Predictions on the core mass of Jupiter and of giant planets in general

More than 80 giant planets are known by mass and radius. Their interior structure in terms of core mass, number of layers, and composition however is still poorly known. An overview is presented about the core mass Mcore and envelope mass of metals MZ in Jupiter as predicted by various equations of state. It is argued that the uncertainty about the true H/He EOS in a pressure regime where the gravitational moments J2 and J4 are most sensitive, i.e. between 0.5 and 4 Mbar, is in part responsible for the broad range Mcore=0-18 Mearth, MZ=0-38 Mearth, and Mcore+MZ=14-38 Mearth currently offered for Jupiter. We then compare the Jupiter models obtained when we only match J2 with the range of solutions for the exoplanet GJ436b, when we match an assumed tidal Love number k2 value.Comment: Accepted for publication in Astrophyics and Space Scienc

Low- and high-order gravitational harmonics of rigidly rotating Jupiter

The Juno Orbiter has provided improved estimates of the even gravitational harmonics J2 to J8 of Jupiter. To compute higher-order moments, new methods such as the Concentric Maclaurin Spheroids (CMS) method have been developed which surpass the so far commonly used Theory of Figures (ToF) method in accuracy. This progress rises the question whether ToF can still provide a useful service for deriving the internal structure of giant planets in the Solar system. In this paper, I apply both the ToF and the CMS method to compare results for polytropic Jupiter and for the physical equation of state H/He-REOS.3 based models. An accuracy in the computed values of J2 and J4 of 0.1% is found to be sufficient in order to obtain the core mass safely within 0.5 Mearth numerical accuracy and the atmospheric metallicity within about 0.0004. ToF to 4th order provides that accuracy, while ToF to 3rd order does not for J4. Furthermore, I find that the assumption of rigid rotation yields J6 and J8 values in agreement with the current Juno estimates, and that higher order terms (J10 to J18) deviate by about 10% from predictions by polytropic models. This work suggests that ToF4 can still be applied to infer the deep internal structure, and that the zonal winds on Jupiter reach less deep than 0.9 RJup.Comment: 8 pages, accepted to A&

Thermal evolution and structure models of the transiting super-Earth GJ 1214b

The planet GJ 1214b is the second known super-Earth with a measured mass and radius. Orbiting a quiet M-star, it receives considerably less mass-loss driving X-ray and UV radiation than CoRoT-7b, so that the interior may be quite dissimilar in composition, including the possibility of a large fraction of water. We model the interior of GJ 1214b assuming a two-layer (envelope+rock core) structure where the envelope material is either H/He, pure water, or a mixture of H/He and H2O. Within this framework we perform models of the thermal evolution and contraction of the planet. We discuss possible compositions that are consistent with Mp=6.55 ME, Rp=2.678 RE, an age tau=3-10 Gyr, and the irradiation level of the atmosphere. These conditions require that if water exists in the interior, it must remain in a fluid state, with important consequences for magnetic field generation. These conditions also require the atmosphere to have a deep isothermal region extending down to 80-800 bar, depending on composition. Our results bolster the suggestion of a metal-enriched H/He atmosphere for the planet, as we find water-world models that lack an H/He atmosphere to require an implausibly large water-to-rock ratio of more than 6:1. We instead favor a H/He/H2O envelope with high water mass fraction (~0.5-0.85), similar to recent models of the deep envelope of Uranus and Neptune. Even with these high water mass fractions in the H/He envelope, generally the bulk composition of the planet can have subsolar water:rock ratios. Dry, water-enriched, and pure water envelope models differ to an observationally significant level in their tidal Love numbers k2 of respectively ~0.018, 0.15, and 0.7.Comment: 11 pages, 6 figures, 1 table, accepted to Ap

What do we Really Know about Uranus and Neptune?

The internal structures and compositions of Uranus and Neptune are not well constrained due to the uncertainty in rotation period and flattening, as well as the relatively large error bars on the gravitational coefficients. While Uranus and Neptune are similar in mass and radius, they differ in other physical properties such as thermal emission, obliquity, and inferred atmospheric enrichment. In this letter we consider the uncertainty in the planetary rotation periods, show that rotation periods more consistent with the measured oblateness imply that Uranus and Neptune have different internal structures, and speculate on the source of that difference. We conclude that Uranus and Neptune might have very different structures and/or compositions despite their similar masses and radii. We point out that understanding these differences can have important implications for our view of the formation and evolution of Uranus and Neptune as well as intermediate-mass extra-solar planets in general.Comment: Accepted for publication in ApJ

New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data

Since the Voyager fly-bys of Uranus and Neptune, improved gravity field data have been derived from long-term observations of the planets' satellite motions, and modified shape and solid-body rotation periods were suggested. A faster rotation period (-40 min) for Uranus and a slower rotation period (+1h20) of Neptune compared to the Voyager data were found to minimize the dynamical heights and wind speeds. We apply the improved gravity data, the modified shape and rotation data, and the physical LM-R equation of state to compute adiabatic three-layer structure models, where rocks are confined to the core, and homogeneous thermal evolution models of Uranus and Neptune. We present the full range of structure models for both the Voyager and the modified shape and rotation data. In contrast to previous studies based solely on the Voyager data or on empirical EOS, we find that Uranus and Neptune may differ to an observationally significant level in their atmospheric heavy element mass fraction Z1 and nondimensional moment of inertia, nI. For Uranus, we find Z1 < 8% and nI=0.2224(1), while for Neptune Z1 < 65% and nI=0.2555(2) when applying the modified shape and rotation data, while for the unmodified data we compute Z1 < 17% and nI=0.230(1) for Uranus and Z1 < 54% and nI=0.2410(8) for Neptune. In each of these cases, solar metallicity models (Z1=0.015) are still possible. The cooling times obtained for each planet are similar to recent calculations with the Voyager rotation periods: Neptune's luminosity can be explained by assuming an adiabatic interior while Uranus cools far too slowly. More accurate determinations of these planets' gravity fields, shapes, rotation periods, atmospheric heavy element abundances, and intrinsic luminosities are essential for improving our understanding of the internal structure and evolution of icy planets.Comment: accepted to Planet. Space Sci., special editio

Forward and Inverse Modeling for Jovian Seismology

Jupiter is expected to pulsate in a spectrum of acoustic modes and recent re-analysis of a spectroscopic time series has identified a regular pattern in the spacing of the frequencies \citep{gaulme2011}. This exciting result can provide constraints on gross Jovian properties and warrants a more in-depth theoretical study of the seismic structure of Jupiter. With current instrumentation, such as the SYMPA instrument \citep{schmider2007} used for the \citet{gaulme2011} analysis, we assume that, at minimum, a set of global frequencies extending up to angular degree $\ell=25$ could be observed. In order to identify which modes would best constrain models of Jupiter's interior and thus help motivate the next generation of observations, we explore the sensitivity of derived parameters to this mode set. Three different models of the Jovian interior are computed and the theoretical pulsation spectrum from these models for $\ell\leq 25$ is obtained. We compute sensitivity kernels and perform linear inversions to infer details of the expected discontinuities in the profiles in the Jovian interior. We find that the amplitude of the sound-speed jump of a few percent in the inner/outer envelope boundary seen in two of the applied models should be reasonably inferred with these particular modes. Near the core boundary where models predict large density discontinuities, the location of such features can be accurately measured, while their amplitudes have more uncertainty. These results suggest that this mode set would be sufficient to infer the radial location and strength of expected discontinuities in Jupiter's interior, and place strong constraints on the core size and mass. We encourage new observations to detect these Jovian oscillations.Comment: 31 pages, 12 figures, accepted to Icaru

First year growth in the lithodids Lithodes santolla and Paralomis granulosa reared at different temperatures

The southern king crab, Lithodes santolla Molina, and stone crab, Paralomis granulosa Jacquinot, inhabit the cold-temperate waters of southernmost South America (southern Chile and Argentina), where stocks of both species are endangered by overfishing. Recent investigations have shown that these crabs show life-cycle adaptations to scarcity of food and low temperatures prevailing in subantarctic regions, including complete lecithotrophy of all larval stages and prolonged periods of brooding and longevity. However, growth and development to maturity are slow under conditions of low temperatures, which may explain the particular vulnerability of subpolar lithodids to fisheries. In the present study, juvenile L. santolla and P. granulosa were individually reared in the laboratory at constant temperatures ranging from 3–15 °C, and rates of survival and development through successive instars were monitored throughout a period of about nine months from hatching. When the experiments were terminated, L. santolla had maximally reached juvenile instar IV (at 6 °C), V (9 °C), or VII (15 °C). In P. granulosa the maximum crab instar reached was II (at 3 °C), V (6 °C), V (9 °C), or VII (15 °C). The intermoult period decreased with increasing temperature, while it increased in successively later instars. In consequence, growth rate showed highly significant differences among temperatures (P&lt;0.001). Growth-at-moult was highest at 9 °C. Rates of survival decreased significantly in juvenile P. granulosa with increasing temperature. Only at 15 °C in L. santolla, was a significantly enhanced mortality found compared with lower temperatures. Our results indicate that juvenile stages of L. santolla and P. granulosa are well adapted to 5–10°C, the range of temperatures typically prevailing in subantarctic marine environments. In spite of causing higher mortality rates, higher rearing temperatures (12–15 °C) should accelerate the rates of growth and maturation, which may be favourable for projects aiming at aquaculture or repopulation of overexploited king crab stocks

Formation and Structure of Low Density Exo-Neptunes

Kepler has found hundreds of Neptune-size (2-6 R_Earth) planet candidates within 0.5 AU of their stars. The nature of the vast majority of these planets is not known because their masses have not been measured. Using theoretical models of planet formation, evolution and structure, we explore the range of minimum plausible masses for low-density exo-Neptunes. We focus on highly irradiated planets with T_eq>=500K. We consider two separate formation pathways for low-mass planets with voluminous atmospheres of light gases: core nucleated accretion and outgassing of hydrogen from dissociated ices. We show that Neptune-size planets at T_eq=500K with masses as small as a few times that of Earth can plausibly be formed core nucleated accretion coupled with subsequent inward migration. We also derive a limiting low-density mass-radius relation for rocky planets with outgassed hydrogen envelopes but no surface water. Rocky planets with outgassed hydrogen envelopes typically have computed radii well below 3 R_Earth. For both planets with H/He envelopes from core nucleated accretion and planets with outgassed hydrogen envelopes, we employ planet interior models to map the range of planet mass--envelope mass--equilibrium temperature parameter space that is consistent with Neptune-size planet radii. Atmospheric mass loss mediates which corners of this parameter space are populated by actual planets and ultimately governs the minimum plausible mass at a specified transit radius. We find that Kepler's 2-6 R_Earth planet candidates at T_eq=500--1000K could potentially have masses less than ~4 M_Earth. Although our quantitative results depend on several assumptions, our qualitative finding that warm Neptune-size planets can have masses substantially smaller than those given by interpolating the masses and radii of planets within our Solar System is robust.Comment: 17 pages, 9 figures, accepted for publication in Ap