\frac{GM_{\rm p}}{c_{\rm s}^2} \right)^2  \end{aligned}$$ where $\rho_{\rm p}$ is the disc midplane mass density near the planet, $c_{\rm s}$ is the disc sound speed, $R_{\rm B} = GM_{\rm p}/c_{\rm s}^2$ is the Bondi radius, $H = c_{\rm s}/\Omega$ is the disc scale height, $\Omega$ is the orbital angular frequency, and $G$ is the gravitational constant. Then $$\label{eqn:A}
A_{\rm Bondi} \sim \frac{m^2}{h^4} \Omega r^2$$ where $m \equiv M_{\rm p}/M_\star$ is the planet-to-star mass ratio, and $h\equiv H/r$ is the disc aspect ratio. Ginzburg & Chiang ([-@gc_2019a], their section 1.1) discusses how Bondi accretion may be valid for “sub-thermal” planets whose masses are less than $$\label{eqn:thermalmass_0}
M_{\rm thermal} \sim h^3 M_\star$$ the mass for which the Bondi radius $R_{\rm B}$, the Hill radius $R_{\rm H} \sim m^{1/3} r$, and the disc scale height $H$ are all equal. A sub-thermal planet has $R_{\rm B} < R_{\rm H} < H$—its gravitational sphere of influence has radius $R_{\rm B}$, set by gravity and thermal pressure—and should accrete at the Bondi rate, isotropically from the all-surrounding disc (@gc_2019a; see also fig. 1 of @tt_2016 for evidence supporting the Bondi $m^2$ scaling, taken from the 3D simulations of @dkh_2003). For a super-thermal planet having $M>M_{\rm thermal}$, the 