arXiv subjects

Morris Podolak

Publications and source records attributed to Morris Podolak.

At least 19 recordsLinked to original sources

arXiv2024

Detailed Calculations of the Efficiency of Planetesimal Accretion in the Core-Accretion Model -III: The Contribution of Planetesimals Beyond Saturn

Continuing our initiative on advancing the calculations of planetesimal accretion in the core-accretion model, we present here the results of our recent study of the contributions of planetesimals around and beyond the orbit of Saturn. In our first two papers [ApJ, 899:45; 941:117], where our focus was on the effects of the Sun and Saturn, the initial distribution of planetesimals was limited to the regions around the accretion zone of a growing Jupiter. In this paper, we expanded that distribution to regions beyond the accretion zone of Saturn. We integrated the orbits of a large ensemble of planetesimals and studied the rate of their capture by the growing proto-Jupiter. In order to be consistent with our previous studies, we did not consider the effect of the nebular gas. Results demonstrated that the exterior planetesimals, especially those beyond 8 AU, have only slight contributions to the growth and metallicity of the growing Jupiter. The final mass and composition of this planet is mainly due to the planetesimals inside and around its accretion zone. Our study shows that although the rate of capture varies slightly by the size and composition of planetesimals, in general, the final results are independent of the size and material of these bodies. Results also pointed to a new finding: the rate of accretion follows the same trend as that of the evolution of Jupiter's envelope, with the largest accretion occurring during the envelope's collapse. We present details of our analysis and discuss the implications of their results.

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arXiv2024

Uranus and Neptune as methane planets: producing icy giants from refractory planetesimals

Uranus and Neptune are commonly considered ice giants, and it is often assumed that, in addition to a solar mix of hydrogen and helium, they contain roughly twice as much water as rock. This classical picture has led to successful models of their internal structure and has been understood to be compatible with the composition of the solar nebula during their formation (Reynolds and Summers 1965; Podolak and Cameron 1974; Podolak and Reynolds 1984; Podolak et al. 1995; Nettelmann et al. 2013). However, the dominance of water has been recently questioned (Teanby et al. 2020; Helled and Fortney 2020; Podolak et al. 2022). Planetesimals in the outer solar system are composed mainly of refractory materials, leading to an inconsistency between the icy composition of Uranus and Neptune and the ice-poor planetesimals they accreted during formation (Podolak et al. 2022). Here we elaborate on this problem, and propose a new potential solution. We show that chemical reactions between planetesimals dominated by organic-rich refractory materials and the hydrogen in gaseous atmospheres of protoplanets can form large amounts of methane 'ice'. Uranus and Neptune could thus be compatible with having accreted refractory-dominated planetesimals, while still remaining icy. Using random statistical computer models for a wide parameter space, we show that the resulting methane-rich internal composition could be a natural solution, giving a good match to the size, mass and moment of inertia of Uranus and Neptune, whereas rock-rich models appear to only work if a rocky interior is heavily mixed with hydrogen. Our model predicts a lower than solar hydrogen to helium ratio, which can be tested. We conclude that Uranus, Neptune and similar exoplanets could be methane-rich, and discuss why Jupiter and Saturn cannot.

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arXiv2023

About the loss of a primordial atmosphere of super-Earths by planetesimal impacts

We consider planets composed of water ice and rock, located far from a central star. In an earlier study, computing the growth of planets by continuous accretion, we found that a large fraction of the ice evaporates upon accretion, creating a water vapor atmosphere. Here we consider accretion as a discrete series of planetesimal impacts (of order $10^8$), at the same time-dependent accretion rate, and investigate the fate of the vapor, as a result of its interaction with the accreting planetesimals. We find that a large fraction of the vapor escapes. The remaining fraction may form an outer layer of ice after the termination of accretion and cooling of the surface. The escaped water mass may significantly alter the ice-to-rock ratio of the planet. We investigate the effect of different choices of parameters such as the ice-to-rock ratio, the planetesimal size distribution, and the impact velocities. We find that the planetesimal size distribution has a negligible effect and explain why. By contrast, the ice-to-rock ratio and impact velocities affect the fraction of retained water masses considerably.

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arXiv2023

An Equation of State of CO for use in Planetary Modeling

Although carbon monoxide (CO) is an abundant molecule and may have great importance for planetary interiors, measurements of its properties are difficult due to its extreme volatility. We calculate the equation of state for CO over a range of temperature and density that is applicable to the conditions in planetary interiors. Previous experimental and theoretical studies cover only a limited temperature-density range. Our calculations match these early results well, but now cover the full range of relevance. The method of calculation is based on the general-purpose quotidian equation of state described by More et al. (1988), which is here used in order to generate a freely downloadable look-up table to be used by the community.

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arXiv2022

Detailed Calculations of the Efficiency of Planetesimal Accretion in the Core-Accretion Model -II: The effect of Saturn

As part of our ongoing initiative on accurately calculating the accretion rate of planetesimals in the core-accretion model, we demonstrated in a recent article that when the calculations include the gravitational force of the Sun (the original core-accretion model did not include solar gravity), results change considerably [ApJ, 899:45]. In this paper, we have advanced our previous study by including the effect of Saturn. To maintain focus on the effect of this planet, and in order to be consistent with previous studies, we did not include the effect of the nebular gas. Results demonstrated that as expected, Saturn's perturbation decreases the rate of accretion by scattering many planetesimals out of Jupiter's accretion zone. It also increases the velocities with which planetesimals encounter the envelope, which in agreement with our previous findings, enhances their break-up due to the ram-pressure. Results also show that, because the effect of Saturn in scattering of planetesimals increases with its mass, this planet might not have played a significant role in the accretion of planetesimals by proto-Jupiter during the early stage of its growth. Finally, the late accretion of planetesimals, as obtained in our previous study, appears in our new results as well, implying that combined with the rapid in-fall of the gas, it can result in the mixing of material in the outer regions of the envelope which may explain the enhancement of the envelope's high-Z material.

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arXiv2022

The Effect of Accretion Rate and Composition on the Structure of Ice-rich Super-Earths

It is reasonable to assume that the structure of a planet and the interior distribution of its components are determined by its formation history. We thus follow the growth of a planet from a small embryo through its subsequent evolution. We estimate the accretion rate range based on a protoplanetary disk model at a large enough distance from the central star, for water ice to be a major component. We assume the accreted material to be a mixture of silicate rock and ice, with no H-He envelope, as the accretion timescale is much longer than the time required for the nebular gas to dissipate. We adopt a thermal evolution model that includes accretional heating, radioactive energy release, and separation of ice and rock. Taking the Safronov parameter and the ice-to-rock ratio as free parameters, we compute growth and evolutionary sequences for different parameter combinations, for 4.6 Gyr. We find the final structure to depend significantly on both parameters. Low initial ice to rock ratios and high accretion rates, each resulting in increased heating rate, lead to the formation of extended rocky cores, while the opposite conditions leave the composition almost unchanged and result in relatively low internal temperatures. When rocky cores form, the ice-rich outer mantles still contain rock mixed with the ice. We find that a considerable fraction of the ice evaporates upon accretion, depending on parameters, and assume it is lost, thus the final surface composition and bulk density of the planet do not necessarily reflect the protoplanetary disk composition.

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arXiv2022

Random Models for Exploring Planet Compositions I: Uranus as an Example

Modeling the interior of a planet is difficult because the small number of measured parameters is insufficient to constrain the many variables involved in describing the interior structure and composition. One solution is to invoke additional constraints based on arguments about how the planet formed. However, a planet's actual structure and composition may hold clues to its formation which would be lost if this structure were not allowed by the initial assumptions. It is therefore interesting to explore the space of allowable compositions and structures in order to better understand which cosmogonic constraints are absolutely necessary. To this end, we describe a code for generating random, monotonic, density distributions, rho(r), that fit a given mass, radius, and moment of inertia. Integrating the equation of hydrostatic equilibrium gives the pressure, P(r), at each point in the body. We then provide three algorithms for generating a monotonic temperature distribution, T(r), and an associated composition that is consistent with the rho-P relation, and realistic equations of state. We apply this code to Uranus as a proof of concept, and show that the ratio of rock to water cannot be much larger than 2.

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arXiv2022

On the structure and long-term evolution of ice-rich bodies

The interest in the structure of ice-rich planetary bodies, in particular the differentiation between ice and rock, has grown due to the discovery of Kuiper belt objects and exoplanets. We thus carry out a parameter study for a range of planetary masses $M$, yielding radii $50 \aplt R \aplt 3000$~km, and for rock/ice mass ratios between 0.25 and 4, evolving them for 4.5~Gyr in a cold environment, to obtain the present structure. We use a thermal evolution model that allows for liquid and vapor flow in a porous medium, solving mass and energy conservation equations under hydrostatic equilibrium for a spherical body in orbit around a central star. The model includes the effect of pressure on porosity and on the melting temperature, heating by long-lived radioactive isotopes, and temperature-dependent serpentinization and dehydration. We obtain the boundary in parameter space [size, rock-content] between bodies that differentiate, forming a rocky core, and those which remain undifferentiated: small bodies, bodies with a low rock content, and the largest bodies considered, which develop high internal pressures and barely attain the melting temperature. The final differentiated structure comprises a rocky core, an ice-rich mantle, and a thin dense crust below the surface. We obtain and discuss the bulk density-radius relationship. The effect of a very cold environment is investigated and we find that at an ambient temperature of $\sim$20~K, small bodies preserve the ice in amorphous form to the present.

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arXiv2020

Detailed Calculations of the Efficiency of Planetesimal Accretion in the Core-Accretion Model

We present results of a detailed study of the rate of the accretion of planetesimals by a growing proto-Jupiter in the core-accretion model. Using a newly developed code, we accurately combine a detailed three-body trajectory calculation with gas drag experienced during the passage of planetesimals in the protoplanet's envelope. We find that the motion of planetesimals is excited to the extent that encounters with the proto-planetary envelope become so fast that ram pressure breaks up the planetesimals in most encounters. As a result, the accretion rate is largely independent of the planetesimal size and composition. For the case we explored of a planet forming at 5.2 AU from the Sun in a disk with a solid surface density of 6 g/cm^2 (Lozovsky et al. 2017) the accretion rate we compute differs in several respects from that assumed by those authors. We find that only 4-5 M_Earth is accreted in the first 1.5x10^6 years before the onset of rapid gas accretion. Most of the mass, some 10 M_Earth, is accreted simultaneously with this rapid gas accretion. In addition, we find that the mass accretion rate remains small, but non-zero for at least a million years after this point, and an additional 0.3-0.4 M_Earth is accreted during that time. This late accretion, together with a rapid infall of gas could lead to the accreted material being mixed throughout the outer regions, and may account for the enhancement of high-Z material in Jupiter's envelope.

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arXiv2019

Effect of Non-Adiabatic Thermal Profiles on the Inferred Compositions of Uranus and Neptune

It has been a common assumption of interior models that the outer planets of our solar system are convective, and that the internal temperature distributions are therefore adiabatic. This assumption is also often applied to exoplanets. However, if a large portion of the thermal flux can be transferred by conduction, or if convection is inhibited, the thermal profile could be substantially different and would therefore affect the inferred planetary composition. Here we investigate how the assumption of non-adiabatic temperature profiles in Uranus and Neptune affects their internal structures and compositions. We use a set of plausible temperature profiles together with density profiles that match the measured gravitational fields to derive the planets' compositions. We find that the inferred compositions of both Uranus and Neptune are quite sensitive to the assumed thermal profile in the outer layers, but relatively insensitive to the thermal profile in the central, high pressure region. The overall value of the heavy element mass fraction, $Z$, for these planets is between 0.8 and 0.9. Finally, we suggest that large parts of Uranus' interior might be conductive, a conclusion that is consistent with Uranus dynamo models and a hot central inner region.

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arXiv2017

H-Atmospheres of Icy Super-Earths Formed in situ in the Outer Solar System: An Application to a Possible Planet Nine

We examine the possibility that icy super-Earth mass planets, formed over long time scales (0.1--1~Gyr) at large distances ($\sim$ 200--1000~AU) from their host stars, will develop massive H-rich atmospheres. Within the interior of these planets, high pressure converts CH$_4$ into ethane, butane, or diamond and releases H$_2$. Using simplified models which capture the basic physics of the internal structure, we show that the physical properties of the atmosphere depend on the outflux of H$_2$ from the mantle. When this outflux is $\lesssim 10^{10}$ [molec cm$^{-2}$ s$^{-1}$], the outgassed atmosphere has base pressure $\lesssim$ 1 bar. Larger outflows result in a substantial atmosphere where the base pressure may approach $10^3 - 10^4$ bar. For any pressure, the mean density of these planets, 2.4--3 [g cm$^{-3}$], is much larger than the mean density of Uranus and Neptune, 1.3--1.6 [g cm$^{-3}$]. Thus, observations can distinguish between a Planet Nine with a primordial H/He-rich atmosphere accreted from the protosolar nebula and one with an atmosphere outgassed from the core.

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arXiv2016

The Abundance of Atmospheric CO2 in Ocean Exoplanets: A Novel CO2 Deposition Mechanism

We consider super-Earth sized planets which have a water mass fraction that is large enough to form an external mantle composed of high pressure water ice polymorphs and that lack a substantial H/He atmosphere. We consider such planets in their habitable zone so that their outermost condensed mantle is a global deep liquid ocean. For these ocean planets we investigate potential internal reservoirs of CO2; the amount of CO2 dissolved in the ocean for the various saturation conditions encountered, and the ocean-atmosphere exchange flux of CO2. We find that in steady state the abundance of CO2 in the atmosphere has two possible states. When the wind-driven circulation is the dominant CO2 exchange mechanism, an atmosphere of tens of bars of CO2 results, where the exact value depends on the subtropical ocean surface temperature and the deep ocean temperature. When sea-ice formation, acting on these planets as a CO2 deposition mechanism, is the dominant exchange mechanism, an atmosphere of a few bars of CO2 is established. The exact value depends on the subpolar surface temperature. Our results suggest the possibility of a negative feedback mechanism, unique to water planets, where a reduction in the subpolar temperature drives more CO2 into the atmosphere to increase the greenhouse effect.

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arXiv2016

A Simple Model for Understanding the DIM Dust Measurement at Comet 67P/Churyumov-Gerasimenko

We present a simple model for gas and dust flow from 67P/Churyumov-Gerasimenko that can be used to understand the grain impact observed by the DIM instrument on Philae (Krueger et al. 2015) We show how model results when applied to the GIADA measurements (Rotundi et al. 2015; Della Corte et al. 2015) can be used, in conjunction with the results found by the MIRO (Schloerb et al. 2015) and VIRTIS (De Sanctis et al. 2015) instruments to infer surface properties such as surface temperature and surface ice fraction.

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arXiv2015

Dust Impact Monitor (SESAME-DIM) Measurements at Comet 67P/Churyumov-Gerasimenko

The Rosetta lander Philae successfully landed on the nucleus of comet 67P/Churyumov-Gerasimenko on 12 November 2014. Philae carries the Dust Impact Monitor (DIM) on board, which is part of the Surface Electric Sounding and Acoustic Monitoring Experiment (SESAME). DIM employs piezoelectric PZT sensors to detect impacts by sub-millimeter and millimeter-sized ice and dust particles that are emitted from the nucleus and transported into the cometary coma. The DIM sensor measures dynamical data like flux and the directionality of the impacting particles. Mass and speed of the particles can be constrained assuming density and elastic particle properties. DIM was operated during three mission phases of Philae at the comet: (1) Before Philae's separation from Rosetta at distances of about 9.6 km, 11.8 km, and 25.3 km from the nucleus barycenter. In this mission phase particles released from the nucleus on radial trajectories remained undetectable because of significant obscuration by the structures of Rosetta, and no dust particles were indeed detected. (2) During Philae's descent to its nominal landing site Agilkia, DIM detected one approximately millimeter-sized particle at a distance of 5.0 km from the nucleus' barycenter, corresponding to an altitude of 2.4 km from the surface. This is the closest ever dust detection at a cometary nucleus by a dedicated in-situ dust detector. (3) At Philae's final landing site, Abydos, DIM detected no dust impact which may be due to low cometary activity in the vicinity of Philae, or due to shading by obstacles close to Philae, or both. Laboratory calibration experiments showed that the material properties of the detected particle are compatible with a porous particle having a bulk density of approximately $250\, \mathrm{kg\,m^{-3}}$. The particle could have been lifted off from the comet's surface by sublimating water ice.

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arXiv2015

Methane Planets and their Mass-Radius Relation

Knowledge of both the mass and radius of an exoplanet allows us to estimate its mean density, and therefore its composition. Exoplanets seem to fill a very large parameter space in terms of mass and composition, and unlike the solar-system's planets, exoplanets also have intermediate masses (~ 5 - 50 M_Earth) with various densities. In this letter, we investigate the behavior of the Mass-Radius relation for methane (CH_4) planets and show that when methane planets are massive enough (Mp >~ 15 M_Earth), the methane can dissociate and lead to a differentiated planet with a carbon core, a methane envelope, and a hydrogen atmosphere. The contribution of a rocky core to the behavior of CH_4 planet is considered as well. We also develop interior models for several detected intermediate-mass planets that could, in principle, be methane/methane-rich planets. The example of methane planets emphasizes the complexity of the Mass-Radius relation and the challenge involved in uniquely inferring the planetary composition.

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arXiv2015

Capture and Evolution of Planetesimals in Circumjovian Disks

We study the evolution of planetesimals in evolved gaseous disks, which orbit a solar-mass star and harbor a Jupiter-mass planet at a_p~5AU. The gas dynamics is modeled with a three-dimensional hydrodynamics code that employes nested-grids and achieves a resolution of one Jupiter's radius in the circumplanetary disk. The code models solids as individual particles. Planetesimals are subjected to gravitational forces by the star and the planet, drag force by the gas, disruption via ram pressure, and mass loss through ablation. The mass evolution of solids is calculated self-consistently with their temperature, velocity, and position. We consider icy and icy/rocky bodies of radius 0.1-100km, initially deployed on orbits around the star within a few Hill radii (Rhill) of the planet's orbit. Planetesimals are scattered inward, outward, and toward disk regions of radius r>>a_p. Scattering can relocate significant amounts of solids, provided that regions |r-a_p|~ 3Rhill are replenished with planetesimals. Scattered bodies can be temporarily captured on planetocentric orbits. Ablation consumes nearly all solids at gas temperatures > ~220K. Super-keplerian rotation around and beyond the outer edge of the gas gap can segregate < ~0.1km bodies, producing solid gap edges at size-dependent radial locations. Capture, break-up, and ablation of solids result in a dust-laden circumplanetary disk with low surface densities of km-size planetesimals, implying relatively long timescales for satellite formation. After a giant planet acquires most of its mass, accretion of solids is unlikely to alter significantly its heavy-element content. The luminosity generated by solids' accretion can be of a similar order of magnitude to the contraction luminosity.

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arXiv2015

Convection and Mixing in Giant Planet Evolution

The primordial internal structures of gas giant planets are unknown. Often giant planets are modeled under the assumption that they are adiabatic, convective, and homogeneously mixed, but this is not necessarily correct. In this work, we present the first self-consistent calculation of convective transport of both heat and material as the planets evolve. We examine how planetary evolution depends on the initial composition and its distribution, whether the internal structure changes with time, and if so, how it affects the evolution. We consider various primordial distributions, different compositions, and different mixing efficiencies and follow the distribution of heavy elements in a Jupiter-mass planet as it evolves. We show that a heavy-element core cannot be eroded by convection if there is a sharp compositional change at the core-envelope boundary. If the heavy elements are initially distributed within the planet according to some compositional gradient, mixing occurs in the outer regions resulting in a compositionally homogeneous outer envelope. Mixing of heavy materials that are injected in a convective gaseous envelope are found to mix efficiently. Our work demonstrates that the primordial internal structure of a giant planet plays a substantial role in determining its long-term evolution and that giant planets can have non-adiabatic interiors. These results emphasize the importance of coupling formation, evolution, and internal structure models of giant planets self-consistently.

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arXiv2014

Structure and Dynamics of Cold Water Super-Earths: The Case of Occluded CH4 and its Outgassing

We study the transport of methane in the external water envelopes surrounding water-rich super-Earths and estimate its outgassing into the atmosphere. We investigate the influence of methane on the thermodynamics and mechanics of the water mantle. We find that including methane in the water matrix introduces a new phase (filled ice) resulting in hotter planetary interiors. This effect renders the super-ionic and reticulating phases accessible to relatively low mass planets lacking a H/He atmosphere. We model the thermal and structural profile of the planetary crust and discuss five possible crustal regimes. The formation of methane clathrate in the subsurface is shown to inhibit the formation of a subterranean ocean. This effect results in increased stresses on the lithosphere making modes of ice plate tectonics possible. The dynamics of the tectonic plates are analysed. We derive overturn and resurfacing time scales as well as the melt fraction underneath spreading centers. Ice mantle dynamics is found to be important for assessing the composition of the atmosphere. We formulate the relation between the outgassing flux of methane and the tectonic mode dynamics. We give numerical estimates for the global outgassing rate of methane into the atmosphere.

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