2023MNRAS.525.2806C

The hunt is on for dozens of protoplanets hypothesized to reside in protoplanetary discs with imaged gaps. How bright these planets are, and what they will grow to become, depend on their accretion rates, which may be in the runaway regime. Using 3D global simulations, we calculate maximum gas accretion rates for planet masses M_p from 1$\, \mathrm{ M}_{{\oplus }}$ to $10\, \mathrm{ M}_{\rm J}$. When the planet is small enough that its sphere of influence is fully embedded in the disc, with a Bondi radius r_Bondi smaller than the disc's scale height H_p - such planets have thermal mass parameters q_th ≡ (M_p/M_⋆)/(H_p/R_p)³ ≲ 0.3, for host stellar mass M_⋆ and orbital radius R_p - the maximum accretion rate follows a Bondi scaling, with $\max \dot{M}_{\rm p} \propto \rho _{\rm g}M_{\rm p}^2 / (H_{\rm p}/R_{\rm p})^3$ for ambient disc density ρ_g. For more massive planets with 0.3 ≲ q_th ≲ 10, the Hill sphere replaces the Bondi sphere as the gravitational sphere of influence, and $\max \dot{M}_{\rm p} \propto \rho _{\rm g}M_{\rm p}^1$, with no dependence on H_p/R_p. In the strongly superthermal limit when q_th ≳ 10, the Hill sphere pops well out of the disc, and $\max \dot{M}_{\rm p} \propto \rho _{\rm g}M_{\rm p}^{2/3} (H_{\rm p}/R_{\rm p})^1$. Applied to the two confirmed protoplanets PDS 70b and c, our numerically calibrated maximum accretion rates imply that their Jupiter-like masses may increase by up to a factor of ∼2 before their parent disc dissipates.