Ambient density profiles for different redshifts (z = 0 in blue, z = 3 in orange and z = 6 in green) and for different values of the exponents β (β_g = −1.6 and β_c = −1.1 in solid curves, β_g = −1.8 and β_c = −1.3 in dashed curves, and β_g = −2 and β_c = −1.5 in dotted curves). The radius of the core at z = 0 are fixed at a_g, 0 = 1.25 kpc and a_c = 45 kpc, and the central densities at ρ_g, 0 = 1.673 × 10⁻²¹ kg/m³ (≈1 proton/cm³) and ρ_c, 0 = 1.673 × 10⁻²³ kg/m³ (≈0.01 proton/cm³).