A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes

We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star's photospheric composition. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius, (2) atmospheric model, (3) data uncertainties, (4) semi-major axes, (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes), and (6) prior distributions are varied. Our main conclusions are: [...]Comment: Astronomy & Astrophysics, 597, A37, 17 pages, 11 figure

Lunar Seismology: An Update on Interior Structure Models

An international team of researchers gathered, with the support of the Interna- tional Space Science Institute (ISSI), (1) to review seismological investigations of the lunar interior from the Apollo-era and up until the present and (2) to re-assess our level of knowl- edge and uncertainty on the interior structure of the Moon. A companion paper (Nunn et al. in Space Sci. Rev., submitted) reviews and discusses the Apollo lunar seismic data with the aim of creating a new reference seismic data set for future use by the community. In this study, we first review information pertinent to the interior of the Moon that has become available since the Apollo lunar landings, particularly in the past ten years, from orbiting spacecraft, continuing measurements, modeling studies, and laboratory experiments. Fol- lowing this, we discuss and compare a set of recent published models of the lunar interior, including a detailed review of attenuation and scattering properties of the Moon. Common features and discrepancies between models and moonquake locations provide a first esti- mate of the error bars on the various seismic parameters. Eventually, to assess the influence of model parameterisation and error propagation on inverted seismic velocity models, an inversion test is presented where three different parameterisations are considered. For this purpose, we employ the travel time data set gathered in our companion paper (Nunn et al. in Space Sci. Rev., submitted). The error bars of the inverted seismic velocity models demon- strate that the Apollo lunar seismic data mainly constrain the upper- and mid-mantle struc- ture to a depth of ∼1200 km. While variable, there is some indication for an upper mantle low-velocity zone (depth range 100–250 km), which is compatible with a temperature gradi- ◦ent around 1.7 C/km. This upper mantle thermal gradient could be related to the presence of the thermally anomalous region known as the Procellarum Kreep Terrane, which contains a large amount of heat producing elements

Seismic detection of the martian core by InSight

A plethora of geophysical, geo- chemical, and geodynamical observations indicate that the terrestrial planets have differentiated into silicate crusts and mantles that surround a dense core. The latter consists primarily of Fe and some lighter alloying elements (e.g., S, Si, C, O, and H) [1]¿. The Martian meteorites show evidence of chalcophile element depletion, suggesting that the otherwise Fe-Ni- rich core likely contains a sulfide component, which influences physical state

Seismic Constraints on the Thickness and Structure of the Martian Crust from InSight

NASA¿s InSight mission [1] has for the first time placed a very broad-band seismometer on the surface of Mars. The Seismic Experiment for Interior Structure (SEIS) [2] has been collecting continuous data since early February 2019. The main focus of InSight is to enhance our understanding of the internal structure and dynamics of Mars, which includes the goal to better constrain the crustal thickness of the planet [3]. Knowing the present-day crustal thickness of Mars has important implications for its thermal evolution [4] as well as for the partitioning of silicates and heat-producing elements between the different layers of Mars. Current estimates for the crustal thickness of Mars are based on modeling the relationship between topography and gravity [5,6], but these studies rely on different assumptions, e.g. on the density of the crust and upper mantle, or the bulk silicate composition of the planet and the crust. The resulting values for the average crustal thickness differ by more than 100%, from 30 km to more than 100 km [7]. New independent constraints from InSight will be based on seismically determining the crustal thickness at the landing site. This single firm measurement of crustal thickness at one point on the planet will allow to constrain both the average crustal thickness of Mars as well as thickness variations across the planet when combined with constraints from gravity and topography [8]. Here we describe the determination of the crustal structure and thickness at the InSight landing site based on seismic receiver functions for three marsquakes compared with autocorrelations of InSight data [9].We acknowledge NASA, CNES, partner agencies and institutions (UKSA, SSO,DLR, JPL, IPGP-CNRS, ETHZ, IC, MPS-MPG) and the operators of JPL, SISMOC, MSDS, IRIS-DMC and PDS for providing SEED SEIS data. InSight data is archived in the PDS, and a full list of archives in the Geosciences, Atmospheres, and Imaging nodes is at https://pds-geosciences.wustl.edu/missions/insight/. This work was partially carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. ©2021, California Institute of Technology. Government sponsorship acknowledge

Mercury's Interior Structure Constrained by Density and P-Wave Velocity Measurements of Liquid Fe-Si-C Alloys

peer reviewe

Seismic detection of the martian core

Clues to a planet's geologic history are contained in its interior structure, particularly its core. We detected reflections of seismic waves from the core-mantle boundary of Mars using InSight seismic data and inverted these together with geodetic data to constrain the radius of the liquid metal core to 1830 +/- 40 kilometers. The large core implies a martian mantle mineralogically similar to the terrestrial upper mantle and transition zone but differing from Earth by not having a bridgmanite-dominated lower mantle. We inferred a mean core density of 5.7 to 6.3 grams per cubic centimeter, which requires a substantial complement of light elements dissolved in the iron-nickel core. The seismic core shadow as seen from InSight's location covers half the surface of Mars, including the majority of potentially active regions-e.g., Tharsis-possibly limiting the number of detectable marsquakes.This is InSight contribution 200. We acknowledge NASA, CNES, and partner agencies and institutions (UKSA, SSO, ESA-PRODEX, DLR, JPL, IPGP-CNRS, ETHZ, IC, and MPS-MPG) for the development of SEIS. Numerical simulations were supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID s922 as well as HPC resources of CINES under the allocation A0090407341, made by GENCI. We thank B. Dintrans, director of CINES, for his efficient handling of our request for computational time. Figures were created using matplotlib (83), seismic data processing was done in ObsPy (84), and numerical evaluation was done in NumPy and SciPy (85, 86). Funding: S.C.S., A.K., D.G., J.C., A.C.D., G.Z., and N.D. acknowledge support from ETHZ through the ETH+ funding scheme (ETH+2 19-1: “Planet MARS”). S.C.S. acknowledges funding from ETH research grant ETH-10 17-3. W.B.B., A.G.M., M.P.P., and S.E.S. were supported by the NASA InSight mission and funds from the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). D.A. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement 724690). The French teams acknowledge support from CNES as well as Agence Nationale de la Recherche (ANR-14-CE36-0012-02 and ANR-19-CE31-0008-08). A.R. was financially supported by the Belgian PRODEX program managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office. M.S. wishes to thank SANIMS (RTI2018-095594-B-I00). M.v.D. received support from the ERC under the European Union’s Horizon 2020 program (grant no. 714069). D.S. and C.S. acknowledge funding from ETH research grant ETH-06 17-02. J.C.E.I. acknowledges support from NASA grant 80NSSC18K1633. N.S., D.K., Q.H., R.M., V.L., and A.G.M. acknowledge NASA grant 80NSSC18K1628 for support. V.L. acknowledges support from the Packard Foundation. W.T.P. and C.C. received funding from the UK Space Agency, grant ST/S001239/1. A.H. was funded by the UK Space Agency (grant ST/R002096/1). A.-C.P. acknowledges the financial support and endorsement from the DLR Management Board Young Research Group Leader Program and the Executive Board Member for Space Research and Technology. Author contributions: S.C.S., D.G., S.C., R.F.G., Q.H., D.K., V.L., M.S., N.S., D.S., É.S., C.S., and G.Z. analyzed the seismic data and made ScS arrival time picks. S.C.S., P.L., D.G., Z.X., C.C., and W.T.P. performed the statistical analysis of the observed signals. S.C.S., Q.H., N.S., R.M., and A.G.M. identified the arrivals as ScS waves based on interior models from A.K., H.S., and A.R. A.K., M.D., A.C.D., and H.S. performed the inversions. S.C.S., A.K., P.L., D.G., D.A., J.C.E.I., M.K., C.P., A.-C.P., A.R., T.G., and S.E.S. participated and contributed to the interpretation of the results. Review of the continuous data and detection of marsquakes was done by S.C.S., S.C., G.Z., C.C., N.D., J.C., M.v.D., T.K., M.P., and A.H. with operational support by É.B., C.P., and P.M.D. S.C.S. and A.K. wrote the central part of the paper with contributions from H.S., N.S., D.A., J.C.E.I., A.G.M., A.-C.P., A.R., J.C., and M.v.D. J.C.E.I., R.M., M.K., and V.L. reviewed the contributions to the supplementary materials. The InSight mission is managed by W.B.B., M.P.P., and S.E.S. The SEIS instrument development was led by P.L., D.G., W.T.P., and W.B.B. Supplementary section 1 was written by M.S., D.S., and É.S. with contributions from S.C.S., C.S., and Z.X. Supplementary section 2 was written by D.K. and V.L. with contributions from J.C.E.I. and N.S. Supplementary section 3 was written by M.S. and É.S. Supplementary section 4 was written by R.F.G. with contributions from M.D. Supplementary section 5 was written by Q.H. with contributions from N.S. Supplementary section 6 was written by S.C.S. with contributions from the authors of the other supplements. Supplementary section 7 was written by Z.X. and C.C. with contributions from P.L. and W.T.P. Supplementary section 8 was written by A.K., M.D., A.C.D., and H.S. Supplementary section 9 was written by M.D. Supplementary section 10 was written by A.C.D., A.K., and M.D. Supplementary section 11 was written by D.A. and A.R. with contributions from A.K. Competing interests: The authors declare that they have no competing interests. Data and materials availability: We thank the operators of JPL, SISMOC, MSDS, IRIS-DMC, and PDS for providing SEED SEIS data (87). Three hundred interior models derived in this study are available from MSDS (88)

The phase diagram of NiSi under the conditions of small planetary interiors

The phase diagram of NiSi has been determined using in situ synchrotron X-ray powder diffraction multi-anvil experiments to 19 GPa, with further preliminary results in the laser-heated diamond cell reported to 60 GPa. The low-pressure MnP-structured phase transforms to two different high-pressure phases depending on the temperature: the ε-FeSi structure is stable at temperatures above ∼1100 K and a previously reported distorted-CuTi structure (with Pmmn symmetry) is stable at lower temperature. The invariant point is located at 12.8 ± 0.2 GPa and 1100 ± 20 K. At higher pressures, ε -FeSi-structured NiSi transforms to the CsCl structure with CsCl-NiSi as the liquidus phase above 30 GPa. The Clapeyron slope of this transition is -67 MPa/K. The phase boundary between the ε -FeSi and Pmmn structured phases is nearly pressure independent implying there will be a second sub-solidus invariant point between CsCl, ε -FeSi and Pmmn structures at higher pressure than attained in this study. In addition to these stable phases, the MnP structure was observed to spontaneously transform at room temperature to a new orthorhombic structure (also with Pnma symmetry) which had been detailed in previous ab initio simulations. This new phase of NiSi is shown here to be metastable

The interior of Mars as seen by InSight (Invited)

InSight is the first planetary mission dedicated to exploring the whole interior of a planet using geophysical methods, specifically seismology and geodesy. To this end, we observed seismic waves of distant marsquakes and inverted for interior models using differential travel times of phases reflected at the surface (PP, SS...) or the core mantle-boundary (ScS), as well as those converted at crustal interfaces. Compared to previous orbital observations1-3, the seismic data added decisive new insights with consequences for the formation of Mars: The global average crustal thickness of 24-75 km is at the low end of pre-mission estimates5. Together with the the thick lithosphere of 450-600 km5, this requires an enrichment of heat-producing elements in the crust by a factor of 13-20, compared to the primitive mantle. The iron-rich liquid core is 1790-1870 km in radius6, which rules out the existence of an insulating bridgmanite-dominated lower mantle on Mars. The large, and therefore low-density core needs a high amount of light elements. Given the geochemical boundary conditions, Sulfur alone cannot explain the estimated density of ~6 g/cm3 and volatile elements, such as oxygen, carbon or hydrogen are needed in significant amounts. This observation is difficult to reconcile with classical models of late formation from the same material as Earth. We also give an overview of open questions after three years of InSight operation on the surface of Mars, such as the potential existence of an inner core or compositional layers above the CM

PADME (Phobos and Deimos and Mars Environment): A Proposed NASA Discovery Mission to Investigate the Two Moons of Mars

PADME is a proposed NASA Discovery mission to investigate the origin of two remarkable and enigmatic small bodies, Phobos and Deimos, the two moons of Mars

An Autonomous Lunar Geophysical Experiment Package (ALGEP) for future space missions

Geophysical observations will provide key information about the inner structure of the planets and satellites and understanding the internal structure is a strong constraint on the bulk composition and thermal evolution of these bodies. Thus, geophysical observations are a key to uncovering the origin and evolution of the Moon. In this article, we propose the development of an autonomous lunar geophysical experiment package, composed of a suite of instruments and a central station with standardized interface, which can be installed on various future lunar missions. By fixing the interface between instruments and the central station, it would be possible to easily configure an appropriate experiment package for different missions. We describe here a series of geophysical instruments that may be included as part of the geophysical package: a seismometer, a magnetometer, a heat flow probe, and a laser reflector. These instruments will provide mechanical, thermal, and geodetic parameters of the Moon that are strongly related to the internal structure. We discuss the functionality required for future geophysical observations of the Moon, including the development of the central station that will be used commonly by different payloads