Tides between the TRAPPIST-1 planets

The TRAPPIST-1 system is sufficiently closely packed that tides raised by one planet on another are significant. We investigate whether this source of tidal heating is comparable to eccentricity tides raised by the star. Assuming a homogeneous body with a Maxwell rheology, we find that energy dissipation from stellar tides always dominates over that from planet-planet tides across a range of viscosities. TRAPPIST-1 g may experience the greatest proportion of planet-planet tidal heating, where it can account for between 2% and 20% of the total amount of tidal heating, for high ($10^{21}$ Pa s) and low viscosity ($10^{14}$ Pa s) regimes, respectively. If planet-planet tidal heating is to exceed that from stellar eccentricity tides, orbital eccentricities must be no more than e=$10^{-3}$ to $10^{-4}$ for most of the TRAPPIST-1 planets.Comment: 14 pages - 7 figures - accepted to Ap

True polar wander driven by late-stage volcanism and the distribution of paleopolar deposits on Mars

The areal centroids of the youngest polar deposits on Mars are offset from those of adjacent paleopolar deposits by 5-10 degrees. We test the hypothesis that the offset is the result of true polar wander (TPW), the motion of the solid surface with respect to the spin axis, caused by a mass redistribution within or on the surface of Mars. In particular, we consider TPW driven by late-stage volcanism during the late Hesperian to Amazonian. There is observational and qualitative support for this hypothesis: in both North and South, observed offsets lie close to a great circle 90 degrees from Tharsis, as expected for polar wander after Tharsis formed. We calculate the magnitude and direction of TPW produced by mapped late-stage lavas for a range of lithospheric thicknesses, lava thicknesses, eruption histories, and prior polar wander events. If Tharsis formed close to the equator, the stabilizing effect of a fossil rotational bulge located close to the equator leads to predicted TPW of <2 degrees, too small to account for observed offsets. If, however, Tharsis formed far from the equator, late-stage TPW driven by low-latitude, late-stage volcanism would be 6-33 degrees, similar to that inferred from the location of paleopolar deposits. 4.4+/-1.3x10^19 kg of young erupted lava can account for the offset of the Dorsa Argentea Formation from the present-day south rotation pole. This mass is consistent with prior mapping-based estimates and would imply a mass release of CO2 by volcanic degassing similar to that in the atmosphere at the present time. The South Polar Layered Deposits are offset from the spin axis in the opposite sense to the other paleopolar deposits. This can be explained by an additional contribution from a plume beneath Elysium. We conclude with a list of observational tests of the TPW hypothesis.Comment: Accepted by Earth and Planetary Science Letters. 3 tables, 8 figure

The thermal-orbital evolution of the Earth-Moon system with a subsurface magma ocean and fossil figure

Various theories have been proposed to explain the Moon's current inclined orbit. We test the viability of these theories by reconstructing the thermal-orbital history of the Moon. We build on past thermal-orbital models and incorporate the evolution of the lunar figure including a fossil figure component. Obliquity tidal heating in the lunar magma ocean would have produced rapid inclination damping, making it difficult for an early inclination to survive to the present-day. An early inclination is preserved only if the solid-body of the early Moon were less dissipative than at present. If instabilities at the Laplace plane transition were the source of the inclination, then the Moon had to recede slowly, which is consistent with previous findings of a weakly dissipative early Earth. If collisionless encounters with planetesimals up to 140 Myr after Moon formation excited the inclination, then the Moon had to migrate quickly to pass through the Cassini state transition at 33 Earth radii and reach a period of limited inclination damping. The fossil figure was likely established before 16 Earth radii to match the present-day degree-2 gravity field observations.Comment: 18 pages, 6 figure

A Spectral Method to Compute the Tides of Laterally-Heterogeneous Bodies

Body tides reveal information about planetary interiors and affect their evolution. Most models to compute body tides rely on the assumption of a spherically-symmetric interior. However, several processes can lead to lateral variations of interior properties. We present a new spectral method to compute the tidal response of laterally-heterogeneous bodies. Compared to previous spectral methods, our approach is not limited to small-amplitude lateral variations; compared to finite element codes, the approach is more computationally-efficient. While the tidal response of a spherically-symmetric body has the same wave-length as the tidal force; lateral heterogeneities produce an additional tidal response with an spectra that depends on the spatial pattern of such variations. For Mercury, the Moon and Io the amplitude of this signal is as high as $1\%-10\%$ the main tidal response for long-wavelength shear modulus variations higher than $\sim 10\%$ the mean shear modulus. For Europa, Ganymede and Enceladus, shell-thickness variations of $50\%$ the mean shell thickness can cause an additional signal of $\sim 1\%$ and $\sim 10\%$ for the Jovian moons and Encelaudus, respectively. Future missions, such as $\textit{BepiColombo}$ and $\textit{JUICE}$, might measure these signals. Lateral variations of viscosity affect the distribution of tidal heating. This can drive the thermal evolution of tidally-active bodies and affect the distribution of active regions.Comment: 30 pages, 8 figure

Powering the Galilean Satellites with Moon-Moon Tides

There is compelling evidence for subsurface water oceans among the three outer Galilean satellites, and evidence for an internal magma ocean in the innermost moon, Io. Tidal forces from Jupiter periodically deform these bodies, causing heating and deformation that, if measured, can probe their interior structures. In addition to Jupiter-raised tides, each moon also raises tides on the others. We investigate moon-moon tides for the first time in the Galilean moons, and show that they can cause significant heating through the excitation of high-frequency resonant tidal waves in their subsurface oceans. The heating occurs both in the crust and ocean, and can exceed that of other tidal sources and radiogenic decay if the ocean is inviscid enough. The resulting tidal deformation can be used to constrain subsurface ocean thickness. Our understanding of the thermal-orbital evolution and habitability of the Jovian system may be fundamentally altered as a result

Viscous diffusion and photoevaporation of stellar disks

The evolution of a stellar disk under the influence of viscous evolution, photoevaporation from the central source, and photoevaporation by external stars is studied. We take the typical parameters of TTSs and the Trapezium Cluster conditions. The photoionizing flux from the central source is assumed to arise both from the quiescent star and accretion shocks at the base of stellar magnetospheric columns, along which material from the disk accretes. The accretion flux is calculated self-consistently from the accretion mass loss rate. We find that the disk cannot be entirely removed using only viscous evolution and photoionization from the disk-star accretion shock. However, when FUV photoevaporation by external massive stars is included the disk is removed in 10^6 -10^7yr; and when EUV photoevaporation by external massive stars is included the disk is removed in 10^5 - 10^6yr. An intriguing feature of photoevaporation by the central star is the formation of a gap in the disk at late stages of the disk evolution. As the gap starts forming, viscous spreading and photoevaporation work in resonance. There is no gap formation for disks nearby external massive stars because the outer annuli are quickly removed by the dominant EUV flux. On the other hand, at larger, more typical distances (d>>0.03pc) from the external stars the flux is FUV dominated. As a consequence, the disk is efficiently evaporated at two different locations; forming a gap during the last stages of the disk evolution.Comment: 27 pages, 11 figures, accepted for publication in Ap

Halting planet migration by photoevaporation from the central source

The recent discovery of Jupiter-mass planets orbiting at a few AU from their stars compliments earlier detections of massive planets on very small orbits. The short period orbits strongly suggest that planet migration has occurred, with the likely mechanism being tidal interactions between the planets and the gas disks out of which they formed. The newly discovered long period planets, together with the gas giant planets in our solar system, show that migration is either absent or rapidly halted in at least some systems. We propose a mechanism for halting type-II migration at several AU in a gas disk. Photoevaporation of the disk by irradiation from the central star can produce a gap in the disk at a few AU, preventing planets outside the gap from migrating down to the star. This would result in an excess of systems with planets at or just outside the photoevaporation radius.Comment: 12 pages, 3 figures, accepted for publication by ApJ Letter

Ocean tidal heating in icy satellites with solid shells

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%.The time-averaged 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 thicknessComment: Icarus, accepted for publicatio

Indications for grain growth and mass decrease in cold dust disks around Classical T Tauri stars in the MBM 12 young association

We report detection of continuum emission at 850 and 450 micron from disks around four Classical T Tauri stars in the MBM 12 (L1457) young association. Using a simple model we infer masses of 0.0014-0.012 M_sun for the disk of LkHa 263 ABC, 0.005-0.021 M_sun for S18 ABab, 0.03-0.18 M_sun for LkHa 264 A, and 0.023-0.23 M_sun for LkHa 262. The disk mass found for LkHa 263 ABC is consistent with the 0.0018 M_sun inferred from the scattered light image of the edge-on disk around component C. Comparison to earlier 13CO line observations indicates CO depletion by up to a factor 300 with respect to dark-cloud values. The spectral energy distributions (SED) suggest grain growth, possibly to sizes of a few hundred micron, but our spatially unresolved data cannot rule out opacity as an explanation for the SED shape. Our observations show that these T Tauri stars are still surrounded by significant reservoirs of cold material at an age of 1-5 Myr. We conclude that the observed differences in disk mass are likely explained by binary separation affecting the initial value. With available accretion rate estimates we find that our data are consistent with theoretical expectations for viscously evolving disks having decreased their masses by ~30%.Comment: 15 pages, 3 figures, uses aastex. ApJ Letters, in pres