To Cool is to Accrete: Analytic Scalings for Nebular Accretion of Planetary Atmospheres

摘要: Planets acquire atmospheres from their parent circumstellar disks. We derive a general analytic expression for how the atmospheric mass grows with time $t$, as function of underlying core $M_{\rm core}$ and nebular conditions, including gas metallicity $Z$. accrete much can cool: an atmosphere's doubling is given by its Kelvin-Helmholtz time. Dusty behave differently made dust-free grain growth sedimentation. The gas-to-core ratio (GCR) dusty atmosphere scales GCR $\propto t^{0.4} M_{\rm core}^{1.7} Z^{-0.4} \mu_{\rm rcb}^{3.4}$, where $\mu_{\rm rcb} \propto 1/(1-Z)$ (for $Z$ not too close to 1) mean molecular weight at innermost radiative-convective boundary. This scaling applies across all orbital distances conditions atmospheres; boundaries, which regulate cooling, are set external environment, but rather internal microphysics dust sublimation, H$_2$ dissociation, formation H$^-$. By contrast, have radiative boundaries temperatures $T_{\rm rcb}$ out}$, grow faster larger cooler temperatures, extension lower opacities, prevail. At 0.1 AU in gas-poor nebula, T_{\rm rcb}^{-1.9} core}^{1.6} rcb}^{3.3}$, while beyond 1 gas-rich rcb}^{-1.5} core}^1 Z^{-0.4}\mu_{\rm rcb}^{2.2}$. confirm our scalings against detailed numerical models objects ranging Mars (0.1 $M_\oplus$) most extreme super-Earths (10-20 $M_\oplus$), explain why heating planetesimal accretion cannot prevent latter undergoing runaway accretion.