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 temperaturedependent 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 ⊕ ), pebbles impact the core without significant ablation. During the second phase (M core < 0.5 M ⊕ ), 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 ⊕ ), 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 ⊕ , terminating direct core growth. In the case of icy H 2 O pebbles, this happens before 0.1 M ⊕ . Conclusions. Our results indicate that pebble accretion can directly form rocky cores up to only 0.6 M ⊕ , 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.

During their formation, planets form large, hot atmospheres due to the ongoing accretion of solids. It has been customary to assume that all solids end up at the center, constituting a “core” of refractory materials, whereas the envelope remains metal-free. However, recent work, as well as observations by the Juno mission, indicate that the distinction may not be so clear cut. Indeed, small silicate, pebble-sized particles will sublimate in the atmosphere when they hit the sublimation temperature (T ~ 2000 K). In this paper we extend previous analytical work to compute the properties of planets within such a pebble accretion scenario. We conduct 1D numerical calculations of the atmosphere of an accreting planet, solving the stellar structure equations, augmented by a nonideal equation of state that describes a hydrogen and helium-silicate vapor mixture. Calculations terminate at the point where the total mass in metal is equal to that of the H+He gas, which we numerically confirm as the onset of runaway gas accretion. When pebbles sublimate before reaching the core, insufficient (accretion) energy is available to mix dense, vapor-rich lower layers with the higher layers of lower metallicity. A gradual structure in which Z decreases with radius is therefore a natural outcome of planet formation by pebble accretion. We highlight, furthermore, that (small) pebbles can act as the dominant source of opacity, preventing rapid cooling and presenting a channel for (mini-)Neptunes to survive in gas-rich disks. Nevertheless, once pebble accretion subsides, the atmosphere rapidly clears followed by runaway gas accretion. We consider atmospheric recycling to be the most probable mechanism to have stalled the growth of the envelopes of these planets.

White dwarf (WD) pollution is thought to arise from the tidal disruption of planetary bodies. The initial fragment stream is extremely eccentric, while observational evidence suggest that discs are circular or nearly so. Here we propose a novel mechanism to bridge this gap and show that the fragments can rapidly circularise through dust or gas drag when they interact with a pre-existing compact disc. We assume that the tidal stream mainly consists of small cohesive fragments in the size range 10-1000 m, capable of resisting the WD tidal forces, whereas the compact discs span a wide mass range. We provide an analytical model, accompanied by N-body simulations, and find a large parameter space in fragment sizes and orbital separation that leads to full circularization. Partial circularization is possible for compact discs that are several orders of magnitudes less massive. We show that dust-induced circularization inherently produces gas as tidal fragments collisionally vaporize the pre-existing dust along their path. We show that ongoing gas production has a higher probability to occur during the early stages of tidal disruption events, resulting from the fact that smaller fragments are the first to circularize. Intermittent gas production however becomes more likely as the tidal stream matures. This could explain why only a small subset of systems with dusty compact discs also have an observed gaseous component. Additionally, the interaction yields fragment erosion by collisional shattering, sputtering, sublimation and possibly ram-pressure. Material scattered by the collisions might form a thin dusty halo that evolves through PR drag, in compatibility with observed infrared variability.

Context. Proto-planets embedded in their natal disks acquire hot envelopes as they grow and accrete solids. This ensures that the material they accrete – pebbles, as well as (small) planetesimals – will vaporize to enrich their atmospheres. Enrichment modifies an envelope’s structure and significantly alters its further evolution. Aims. Our aim is to describe the formation of planets with polluted envelopes from the moment that impactors begin to sublimate to beyond the disk’s eventual dissipation. Methods. We constructed an analytical interior structure model, characterized by a hot and uniformly mixed high-Z vapor layer surrounding the core, located below the usual unpolluted radiative-convective regions. Our model assumes an ideal equation of state and focuses on identifying trends rather than precise calculations. The expressions we derived are applicable to all single-species pollutants, but we used SiO2 to visualize our results. Results. The evolution of planets with uniformly mixed polluted envelopes follows four potential phases. Initially, the central core grows directly through impacts and rainout until the envelope becomes hot enough to vaporize and absorb all incoming solids. We find that a planet reaches runaway accretion when the sum of its core and vapor mass exceeds a value that we refer to as the critical metal mass – a criterion that supersedes the traditional critical core mass. The critical metal mass scales positively with both the pollutant’s evaporation temperature and with the planet’s core mass. Hence, planets at shorter orbital separations require the accretion of more solids to reach runaway as they accrete less volatile materials. If the solids accretion rate dries up, we identify the decline of the mean molecular weight – dilution – as a mechanism to limit gas accretion during a polluted planet’s embedded cooling phase. When the disk ultimately dissipates, the envelope’s inner temperature declines and its vapor eventually rains out, augmenting the mass of the core. The energy release that accompanies this does not result in significant mass-loss, as it only occurs after the planet has substantially contracted.