This report deals with the quantum field theory of particle oscillations in vacuum. We first review the various controversies regarding quantum-mechanical derivations of the oscillation formula, as well as the different field-theoretical approaches proposed to settle them. We then clear up the contradictions between the existing field-theoretical treatments by a thorough study of the external wave packet model. In particular, we show that the latter includes stationary models as a subcase. In addition, we explicitly compute decoherence terms, which destroy interferences, in order to prove that the coherence length can be increased without bound by more accurate energy measurements. We show that decoherence originates not only in the width and in the separation of wave packets, but also in their spreading through space-time. In this review, we neither assume the relativistic limit nor the stability of oscillating particles, so that the oscillation formula derived with field-theoretical methods can be applied not only to neutrinos but also to neutral K and B mesons. Finally, we discuss oscillations of correlated particles in the same framework.Comment: v2, 124 pages, 10 figures (7 more); updated review of the literature; complete derivation of the oscillation probability at short and large distance; more details on the influence of the spreading of the amplitude on decoherence; submitted to Physics Report

Enceladus's gravity and shape have been explained in terms of a thick isostatic ice shell floating on a global ocean, in contradiction of the thin shell implied by librations. Here we propose a new isostatic model minimizing crustal deviatoric stress and demonstrate that gravity and shape data predict a 38 ± 4 km thick ocean beneath a 23 ± 4 km thick shell agreeing with—but independent of—libration data. Isostatic and tidal stresses are comparable in magnitude. South polar crust is only 7 ± 4 km thick, facilitating the opening of water conduits and enhancing tidal dissipation through stress concentration. Enceladus's resonant companion, Dione, is in a similar state of minimum stress isostasy. Its gravity and shape can be explained in terms of a 99 ± 23 km thick isostatic shell overlying a 65 ± 30 km thick global ocean, thus providing the first clear evidence for a present‐day ocean within Dione.

In a body periodically strained by tides, heating produced by viscous friction is far from homogeneous. I show here that the distribution of the dissipated power within a spherically stratified body is a linear combination of three angular functions. These angular functions depend only on the tidal potential whereas the radial weights are specified by the internal structure of the body. The 3D problem of predicting spatial patterns of dissipation at all radii is thus reduced to the 1D problem of computing weight functions. I compute spatial patterns in various toy models without assuming a specific rheology: a viscoelastic thin shell stratified in conductive and convective layers, an incompressible homogeneous body and a two-layer model of uniform density with a liquid or rigid core. For a body in synchronous rotation undergoing eccentricity tides, dissipation in a mantle surrounding a liquid core is highest at the poles. Within a softer layer (asthenosphere or icy layer), the same tides generate maximum heating in the equatorial region with a significant degree-four structure if the layer is thin. Tidal heating patterns are thus of three main types: mantle dissipation (including the case of a floating icy crust), dissipation in a thin soft layer and dissipation in a thick soft layer. I illustrate the method with applications to Europa, Titan and Io. The formalism described in this paper applies to dissipation within solid layers of planets and satellites for which internal spherical symmetry and viscoelastic linear rheology are good approximations.Comment: 51 pages, 8 figures, accepted for publication in Icaru

Could tidal dissipation within Enceladus' subsurface ocean account for the observed heat flow? Earthlike models of dynamical tides give no definitive answer because they neglect the influence of the crust. I propose here the first model of dissipative tides in a subsurface ocean, by combining the Laplace Tidal Equations with the membrane approach. For the first time, it is possible to compute tidal dissipation rates within the crust, ocean, and mantle in one go. I show that oceanic dissipation is strongly reduced by the crustal constraint, and thus contributes little to Enceladus' present heat budget. Tidal resonances could have played a role in a forming or freezing ocean less than 100 m deep. The model is general: it applies to all icy satellites with a thin crust and a shallow ocean. Scaling rules relate the resonances and dissipation rate of a subsurface ocean to the ones of a surface ocean. If the ocean has low viscosity, the westward obliquity tide does not move the crust. Therefore, crustal dissipation due to dynamical obliquity tides can differ from the static prediction by up to a factor of two.

22Extreme volcanism on Io results from tidal heating, but its tidal dissipation mechanisms and

As a long-term energy source, tidal heating in subsurface oceans of icy satellites can influence their thermal, rotational, and orbital evolution, and the sustainability of oceans. We present a new theoretical treatment for tidal heating in thin subsurface oceans with overlying incompressible elastic shells of arbitrary thickness. The stabilizing effect of an overlying shell damps ocean tides, reducing tidal heating. This effect is more pronounced on Enceladus than on Europa because the effective rigidity on a small body like Enceladus is larger. For the range of likely shell and ocean thicknesses of Enceladus and Europa, the thin shell approximation of Beuthe (2016) is generally accurate to less than about 4%. Explaining Enceladus' endogenic power radiated from the south polar terrain by ocean tidal heating requires ocean and shell thicknesses that are significantly smaller than the values inferred from gravity and topography constraints. The timeaveraged surface distribution of ocean tidal heating is distinct from that due to dissipation in the solid shell, with higher dissipation near the equator and poles for eccentricity and obliquity forcing respectively. This can lead to unique horizontal shell thickness variations if the shell is conductive. The surface displacement driven by eccentricity and obliquity forcing can have a phase lag relative to the forcing tidal potential due to the delayed ocean response. For Europa and Enceladus, eccentricity forcing generally produces greater tidal amplitudes due to the large eccentricity values relative to the obliquity values. Despite the small obliquity values, obliquity forcing generally produces larger phase lags due to the generation of Rossby-Haurwitz waves. If Europa's shell and ocean are respectively 10 and 100 km thick, the tide amplitude and phase lag are 26.5 m and < 1 degree for eccentricity forcing, and < 2.5 m and < 18 degrees for obliquity forcing.Measurement of the obliquity phase lag (e.g. by Europa Clipper) would provide a probe of ocean thickness

Tidal heating is the prime suspect behind Enceladus's south polar heating anomaly and global subsurface ocean. No model of internal tidal dissipation, however, can explain at the same time the total heat budget and the focusing of the energy at the south pole. I study here whether the non-uniform icy shell thickness can cause the north-south heating asymmetry by redistributing tidal heating either in the shell or in the core. Starting from the non-uniform tidal thin shell equations, I compute the volumetric rate, surface flux, and total power generated by tidal dissipation in shell and core. The micro approach is supplemented by a macro approach providing an independent determination of the core-shell partition of the total power. Unless the shell is incompressible, the assumption of a uniform Poisson's ratio implies non-zero bulk dissipation. If the shell is laterally uniform, the thin shell approach predicts shell dissipation with a few percent error while the error on core dissipation is negligible. Variations in shell thickness strongly increase the shell dissipation flux where the shell is thinner. For a hard shell with long-wavelength variations, the shell dissipation flux can be predicted by scaling with the inverse local thickness the flux for a laterally uniform shell. If Enceladus's shell is in conductive thermal equilibrium with isostatic thickness variations, the nominal shell dissipation flux at the south pole is about three times its value for a shell of uniform thickness, which remains negligible compared to the observed flux. The shell dissipation rate should be ten times higher than nominal in order to account for the spatial variations of the observed flux. Dissipation in an unconsolidated core can provide the missing power, but does not generate any significant heating asymmetry as long as the core is homogeneous. Non-steady state models, though not investigated here, face similar difficulties in explaining the asymmetries of tidal heating and shell thickness.

The geologic activity at Enceladus's south pole remains unexplained, though tidal deformations are probably the ultimate cause. Recent gravity and libration data indicate that Enceladus's icy crust floats on a global ocean, is rather thin, and has a strongly non-uniform thickness. Tidal effects are enhanced by crustal thinning at the south pole, so that realistic models of tidal tectonics and dissipation should take into account the lateral variations of shell structure. I construct here the theory of non-uniform viscoelastic thin shells, allowing for depth-dependent rheology and large lateral variations of shell thickness and rheology. Coupling to tides yields two 2D linear partial differential equations of the fourth order on the sphere which take into account self-gravity, density stratification below the shell, and core viscoelasticity. If the shell is laterally uniform, the solution agrees with analytical formulas for tidal Love numbers; errors on displacements and stresses are less than 5% and 15%, respectively, if the thickness is less than 10% of the radius. If the shell is non-uniform, the tidal thin shell equations are solved as a system of coupled linear equations in a spherical harmonic basis. Compared to finite element models, thin shell predictions are similar for the deformations due to Enceladus's pressurized ocean, but differ for the tides of Ganymede. If Enceladus's shell is conductive with isostatic thickness variations, surface stresses are approximately inversely proportional to the local shell thickness. The radial tide is only moderately enhanced at the south pole. The combination of crustal thinning and convection below the poles can amplify south polar stresses by a factor of 10, but it cannot explain the apparent time lag between the maximum plume brightness and the opening of tiger stripes. In a second paper, I will study the impact of a non-uniform crust on tidal dissipation.