Corrected kriging update formulae for batch-sequential data assimilation

Recently, a lot of effort has been spent in the efficient computation of kriging predictors when observations are assimilated sequentially. In particular, kriging update formulae enabling significant computational savings were derived. Taking advantage of the previous kriging mean and variance computations helps avoiding a costly matrix inversion when adding one observation to the TeX already available ones. In addition to traditional update formulae taking into account a single new observation, Emery (2009) proposed formulae for the batch-sequential case, i.e. when TeX new observations are simultaneously assimilated. However, the kriging variance and covariance formulae given in Emery (2009) for the batch-sequential case are not correct. In this paper, we fix this issue and establish correct expressions for updated kriging variances and covariances when assimilating observations in parallel. An application in sequential conditional simulation finally shows that coupling update and residual substitution approaches may enable significant speed-ups.

Modeling the heterogeneous ice and gas coma of Comet 103P/Hartley 2

The spectacular images of Comet 103P/Hartley 2 recorded by the Medium Resolution Instrument (MRI) and High Resolution Instrument (HRI) on board of the Extrasolar Planet Observation and Deep Impact Extended Investigation (EPOXI) spacecraft, as the Deep Impact extended mission, revealed that its bi-lobed very active nucleus outgasses volatiles heterogeneously. Indeed, CO2 is the primary driver of activity by dragging out chunks of pure ice out of the nucleus from the sub-solar lobe that appear to be the main source of water in Hartley 2's coma by sublimating slowly as they go away from the nucleus. However, water vapor is released by direct sublimation of the nucleus at the waist without any significant amount of either CO2 or icy grains. The coma structure for a comet with such areas of diverse chemistry differs from the usual models where gases are produced in a homogeneous way from the surface. We use the fully kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J. 685, 659-677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J. 732, 104-120) applied to Comet 103P/Hartley 2 including sublimating icy grains to reproduce the observations made by EPOXI and ground-based measurements. A realistic bi-lobed nucleus with a succession of active areas with different chemistry was included in the model enabling us to study in details the coma of Hartley 2. The different gas production rates from each area were found by fitting the spectra computed using a line-by-line non-LTE radiative transfer model to the HRI observations. The presence of icy grains with long lifetimes, which are pushed anti-sunward by radiation pressure, explains the observed OH asymmetry with enhancement on the night side of the coma.

Precise Orbit Determination of Low Earth Satellites at AIUB using GPS and SLR data

An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning Sys- tem (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Insti- tute of the University of Bern (AIUB) LEO precise or- bit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numeri- cal integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to effi- ciently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circula- tion Explorer (GOCE).

Theoretical models of planetary system formation: mass vs. semi-major axis

Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims: In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods: We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results: We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ~5 M⊕, simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.

Core formation and mantle differentiation on Mars

Geochemical investigation of Martian meteorites (SNC meteorites) yields important constraints on the chemical and geodynamical evolution of Mars. These samples may not be representative of the whole of Mars; however, they provide constraints on the early differentiation processes on Mars. The bulk composition of Martian samples implies the presence of a metallic core that formed concurrently as the planet accreted. The strong depletion of highly siderophile elements in the Martian mantle is only possible if Mars had a large scale magma ocean early in its history allowing efficient separation of a metallic melt from molten silicate. The solidification of the magma ocean created chemical heterogeneities whose ancient origin is manifested in the heterogeneous 142Nd and 182W abundances observed in different meteorite groups derived from Mars. The isotope anomalies measured in SNC meteorites imply major chemical fractionation within the Martian mantle during the life time of the short-lived isotopes 146Sm and 182Hf. The Hf-W data are consistent with very rapid accretion of Mars within a few million years or, alternatively, a more protracted accretion history involving several large impacts and incomplete metal-silicate equilibration during core formation. In contrast to Earth early-formed chemical heterogeneities are still preserved on Mars, albeit slightly modified by mixing processes. The preservation of such ancient chemical differences is only possible if Mars did not undergo efficient whole mantle convection or vigorous plate tectonic style processes after the first few tens of millions of years of its history.

The Science of Exoplanets and Their Systems

A scientific forum on “The Future Science of Exoplanets and Their Systems,” sponsored by Europlanet* and the International Space Science Institute (ISSI)† and co-organized by the Center for Space and Habitability (CSH)‡ of the University of Bern, was held during December 5 and 6, 2012, in Bern, Switzerland. It gathered 24 well-known specialists in exoplanetary, Solar System, and stellar science to discuss the future of the fast-expanding field of exoplanetary research, which now has nearly 1000 objects to analyze and compare and will develop even more quickly over the coming years. The forum discussions included a review of current observational knowledge, efforts for exoplanetary atmosphere characterization and their formation, water formation, atmospheric evolution, habitability aspects, and our understanding of how exoplanets interact with their stellar and galactic environment throughout their history. Several important and timely research areas of focus for further research efforts in the field were identified by the forum participants. These scientific topics are related to the origin and formation of water and its delivery to planetary bodies and the role of the disk in relation to planet formation, including constraints from observations as well as star-planet interaction processes and their consequences for atmosphere-magnetosphere environments, evolution, and habitability. The relevance of these research areas is outlined in this report, and possible themes for future ISSI workshops are identified that may be proposed by the international research community over the coming 2–3 years.

REE and Hf distribution among mineral phases in the CV-CK clan : a way to explain present-day Hf isotopic variations in chondrites

Chondrites are among the most primitive objects in the Solar System and constitute the main building blocks of telluric planets. Among the radiochronometers currently used for dating geological events, Sm–Nd and Lu–Hf are both composed of refractory, lithophile element. They are thought to behave similarly as the parent elements (Sm and Lu) are generally less incompatible than the daughter elements (Nd and Hf) during geological processes. As such, their respective average isotopic compositions for the solar system should be well defined by the average of chondrites, called Chondritic Uniform Reservoir (CHUR). However, while the Sm–Nd isotopic system shows an actual spread of less than 4% in the average chondritic record, the Lu–Hf system shows a larger variation range of 28% [Bouvier A., Vervoort J. D. and Patchett P. J. (2008) The Lu–Hf and Sm–Nd isotopic composition of CHUR: Constraints from unequilibrated chondrites and implications for the bulk composition of terrestrial planets. Earth Planet. Sci. Lett.273, 48–57]. To better understand the contrast between Sm–Nd and Lu–Hf systems, the REE and Hf distribution among mineral phases during metamorphism of Karoonda (CK) and Vigarano-type (CV) carbonaceous chondrites has been examined. Mineral modes were determined from elemental mapping on a set of five CK chondrites (from types 3–6) and one CV3 chondrite. Trace-element patterns are obtained for the first time in all the chondrite-forming minerals of a given class (CK chondrites) as well as one CV3 sample. This study reveals that REE are distributed among both phosphates and silicates. Only 30–50% of Sm and Nd are stored in phosphates (at least in chondrites types 3–5); as such, they are not mobilized during early stages of metamorphism. The remaining fraction of Sm and Nd is distributed among the same mineral phases; these elements are therefore not decoupled during metamorphism. Of the whole-rock total of Lu, the fraction held in phosphate decreases significantly as the degree of metamorphism increases (30% for types 3 and 4, less than 5% in type 6). In contrast to Lu, Hf is mainly hosted by silicates with little contribution from phosphates throughout the CK metamorphic sequence. A significant part of Sm and Nd are stored in phosphates in types 3–5, and these elements behave similarly during CK chondrite metamorphism. That explains the robustness of the Sm/Nd ratios in chondrites through metamorphism, and the slight discrepancies observed in the present-day isotopic Nd values in chondrites. On the contrary, Lu and Hf are borne by several different minerals and consequently they are redistributed during metamorphism–induced recrystallization. The Lu/Hf ratios are therefore significantly disturbed during chondrites metamorphism, leading to the high discrepancies observed in present-day Hf isotopic values in chondrites.