arXiv subjects

B. Militzer

Publications and source records attributed to B. Militzer.

At least 19 recordsLinked to original sources

arXiv2023

Saturn's Interior After the Cassini Grand Finale

We present a review of Saturn's interior structure and thermal evolution, with a particular focus on work in the past 5 years. Data from the Cassini mission, including a precise determination of the gravity field from the Grand Finale orbits, and the still ongoing identification of ring wave features in Saturn's C-ring tied to seismic modes in the planet, have led to dramatic advances in our understanding of Saturn's structure. Models that match the gravity field suggest that differential rotation, as seen in the visible atmosphere, extends down to at least a depth of 10,000 km (1/6$^{\rm th}$ the planet's radius). At greater depths, a variety of different investigations all now point to a deep Saturn rotation rate of 10 hours and 33 minutes. There is very compelling evidence for a central heavy element concentration (``core''), that in most recent models is 12-20 Earth masses. Ring seismology strongly suggests that the core is not entirely compact, but is dilute (mixed in with the overlying H/He), and has a substantial radial extent, perhaps out to around one-half of the planet's radius. A wide range of thermal evolution scenarios can match the planet's current luminosity, with progress on better quantifying the helium rain scenario hampered by Saturn's poorly known atmospheric helium abundance. We discuss the relevance of magnetic field data on understanding the planet's current interior structure. We point towards additional future work that combines seismology and gravity within a framework that includes differential rotation, and the utility of a Saturn entry probe.

astro-ph.EP↗

arXiv2023

Jupiter's interior from Juno: Equation-of-state uncertainties and dilute core extent

The Juno mission has provided measurements of Jupiter s gravity field with an outstanding level of accuracy, leading to better constraints on the interior of the planet. Improving our knowledge of the internal structure of Jupiter is key to understanding its formation and evolution but is also important in the framework of exoplanet exploration. In this study, we investigated the differences between the state-of-the-art equations of state and their impact on the properties of interior models. Accounting for uncertainty on the hydrogen and helium equation of state, we assessed the span of the interior features of Jupiter. We carried out an extensive exploration of the parameter space and studied a wide range of interior models using Markov chain Monte Carlo (MCMC) simulations. To consider the uncertainty on the equation of state, we allowed for modifications of the equation of state in our calculations. Our models harbour a dilute core and indicate that Jupiter s internal entropy is higher than what is usually assumed from the Galileo probe measurements. We obtain solutions with extended dilute cores, but contrary to other recent interior models of Jupiter, we also obtain models with small dilute cores. The dilute cores in such solutions extend to 20% of Jupiter s mass, leading to better agreement with formation evolution models. We conclude that the equations of state used in Jupiter models have a crucial effect on the inferred structure and composition. Further explorations of the behaviour of hydrogen helium mixtures at the pressure and temperature conditions in Jupiter will help to constrain the interior of the planet, and therefore its origin.

astro-ph.EP↗

arXiv2022

Jupiter's inhomogeneous envelope

While Jupiter's massive gas envelope consists mainly of hydrogen and helium, the key to understanding Jupiter's formation and evolution lies in the distribution of the remaining (heavy) elements. Before the Juno mission, the lack of high-precision gravity harmonics precluded the use of statistical analyses in a robust determination of the heavy-elements distribution in Jupiter's envelope. In this paper, we assemble the most comprehensive and diverse collection of Jupiter interior models to date and use it to study the distribution of heavy elements in the planet's envelope. We apply a Bayesian statistical approach to our interior model calculations, reproducing the Juno gravitational and atmospheric measurements and constraints from the deep zonal flows. Our results show that the gravity constraints lead to a deep entropy of Jupiter corresponding to a 1 bar temperature 5-15 K higher than traditionally assumed. We also find that uncertainties in the equation of state are crucial when determining the amount of heavy elements in Jupiter's interior. Our models put an upper limit to the inner compact core of Jupiter of 7 Earth masses, independently on the structure model (with or without dilute core) and the equation of state considered. Furthermore, we robustly demonstrate that Jupiter's envelope is inhomogenous, with a heavy-element enrichment in the interior relative to the outer envelope. This implies that heavy element enrichment continued through the gas accretion phase, with important implications for the formation of giant planets in our solar system and beyond.

astro-ph.EP↗

arXiv2021

Reconciling ionization energies and band gaps of warm dense matter derived with ab initio simulations and average atom models

Average atom (AA) models allow one to efficiently compute electronic and optical properties of materials over a wide range of conditions and are often employed to interpret experimental data. However, at high pressure, predictions from AA models have been shown to disagree with results from ab initio computer simulations. Here we reconcile these deviations by developing an innovative type of AA model, AVION, that computes the electronic eigenstates with novel boundary conditions within the ion sphere. Bound and free states are derived consistently. We drop the common AA image that the free-particle spectrum starts at the potential threshold, which we found to be incompatible with ab initio calculations. We perform ab initio simulations of crystalline and liquid carbon and aluminum over a wide range of densities and show that the computed band structure is in very good agreement with predictions from AVION.

physics.plasm-ph↗

arXiv2019

Models of Saturn's Interior Constructed with Accelerated Concentric Maclaurin Spheroid Method

The Cassini spacecraft's Grand Finale orbits provided a unique opportunity to probe Saturn's gravity field and interior structure. Doppler measurements yielded unexpectedly large values for the gravity harmonics J_6, J_8, and J_10 that cannot be matched with planetary interior models that assume uniform rotation. Instead we present a suite of models that assume the planet's interior rotates on cylinders, which allows us to match all the observed even gravity harmonics. For every interior model, the gravity field is calculated self-consistently with high precision using the Concentric Maclaurin Spheroid (CMS) method. We present an acceleration technique for this method, which drastically reduces the computational cost, allows us to efficiently optimize model parameters, map out allowed parameter regions with Monte Carlo sampling, and increases the precision of the calculated J_2n gravity harmonics to match the error bars of the observations, which would be difficult without acceleration. Based on our models, Saturn is predicted to have a dense central core of 15-18 Earth masses and an additional 1.5-5 Earth masses of heavy elements in the envelope. Finally, we vary the rotation period in the planet's deep interior and determine the resulting oblateness, which we compare with the value from radio occultation measurements by the Voyager spacecraft. We predict a rotation period of 10:33:34 h +- 55s, which is in agreement with recent estimates derived from ring seismology.

astro-ph.EP↗

arXiv2017

Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core

The Juno spacecraft has measured Jupiter's low-order, even gravitational moments, $J_2$--$J_8$, to an unprecedented precision, providing important constraints on the density profile and core mass of the planet. Here we report on a selection of interior models based on ab initio computer simulations of hydrogen-helium mixtures. We demonstrate that a dilute core, expanded to a significant fraction of the planet's radius, is helpful in reconciling the calculated $J_n$ with Juno's observations. Although model predictions are strongly affected by the chosen equation of state, the prediction of an enrichment of $Z$ in the deep, metallic envelope over that in the shallow, molecular envelope holds. We estimate Jupiter's core to contain an 7--25 Earth mass of heavy elements. We discuss the current difficulties in reconciling measured $J_n$ with the equations of state, and with theory for formation and evolution of the planet.

astro-ph.EP↗

arXiv2017

First-Principles Simulations of Warm Dense Lithium Fluoride

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of LiF. Our simulations cover a wide density-temperature range of $2.08-15.70$~g$\,$cm$^{-3}$ and $10^4-10^9$~K. Since PIMC and DFT-MD accurately treat effects of atomic shell structure, we find a pronounced compression maximum and a shoulder on the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely-used EOS tables, such as SESAME, LEOS, and models. In addition, we compute pair-correlation functions that reveal an evolving plasma structure and ionization process that is driven by thermal and pressure ionization. Finally, we compute electronic density of states of liquid LiF from DFT-MD simulations and find that the electronic gap can remain open with increasing density and temperature to at least 15.7 g$~$cm$^{-3}$.

physics.plasm-ph↗

arXiv2016

First-Principles Prediction of the Softening of the Silicon Shock Hugoniot Curve

Shock compression of silicon (Si) under extremely high pressures (>100 Mbar) was investigated by using two first-principles methods of orbital-free molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures from the two methods agree very well, PIMC predicts a second compression maximum because of 1s electron ionization that is absent in OFMD calculations since Thomas-Fermi-based theories lack shell structure. The Kohn-Sham density functional theory is used to calculate the equation of state (EOS) of warm dense silicon for low-pressure loadings (P < 100 Mbar). Combining these first-principles EOS results, the principal shock Hugoniot curve of silicon for pressures varying from 1 Mbar to above 10 Gbar was derived. We find that silicon is 20% or more softer than what was predicted by widely-used EOS models. Existing high-pressure experimental data (P = 1 - 2 Mbar) seem to indicate this softening behavior of Si, which calls for future strong-shock experiments (P > 10 Mbar) to benchmark our results.

cond-mat.mtrl-sci↗

arXiv2016

A Preliminary Jupiter Model

In anticipation of new observational results for Jupiter's axial moment of inertia and gravitational zonal harmonic coefficients from the forthcoming Juno orbiter, we present a number of preliminary Jupiter interior models. We combine results from ab initio computer simulations of hydrogen-helium mixtures, including immiscibility calculations, with a new nonperturbative calculation of Jupiter's zonal harmonic coefficients, to derive a self-consistent model for the planet's external gravity and moment of inertia. We assume helium rain modified the interior temperature and composition profiles. Our calculation predicts zonal harmonic values to which measurements can be compared. Although some models fit the observed (pre-Juno) second- and fourth-order zonal harmonics to within their error bars, our preferred reference model predicts a fourth-order zonal harmonic whose absolute value lies above the pre-Juno error bars. This model has a dense core of about 12 Earth masses, and a hydrogen-helium-rich envelope with approximately 3 times solar metallicity.

astro-ph.EP↗

arXiv2016

First-Principles Equation of State and Electronic Properties of Warm Dense Oxygen

We perform all-electron path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of oxygen. Our simulations cover a wide density-temperature range of $1-100$~g$\,$cm$^{-3}$ and $10^4-10^9$~K. By combining results from PIMC and DFT-MD, we are able to compute pressures and internal energies from first-principles at all temperatures and provide a coherent equation of state. We compare our first-principles calculations with analytic equations of state, which tend to agree for temperatures above 8$\times$10$^6$~K. Pair-correlation functions and the electronic density of states reveal an evolving plasma structure and ionization process that is driven by temperature and density. As we increase the density at constant temperature, we find that the ionization fraction of the 1s state decreases while the other electronic states move towards the continuum. Finally, the computed shock Hugoniot curves show an increase in compression as the first and second shells are ionized.

physics.plasm-ph↗

arXiv2016

First-Principles Equation of State Calculations of Warm Dense Nitrogen

Using path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD) simulation methods, we compute a coherent equation of state (EOS) of nitrogen that spans the liquid, warm dense matter (WDM), and plasma regimes. Simulations cover a wide range of density-temperature space, $1.5-13.9$~g$~$cm$^{-3}$ and $10^3-10^9$~K. In the molecular dissociation regime, we extend the pressure-temperature phase diagram beyond previous studies, providing dissociation and Hugoniot curves in good agreement with experiments and previous DFT-MD work. Analysis of pair-correlation functions and the electronic density of states in the WDM regime reveals an evolving plasma structure and ionization process that is driven by temperature and pressure. Our Hugoniot curves display a sharp change in slope in the dissociation regime and feature two compression maxima as the K and L shells are ionized in the WDM regime, which have some significant differences from the predictions of plasma models.

physics.plasm-ph↗

arXiv2013

Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation

Using density functional molecular dynamics simulations, we determine the equation of state for hydrogen-helium mixtures spanning density-temperature conditions typical of giant planet interiors, ~0.2-9 g/cc and 1000-80000 K for a typical helium mass fraction of 0.245. In addition to computing internal energy and pressure, we determine the entropy using an ab initio thermodynamic integration technique. A comprehensive equation of state (EOS) table with 391 density-temperature points is constructed and the results are presented in form of two-dimensional free energy fit for interpolation. Deviations between our ab initio EOS and the semi-analytical EOS model by Saumon and Chabrier are analyzed in detail, and we use the results for initial revision of the inferred thermal state of giant planets with known values for mass and radius. Changes are most pronounced for planets in the Jupiter mass range and below. We present a revision to the mass-radius relationship which makes the hottest exoplanets increase in radius by ~0.2 Jupiter radii at fixed entropy and for masses greater than ~0.5 Jupiter mass. This change is large enough to have possible implications for some discrepant "inflated giant exoplanets".

astro-ph.EP↗

arXiv2011

FPEOS: A First-Principles Equation of State Table of Deuterium for Inertial Confinement Fusion Applications

Understanding and designing inertial confinement fusion (ICF) implosions through radiation-hydrodynamics simulations rely on the accurate knowledge of the equation of state (EOS) of the deuterium and tritium fuels. To minimize the drive energy for ignition, the imploding shell of DT fuel must be kept as cold as possible. Such low-adiabat ICF implosions can access to coupled and degenerate plasma conditions, in which the analytical or chemical EOS models become inaccurate. Using the path-integral Monte Carlo (PIMC) simulations we have derived a first-principles EOS (FPEOS) table of deuterium that covers typical ICF fuel conditions at densities ranging from 0.002 to 1596 g/cm3 and temperatures of 1.35 eV to 5.5 keV. We report the internal energy and the pressure, and discuss the structure of the plasma in terms of pair-correlation functions. When compared with the widely used SESAME table and the revised Kerley03 table, discrepancies in the internal energy and in the pressure are identified for moderately coupled and degenerate plasma conditions. In contrast to the SESAME table, the revised Kerley03 table is in better agreement with our FPEOS results over a wide range of densities and temperatures. Although subtle differences still exist for lower temperatures (T < 10 eV) and moderate densities (1 to 10 g/cc), hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table and the Kerley03 table have resulted in similar results for the peak density, areal density (ρR), and neutron yield, which are significantly different from the SESAME simulations.

cond-mat.mtrl-sci↗

arXiv2011

Bonding and Electronic Properties of Ice at High Pressure

The properties of water ice at megabar pressure are characterized with ab initio computer simulations. The focus lies on the metallic Cmcm phase and its insulating distorted analogue with Pnma symmetry. Both phases were recently predicted to occur at 15.5 and 12.5 Mbar respectively [Phys. Rev. Lett. 105 (2010) 195701]. The Fermi surface of the Cmcm phase is analyzed and possibility of Fermi nesting to occur is discussed. The Wannier orbital are computed for the Pnma structure and compared to ice X. While ice X shows typical sp3 hybridization, in the Pnma structure, the orbitals are deformed and no longer all aligned with the hydrogen bonds.

cond-mat.mtrl-sci↗

arXiv2010

Quantum Monte Carlo for minerals at high pressure: Phase stability, equations of state, and elasticity of silica

Silica is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. As the simplest silicates, understanding pure silica is a prerequisite to understanding the rocky part of the Earth, its majority. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals, but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrodinger's equation. Using ground state QMC plus phonons within the quasiharmonic approximation from density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth's core-mantle boundary. Our results provide the most well-constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the most dense alpha-PbO2 structure above the core-insulating D" layer, suggesting the absence of significant free silica in the bulk lower mantle, which has been assumed but never proven. We also find an accurate shear elastic constant and its geophysically important softening with pressure.

cond-mat.mtrl-sci↗

arXiv2010

Fundamental high pressure calibration from all-electron quantum Monte Carlo calculations

We develop an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and use it to construct a primary ultra-high pressure calibration based the equation of state of cubic boron nitride(c-BN). We compute the static contribution to the free energy with QMC, and obtain the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. Furthermore, we compute the anharmonic Raman frequency shift with QMC as a function of pressure and temperature, allowing optical pressure calibration in table-top experiments. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron methodology is generally applicable to first-row solids, and can be used to provide a new reference for ab initio calculations of solids and to benchmark pseudopotential accuracy.

cond-mat.mtrl-sci↗

arXiv2009

Computation of the High Temperature Coulomb Density Matrix in Periodic Boundary Conditions

The high temperature many-body density matrix is fundamental to path integral computation. The pair approximation, where the interaction part is written as a product of pair density matrices, is commonly used and is accurate to order tau squared, where tau is the step size in the imaginary time. Here we present a method for systems with Coulomb interactions in periodic boundary conditions that consistently treats the all interactions with the same level of accuracy. It shown that this leads to a more accurate high temperature solution of the Bloch equation. The method is applied to many-body simulation and tests for the isolated hydrogen atom and molecule are presented.

cond-mat.mtrl-sci↗

arXiv2009

Frontiers of the physics of dense plasmas and planetary interiors: experiments, theory, applications

Recent developments of dynamic x-ray characterization experiments of dense matter are reviewed, with particular emphasis on conditions relevant to interiors of terrestrial and gas giant planets. These studies include characterization of compressed states of matter in light elements by x-ray scattering and imaging of shocked iron by radiography. Several applications of this work are examined. These include the structure of massive "Super Earth" terrestrial planets around other stars, the 40 known extrasolar gas giants with measured masses and radii, and Jupiter itself, which serves as the benchmark for giant planets.

astro-ph.EP↗