Density and one-dimensional velocity dispersion for a DM density spike as a function of radius according to Eq. (2). We assume r_sp = 1 μpc, ρ_sp = 5.45 × 10⁻³ M_⊙ μpc⁻³, α_sp = 7/3, and M_BH = 10³ M_⊙. In addition, we indicate the Schwarzschild radius R_s = 2GM/c². For computing the velocity dispersion, we followed Kremer (2022). Here, we assumed an isotropic velocity distribution. In contrast to Kremer (2022), we solved their Eq. (27) including higher-order terms instead of Eq. (28). Moreover, we show the results for m/(k_BT)≈6.53 × 10³ s² km⁻², with m being the rest mass of a physical DM particle, k_B the Boltzmann constant and T the absolute temperature of the system.