Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. In this formulation the effective or eddy diffusivity depends on the entropy gradient, $\partial S/\partial r$, as well as entropy. First we present a simplified model with semi-analytical solutions, highlighting the large dynamic range of $\partial S/\partial r$, around 12 orders of magnitude, for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple, stable numerical scheme able to capture the large dynamic range of $\partial S/\partial r$ and provide a flexible and robust method for time-integrating the energy equation. We then consider a full model including energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using $\partial S/\partial r$ as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. Our computational framework is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations arising in other disciplines, particularly for non-linear functional forms of the diffusion coefficient

Linking the evolution of terrestrial interiors and an early outgassed atmosphere to astrophysical observations

A terrestrial planet is molten during formation and may remain so if subject to intense insolation or tidal forces. Observations continue to favour the detection and characterisation of hot planets, potentially with large outgassed atmospheres. We aim to determine the radius of hot Earth-like planets with large outgassed atmospheres and explore differences between molten and solid silicate planets and their influence on the mass-radius relationship and transmission and emission spectra. An interior-atmosphere model, combined with static structure calculations, tracks the evolving radius of a rocky mantle that is outgassing CO$_2$ and H$_2$O. Synthetic emission and transmission spectra are generated for CO$_2$ and H$_2$O dominated atmospheres. Atmospheres dominated by CO$_2$ suppress the outgassing of H$_2$O to a greater extent than previously realised, as previous studies have applied an erroneous relationship between volatile mass and partial pressure. We therefore predict more H$_2$O can be retained by the interior during the later stages of magma ocean crystallisation. Furthermore, formation of a lid at the surface can tie outgassing of H$_2$O to the efficiency of heat transport through the lid, rather than the atmosphere's radiative timescale. Contraction of the mantle as it solidifies gives $\sim5\%$ radius decrease, which can partly be offset by addition of a relatively light species to the atmosphere. We conclude that a molten silicate mantle can increase the radius of a terrestrial planet by around $5\%$ compared to its solid counterpart, or equivalently account for a $13\%$ decrease in bulk density. An outgassing atmosphere can perturb the total radius according to its speciation. Atmospheres of terrestrial planets around M-stars that are dominated by CO$_2$ or H$_2$O can be distinguished by observing facilities with extended wavelength coverage (e.g., JWST).Comment: 19 pages, published in A&A, abstract shortene

A determination of the spin-orbit alignment of the anomalously dense planet orbiting HD 149026

We report 35 radial velocity measurements of HD 149026 taken with the Keck Telescope. Of these measurements, 15 were made during the transit of the companion planet HD 149026b, which occurred on 2005 June 25. These velocities provide a high-cadence observation of the Rossiter-McLaughlin effect, the shifting of photospheric line profiles that occurs when a planet occults a portion of the rotating stellar surface. We combine these radial velocities with previously published radial velocity and photometric data sets and derive a composite best-fit model for the star-planet system. This model confirms and improves previously published orbital parameters, including the remarkably small planetary radius, the planetary mass, and the orbital inclination, found to be Rp/RJup = 0.718 ± 0.065, Mp/MJup = 0.352 ± 0.025, and I = 86.1° ± 1.4°, respectively. Together the planetary mass and radius determinations imply a mean planetary density of 1.18(-0.30)(+0.38)g cm(-3). The new data also allow for the determination of the angle between the apparent stellar equator and the orbital plane, which we constrain to be λ = -12° ± 15°

VapoRock: Thermodynamics of vaporized silicate melts for modeling volcanic outgassing and magma ocean atmospheres

Silicate vapors play a key role in planetary evolution, especially dominating early stages of rocky planet formation through outgassed magma ocean atmospheres. Our open-source thermodynamic modeling software "VapoRock" combines the MELTS liquid model (Ghiorso et al., 1995) with gas-species properties from multiple thermochemistry tables (e.g., Chase et al., 1998). VapoRock calculates the partial pressures of 34 gaseous species in equilibrium with magmatic liquid in the system Si-Mg-Fe-Al-Ca-Na-K-Ti-Cr-O at desired temperatures and oxygen fugacities (fO2, or partial pressure of O2). Comparison with experiments shows that pressures and melt-oxide activities (which vary over many orders of magnitude) are reproduced to within a factor of ~3, consistent with measurement uncertainties. We also benchmark the model against a wide selection of igneous rock compositions including bulk silicate Earth, predicting elemental vapor abundances that are comparable (Na, Ca, & Al) or more realistic (K, Si, Mg, Fe, & Ti) than those of the closed-source MAGMA code (with maximum deviations by factors of 10-300 for K & Si). Vapor abundances depend critically on the activities of liquid components. The MELTS model underpinning VapoRock was calibrated and extensively tested on natural igneous liquids. In contrast, MAGMA's liquid model assumes ideal mixtures of a limited set of chemically simplified pseudo-species, which only roughly approximates the non-ideal compositional interactions typical of many-component natural silicate melts. Finally, we explore how relative abundances of SiO and SiO2 provide a spectroscopically measurable proxy for oxygen fugacity in devolatilized exoplanetary atmospheres, potentially constraining fO2 in outgassed exoplanetary mantles

The thermal equation of state of (Mg, Fe)SiO3 bridgmanite (perovskite) and implications for lower mantle structures

The high‐pressure/high‐temperature equation of state (EOS) of synthetic 13% Fe‐bearing bridgmanite (Mg silicate perovskite) is measured using powder X‐ray diffraction in a laser‐heated diamond anvil cell with a quasi‐hydrostatic neon pressure medium. We compare these results, which are consistent with previous 300 K sound speed and compression studies, with a reanalysis of Fe‐free Mg end‐member data from Tange et al. (2012) to determine the effect of iron on bridgmanite’s thermoelastic properties. EOS parameters are incorporated into an ideal lattice mixing model to probe the behavior of bridgmanite at deep mantle conditions. With this model, a nearly pure bridgmanite mantle composition is shown to be inconsistent with density and compressibility profiles of the lower mantle. We also explore the buoyant stability of bridgmanite over a range of temperatures and compositions expected for Large Low‐Shear Velocity Provinces, concluding that bridgmanite‐dominated thermochemical piles are more likely to be passive dense layers externally supported by convection, rather than internally supported metastable domes. The metastable dome scenario is estimated to have a relative likelihood of only 4–7%, given the narrow range of compositions and temperatures consistent with seismic constraints. If buoyantly supported, such structures could not have remained stable with greater thermal contrast early in Earth’s history, ruling out formation scenarios involving a large concentration of heat producing elements.Key PointsHigh P‐T equation of state of 13% and 0% Fe bridgmanite (perovksite) is obtainedPure bridgmanite mantle is inconsistent with PREM at any Fe contentBuoyant stability of LLSVPs favors passive chemical piles over metastable domesPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141021/1/jgrb51327.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/141021/2/jgrb51327_am.pd

Spectropolarimetry and Modeling of the Eclipsing T Tauri Star KH 15D

KH 15D is a strongly variable T Tauri star in the young star cluster NGC 2264 that shows a decrease in flux of 3.5 magnitudes lasting for 18 days and repeating every 48 days. The eclipsing material is likely due to orbiting dust or rocky bodies in a partial ring or warped disk that periodically occults the star. We measured the polarized spectrum in and out of eclipse at the Keck and Palomar observatories. Outside of the eclipse, the star exhibited low polarization consistent with zero. During eclipse, the polarization increased dramatically to ~2% across the optical spectrum, while the spectrum had the same continuum shape as outside of eclipse and exhibited emission lines of much larger equivalent width, as previously seen. From the data, we conclude that (a) the scattering region is uneclipsed; (b) the scattering is nearly achromatic; (c) the star is likely completely eclipsed so that the flux during eclipse is entirely due to scattered light, a conclusion also argued for by the shape of the ingress and egress. We argue that the scattering is not due to electrons, but may be due to large dust grains of size ~10 micron, similar to the interplanetary grains which scatter the zodiacal light. We construct a warped-disk model with an extended dusty atmosphere which reproduces the main features of the lightcurve, namely (a) a gradual decrease before ingress due to extinction in the atmosphere (similar for egress); (b) a sharper decrease within ingress due to the optically-thick base of the atmosphere; (c) a polarized flux during eclipse which is 0.1% of the total flux outside of eclipse, which requires no fine-tuning of the model. (abridged)Comment: 9 pages, 7 figures, accepted for publication in ApJ, MPEG simulation available at http://www.astro.washington.edu/agol/scatter2.mp

Venus: Interpreting the spatial distribution of volcanically modified craters

To understand the impact cratering record on Venus, we investigate two distinct resurfacing styles: localized, thin flows and large shield volcanoes. We statistically analyze the size-frequency distribution of volcanically modified craters and, using Monte Carlo simulations, their spatial distribution. Lava flows partially fill most craters, darkening their floors in radar images. We find that a model featuring localized, thin flows occurring throughout geologic time predicts their observed distribution. Individual flows may be morphologically indistinguishable, but, combined, they cover large provinces. Recent mantle plumes may drive a small amount of hot spot magmatism that produces the observed clusters of large shield volcanoes and obviously embayed craters. Ultimately, our analysis demonstrates that two styles of volcanism are needed to explain the observed properties of impact craters and that catastrophic resurfacing is not required

Data from: Genotyping-by-Sequencing for Populus Population Genomics: An Assessment of Genome Sampling Patterns and Filtering Approaches

Continuing advances in nucleotide sequencing technology are inspiring a suite of genomic approaches in studies of natural populations. Researchers are faced with data management and analytical scales that are increasing by orders of magnitude. With such dramatic advances comes a need to understand biases and error rates, which can be propagated and magnified in large-scale data acquisition and processing. Here we assess genomic sampling biases and the effects of various population-level data filtering strategies in a genotyping-by-sequencing (GBS) protocol. We focus on data from two species of Populus, because this genus has a relatively small genome and is emerging as a target for population genomic studies. We estimate the proportions and patterns of genomic sampling by examining the Populus trichocarpa genome (Nisqually-1), and demonstrate a pronounced bias towards coding regions when using the methylation-sensitive ApeKI restriction enzyme in this species. Using population-level data from a closely related species (P. tremuloides), we also investigate various approaches for filtering GBS data to retain high-depth, informative SNPs that can be used for population genetic analyses. We find a data filter that includes the designation of ambiguous alleles resulted in metrics of population structure and Hardy-Weinberg equilibrium that were most consistent with previous studies of the same populations based on other genetic markers. Analyses of the filtered data (27,910 SNPs) also resulted in patterns of heterozygosity and population structure similar to a previous study using microsatellites. Our application demonstrates that technically and analytically simple approaches can readily be developed for population genomics of natural populations

Separating the influence of temperature, drought, and fire on interannual variability in atmospheric CO 2

The response of the carbon cycle in prognostic Earth system models (ESMs) contributes significant uncertainty to projections of global climate change. Quantifying contributions of known drivers of interannual variability in the growth rate of atmospheric carbon dioxide (CO 2 ) is important for improving the representation of terrestrial ecosystem processes in these ESMs. Several recent studies have identified the temperature dependence of tropical net ecosystem exchange (NEE) as a primary driver of this variability by analyzing a single, globally averaged time series of CO 2 anomalies. Here we examined how the temporal evolution of CO 2 in different latitude bands may be used to separate contributions from temperature stress, drought stress, and fire emissions to CO 2 variability. We developed atmospheric CO 2 patterns from each of these mechanisms during 1997–2011 using an atmospheric transport model. NEE responses to temperature, NEE responses to drought, and fire emissions all contributed significantly to CO 2 variability in each latitude band, suggesting that no single mechanism was the dominant driver. We found that the sum of drought and fire contributions to CO 2 variability exceeded direct NEE responses to temperature in both the Northern and Southern Hemispheres. Additional sensitivity tests revealed that these contributions are masked by temporal and spatial smoothing of CO 2 observations. Accounting for fires, the sensitivity of tropical NEE to temperature stress decreased by 25% to 2.9 ± 0.4 Pg C yr −1  K −1 . These results underscore the need for accurate attribution of the drivers of CO 2 variability prior to using contemporary observations to constrain long‐term ESM responses. Key Points Accurate attribution of CO 2 variability is required to constrain coupled models Combined influence of drought and fire exceed ecosystem responses to temperature Temporal and spatial smoothing of CO 2 observations masks variability from firePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109962/1/gbc20215.pd