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

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 Origin of the Intrinsic Scatter in the Relation Between Black Hole Mass and Bulge Luminosity for Nearby Active Galaxies

We investigate the origin of the intrinsic scatter in the correlation between black hole mass (MBH) and bulge luminosity [L(bulge)] in a sample of 45 massive, local (z < 0.35) type~1 active galactic nuclei (AGNs). We derive MBH from published optical spectra assuming a spherical broad-line region, and L(bulge) from detailed two-dimensional decomposition of archival optical Hubble Space Telescope images. AGNs follow the MBH-L(bulge) relation of inactive galaxies, but the zero point is shifted by an average of \Delta log MBH ~ -0.3 dex. We show that the magnitude of the zero point offset, which is responsible for the intrinsic scatter in the MBH-L(bulge) relation, is correlated with several AGN and host galaxy properties, all of which are ultimately related to, or directly impact, the BH mass accretion rate. At a given bulge luminosity, sources with higher Eddington ratios have lower MBH. The zero point offset can be explained by a change in the normalization of the virial product used to estimate MBH, in conjunction with modest BH growth (~ 10%--40%) during the AGN phase. Galaxy mergers and tidal interactions appear to play an important role in regulating AGN fueling in low-redshift AGNs.Comment: To appear in ApJ; 67 pages, 56 figures, 4 tables, version with full resolution figures at http://users.ociw.edu/mjkim/papers/scatter.pd

Biomarkers of aging associated with past treatments in breast cancer survivors.

Radiation and chemotherapy are effective treatments for cancer, but are also toxic to healthy cells. Little is known about whether prior exposure to these treatments is related to markers of cellular aging years later in breast cancer survivors. We examined whether past exposure to chemotherapy and/or radiation treatment was associated with DNA damage, telomerase activity, and telomere length 3-6 years after completion of primary treatments in breast cancer survivors (stage 0-IIIA breast cancer at diagnosis). We also examined the relationship of these cellular aging markers with plasma levels of Interleukin (IL)-6, soluble TNF-receptor-II (sTNF-RII), and C-reactive protein (CRP). Ninety-four women (36.4-69.5 years; 80% white) were evaluated. Analyses adjusting for age, race, BMI, and years from last treatment found that women who had prior exposure to chemotherapy and/or radiation compared to women who had previously received surgery alone were more likely to have higher levels of DNA damage (P = .02) and lower telomerase activity (P = .02), but did not have differences in telomere length. More DNA damage and lower telomerase were each associated with higher levels of sTNF-RII (P's &lt; .05). We found that exposure to chemotherapy and/or radiation 3-6 years prior was associated with markers of cellular aging, including higher DNA damage and lower telomerase activity, in post-treatment breast cancer survivors. Furthermore, these measures were associated with elevated inflammatory activation, as indexed by sTNF-RII. Given that these differences were observed many years after the treatment, the findings suggest a long lasting effect of chemotherapy and/or radiation exposure

Design and Assembly of an Integrated Metabolic Heat Regenerated Temperature Swing Adsorption (MTSA) Subassembly Engineering Development Unit

Metabolic heat regenerated Temperature Swing Adsorption (MTSA) technology is being developed for thermal and carbon dioxide (CO2) control for a Portable Life Support System (PLSS), as well as water recycling. The core of the MTSA technology is a sorbent bed that removes CO2 from the PLSS ventilation loop gas via a temperature swing. A Condensing Icing Heat eXchanger (CIHX) is used to warm the sorbent while also removing water from the ventilation loop gas. A Sublimation Heat eXchanger (SHX) is used to cool the sorbent. Research was performed to explore an MTSA designed for both lunar and Martian operations. Previously the sorbent bed, CIHX, and SHX had been built and tested individually on a scale relevant to PLSS operations, but they had not been done so as an integrated subassembly. Design and analysis of an integrated subassembly was performed based on this prior experience and an updated transient system model. Focus was on optimizing the design for Martian operations, but the design can also be used in lunar operations. An Engineering Development Unit (EDU) of an integrated MTSA subassembly was assembled based on the design. Its fabrication is discussed. Some details on the differences between the as-assembled EDU and the future flight unit are considered

Metabolic Heat Regenerated Temperature Swing Adsorption for CO2 and Heat Removal/Rejection in a Martian PLSS

Two of the fundamental problems facing the development of a Portable Life Support System (PLSS) for use on Mars, are (i) heat rejection (because traditional technologies use sublimation of water, which wastes a scarce resource and contaminates the premises), and (ii) rejection of carbon dioxide (CO2) in an environment with a CO2 partial pressure (ppCO2) of 0.4-0.9 kPa. Patent-pending Metabolic heat regenerated Temperature Swing Adsorption (MTSA) technology is being developed to address both these challenges. The technology utilizes an adsorbent that when cooled with liquid CO2 to near sublimation temperatures (~195K) removes metabolically-produced CO2 in the ventilation loop. Once fully loaded, the adsorbent is then warmed externally by the ventilation loop (~300K), rejecting the captured CO2 to Mars ambient. Two beds are used to provide a continuous cycle of CO2 removal/rejection as well as facilitate heat exchange out of the ventilation loop. Any cryogenic fluid can be used in the application; however, since CO2 is readily available on Mars and can be easily produced and stored on the Martian surface, the solution is rather elegant and less complicated when employing liquid CO2. As some metabolic heat will need to be rejected anyway, finding a practical use for metabolic heat is also an overall benefit to the PLSS. To investigate the feasibility of the technology, a series of experiments were conducted which lead to the selection and partial characterization of an appropriate adsorbent. The Molsiv Adsorbents 13X 8x12 (also known as NaX zeolite) successfully removed CO2 from a simulated ventilation loop at the prescribed temperature swing anticipated during PLSS operating conditions on Mars using a cryogenic fluid. Thermal conductivity of the adsorbent was also measured to eventually aid in a demonstrator design of the technology. These results provide no show stoppers to the development of MTSA technology and allow its development to focus on other design challenges as listed in the conclusions section of this paper

Mass transport by buoyant bubbles in galaxy clusters

We investigate the effect of three important processes by which AGN-blown bubbles transport material: drift, wake transport and entrainment. The first of these, drift, occurs because a buoyant bubble pushes aside the adjacent material, giving rise to a net upward displacement of the fluid behind the bubble. For a spherical bubble, the mass of upwardly displaced material is roughly equal to half the mass displaced by the bubble, and should be ~ 10^{7-9} solar masses depending on the local ICM and bubble parameters. We show that in classical cool core clusters, the upward displacement by drift may be a key process in explaining the presence of filaments behind bubbles. A bubble also carries a parcel of material in a region at its rear, known as the wake. The mass of the wake is comparable to the drift mass and increases the average density of the bubble, trapping it closer to the cluster centre and reducing the amount of heating it can do during its ascent. Moreover, material dropping out of the wake will also contribute to the trailing filaments. Mass transport by the bubble wake can effectively prevent the build-up of cool material in the central galaxy, even if AGN heating does not balance ICM cooling. Finally, we consider entrainment, the process by which ambient material is incorporated into the bubble. AbridgedComment: Accepted for publication in MNRAS. 17 pages, 4 figures, 2 tables. Formatted for letter paper and adjusted author affiliations

Patient-reported symptoms and discontinuation of adjuvant aromatase inhibitor therapy

BACKGROUND: Aromatase inhibitor (AI) therapy results in substantial survival benefits for patients with hormone receptor-positive breast cancer. The rates of poor adherence and discontinuation of AI therapy are high, primarily because of treatment-related toxicities like musculoskeletal pain. Although pain-related symptoms may worsen during AI therapy, the authors hypothesized that nonpersistence with AI therapy was associated with symptoms that were present before treatment initiation. METHODS: Postmenopausal women initiating AI therapy who were enrolled in a prospective clinical trial completed questionnaires at baseline to assess sleep, fatigue, mood, and pain. Reasons for treatment discontinuation during the first year of treatment were recorded. Associations between baseline patient-reported symptoms and treatment discontinuation because of toxicity were identified using logistic regression. RESULTS: Four hundred forty-nine patients were evaluable. The odds of treatment discontinuation were higher in patients who reported a greater number of symptoms before AI initiation. Baseline poor sleep quality was associated with early treatment discontinuation, with an odds ratio (OR) of 1.91 (95% confidence interval [CI], 1.26-2.89; P = .002). Baseline presence of tired feeling and forgetfulness had similar ORs for discontinuation (tired feeling: OR, 1.76; 95% CI, 1.15-2.67; P = .009; forgetfulness: OR, 1.66; 95% CI, 1.11-2.48; P = .015). An increasing total number of baseline symptoms was associated with an increased likelihood of treatment discontinuation, with an OR of 1.89 (95% CI, 1.20-2.96; P = .006) for 3 to 5 symptoms versus 0 to 2 symptoms. CONCLUSIONS: Symptom clusters in breast cancer survivors that are present before the initiation of adjuvant AI therapy may have a negative impact on a patient's persistence with therapy. Interventions to manage these symptoms may improve breast cancer outcomes and quality of life