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ABSTRACT 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.
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Effective two-body scatterings around a massive object
ABSTRACT Two-body scatterings under the potential of a massive object are very common in astrophysics. If the massive body is far enough away that the two small bodies are in their own gravitational sphere of influence, the gravity of the massive body can be temporarily ignored. However, this requires the scattering process to be fast enough that the small objects do not spend too much time at distances near the surface of the sphere of influence. In this paper, we derive the validation criteria for effective two-body scattering and establish a simple analytical solution for this process, which we verify through numerical scattering experiments. We use this solution to study star–black hole scatterings in the discs of active galactic nuclei and planet–planet scatterings in planetary systems, and calculate their one-dimensional cross-section analytically. Our solution will be valuable in reducing computational time when treating two-body scatterings under the potential of a much more massive third body, provided that the problem settings are in the valid parameter space region identified by our study.
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- PAR ID:
- 10418039
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 523
- Issue:
- 2
- ISSN:
- 0035-8711
- Format(s):
- Medium: X Size: p. 2014-2026
- Size(s):
- p. 2014-2026
- Sponsoring Org:
- National Science Foundation
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