Probing dark matter halo profiles with multiband observations of gravitational waves

In this paper, we evaluate the potential of multiband gravitational wave observations from a dHz space-based detector and third-generation ground-based gravitational wave detectors to constrain the properties of dark matter spikes around intermediate-mass ratio inspirals. The presence of dark matter influences the orbital evolution of the secondary compact object through dynamic friction, which leads to a phase shift in the gravitational waveform compared to the vacuum case. Our analysis shows that the proposed Indian space-based detector GWSat, operating in the dHz frequency band, provides the most stringent constraints on the dark matter spike parameters, as IMRIs spend a significant portion of their inspiral phase within its sensitivity range. While third-generation ground-based detectors such as the Einstein Telescope and Cosmic Explorer offer additional constraints, their contribution is somewhat limited, particularly for higher mass systems where the signal duration in their frequency bands is shorter. However, for systems with detector-frame total masses ${M}_{z}<400{M}_{\ensuremath{\bigodot}}$, Cosmic Explorer and Einstein Telescope could improve the estimation of the chirp mass, symmetric mass ratio, luminosity distance, and dark matter spike power-law index by more than 15%. Nonetheless, their impact on the constraint of spike density is minimal. These results highlight the crucial role of dHz space-based detectors in probing dark matter interactions with gravitational wave sources.