scholarly journals Interior structure models and tidal Love numbers of Titan

2003 ◽  
Vol 108 (E12) ◽  
Author(s):  
F. Sohl ◽  
H. Hussmann ◽  
B. Schwentker ◽  
T. Spohn ◽  
R. D. Lorenz
Keyword(s):  
Interior Structure ◽  
Love Numbers

Gravity constraints on the interior structure of Europa

2020 ◽  
Author(s):  
Isamu Matsuyama ◽  
Antony Trinh
Keyword(s):  
Gravity Field ◽  
Shell Thickness ◽  
Gravity Data ◽  
Equal Mass ◽  
Altimeter Data ◽  
Structure Parameters ◽  
Interior Structure ◽  
Subsurface Ocean ◽  
Love Numbers ◽  
Ice Shell

<p><span>We assess the gravity constraints on the interior structure of Europa in anticipation of the Europa Clipper mission.</span></p><p><span>Moore and Schubert (2000) illustrated that the diurnal tide amplitude, quantified by the diurnal (tidal) Love numbers, k<sub>2</sub><sup>d</sup> and h<sub>2</sub><sup>d</sup>, can be used to determine the presence of a subsurface liquid ocean due to the significant increase in tidal amplitudes associated with the mechanical decoupling of the shell with a subsurface ocean.<span>  </span>However, they considered a limited range of possible interior parameters except the ice shell rigidity, which was assumed to be in the range of 1-10 GPa. We consider a wider range of possible interior structure parameters and a more realistic ice shell rigidity range of 1-4 GPa. Inferring the presence of a subsurface ocean is slightly easier than previously thought (Verma & Margot 2018), with required absolute precisions of 0.08 for k<sub>2</sub><sup>d</sup> , and 0.44 for h<sub>2</sub><sup>d</sup> .</span></p><p><span>Previous work have considered diurnal (tidal) gravity constraints alone or static gravity constraints alone using a forward modeling approach (e.g.<span>  </span>Anderson et al., 1998; Moore and Schubert, 2000; Wahr et al., 2006). We evaluate constraints on interior structure parameters using Bayesian inversion with the mass, static gravity, and diurnal gravity as constraints, allowing a probabilistic view of Europa's interior structure. Given the same relative uncertainties, the static Love numbers provide stronger constraints on the interior structure relative to those from the mean moment of inertia (MOI). Additionally, the static Love numbers can be inferred directly from the static gravity field whereas inferring the MOI requires the Radau-Darwin approximation.</span></p><p><span>Jointly considered with the static shape, the static gravity field can constrain the average and long-wavelength thickness of the shell. For an isostatically compensated shell, it is usual to conceptualize the crust as a series of independently floating columns of equal cross-sectional area which, by application of Archimedes' principle, should have equal mass above the depth of compensation. However, this approach is unphysical in the presence of curvature and self-gravitation. We consider alternative prescriptions of Airy isostasy: the equal-pressure prescription (Hemingway and Matsuyama, 2017), and the minimum-stress prescription (Dahlen 1982; Beuthe et al., 2016; Trinh et al., 2019).<span>  </span>The gravitational coefficients are more sensitive to shell thickness than would be expected from the classical (equal-mass) approach, illustrating that the equal-mass prescription can lead to large errors in the inferred average shell thickness and its lateral variations.</span></p><p><span>Diurnal gravity data alone can only constrain the product of the shell rigidity and thickness (Moore and Schubert, 2000; Wahr et al., 2006). An additional observational constraint that is sensitive to these parameters is the libration amplitude, which can be obtained from direct imaging or from altimeter data. We show that a joint gravity and libration analysis is able to separately constrain the shell thickness and rigidity.</span></p>

scholarly journals Tidal deformation of Ganymede: Sensitivity of Love numbers on the interior structure

2016 ◽  
Vol 121 (7) ◽  
pp. 1362-1375 ◽  
Author(s):  
Shunichi Kamata ◽  
Jun Kimura ◽  
Koji Matsumoto ◽  
Francis Nimmo ◽  
Kiyoshi Kuramoto ◽  
...  
Keyword(s):  
Interior Structure ◽  
Tidal Deformation ◽  
Love Numbers

scholarly journals Matrix-propagator approach to compute fluid Love numbers and applicability to extrasolar planets

2018 ◽  
Vol 620 ◽  
pp. A178 ◽  
Author(s):  
S. Padovan ◽  
T. Spohn ◽  
P. Baumeister ◽  
N. Tosi ◽  
D. Breuer ◽  
...  
Keyword(s):  
Density Profile ◽  
Extrasolar Planets ◽  
Nonlinear Effects ◽  
Extrasolar Planet ◽  
Interior Structure ◽  
Love Number ◽  
Hot Jupiters ◽  
Linear Approach ◽  
Love Numbers ◽  
The Matrix

Context.The mass and radius of a planet directly provide its bulk density, which can be interpreted in terms of its overall composition. Any measure of the radial mass distribution provides a first step in constraining the interior structure. The fluid Love numberk2provides such a measure, and estimates ofk2for extrasolar planets are expected to be available in the coming years thanks to improved observational facilities and the ever-extending temporal baseline of extrasolar planet observations.Aims.We derive a method for calculating the Love numbersknof any object given its density profile, which is routinely calculated from interior structure codes.Methods.We used the matrix-propagator technique, a method frequently used in the geophysical community.Results.We detail the calculation and apply it to the case of GJ 436b, a classical example of the degeneracy of mass-radius relationships, to illustrate how measurements ofk2can improve our understanding of the interior structure of extrasolar planets. We implemented the method in a code that is fast, freely available, and easy to combine with preexisting interior structure codes. While the linear approach presented here for the calculation of the Love numbers cannot treat the presence of nonlinear effects that may arise under certain dynamical conditions, it is applicable to close-in gaseous extrasolar planets like hot Jupiters, likely the first targets for whichk2will be measured.

scholarly journals Interior structure models and fluid Love numbers of exoplanets in the super-Earth regime

2018 ◽  
Vol 615 ◽  
pp. A39 ◽  
Author(s):  
C. Kellermann ◽  
A. Becker ◽  
R. Redmer
Keyword(s):  
Extrasolar Planets ◽  
Water Layer ◽  
Parameter Study ◽  
Interior Structure ◽  
Tidal Interactions ◽  
Love Numbers ◽  
Mass Fractions ◽  
Successful Technique ◽  
Outer Water ◽  
Measured Mass

Space missions such as CoRoT and Kepler have made the transit method the most successful technique in observing extrasolar planets. However, although the mean density of a planet can be derived from its measured mass and radius, no details about its interior structure, such as the density profile, can be inferred so far. If determined precisely enough, the shape of the transiting light curve might, in principle, reveal the shape of the planet, and in particular, its deviation from spherical symmetry. These deformations are caused, for instance, by the tidal interactions of the planet with the host star and by other planets that might orbit in the planetary system. The deformations depend on the interior structure of the planet and its composition and can be parameterized as Love numbers kn. This means that the diversity of possible interior models for extrasolar planets might be confined by measuring this quantity. We present results of a wide-ranging parameter study in planet mass, surface temperature, and layer mass fractions on such models for super-Earths and their corresponding Love numbers. Based on these data, we find that k2 is most useful in assessing the ratio of rocky material to iron and in ruling out certain compositional configurations for measured mass and radius values, such as a prominent core consisting of rocky material. Furthermore, we apply the procedure to exoplanets K2-3b and c and predict that K2-3c probably has a thick outer water layer.

The interior structure of Camarophoria King

1936 ◽  
Vol s5-32 (187) ◽  
pp. 55-69
Author(s):  
B. Licharew
Keyword(s):  
Interior Structure

INITIAL GEOPHYSICAL SURVEY FINDINGS ON THE INTERIOR STRUCTURE OF THE BLACKHAWK LANDSLIDE

2020 ◽  
Author(s):  
Ashley Rivera ◽  
◽  
Alejandro Razo ◽  
Jonathon Martinez ◽  
Jascha Polet
Keyword(s):  
Geophysical Survey ◽  
Interior Structure

Venus Interior Structure and Dynamics

2018 ◽  
Vol 214 (5) ◽  
Author(s):  
Suzanne E. Smrekar ◽  
Anne Davaille ◽  
Christophe Sotin
Keyword(s):  
Interior Structure ◽  
Structure And Dynamics

scholarly journals The interiors of Uranus and Neptune: current understanding and open questions

2020 ◽  
Vol 378 (2187) ◽  
pp. 20190474 ◽  
Author(s):  
Ravit Helled ◽  
Jonathan J. Fortney
Keyword(s):  
Solar System ◽  
Internal Structure ◽  
Planetary Systems ◽  
Space Missions ◽  
Current Understanding ◽  
Interior Structure ◽  
Distinct Class ◽  
Open Questions

Uranus and Neptune form a distinct class of planets in our Solar System. Given this fact, and ubiquity of similar-mass planets in other planetary systems, it is essential to understand their interior structure and composition. However, there are more open questions regarding these planets than answers. In this review, we concentrate on the things we do not know about the interiors of Uranus and Neptune with a focus on why the planets may be different, rather than the same. We next summarize the knowledge about the planets’ internal structure and evolution. Finally, we identify the topics that should be investigated further on the theoretical front as well as required observations from space missions. This article is part of a discussion meeting issue ‘Future exploration of ice giant systems’.

scholarly journals Flux transfer events: Scale size and interior structure

1984 ◽  
Vol 11 (2) ◽  
pp. 131-134 ◽  
Author(s):  
M. A. Saunders ◽  
C. T. Russell ◽  
N. Sckopke
Keyword(s):  
Interior Structure ◽  
Flux Transfer Events ◽  
Scale Size ◽  
Flux Transfer
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