scholarly journals Connecting gravity field, moment of inertia, and core properties in Jupiter through empirical structure models

2021 ◽  
Author(s):  
Benno A. Neuenschwander ◽  
Ravit Helled ◽  
Naor Movshovitz ◽  
Jonathan J. Fortney
Keyword(s):  
Equations Of State ◽  
Moment Of Inertia ◽  
Independent Measurement ◽  
Core Mass ◽  
Density Profiles ◽  
Formation And Evolution ◽  
Standard Models ◽  
Fuzzy Core ◽  
Similar Density ◽  
Better Than

<p>Constraining Jupiter's internal structure is crucial for understanding its formation and evolution history. Recent interior models of Jupiter that fit Juno's measured gravitational field suggest an inhomogeneous interior and potentially the existence of a diluted core. These models, however, strongly depend on the model assumptions and the equations of state used. A complementary modelling approach is to use empirical structure models. <br>These can later be used to reveal new insights on the planetary interior and be compared to standard models. <br>Here we present empirical structure models of Jupiter where the density profile is constructed by piecewise-polytropic equations. With these models we investigate the relation between the normalized moment of inertia (MoI) and the gravitational moments J<sub>2</sub> and J<sub>4</sub>. <br>Given that only the first few gravitational moments of Jupiter are measured with high precision, we show that an accurate and independent measurement of the MoI value could be used to further constrain Jupiter's interior. An independent measurement of the MoI with an accuracy better than ~0.1% could constrain Jupiter's core region and density discontinuities in its envelope. <br>We find that models with a density discontinuity at ~1 Mbar, as would produce a presumed hydrogen-helium separation, correspond to a fuzzy core in Jupiter. <br>We next test the appropriateness of using polytropes, by comparing them with empirical models based on polynomials. <br>We conclude that both representations result in similar density profiles and ranges of values for quantities like core mass and MoI.</p>

scholarly journals Empirical models of Jupiter’s interior from Juno data

2018 ◽  
Vol 613 ◽  
pp. A32 ◽  
Author(s):  
Dongdong Ni
Keyword(s):  
Gravity Field ◽  
Equations Of State ◽  
Moment Of Inertia ◽  
Radial Density ◽  
Love Number ◽  
Core Mass ◽  
The Core ◽  
Theoretical Approaches ◽  
Radial Density Profile ◽  
History Of

Context. The Juno spacecraft has significantly improved the accuracy of gravitational harmonic coefficients J4, J6 and J8 during its first two perijoves. However, there are still differences in the interior model predictions of core mass and envelope metallicity because of the uncertainties in the hydrogen-helium equations of state. New theoretical approaches or observational data are hence required in order to further constrain the interior models of Jupiter. A well constrained interior model of Jupiter is helpful for understanding not only the dynamic flows in the interior, but also the formation history of giant planets. Aims. We present the radial density profiles of Jupiter fitted to the Juno gravity field observations. Also, we aim to investigate our ability to constrain the core properties of Jupiter using its moment of inertia and tidal Love number k2 which could be accessible by the Juno spacecraft. Methods. In this work, the radial density profile was constrained by the Juno gravity field data within the empirical two-layer model in which the equations of state are not needed as an input model parameter. Different two-layer models are constructed in terms of core properties. The dependence of the calculated moment of inertia and tidal Love number k2 on the core properties was investigated in order to discern their abilities to further constrain the internal structure of Jupiter. Results. The calculated normalized moment of inertia (NMOI) ranges from 0.2749 to 0.2762, in reasonable agreement with the other predictions. There is a good correlation between the NMOI value and the core properties including masses and radii. Therefore, measurements of NMOI by Juno can be used to constrain both the core mass and size of Jupiter’s two-layer interior models. For the tidal Love number k2, the degeneracy of k2 is found and analyzed within the two-layer interior model. In spite of this, measurements of k2 can still be used to further constrain the core mass and size of Jupiter’s two-layer interior models.

scholarly journals Simulations of the IMF in Clusters

2010 ◽  
Vol 6 (S270) ◽  
pp. 151-158
Author(s):  
Ralph E. Pudritz
Keyword(s):  
Equations Of State ◽  
Stellar Dynamics ◽  
Mass Function ◽  
Initial Mass Function ◽  
Core Mass ◽  
Numerical Work ◽  
Computational Approaches ◽  
The Core ◽  
The Imf

AbstractWe review computational approaches to understanding the origin of the Initial Mass Function (IMF) during the formation of star clusters. We examine the role of turbulence, gravity and accretion, equations of state, and magnetic fields in producing the distribution of core masses - the Core Mass Function (CMF). Observations show that the CMF is similar in form to the IMF. We focus on feedback processes such as stellar dynamics, radiation, and outflows can reduce the accreted mass to give rise to the IMF. Numerical work suggests that filamentary accretion may play a key role in the origin of the IMF.

scholarly journals Astrometric Tests of Galactic Evolution

1995 ◽  
Vol 166 ◽  
pp. 251-258
Author(s):  
Gerard Gilmore
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Galactic Evolution ◽  
Critical Test ◽  
Current Standard ◽  
High Quality ◽  
Stellar Velocity ◽  
Formation And Evolution ◽  
Standard Models

There are many fundamental aspects of Galactic structure and evolution which can be studied best or exclusively with high quality three dimensional kinematics. Amongst these we note as examples determination of the orientation of the stellar velocity ellipsoid, and the detection of structure in velocity-position phase space. The first of these is the primary limitation at present to reliable and accurate measurement of the Galactic gravitational potential. The second is a critical test of current standard models of Galactic formation and evolution.

Mixing-rules calculations and AAMD simulations for EOSs of deuterium–xenon mixtures

2018 ◽  
Vol 96 (12) ◽  
pp. 1404-1408
Author(s):  
Zhencen He ◽  
Zhimin Hu ◽  
Yong Hou ◽  
Jiamin Yang ◽  
Jianmin Yuan ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Equations Of State ◽  
Mixing Rules ◽  
Self Consistency ◽  
Better Than ◽  
The Ideal

We present the calculated equations of state (EOSs) for deuterium–xenon mixtures using mixing rules. Three mixing rules, which are the ideal rule, volume rule, and pressure rule, were used for the calculations, and the thermodynamic self-consistency was evaluated. The volume rule predicts the pressures of mixtures rather accurately, but it fails in the predictions of energies. The pressure ionization has an impact on energy and pressure. Furthermore, the calculated results of the mixing rules were compared with average-atom molecular dynamics (AAMD) simulations, and the pressure rule performs better than the ideal and volume rules over the investigated range.

scholarly journals Revisited mass-radius relations for exoplanets below 120 M⊕

2020 ◽  
Vol 634 ◽  
pp. A43 ◽  
Author(s):  
J. F. Otegi ◽  
F. Bouchy ◽  
R. Helled
Keyword(s):  
Pure Water ◽  
Mass Range ◽  
Planetary Formation ◽  
Core Mass ◽  
Transiting Planets ◽  
Small Density ◽  
Different Populations ◽  
Formation And Evolution ◽  
The Masses ◽  
Two Populations

The masses and radii of exoplanets are fundamental quantities needed for their characterisation. Studying the different populations of exoplanets is important for understanding the demographics of the different planetary types, which can then be linked to planetary formation and evolution. We present an updated exoplanet catalogue based on reliable, robust, and, as much as possible accurate mass and radius measurements of transiting planets up to 120 M⊕. The resulting mass-radius (M-R) diagram shows two distinct populations, corresponding to rocky and volatile-rich exoplanets which overlap in both mass and radius. The rocky exoplanet population shows a relatively small density variability and ends at mass of ~25 M⊕, possibly indicating the maximum core mass that can be formed. We use the composition line of pure water to separate the two populations, and infer two new empirical M-R relations based on this data: M = (0.9 ± 0.06) R(3.45±0.12) for the rocky population, and M = (1.74 ± 0.38) R(1.58±0.10) for the volatile-rich population. While our results for the two regimes are in agreement with previous studies, the new M-R relations better match the population in the transition region from rocky to volatile-rich exoplanets, which correspond to a mass range of 5–25 M⊕, and a radius range of 2–3 R⊕.

scholarly journals Critical Angle Refractometry for Lossy Media with a Priori Known Extinction Coefficient

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 569-578
Author(s):  
Spyridon Koutsoumpos ◽  
Panagiotis Giannios ◽  
Konstantinos Moutzouris
Keyword(s):  
Extinction Coefficient ◽  
Critical Angle ◽  
Incidence Angle ◽  
A Priori ◽  
Sufficient Accuracy ◽  
Independent Measurement ◽  
Reflectance Measurement ◽  
Lossy Media ◽  
Established Technique ◽  
Better Than

Critical angle refractometry is an established technique for determining the refractive index of liquids and solids. For transparent samples, the critical angle refractometry precision is limited by incidence angle resolution. For lossy samples, the precision is also affected by reflectance measurement error. In the present study, it is demonstarted that reflectance error can be practically eliminated, provided that the sample’s extinction coefficient is a priori known with sufficient accuracy (typically, better than 5%) through an independent measurement. Then, critical angle refractometry can be as precise with lossy media as with transparent ones.

NeQuick2 and IRI2012 models applied to mid and high latitudes, and the Antarctic ionosphere

2017 ◽  
Vol 29 (3) ◽  
pp. 265-276 ◽  
Author(s):  
M. Pietrella ◽  
B. Nava ◽  
M. Pezzopane ◽  
Y. Migoya Orue ◽  
A. Ippolito ◽  
...  
Keyword(s):  
Electron Density ◽  
Activity Index ◽  
High Latitudes ◽  
Limited Sample ◽  
Density Profiles ◽  
Solar Activity Index ◽  
Macquarie Island ◽  
Electron Density Profiles ◽  
The Antarctic ◽  
Better Than

AbstractWithin the framework of the AUSPICIO (AUtomatic Scaling of Polar Ionograms and Co-operative Ionospheric Observations) project, a limited sample of ionograms recorded mostly in 2001 and 2009, and to a lesser extent in 2006–07 and 2012–15, at the ionospheric observatories of Hobart and Macquarie Island (mid-latitude), Comandante Ferraz and Livingstone Island (high latitude), and Casey, Mawson, Davis and Scott Base (inside the Antarctic Polar Circle (APC)) were considered to study the capability of the NeQuick2 and IRI2012 models for predicting the behaviour of the ionosphere at mid- and high latitudes and over the Antarctic area. The applicability of NeQuick2 and IRI2012 was evaluated as i) climatological models taking as input the F10.7 solar activity index and ii) assimilative models ingesting the foF2 and hmF2 measurements obtained from the electron density profiles provided by the Adaptive Ionospheric Profiler (AIP). The statistical analysis results reveal that the best description of the ionosphere’s electron density is achieved when the AIP measurements are ingested into the NeQuick2 and IRI2012 models. Moreover, NeQuick2 performance is far better than IRI2012 performance outside the APC. Conversely, the IRI2012 model performs better than the NeQuick2 model inside the APC.

Mass, radius, and moment of inertia for neutron stars

1991 ◽  
Vol 69 (1) ◽  
pp. 8-15 ◽  
Author(s):  
Tommy Øvergård ◽  
Erlend Østgaard
Keyword(s):  
Total Mass ◽  
Nuclear Energy ◽  
Equations Of State ◽  
Mass Density ◽  
Moment Of Inertia ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Mass Energy ◽  
Energy Calculations ◽  
Models Comparison

Using results from energy calculations of "neutron matter," we construct various equations of state. From these equations of state, together with the Tolman–Oppenheimer–Volkoff equations derived from Einstein's general theory of relativity, we calculate quantities such as pressure, mass density, mass energy density, total mass, radius, and moment of inertia for configurations described in the models. Comparison is made with calculations based on other nuclear potentials and nuclear energy calculations, and our results are in reasonable agreement with results from observational data.

scholarly journals The Unpredictability of Floods, Erosion, and Channel Migration

Eos ◽  
2019 ◽  
Vol 100 ◽  
Author(s):  
Aaron Sidder
Keyword(s):  
Channel Formation ◽  
Channel Migration ◽  
Stream Channel ◽  
Standard Models ◽  
Better Than

A new algorithm incorporates randomness into stream channel formation and suggests the approach represents regions with variable flood magnitudes better than standard models.

scholarly journals Understanding Saturn’s interior from the Cassini Grand Finale gravity measurements

2020 ◽  
Vol 639 ◽  
pp. A10 ◽  
Author(s):  
Dongdong Ni
Keyword(s):  
Rotation Rate ◽  
Mass Fraction ◽  
Heavy Element ◽  
Equations Of State ◽  
Layer Structure ◽  
Element Abundance ◽  
Structure Model ◽  
Core Mass ◽  
Induced Gravity ◽  
Gravity Measurements

Context. Measurements of Saturn’s gravity field by Cassini Grand Finale have been acquired with high precision. It has been demonstrated that the even gravitational harmonics J6–J10 have larger absolute values than the predictions by typical rigid-body interior models. A four-layer structure model, proposed to interpret Juno’s gravity measurements for Jupiter, has been applied to Saturn, but great attention was paid to the depth of zonal flows in order to interpret the large absolute values of J6–J10. Aims. We aim to understand the internal structure and interior composition of Saturn with a similar model for Jupiter. The additional uncertainties in Saturn’s structure and composition are investigated in detail, such as rotation periods, atmospheric helium mass fractions, and flow-induced gravity corrections. Also, we investigate the effect of equations of state for hydrogen and helium on the predictions of the core mass and heavy element abundance. Methods. In the four-layer structure model, we adjusted the heavy element abundances in the outer two envelopes and the mass of the compact core in order to reproduce Saturn’s equatorial radius as well as the Cassini Grand Finale gravity measurements corrected by the flow-induced gravity signals. Different four-layer interior models are specified in terms of the rotation period, the atmospheric helium mass fraction, and the flow-induced gravity corrections. Two different ab initio equations of state for hydrogen and helium were used in interior structure calculations. Optimized calculations were then performed to explore Saturn’s internal structure and composition. Results. It is found that the absolute values of J6–J10 tend to increase with increasing deep rotation rate and depend on the equations of state adopted in interior calculations. Saturn’s deep rotation rate and atmospheric helium mass fraction are important to determine the distribution of helium and heavy elements in the outer envelopes. We also show that the core mass and heavy element abundance in Saturn are dependent upon the deep rotation rate, the atmospheric helium mass fraction, the flow-induced gravity corrections, and the equations of state for hydrogen and helium.

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