Spike density profile in the inner regions at various times for a DM spike set-up initially with two different spike indices. The left and right panels correspond to {γ, σ/m_χ} of {1/2, 1.0 cm²g⁻¹} and {7/4, 2 ⋅ 10⁻⁵ cm²g⁻¹}, respectively. In both panels, the dotted lines are the initial density profile that is sampled and the dashed lines correspond to a spike profile with an index of 3/4. For both steeper and shallower starting profiles, we see that the spike index evolves towards γ = 3/4.