Radiating Bondi Flows I: Dimensionless Framework and Constant Opacity Solutions

Abstract

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 $\tilde{L}_\infty$, and a characteristic dimensionless cooling time β. We present numerical solutions across the dimensionless parameter space $(\tau _B, \tilde{L}_\infty , \beta )\in [10^{-3}, 10^3]$. Contrary to radiation-pressure-dominated environments, radiative feedback primarily operates to suppress accretion – particularly at high τB, $\tilde{L}_\infty$, and/or β. We also present analytic descriptions confirming the suppressive nature of this feedback and give the scalings for the accretion rate $\dot{M}\sim \tilde{L}_\infty ^{-5/4}$ at large $\tilde{L}_\infty$, $\dot{M}\sim \tau _B^{-10/11}\beta ^{-5/11}$ at large τB, and $\dot{M}\sim (\tilde{L}_\infty \tau _B)^{-5/8}$ for large $\tilde{L}_\infty \tau _B$. 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.