Radiating Bondi Flows I: Dimensionless Framework and Constant Opacity Solutions

Abstract

In this paper, we extend the foundational work of Bondi (1952) 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 ${\hat{I}}^3$, optical depth through the Bondi radius $\ddot{I}{„}_B$, dimensionless luminosity at infinity ${\tilde{L}}_{\infty }$, and a characteristic dimensionless cooling time ${\hat{I}}^2$. We present numerical solutions across the dimensionless parameter space $(\ddot{I}{„}_B,{\tilde{L}}_{\infty },{\hat{I}}^2)\in [10^{-3},10^3]$. Contrary to radiation-pressure-dominated environments, radiative feedback primarily operates to suppress accretion -- particularly at high $\ddot{I}{„}_B$, ${\tilde{L}}_{\infty }$, and/or ${\hat{I}}^2$. 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 ${\tilde{L}}_{\infty }$, $\dot{M}\sim τ_B^{-10/11}β^{-5/11}$ at large $\ddot{I}{„}_B$, and $\dot{M}\sim ({\tilde{L}}_{\infty }\ddot{I}{„}_B{)}^{-5/8}$ for large ${\tilde{L}}_{\infty }\ddot{I}{„}_B$. 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.

First paper in a series. See accompanying Paper II for applications to planet formation. Submitted to MNRAS; 22 pages, 11 figures