Dark Matter Spikes at Sgr A* Retain 82% Central Density After 10 Gyr of EMRIs

The authors treat the Galactic Center as an observationally anchored laboratory. They integrate the cumulative effect of the nuclear star cluster on DM orbits at 0.1 pc, then add the known S-stars at 10^{-3} pc, and finally inject a realistic EMRI population of ~10 M⊙ compact objects drawn from the expected 10 Gyr merger rate. The calculation follows the evolution of the DM phase-space distribution under successive gravitational scatterings without assuming a static background potential.

At radii relevant to LISA-band EMRIs the spike survives because the perturbers are either too distant or too few. The nuclear cluster removes DM at larger radii, but the innermost 10^{-5} pc experiences only gentle heating; after hundreds of mergers the density drops by just 18%. This result directly contradicts earlier analytic estimates that assumed continuous stellar heating would erase spikes entirely.

The finding tightens the link between DM microphysics and GW observables. A surviving spike boosts the EMRI event rate and imprints a measurable dephasing on the waveform; non-detection of that signature would therefore constrain both the DM density slope and the EMRI rate itself. Future work must incorporate resonant relaxation and possible DM self-interactions to test whether the 82% floor is robust.

Next steps require population-synthesis runs that vary the EMRI mass function and include a live stellar cusp, followed by injection into LISA mock data to quantify the minimum detectable spike contrast.