter spikes with large densities. When a massive black hole within a dark-matter environment is part of a binary with a second compact object, the environmental effects will be imprinted on the system's dynamics. Past work studying these systems has demonstrated that matter effects like dynamical friction and accretion effects from the dark-matter distribution can have measurable impacts on the binary inspiral rate. The emitted gravitational waves will be affected in turn; given that they will be in the observable band for upcoming space-based detectors like LISA, the dynamics of dark matter on these scales can be understood precisely. We discuss progress in evolving these systems on three fronts, focusing on inspirals of stellar-mass black holes with supermassive black holes, forming intermediate mass-ratio and extreme mass-ratio inspirals.
First, we present refinements on the effects of dark-matter accretion onto the stellar-mass secondary in a self-consistent framework. We demonstrate that prior estimates for the dephasing due to accretion were overestimated (due to the adoption of a static, unchanging dark-matter distribution) and develop a method to remove accreted dark-matter particles from the distribution via accretion feedback. This method reduces the dephasing against vacuum when compared against comparable simulations without self-consistent feedback, though enough to be inferred from measurements for the systems examined.
Second, we discuss the impacts of two aspects of the formation history of the system on both the resulting dark-matter distribution and the gravitational wave dephasing. Specifically, we examine accretion onto the primary and prior merger events in the system. We model accretion by removing low angular momentum particles from the distribution and find a decrease in dephasing when compared to systems without this cutoff in angular-momentum space, particularly for more extreme mass-ratios. We then simulate an inspiral that takes place within a dark-matter distribution that remains after a prior merger, and find a decrease in dephasing more pronounced for less extreme mass-ratios. In all cases, the dephasing is still expected to be measurable by future detectors.
Finally, we overview a generalization of dynamical friction suitable for spherical systems, and its applications to inspirals. Motivated by the observation that the Chandrasekhar formula fails to capture some detailed features of dynamical friction for spherical systems of finite size, we explore and apply the theory of spherical torques. After outlining the derivation of the torque formula, we present strategies to evaluate the torque. With a careful combination of these integration strategies, we present a methodology for determining the torque, including contributions at high multipole and Fourier mode order while maintaining computational efficiency.
