Steady-state radial profiles from the time-dependent Euler solver for M_BH = 10⁻¹⁶, 10⁻¹³, and 10⁻¹¹ M_⊙. (a) Temperature, (b) infall velocity, (c) density, and (d) Mach number as a function of r/r_S. Dashed gray lines show the adiabatic Bondi solution. The vertical dashed line marks r_B. The thin horizontal dashed lines mark the ambient density ρ_∞ = 150 g cm⁻³ in panel (c) and the sonic condition ﹩{ \mathcal M }=1﹩ in panel (d). The transition from near-adiabatic (low mass) to nearly isothermal (high mass) flow is evident in the temperature panel, while the density and velocity profiles show the enhanced accretion rate in the isothermal limit.