Physics of Planet Trapping with Applications to HL Tau

Abstract

We explore planet formation in the HL Tau disk and possible origins of the prominent gaps and rings observed by ALMA. We investigate whether dust gaps are caused by dynamically trapped planetary embryos at the ice lines of abundant volatiles. The global properties of the HL Tau disk (total mass, size) at its current age are used to constrain an evolving analytic disk model describing its temperature and density profiles. By performing a detailed analysis of the planet-disk interaction for a planet near the water ice line including a rigorous treatment of the dust opacity, we confirm that water is sufficiently abundant (1.5x10^-4 molecules per H) to trap planets at its ice line due to an opacity transition. When the abundance of water is reduced by 50% planet trapping disappears. We extend our analysis to other planet traps: the heat transition, dead zone edge, and the CO_2 ice line and find similar trapping. The formation of planets via planetesimal accretion is computed for dynamically trapped embryos at the water ice line, dead zone, and heat transition. The end products orbit in the inner disk (R < 3 AU), unresolved by ALMA, with masses that range between sub-Earth to 5 Jupiter masses. While we find that the dust gaps correspond well with the radial positions of the CO_2 , CH_4 , and CO ice lines, the planetesimal accretion rates at these radii are too small to build large embryos within 1 Myr.