How cores grow by pebble accretion I. Direct core growth

Context. Planet formation by pebble accretion is an alternative to planetesimal-driven core accretion. In this scenario, planets grow by the accretion of cm- to m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. This can provide early enrichment to the planet's envelope, which influences its subsequent evolution and changes the process of core growth. Aims. We aim to predict core masses and envelope compositions of planets that form by pebble accretion and compare mass deposition of pebbles to planetesimals. Specifically, we calculate the core mass where pebbles completely evaporate and are absorbed before reaching the core, which signifies the end of direct core growth. Methods. We model the early growth of a protoplanet by calculating the structure of its envelope, taking into account the fate of impacting pebbles or planetesimals. The region where high-Z material can exist in vapor form is determined by the temperature-dependent vapor pressure. We include enrichment effects by locally modifying the mean molecular weight of the envelope. Results. In the pebble case, three phases of core growth can be identified. In the first phase (M-core < 0.23-0.39 M-circle plus), pebbles impact the core without significant ablation. During the second phase (M-core < 0.5 M-circle plus), ablation becomes increasingly severe. A layer of high-Z vapor starts to form around the core that absorbs a small fraction of the ablated mass. The rest of the material either rains out to the core or instead mixes outwards, slowing core growth. In the third phase (M-core > 0.5 M-circle plus), the high-Z inner region expands outwards, absorbing an increasing fraction of the ablated material as vapor. Rainout ends before the core mass reaches 0.6 M-circle plus, terminating direct core growth. In the case of icy H2O pebbles, this happens before 0.1 M-circle plus. Conclusions. Our results indicate that pebble accretion can directly form rocky cores up to only 0.6 M-circle plus, and is unable to form similarly sized icy cores. Subsequent core growth can proceed indirectly when the planet cools, provided it is able to retain its high-Z material.