Radiating Bondi Flows I: Dimensionless Framework and Constant Opacity Solutions

In this paper, we extend the physics of Bondi accretion to include the effects of radiative feedback in gas-pressure-dominated environments. We construct steady-state spherically symmetric accretion solutions including radiative heating and cooling. Under the simplifying assumption of a constant opacity, the solutions are controlled by four dimensionless parameters: the adiabatic index γ, optical depth through the Bondi radius τB, dimensionless luminosity at infinity L̃_∞, and a characteristic dimensionless cooling time β. We present numerical solutions across the dimensionless parameter space (τ B, L̃_∞ , β )∈ [10⁻³, 10³]. Contrary to radiation-pressure-dominated environments, radiative feedback primarily operates to suppress accretion – particularly at high τB, L̃_∞, and/or β. We also present analytic descriptions confirming the suppressive nature of this feedback and give the scalings for the accretion rate Ṁ~ L̃_∞ -5/4 at large L̃_∞, Ṁ~ τ B-10/11β -5/11 at large τB, and Ṁ~ (L̃_∞ τ B)-5/8 for large L̃_∞ τ B. We discuss the potential role of convection in these steady-state solutions, and the particular relevance to problems of planet formation where radiative heating is significant, but the system remains in the gas-pressure-dominated regime.