  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.
