How Atmospheres Form for Exoplanets With Masses Between .1 & 5 Earth

DYNAMICAL ACCRETION OF PRIMORDIAL ATMOSPHERES AROUND PLANETS WITH MASSES BETWEEN 0.1 AND 5 M ⊕ IN THE HABITABLE ZONE

Authors:

Stökl et al

Abstract:

In the early, disk-embedded phase of evolution of terrestrial planets, a protoplanetary core can accumulate gas from the circumstellar disk into a planetary envelope. In order to relate the accumulation and structure of this primordial atmosphere to the thermal evolution of the planetary core, we calculated atmosphere models characterized by the surface temperature of the core. We considered cores with masses between 0.1 and 5 M ⊕ situated in the habitable zone around a solar-like star. The time-dependent simulations in 1D-spherical symmetry include the hydrodynamics equations, gray radiative transport, and convective energy transport. Using an implicit time integration scheme, we can use large time steps and and thus efficiently cover evolutionary timescales. Our results show that planetary atmospheres, when considered with reference to a fixed core temperature, are not necessarily stable, and multiple solutions may exist for one core temperature. As the structure and properties of nebula-embedded planetary atmospheres are an inherently time-dependent problem, we calculated estimates for the amount of primordial atmosphere by simulating the accretion process of disk gas onto planetary cores and the subsequent evolution of the embedded atmospheres. The temperature of the planetary core is thereby determined from the computation of the internal energy budget of the core. For cores more massive than about one Earth mass, we obtain that a comparatively short duration of the disk-embedded phase (~105 years) is sufficient for the accumulation of significant amounts of hydrogen atmosphere that are unlikely to be removed by later atmospheric escape processes.

How Terrestrial Exoplanets Lose Their Hydrogen to oft X-ray and Extreme Ultraviolet Flux

Thermal mass loss of protoplanetary cores with hydrogen-dominated atmospheres: The influences of ionization and orbital distance

Authors:

Erkaev et al

Abstract:

We investigate the loss rates of the hydrogen atmospheres of terrestrial planets with a range of masses and orbital distances by assuming a 100 times stronger soft X-ray and extreme ultraviolet (XUV) flux. We apply a 1D upper atmosphere radiation absorption and hydrodynamic escape model that takes into account ionization, dissociation and recombination to calculate hydrogen mass loss rates. We study the effect of the ionization, dissociation and recombination on the thermal mass loss rates of hydrogen-dominated super-Earths and compare the results with those obtained by the energy-limited escape formula which is widely used for mass loss evolution studies. Our results indicate that the energy-limited formula can to a great extent over- or underestimate the hydrogen mass loss rates by amounts that depend on the stellar XUV flux and planetary parameters such as mass, size, effective temperature, and XUV absorption radii.

How Exoplanets Accrete Their Atmospheres From Protoplanetary Disks

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

Authors:

Lee et al

Abstract:

Planets acquire atmospheres from their parent circumstellar disks. We derive a general analytic expression for how the atmospheric mass grows with time t, as a function of the underlying core mass Mcore and nebular conditions, including the gas metallicity Z. Planets accrete as much gas as can cool: an atmosphere's doubling time is given by its Kelvin-Helmholtz time. Dusty atmospheres behave differently from atmospheres made dust-free by grain growth and sedimentation. The gas-to-core mass ratio (GCR) of a dusty atmosphere scales as GCR ∝t0.4M1.7coreZ−0.4μ3.4rcb, where μrcb∝1/(1−Z) (for Z not too close to 1) is the mean molecular weight at the innermost radiative-convective boundary. This scaling applies across all orbital distances and nebular conditions for dusty atmospheres; their radiative-convective boundaries, which regulate cooling, are not set by the external environment, but rather by the internal microphysics of dust sublimation, H2 dissociation, and the formation of H−. By contrast, dust-free atmospheres have their radiative boundaries at temperatures Trcb close to nebular temperatures Tout, and grow faster at larger orbital distances where cooler temperatures, and by extension lower opacities, prevail. At 0.1 AU in a gas-poor nebula, GCR ∝t0.4T−1.9rcbM1.6coreZ−0.4μ3.3rcb, while beyond 1 AU in a gas-rich nebula, GCR ∝t0.4T−1.5rcbM1coreZ−0.4μ2.2rcb. We confirm our analytic scalings against detailed numerical models for objects ranging in mass from Mars (0.1 M⊕) to the most extreme super-Earths (10-20 M⊕), and explain why heating from planetesimal accretion cannot prevent the latter from undergoing runaway gas accretion.

Hydrodynamic Simulations of Terrestrial Exoplanetary Protoatmospheres

Hydrodynamic simulations of captured protoatmospheres around Earth-like planets

Authors:

Stökl et al

Abstract:

Context.

Young terrestrial planets, when they are still embedded in a circumstellar disk, accumulate an atmosphere of nebula gas. The evolution and eventual evaporation of the protoplanetary disk affect the structure and dynamics of the planetary atmosphere. These processes, combined with other mass loss mechanisms, such as thermal escape driven by extreme ultraviolet and soft X-ray radiation from the young host star, determine how much of the primary atmosphere, if anything at all, survives into later stages of planetary evolution.

Aims.

Our aim is to explore the structure and the dynamic outflow processes of nebula-accreted atmospheres in dependency on changes in the planetary environment.

Methods.

We integrate stationary hydrostatic models and perform time-dependent dynamical simulations to investigate the effect of a changing nebula environment on the atmospheric structure and the timescales on which the protoatmosphere reacts to these changes.

Results.

We find that the behavior of the atmospheres strongly depends on the mass of the planetary core. For planets of about Mars-mass the atmospheric structure, and in particular the atmospheric mass, changes drastically and on very short timescales whereas atmospheres around higher mass planets are much more robust and inert.

Simulating SuperEarth & Mini Neptune ProtoAtmospheres

Hydrodynamics of Embedded Planets' First Atmospheres. II. A Rapid Recycling of Atmospheric Gas

Authors:

Ormel et al

Abstract:

Following Paper I we investigate the properties of atmospheres that form around small protoplanets embedded in a protoplanetary disc by conducting hydrodynamical simulations. These are now extended to three dimensions, employing a spherical grid centred on the planet. Compression of gas is shown to reduce rotational motions. Contrasting the 2D case, no clear boundary demarcates bound atmospheric gas from disc material; instead, we find an open system where gas enters the Bondi sphere at high latitudes and leaves through the midplane regions, or, vice versa, when the disc gas rotates sub-Keplerian. The simulations do not converge to a time-independent solution; instead, the atmosphere is characterized by a time-varying velocity field. Of particular interest is the timescale to replenish the atmosphere by nebular gas, treplenish. It is shown that the replenishment rate, Matm/treplenish, can be understood in terms of a modified Bondi accretion rate, ∼R2BondiρgasvBondi, where vBondi is set by the Keplerian shear or the magnitude of the sub-Keplerian motion of the gas, whichever is larger. In the inner disk, the atmosphere of embedded protoplanets replenishes on a timescale that is shorter than the Kelvin-Helmholtz contraction (or cooling) timescale. As a result, atmospheric gas can no longer contract and the growth of these atmospheres terminates. Future work must confirm whether these findings continue to apply when the (thermodynamical) idealizations employed in this study are relaxed. But if shown to be broadly applicable, replenishment of atmospheric gas provides a natural explanation for the preponderance of gas-rich but rock-dominant planets like super-Earths and mini-Neptunes.

Simulating Exoplanet Protoatmospheres

Hydrodynamics of Embedded Planets' First Atmospheres. I. A Centrifugal Growth Barrier for 2D Flows

Authors:

Ormel et al

Abstract:

In the core accretion paradigm of planet formation, gas giants only form a massive atmosphere after their progenitors exceeded a threshold mass: the critical core mass. Most (exo)planets, being smaller and rock/ice-dominated, never crossed this line. Nevertheless, they were massive enough to attract substantial amounts of gas from the disc, while their atmospheres remained in pressure-equilibrium with the disc. Our goal is to characterise the hydrodynamical properties of the atmospheres of such embedded planets and their implication for their (long-term) evolution. In this paper -- the first in series -- we start to investigate the properties of an isothermal and inviscid flow past a small, embedded planet by conducting local, 2D hydrodynamical simulations. Using the PLUTO code we confirm that the flow is steady and bound. This steady outcome is most apparent for the log-polar grid (with the grid spacing proportional to the distance from the planet). For low-mass planets, Cartesian grids are somewhat less efficient as they have difficulty to follow the circular, large speeds in the deep atmosphere. Relating the amount of rotation to the gas fraction of the atmosphere, we find that more massive atmospheres rotate faster -- a finding consistent with Kelvin's circulation theorem. Rotation therefore limits the amount of gas that planets can acquire from the nebula. Dependent on the Toomre-Q parameter of the circumstellar disc, the planet's atmosphere will reach Keplerian rotation before self-gravity starts to become important.

Atmospheric Mass Reduction During Planet Formation

Atmospheric Mass Loss During Planet Formation

Authors:

Schlichting et al

Abstract:

We quantify the atmospheric mass loss during planet formation by examining the contributions to atmospheric loss from both giant impacts and planetesimal accretion. Giant impacts cause global motion of the ground. Using analytic self-similar solutions and full numerical integrations we find (for isothermal atmospheres with adiabatic index (γ=5/3) that the local atmospheric mass loss fraction for ground velocities vg less than 0.25vesc is given by χloss=(1.71vg/vesc)4.9, where vesc is the escape velocity from the target. Yet, the global atmospheric mass loss is a weaker function of the impactor velocity vImp and mass mImp and given by Xloss 0.4x+1.4x2−0.8x3 (isothermal atmosphere) and Xloss 0.4x+1.8x2−1.2x3 (adiabatic atmosphere), where x=(vImpm/vescM). Atmospheric mass loss due to planetesimal impacts proceeds in two different regimes: 1) Large enough impactors m greater than 2‾√ρ0(πhR)3/2 (25~km for the current Earth), are able to eject all the atmosphere above the tangent plane of the impact site, which is h/2R of the whole atmosphere, where h, R and ρ0 are the atmospheric scale height, radius of the target, and its atmospheric density at the ground. 2) Smaller impactors, but above m greater than 4πρ0h3 (1~km for the current Earth) are only able to eject a fraction of the atmospheric mass above the tangent plane. We find that the most efficient impactors (per unit impactor mass) for atmospheric loss are planetesimals just above that lower limit and that the current atmosphere of the Earth could have resulted from an equilibrium between atmospheric erosion and volatile delivery to the atmosphere from planetesimals. We conclude that planetesimal impacts are likely to have played a major role in atmospheric mass loss over the formation history of the terrestrial planets. (Abridged)

Opacity in Protoplanetary Atmospheres

Grain opacity and the bulk composition of extrasolar planets. II. An analytical model for the grain opacity in protoplanetary atmospheres

Authors:

Mordasini et al

Abstract:

Context.

We investigate the grain opacity k_gr in the atmosphere of protoplanets. This is important for the planetary mass-radius relation since k_gr affects the H/He envelope mass of low-mass planets and the critical core mass of giant planets.

Aims.

The goal of this study is to derive an analytical model for k_gr. Methods. Our model is based on the comparison of the timescales of microphysical processes like grain settling in the Stokes and Epstein regime, growth by Brownian motion coagulation and differential settling, grain evaporation, and grain advection due to envelope contraction. With these timescales we derive the grain size, abundance, and opacity.

Results.

We find that the main growth process is differential settling. In this regime, k_gr has a simple functional form and is given as 27 Q/8 H rho in the Epstein regime and as 2 Q/H rho for Stokes drag. Grain dynamics lead to a typical radial structure of k_gr with high ISM-like values in the top layers but a strong decrease in the deeper parts where the grain-free molecular opacities take over.

Conclusions.

In agreement with earlier results we find that k_gr is typically much lower than in the ISM. The equations also show that a higher dust input in the top layer does not strongly increase k_gr with two important implications. First, for a formation of giant planet cores via pebbles, there could be the issue that pebbles increase the grain input high in the atmosphere due to ablation. This could potentially increase k_gr hindering giant planet formation. Our study shows that this adverse effect should not occur. Second, it means that a higher stellar [Fe/H] which presumably leads to a higher surface density of planetesimals only favors giant planet formation without being detrimental to it due to an increased k_gr. This corroborates the result that core accretion explains the increase of the giant planet frequency with [Fe/H].

Protoatmospheric Structure Evolution

An Atmospheric Structure Equation for Grain Growth

Authors:

Ormel et al

Abstract:

We present a method to include the evolution of the grain size and grain opacity κgr in the equations describing the structure of protoplanetary atmospheres. The key assumption of this method is that a single grain size dominates the grain size distribution at any height r. In addition to following grain growth, the method accounts for mass deposition by planetesimals and grain porosity. We illustrate this method by computation of a simplified atmosphere structure model. In agreement with previous works, grain coagulation is seen to be very efficient. The opacity drops to values much below the often-used `ISM-opacities' (∼1 cm2 g−1) and the atmosphere structure profiles for temperature and density resemble that of the grain-free case. Deposition of planetesimals in the radiative part of the atmosphere hardly influences this outcome as the added surface is quickly coagulated away. We observe a modest dependence on the internal structure (porosity), but show that filling factors cannot become too large because of compression by gas drag.

Using Neutrinos to Detect the Early Earth Composition?

Geoneutrinos and Hydridic Earth (or primordially Hydrogen-Rich Planet)

Authors:

Bezrukov et al

Abstract:

Geoneutrino is a new channel of information about geochemical composition of the Earth. We alnalysed here the following problem. What statistics do we need to distinguish between predictions of Bulk Silicate Earth model and Hydridic Earth model for Th/U signal ratio? We obtained the simple formula for estimation of error of Th/U signal ratio. Our calculations show that we need more than 22kt⋅year exposition for Gran-Sasso underground laboratory and Sudbury Neutrino Observatory. We need more than 27kt⋅year exposition for Kamioka site in the case of stopping of all Japanese nuclear power plants.

Mini Neptunes are SuperEarths Which Never Lost Their Protoatmosphere

Origin and Loss of nebula-captured hydrogen envelopes from "sub"- to "super-Earths" in the habitable zone of Sun-like stars

Authors:

Stökl et al

Abstract:

We investigate the origin and loss of captured hydrogen envelopes from protoplanets between `sub-Earth'-like bodies of 0.1M⊕ up to `super-Earths' with 5M⊕ in the HZ of a Sun like G star, assuming their rocky cores had formed before the nebula dissipated. We model the gravitational accumulation of nebula gas around a core as a function of protoplanetary luminosity during accretion and calculate the resulting surface temperature by solving the hydrostatic structure equations for the protoplanetary nebula. Depending on nebular properties and resulting luminosities, for planetary bodies of 0.1--1M⊕ we obtain hydrogen envelopes with masses between ∼2.5×1019--1.5×1026 g. For `super-Earths' with masses between 2--5M⊕ hydrogen envelopes within the mass range of ∼7.5×1023--1.5×1028 g can be captured. To study the escape of these hydrogen-dominated protoatmospheres, we apply a hydrodynamic upper atmosphere model and calculate the loss rates due to the heating by the high XUV flux of the young star. Our results indicate that under most nebula conditions `sub-Earth' and Earth-mass planets can lose their envelopes by thermal escape during the first 100 Myr after the disk dissipated. However, if a nebula has a low dust depletion factor or low accretion rates resulting in low protoplanetary luminosities, it is possible that even protoplanets with Earth-mass cores may keep their hydrogen envelopes during their whole lifetime. In contrast to lower mass protoplanets, `super-Earths' accumulate a huge amount of nebula gas and lose only tiny fractions of their primordial envelopes. Our results agree with the fact that Venus, Earth, and Mars are not surrounded by dense hydrogen envelopes, as well as with the recent discoveries of low density `super-Earths' that most likely could not get rid of their protoatmospheres.