scholarly journals Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

2021 ◽  
Vol 2 (6) ◽  
pp. 241
Author(s):  
N. Nettelmann ◽  
N. Movshovitz ◽  
D. Ni ◽  
J. J. Fortney ◽  
E. Galanti ◽  
...  
Keyword(s):  
Gravity Field ◽  
Heavy Element ◽  
Fast Method ◽  
Wind Speeds ◽  
Deep Interior ◽  
Uncertainty Space ◽  
Cassini Mission ◽  
Classical Models ◽  
Seventh Order ◽  
Juno Mission

Abstract Interior modeling of Jupiter and Saturn has advanced to a state where thousands of models are generated that cover the uncertainty space of many parameters. This approach demands a fast method of computing their gravity field and shape. Moreover, the Cassini mission at Saturn and the ongoing Juno mission delivered gravitational harmonics up to J 12. Here we report the expansion of the theory of figures, which is a fast method for gravity field and shape computation, to the seventh order (ToF7), which allows for computation of up to J 14. We apply three different codes to compare the accuracy using polytropic models. We apply ToF7 to Jupiter and Saturn interior models in conjunction with CMS-19 H/He equation of state. For Jupiter, we find that J 6 is best matched by a transition from an He-depleted to He-enriched envelope at 2–2.5 Mbar. However, the atmospheric metallicity reaches 1 × solar only if the adiabat is perturbed toward lower densities, or if the surface temperature is enhanced by ∼14 K from the Galileo value. Our Saturn models imply a largely homogeneous-in-Z envelope at 1.5–4 × solar atop a small core. Perturbing the adiabat yields metallicity profiles with extended, heavy-element-enriched deep interior (diffuse core) out to 0.4 R Sat, as for Jupiter. Classical models with compact, dilute, or no core are possible as long as the deep interior is enriched in heavy elements. Including a thermal wind fitted to the observed wind speeds, representative Jupiter and Saturn models are consistent with all observed J n values.

Jupiter's Gravity Field Halfway Through the Juno Mission

2020 ◽  
Vol 47 (4) ◽  
Author(s):  
D. Durante ◽  
M. Parisi ◽  
D. Serra ◽  
M. Zannoni ◽  
V. Notaro ◽  
...  
Keyword(s):  
Gravity Field ◽  
Juno Mission

The Gravity Field and Interior Structure of Enceladus

Science ◽  
2014 ◽  
Vol 344 (6179) ◽  
pp. 78-80 ◽  
Author(s):  
L. Iess ◽  
D. J. Stevenson ◽  
M. Parisi ◽  
D. Hemingway ◽  
R. A. Jacobson ◽  
...  
Keyword(s):  
Gravity Field ◽  
Polar Region ◽  
Hydrostatic Equilibrium ◽  
The Body ◽  
Interior Structure ◽  
Negative Mass ◽  
Cassini Mission ◽  
Doppler Data ◽  
The Moment ◽  
South Polar

The small and active Saturnian moon Enceladus is one of the primary targets of the Cassini mission. We determined the quadrupole gravity field of Enceladus and its hemispherical asymmetry using Doppler data from three spacecraft flybys. Our results indicate the presence of a negative mass anomaly in the south-polar region, largely compensated by a positive subsurface anomaly compatible with the presence of a regional subsurface sea at depths of 30 to 40 kilometers and extending up to south latitudes of about 50°. The estimated values for the largest quadrupole harmonic coefficients (106J2= 5435.2 ± 34.9, 106C22= 1549.8 ± 15.6, 1σ) and their ratio (J2/C22= 3.51 ± 0.05) indicate that the body deviates mildly from hydrostatic equilibrium. The moment of inertia is around 0.335MR2, whereMis the mass andRis the radius, suggesting a differentiated body with a low-density core.

scholarly journals Exploration of the structure of giant planets with fast calculations and a bayesian approach

2021 ◽  
Author(s):  
Saburo Howard ◽  
Tristan Guillot ◽  
Michaël Bazot ◽  
Yamila Miguel
Keyword(s):  
Gravity Field ◽  
Internal Structure ◽  
Bayesian Approach ◽  
Equations Of State ◽  
Giant Planets ◽  
Heavy Elements ◽  
Fast Method ◽  
Metallic Hydrogen ◽  
Chemical Abundances ◽  
Wide Range

<p><strong>Abstract</strong></p> <p>The Juno spacecraft is providing measurements of Jupiter's gravity field with an outstanding level of accuracy [3], leading to better constraints on the interior of Jupiter. Improving our knowledge of the internal structure of Jupiter is key, to understand the formation and the evolution of the planet [5,6] but also in the framework of exoplanets exploration. Hence, developing interiors models of Jupiter which are consistent with the observations is essential.</p> <p>Models of giant planets' internal structure are built with the code CEPAM [2] to compute the gravitational moments <em>J<sub>2n</sub></em> [1] and compare them to the observational values. As the numerical calculation of the gravitational moments is crucial, we are here using a fast method based on a 4th order development of the Theory of Figures, coupled with the more precise CMS (Concentric MacLaurin Spheroid) method. This allows us to obtain reliable values of <em>J<sub>2n</sub></em> in a reasonable amount of time.</p> <p>MCMC (Markov chain Monte Carlo) simulations are then run to study a wide range of interior models, using the above way to compute the gravitational moments. This bayesian approach leads to a broad investigation of the parameters range such as the chemical abundances, the 1 bar temperature or the transition pressure between the molecular hydrogen and metallic hydrogen layers.</p> <p>Important questions remain to be clarified like the distribution and amount of the heavy elements inside giant planets, following the hypothesis of a gradual distribution of the heavy elements up to a certain fraction of Jupiter's radius [7]. Throughout this talk, I will pay particular attention on the equations of state used in our models [4]. Indeed, giant planets' internal structure seems strongly linked to the physical properties of its components and it is critical to assess how sensitive to the equations of state our models are.</p> <p><strong>References</strong></p> <p>[1] Guillot, T., Miguel, Y. et al.: A suppression of differential rotation in Jupiter's deep interior, Nature, Vol 555, pp. 227-230, (2018).</p> <p>[2] Guillot, T. and Morel, P.: CEPAM: a code for modeling the interiors of giant planets, Astronomy and Astrophysics Supplement Series 109, 109-123 (1995)</p> <p>[3] Iess, L. et al.: Measurement of Jupiter's asymmetric gravity field, Nature, Vol 555, pp. 220-222, (2018).</p> <p>[4] Miguel, Y., Guillot, T. et al.: Jupiter internal structure: the effect of different equations of state. Astron. Astrophys. 596, A114 (2016)</p> <p>[5] Vazan, A., Helled, R. and Guillot, T.: Jupiter's evolution with primordial composition gradients. Astron. Astrophys. 610, L14 (2018).</p> <p>[6] Venturini, J., Helled, R.: Jupiter's heavy-element enrichment expected from formation models. Astron. Astrophys. 634, A31 (2020).</p> <p>[7] Wahl, S. M. et al.: Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core, Geophys. Res. Lett. Vol 44, pp. 4649-4659, (2017).</p>

Interpretation of lunar potential fields

1977 ◽  
Vol 285 (1327) ◽  
pp. 507-516 ◽  
Keyword(s):  
Magnetic Field ◽  
Gravity Field ◽  
Thermal Convection ◽  
Thermal History ◽  
Second Harmonic ◽  
Iron Core ◽  
The Moon ◽  
Laser Altimeter ◽  
Deep Interior ◽  
History Of

Understanding of the internal dynamics of the Moon must start from the interpretation of the gravitational and magnetic fields, both present and past. It has been long known from the study of Cassini’s laws and its librations that the Moon substantially departs from hydrostatic equilibrium. This is confirmed by the second harmonic of the gravitational field determined by the tracking of orbiting satellites which also reveals anomalies (the mascons) clearly associated with the processes by which the circular mare formed. The mascons must be retained by the finite strength of the lithosphere, although there is evidence that they may have subsided by about 1 km by slippage along cylindrical fault systems around these mare, and these processes may be important in discussing moonquakes and the lunar transient phenomena. The analyses of the present figure of the Moon by the geometrical librations and by the lunar laser altimeter of Apollo 15 and 16 and other space determinations now seem essentially in agreement. The data gives evidence of the figure of the Moon prior to the filling of the mare, i.e. before about 3300 Ma and it can be concluded that the present non-hydrostatic low harmonics of the gravity field were not then present. Comparison between the present figure of the Moon and its gravity field show that there is a low harmonic variation in density in the deep interior. Both these conclusions point to thermal convection described by second degree harmonics as being the cause of the present non-hydrostatic shape of the Moon. The present lunar dipole magnetic field has been shown by successive analyses to be negligible, the most recent value being 0.05 nT at the surface. Yet magnetic anomalies near the surface of the Moon have been discovered: 1 nT at heights of 100 km and 10-30 nT with length scales of 10 km at the surface. These anomalies must arise from the magnetization of the crustal rocks as discovered in the returned samples. These various data conclusively show that the Moon between 4000 and 3200 Ma possessed a field of internal origin, probably dipolar, with an intensity which seemed to have diminished from over 1 Gat 4000 Ma to a few thousand nT at 3.200 Ma. Whether this field arose by dynamo processes in a small iron core of about 300 km radius, which was inferred from the convection theory and is compatible with the now known value of the moment of inertia factor, or whether it was a permanent magnetization of the deep interior produced by a primeval solar system magnetic field must await further understanding of the early thermal history of the Moon. Thermal convection is seen as an essential basis for understanding the thermal history of the Moon, the traces of tectonic evidence in the lithospheric shell and the history of the magnetic field.

scholarly journals Jupiter’s evolution with primordial composition gradients

2018 ◽  
Vol 610 ◽  
pp. L14 ◽  
Author(s):  
Allona Vazan ◽  
Ravit Helled ◽  
Tristan Guillot
Keyword(s):  
Heavy Element ◽  
Bulk Composition ◽  
Outer Part ◽  
Early Evolution ◽  
Composition Gradient ◽  
Outer Envelope ◽  
Deep Interior ◽  
Higher Temperature ◽  
The One ◽  
Composition Gradients

Recent formation and structure models of Jupiter suggest that the planet can have composition gradients and not be fully convective (adiabatic). This possibility directly affects our understanding of Jupiter’s bulk composition and origin. In this Letter we present Jupiter’s evolution with a primordial structure consisting of a relatively steep heavy-element gradient of 40 M⊕. We show that for a primordial structure with composition gradients, most of the mixing occurs in the outer part of the gradient during the early evolution (several 107 yr), leading to an adiabatic outer envelope (60% of Jupiter’s mass). We find that the composition gradient in the deep interior persists, suggesting that ~40% of Jupiter’s mass can be non-adiabatic with a higher temperature than the one derived from Jupiter’s atmospheric properties. The region that can potentially develop layered convection in Jupiter today is estimated to be limited to ~10% of the mass.

First direct measurements of the zonal winds in Saturn's stratosphere

2021 ◽  
Author(s):  
Thibault Cavalié ◽  
Bilal Benmahi ◽  
Thierry Fouchet ◽  
Raphael Moreno ◽  
Emmanuel Lellouch ◽  
...  
Keyword(s):  
General Circulation ◽  
Direct Determination ◽  
General Circulation Models ◽  
Spectral Lines ◽  
Tropical Zone ◽  
Wind Speeds ◽  
Zonal Winds ◽  
Doppler Shifts ◽  
Cassini Mission ◽  
Spectrally Resolved

<p>Saturn's cloud-top zonal winds have been measured since the Voyager days. Contrary to Jupiter, the jets are mostly prograde and with a noticeable broad super-rotating jet between 35°S and 35°N with peak velocities reaching ~450 m/s between 10°S and 10°N (e.g. Sanchez-Lavega et al. 2000). The Cassini mission revealed, during its Grand Finale, that these winds extend as deep as 8000 km below the clouds (Galanti et al. 2019). Above the tropopause, in the stratosphere, there has been no direct determination of the zonal winds, although thermal wind balance calculations have shown the signature of Saturn's semi-annual oscillation (SAO) in the tropical zone (Fouchet et al. 2008, Guerlet et al. 2011, 2018). These derivations lack an initial condition, in terms of wind speeds, located in the sensitivity zone of the temperature measurements. It thus remains unknown if the SAO jets alternate in direction as a function of altitude. In addition, more and more sophisticated general circulation models are being developed to constrain the dynamics of Saturn's stratosphere (Friedson & Moses 2012, Spiga et al. 2020, Bardet et al. 2021). These models now crucially need observational constraints.</p> <p>We used the Atacama Large Millimeter/submillimeter Array (ALMA) to map Saturn's stratospheric zonal winds. We derive the zonal winds as a function of latitude from the Doppler shifts induced by the winds on the spatially and spectrally resolved spectral lines. In this paper, we will present and discuss our results.</p>

Distribution of R- and S-Process Elements in the Galactic Halo

1988 ◽  
Vol 132 ◽  
pp. 501-506
Author(s):  
C. Sneden ◽  
C. A. Pilachowski ◽  
K. K. Gilroy ◽  
J. J. Cowan
Keyword(s):  
Heavy Element ◽  
Galactic Halo ◽  
Low Noise ◽  
Heavy Elements ◽  
Process Synthesis ◽  
Element Abundances ◽  
Halo Stars ◽  
Abundance Patterns ◽  
R Process ◽  
Process Elements

Current observational results for the abundances of the very heavy elements (Z>30) in Population II halo stars are reviewed. New high resolution, low noise spectra of many of these extremely metal-poor stars reveal general consistency in their overall abundance patterns. Below Galactic metallicities of [Fe/H] Ã −2, all of the very heavy elements were manufactured almost exclusively in r-process synthesis events. However, there is considerable star-to-star scatter in the overall level of very heavy element abundances, indicating the influence of local supernovas on element production in the very early, unmixed Galactic halo. The s-process appears to contribute substantially to stellar abundances only in stars more metal-rich than [Fe/H] Ã −2.

Variation of Heavy Element Lines in the Ap Stars

1976 ◽  
Vol 32 ◽  
pp. 311-320 ◽  
Author(s):  
I.A. Aslanov ◽  
Yu. S. Rustamov ◽  
M. Kowalski
Keyword(s):  
Heavy Element ◽  
Ap Stars

SummaryLines of U II were found in the spectrograms of the Ap stars HR 465, 17 Com A and HD 224801. Pm II lines were found in HR 465. These lines vary in intensity in HR 465 with a period of 6h41m, in 17 Com A of 71m, and in HD 224801 of 6h.

Energy-filtered imaging of polymer microstructure

1996 ◽  
Vol 54 ◽  
pp. 162-163
Author(s):  
K. Siangchaew ◽  
J. Bentley ◽  
M. Libera
Keyword(s):  
Energy Loss ◽  
Heavy Element ◽  
Spectroscopic Imaging ◽  
Data Set ◽  
Polymer Microstructure ◽  
Entire Energy ◽  
Staining Methods ◽  
Spectrum Imaging ◽  
Resolution Data

Energy-filtered electron-spectroscopic TEM imaging provides a new way to study the microstructure of polymers without heavy-element stains. Since spectroscopic imaging exploits the signal generated directly by the electron-specimen interaction, it can produce richer and higher resolution data than possible with most staining methods. There are basically two ways to collect filtered images (fig. 1). Spectrum imaging uses a focused probe that is digitally rastered across a specimen with an entire energy-loss spectrum collected at each x-y pixel to produce a 3-D data set. Alternatively, filtering schemes such as the Zeiss Omega filter and the Gatan Imaging Filter (GIF) acquire individual 2-D images with electrons of a defined range of energy loss (δE) that typically is 5-20 eV.

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