Can we constrain the interior structure of rocky exoplanets from mass and radius measurements?

Aims. We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. Methods. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. Results. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii, and to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Conclusions. Our main conclusions are (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are principal constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies, but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structures including hydrogen- and water-rich exoplanets.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.

Global models of planet formation and evolution

Despite the strong increase in observational data on extrasolar planets, the processes that led to the formation of these planets are still not well understood. However, thanks to the high number of extrasolar planets that have been discovered, it is now possible to look at the planets as a population that puts statistical constraints on theoretical formation models. A method that uses these constraints is planetary population synthesis where synthetic planetary populations are generated and compared to the actual population. The key element of the population synthesis method is a global model of planet formation and evolution. These models directly predict observable planetary properties based on properties of the natal protoplanetary disc, linking two important classes of astrophysical objects. To do so, global models build on the simplified results of many specialized models that address one specific physical mechanism. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disc (of gas and solids), those that describe one (proto)planet (its solid core, gaseous envelope and atmosphere), and finally those that describe the interactions (orbital migration and N-body interaction). We compare the approaches taken in different global models, discuss the links between specialized and global models, and identify physical processes that require improved descriptions in future work. We then shortly address important results of planetary population synthesis like the planetary mass function or the mass-radius relationship. With these statistical results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Owing to their nature as meta models, global models depend on the results of specialized models, and therefore on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that the global models will in future undergo significant modifications. Despite these limitations, global models can already now yield many testable predictions. With future global models addressing the geophysical characteristics of the synthetic planets, it should eventually become possible to make predictions about the habitability of planets based on their formation and evolution.

Changes in blood lipids and their associations with changes in measures of height, weight and body mass index from age 8 to 18 years: Project Heartbeat!

A variety of studies indicate that the process of athrosclerosis begins in childhood. There was limited information on the association of the changes in anthropometric variables to blood lipids in school age children and adolescents. Previous longitudinal studies of children typically with insufficient frequency of observation could not provide sound inference on the dynamics of change in blood lipids. The aims of this analysis are (1) to document the sex- and ethnic-specific trajectory and velocity curves of blood lipids (TC, LDL-C, HDL-C and TG); (2) to evaluate the relationship of changes in anthropometric variables, such as height, weight and BMI, to blood lipids from age 8 to 18 years. ^ Project HeartBeat! is a longitudinal study designed to examine the patterns of serial change in major cardiovascular risk factors. Cohort of three different age levels, 8, 11 and 14 years at baseline, with a total of 678 participants were enrolled. Each member of these cohorts was examined three times per year for up to four years. ^ Sex- and ethnic-specific trajectory and velocity curves of blood lipids; demonstrated the complex and polyphasic changes in TC, LDL-C, HDL-C and TG longitudinally. The trajectory curves of TC, LDL-C and HDL-C with age showed curvilinear patterns of change. The velocity change in TC, HDL-C and LDL-C showed U-shaped curves for non-Blacks, and nearly linear lines in velocity of TG for both Blacks and non-Blacks. ^ The relationship of changes in anthropometric variables to blood lipids was evaulated by adding height, weight, or BMI and associated interaction terms separately to the basic age-sex models. Height or height gain had a significant negative association with changes in TC, LDL-C and HDL-C. Weight or BMI gain showed positive associations with TC, LDL-C and TC, and a negative relationship with HDL-C. ^ Dynamic changes of blood lipids in school age children and adolescents observed from this analysis suggested that using fixed screening criteria under the current NCEP guidelines for all ages 2–19 may not be appropriate for this age group. The association of increasing BMI or weight to an adverse blood lipid profile found in this analysis also indicated that weight or BMI monitoring could be a future intervention to be implemented in the pediatric population. ^

Changes in serum lipids with change and fluctuation in body mass index and body fat distribution in Mexican Americans with type 2 diabetes

This dissertation was written in the format of three journal articles. Paper 1 examined the influence of change and fluctuation in body mass index (BMI) over an eleven-year period, on changes in serum lipid levels (total, HDL, and LDL cholesterol, triglyceride) in a population of Mexican Americans with type 2 diabetes. Linear regression models containing initial lipid value, BMI and age, BMI change (slope of BMI), and BMI fluctuation (root mean square error) were used to investigate associations of these variables with change in lipids over time. Increasing BMI over time was associated with gains in total and LDL cholesterol and triglyceride levels in women. Fluctuation of BMI was not associated with detrimental lipid profiles. These effects were independent of age and were not statistically significant in men. In Mexican-American women with type 2 diabetes, weight reduction is likely to result in more favorable levels of total and LDL cholesterol and triglyceride, without concern for possible detrimental effects of weight fluctuation. Weight reduction may not be as effective in men, but does not appear to be harmful either. ^ Paper 2 examined the associations of upper and total body fat with total cholesterol, HDL and LDL cholesterol, and triglyceride levels in the same population. Multilevel analysis was used to predict serum lipid levels from total body fat (BMI and triceps skinfold) and upper body fat (subscapular skinfold), while controlling for the effects of sex, age and self-correlations across time. Body fat was not strikingly associated with trends in serum lipid levels. However, upper body fat was strongly associated with triglyceride levels. This suggests that loss of upper body fat may be more important than weight loss in management of the hypertriglyceridemia commonly seen in type 2 diabetes. ^ Paper 3 was a review of the literature reporting associations between weight fluctuation and lipid levels. Few studies have reported associations between weight fluctuation and total, LDL, and HDL cholesterol and triglyceride levels. The body of evidence to date suggests that weight fluctuation does not strongly influence levels of total, LDL and HDL cholesterol and triglyceride. ^

Relationship between dietary patterns and body mass index in Hispanic children ages 4--19 years of age

Background. In over 30 years, the prevalence of overweight for children and adolescents has increased across the United States (Barlow et al., 2007; Ogden, Flegal, Carroll, & Johnson, 2002). Childhood obesity is linked with adverse physiological and psychological issues in youth and affects ethnic/minority populations in disproportionate rates (Barlow et al., 2007; Butte et al., 2006; Butte, Cai, Cole, Wilson, Fisher, Zakeri, Ellis, & Comuzzie, 2007). More importantly, overweight in children and youth tends to track into adulthood (McNaughton, Ball, Mishra, & Crawford, 2008; Ogden et al., 2002). Childhood obesity affects body functions such as the cardiovascular, respiratory, gastrointestinal, and endocrine systems, including emotional health (Barlow et al., 2007, Ogden et al., 2002). Several dietary factors have been associated with the development of obesity in children; however, these factors have not been fully elucidated, especially in ethnic/minority children. In particular, few studies have been done to determine the effects of different meal patterns on the development of obesity in children. Purpose. The purpose of the study is to examine the relationships between daily proportions of energy consumed and energy derived from fat across breakfast, lunch, dinner, and snack, and obesity among Hispanic children and adolescents. Methods. A cross-sectional design was used to evaluate the relationship between dietary patterns and overweight status in Hispanic children and adolescents 4-19 years of age who participated in the Viva La Familia Study. The goal of the Viva La Familia Study was to evaluate genetic and environmental factors affecting childhood obesity and its co-morbidities in the Hispanic population (Butte et al., 2006, 2007). The study enrolled 1030 Hispanic children and adolescents from 319 families and examined factors related to increased body weight by focusing on a multilevel analysis of extensive sociodemographic, genetic, metabolic, and behavioral data. Baseline dietary intakes of the children were collected using 24-hour recalls, and body mass index was calculated from measured height and weight, and classified using the CDC standards. Dietary data were analyzed using a GEE population-averaged panel-data model with a cluster variable family identifier to include possible correlations within related data sets. A linear regression model was used to analyze associations of dietary patterns using possible covariates, and to examine the percentage of daily energy coming from breakfast, lunch, dinner, and snack while adjusting for age, sex, and BMI z-score. Random-effects logistic regression models were used to determine the relationship of the dietary variables with obesity status and to understand if the percent energy intake (%EI) derived from fat from all meals (breakfast, lunch, dinner, and snacks) affected obesity. Results. Older children (age 4-19 years) consumed a higher percent of energy at lunch and dinner and less percent energy from snacks compared to younger children. Age was significantly associated with percentage of total energy intake (%TEI) for lunch, as well as dinner, while no association was found by gender. Percent of energy consumed from dinner significantly differed by obesity status, with obese children consuming more energy at dinner (p = 0.03), but no associations were found between percent energy from fat and obesity across all meals. Conclusions. Information from this study can be used to develop interventions that target dietary intake patterns in obesity prevention programs for Hispanic children and adolescents. In particular, intervention programs for children should target dietary patterns with energy intake that is spread throughout the day and earlier in the day. These results indicate that a longitudinal study should be used to further explore the relationship of dietary patterns and BMI in this and other populations (Dubois et al., 2008; Rodriquez & Moreno, 2006; Thompson et al., 2005; Wilson et al., in review, 2008). ^

Age models of sediment cores from the Southern Ocean

Recent geochemical models invoke ocean alkalinity changes, particularly in the surface Southern Ocean, to explain glacial age pCO2 reduction. In such models, alkalinity increases in glacial periods are driven by reductions in North Atlantic Deep Water (NADW) supply, which lead to increases in deep-water nutrients and dissolution of carbonate sediments, and to increased alkalinity of Circumpolar Deep Water upwelling in the surface Southern Ocean. We use cores from the Southeast Indian Ridge and from the deep Cape Basin in the South Atlantic to show that carbonate dissolution was enhanced during glacial stages in areas now bathed by Circumpolar Deep Water. This suggests that deep Southern Ocean carbonate ion concentrations were lower in glacial stages than in interglacials, rather than higher as suggested by the polar alkalinity model [Broecker and Peng, 1989, doi:10.1029/GB001i001p00015]. Our observations show that changes in Southern Ocean CaCO3 preservation are coherent with changes in the relative flux of NADW, suggesting that Southern Ocean carbonate chemistry is closely linked to changes in deepwater circulation. The pattern of enhanced dissolution in glacials is consistent with a reduction in the supply of nutrient-depleted water (NADW) to the Southern Ocean and with an increase of nutrients in deep water masses. Carbonate mass accumulation rates on the Southeast Indian Ridge (3200-3800 m), and in relatively shallow cores (<3000 m) from the Kerguelen Plateau and the South Pacific were significantly reduced during glacial stages, by about 50%. The reduced carbonate mass accumulation rates and enhanced dissolution during glacials may be partly due to decreases in CaCO3:Corg flux ratios, acting as another mechanism which would raise the alkalinity of Southern Ocean surface waters. The polar alkalinity model assumes that the ratio of organic carbon to carbonate production on surface alkalinity is constant. Even if overall productivity in the Southern Ocean were held constant, a decrease in the CaCO3:Corg ratio would result in increased alkalinity and reduced pCO2 in Southern Ocean surface waters during glacials. This ecologically driven surface alkalinity change may enhance deepwater-mediated changes in alkalinity, and amplify rapid changes in pCO2.

Age models and stabile isotope ratios from SO35 cores

Stable isotope measurements on the planktonic foraminifer Globigerinoides ruber (white) have been carried out on a number of selected deep-seas sediment cores from the South Lau and Norlh Fiji Basins. The d18O-curves show good correlation with the inter-ocean oraphic correlation composite d18O-record of the standard reference section (Prell et al. 1986), which, in combination with the chronostratigraphic classifications of Herterich & Sarnthein (1984, modified) and Imbrie et al. 1984), allows a detailed dating of the sedimentary sequences. The deepest layers in core no. 119 (southern Lau Basin) could be assigned to Isotope Stage 24. Measurements made on bulk carbonate in two cores show a much higher glacial-interglacial amplitude, allowing the general identification of the conventional oxygen isotope stages. The d13C-values of the benthic foraminifer Cibicidoides wuellerstorfi show progressively lighter values northwards reflecting an increasing contribution of the isotopically lighter CO2 from the remineralisation of organic matter during the general northward movement of the deep water masses. Cyclicities in the sedimentation rates were observed in core nos. 117 and 119 (both southern Lau Basin) where the interglacials exhibit higher levels than the glacials. Calculated new or export paleoproductivity show that the glacials had higher productivity in the euphotic zone. From the oxygen isotope stratigraphy, the five ash layers in core nos. 117 and 119 could be dated as about 530 ka B.P. in Stage 14, 695 ka B.P. in Stage 18, 775 ka B.P. in Stage 21, 790 ka B.P. and 825 ka B.P. in Stage 22. Carbonate dissolution occurred during stages 5, 8 and 10 to 12.

Revised age models and foraminiferal records obtained for the Last Interglacial period in six marine sediment cores

The dataset contains the revised age models and foraminiferal records obtained for the Last Interglacial period in six marine sediment cores: - the Southern Ocean core MD02-2488 (age model, sea surface temperatures, benthic d18O and d13C for the period 136-108 ka), - the North Atlantic core MD95-2042 (age model, planktic d18O, benthic d18O and d13C for the period 135-110 ka), - the North Atlantic core ODP 980 (age model, planktic d18O, sea surface temperatures, seawater d18O, benthic d18O and d13C, ice-rafted detritus for the period 135-110 ka), - the North Atlantic core CH69-K09 (age model, planktic d18O, sea surface temperatures, seawater d18O, benthic d18O and d13C, ice-rafted detritus for the period 135-110 ka), - the Norwegian Sea core MD95-2010 (age model, percentage of Neogloboquadrina pachyderma sinistral, sea surface temperatures, benthic d18O, ice-rafted detritus for the period 134-110 ka), - the Labrador Sea core EW9302-JPC2 (age model, percentage of Neogloboquadrina pachyderma sinistral, sea surface temperatures, benthic d18O for the period 134-110 ka).

Age models of ODP sites from the Barents Sea-Svalbard region

Based on a revised chronostratigraphy, and compilation of borehole data from the Barents Sea continental margin, a coherent glaciation model is proposed for the Barents Sea ice sheet over the past 3.5 million years (Ma). Three phases of ice growth are suggested: (1) The initial build-up phase, covering mountainous regions and reaching the coastline/shelf edge in the northern Barents Sea during short-term glacial intensification, is concomitant with the onset of the Northern Hemisphere Glaciation (3.6-2.4 Ma). (2) A transitional growth phase (2.4-1.0 Ma), during which the ice sheet expanded towards the southern Barents Sea and reached the northwestern Kara Sea. This is inferred from step-wise decrease of Siberian river-supplied smectite-rich sediments, likely caused by ice sheet blockade and possibly reduced sea ice formation in the Kara Sea as well as glacigenic wedge growth along the northwestern Barents Sea margin hampering entrainment and transport of sea ice sediments to the Arctic-Atlantic gateway. (3) Finally, large-scale glaciation in the Barents Sea occurred after 1 Ma with repeated advances to the shelf edge. The timing is inferred from ice grounding on the Yermak Plateau at about 0.95 Ma, and higher frequencies of gravity-driven mass movements along the western Barents Sea margin associated with expansive glacial growth.

Mass estimates and morphometric meassurements of Discoaster species and Sphenolithus from Ceara Rise ODP Site 927

Mass estimates for Late Miocene and Pliocene (8.6-3.25 Ma) Discoaster species and Sphenolithus are determined using samples of the equatorial Atlantic (Ceara Rise: ODP Site 927). Based on morphometric measurements, 3D computer models were created for 11 Discoaster species and their volumes calculated. From these, shape factors (ks) were derived to allow calculation of mass for different-sized discoasters and Sphenolithus abies. The mass estimates were then used to calculate the contribution of nannofossils to the total nannofossil carbonate. The discoaster contribution ranges from 10% to 40%, with a decreasing trend through the investigated interval. However, our estimates of total nannofossil carbonate from size-corrected abundance data are consistently 30-50% lower than estimates from grain-size measurement; this suggests that data based on mass estimates need to be interpreted with caution.

Table 1: Discharge, mass flux, maximum velocity and ice thickness of glaciers from Dronning Maud Land, Antarctica

Mass transport and mass flux values for the different types of glaciers in the Sør-Rondane are calculated from computer models, based upon gravity data and geodetic stake velocity measurements. The results are interpreted in the light of a general flow line analysis, glacial geological investigations and of the ablation terms of the mass balance for Dronning Maud Land and Antarctica.

Age models, accumulation rates, sand and carbonates at DSDP Leg 74 holes

Accumulation rates for the five sites drilled during Leg 74 of the Glomar Challenger are presented on a common timescale based on calibration of datum levels to paleomagnetic records in Leg 74 sediments for the Paleogene, and a new compilation by Berggren et al. (1985), for the Neogene, and using the seafloor-spreading magnetic anomaly timescale of Kent (1985). We present data on accumulation of total sediment, of foraminifers, of the noncarbonate portion, and of fish teeth that give a history of productivity, winnowing, carbonate dissolution, and nonbiogenic input to what was then a part of the South Atlantic at about 30 deg S.

Age models and foraminifer isotopes of four ODP Leg 202 sites

We present benthic isotope stratigraphies for Sites 1236, 1237, 1239, and 1241 that span the late Miocene-Pliocene time interval from 6 to 2.4 Ma. Orbitally tuned timescales were generated for Sites 1237 and 1241 by correlating the high-frequency variations in gamma ray attenuation density, percent sand of the carbonate fraction, and benthic d13C to variations in Earth's orbital parameters. The astronomical timescales for Sites 1237 and 1241 are in agreement with the one from Atlantic Site 925/926 (Ocean Drilling Program Leg 154). The comparison of benthic d18O and d13C records from the east Pacific sites and Atlantic Site 925/926 revealed a surprising clarity of the "41-k.y. signal" in d13C records and a remarkably good correlation between their d13C records. This suggests that the late Miocene-Pliocene amplitudes of obliquity-related d13C cycles reflect a magnitude of global response often larger than that provided by obliquity-related d18O cycles. At Site 1237, the orbitally derived ages of Pliocene magnetic reversal boundaries between the base of Réunion and the top of Thvera confirm astronomical datings of the generally accepted ATNTS2004 timescale, except for the top of Kaena and the base of Sidufjall. Our astronomical age for the top of Kaena is about one obliquity cycle older. The base of Sidufjall appears to be about one precession cycle younger. The age models of Sites 1236 and 1239 were established by correlating their benthic d18O and d13C records directly to the orbitally tuned isotope record of Site 1241.