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 Mp 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 rBondi smaller than the disc’s scale height Hp – such planets have thermal mass parameters qth ≡ (Mp/M⋆)/(Hp/Rp)3 ≲ 0.3, for host stellar mass M⋆ and orbital radius Rp – 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 ρg. For more massive planets with 0.3 ≲ qth ≲ 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 Hp/Rp. In the strongly superthermal limit when qth ≳ 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.
Gaps imaged in protoplanetary discs are suspected to be opened by planets. We compute the present-day mass accretion rates $\dot{M}_{\rm p}$ of seven hypothesized gap-embedded planets, plus the two confirmed planets in the PDS 70 disc. The accretion rates are based on disc gas surface densities Σgas from C18O observations, and planet masses Mp from simulations fitted to observed gaps. Assuming accretion is Bondi-like, we find in eight out of nine cases that $\dot{M}_{\rm p}$ is consistent with the time-averaged value given by the current planet mass and system age, Mp/tage. As system ages are comparable to circumstellar disc lifetimes, these gap-opening planets may be undergoing their last mass doublings, reaching final masses of $M_{\rm p} \sim 10\rm{\!-\!}10^2 \, M_\oplus$ for the non-PDS 70 planets, and $M_{\rm p} \sim 1\!-\!10 \, M_{\rm J}$ for the PDS 70 planets. For another 15 gaps without C18O data, we predict Σgas by assuming their planets are accreting at their time-averaged $\dot{M}_{\rm p}$. Bondi accretion rates for PDS 70b and c are orders of magnitude higher than accretion rates implied by measured U-band and H α fluxes, suggesting most of the accretion shock luminosity emerges in as yet unobserved wavebands, or that the planets are surrounded by dusty, highly extincting, quasi-spherical circumplanetary envelopes. Thermal emission from such envelopes or from circumplanetary discs, on Hill sphere scales, peaks at wavelengths in the mid-to-far-infrared and can reproduce observed mm-wave excesses.
more » « less- NSF-PAR ID:
- 10361200
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 510
- Issue:
- 2
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 1657-1670
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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