Gravitational waves as a probe of dark matter mini-spikes

TL;DR

This paper explores how gravitational wave observations from space-based detectors like eLISA/NGO can precisely measure properties of dark matter mini-spikes around intermediate mass black holes, providing new insights into dark matter distribution.

Contribution

It demonstrates that gravitational wave signals can accurately determine the parameters of dark matter mini-spikes, including the power-law index, which was previously difficult to measure.

Findings

eLISA/NGO can measure the DM mini-spike profile with high precision.

The power-law index of the DM distribution can be determined within 10% accuracy.

Dark matter parameters can be constrained even for flatter profiles.

Abstract

Recent studies show that an intermediate mass black hole (IMBH) may develop a dark matter (DM) mini-halo according to some BH formation scenarios. We consider a binary system composed of an IMBH surrounded by a DM mini-spike and a stellar mass object orbiting around the IMBH. The binary evolves due to gravitational pull and dynamical friction from the DM mini-spike and back-reaction from its gravitational wave (GW) radiation which can be detected by future space-borne GW experiments such as eLISA/NGO. We consider a single power-law model for the DM mini-spike which is assumed to consist of non-annihilating DM particles and demonstrate that an eLISA/NGO detection of GW from such a binary enables us to measure the DM mini-spike parameters very accurately. For instance, in our reference case originally advocated by Zhao and Silk (2005) and Bertone et al. (2005), we could determine the power-law index $\alpha$ of the DM mini-spike radial profile with a 1 $\sigma$ relative error of $\pm 5\times 10^{-6}$ for a GW signal with signal-to-noise-ratio 10 and assuming a 5 year observation with eLISA. We also investigate how accurately the DM parameters can be determined for various DM parameters and the masses of the IMBH-stellar mass object binary surrounded by a DM mini-spike. We find that we can determine the power-law index $\alpha$ at 10 % level even for a slightly flatter radial distribution of $\alpha \sim 1.7$.