Simple convective accretion flows (SCAFs): Explaining the $\approx-1$ density scaling of hot accretion flows around compact accretors

Recent simulations find that hot gas accretion onto compact accretors are often highly turbulent and diskless, and show power-law density profiles with slope $\alpha_\rho\approx-1$. These results are consistent with observational constraints, but do not match existing self-similar solutions of radiatively inefficient accretion flows. We develop a theory for this new class of accretion flows, which we dub simple convective accretion flows (SCAFs). We use a set of hydrodynamic simulations to provide a minimalistic example of SCAFs, and develop an analytic theory to explain and predict key flow properties. We demonstrate that the turbulence in the flow is driven locally by convection, and argue that radial momentum balance, together with an approximate up-down symmetry of convective turbulence, yields $\alpha_\rho=-1\pm~{\rm few}~0.1$. Empirically, for an adiabatic hydrodynamic flow with $\gamma\approx 5/3$, we get $\alpha_\rho\approx-0.8$; the resulting accretion rate (relative to the Bondi accretion rate), $\dot M/\dot M_{\rm B}\sim (r_{\rm acc}/r_{\rm B})^{0.7}$, agrees very well with the observed accretion rates in Sgr A*, M87*, and a number of wind-fed SgXBs. We also argue that the properties of SCAFs are relatively insensitive to additional physical ingredients such as cooling and magnetic field; this explains its common appearance across simulations of different astrophysical systems.