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Melting of Io by Tidal Dissipation
Abstract
The dissipation of tidal energy in Jupiter's satellite Io is likely to have melted a major fraction of the mass. Consequences
of a largely molten interior may be evident in pictures of Io's surface returned by Voyager I.
... Famously, heating within the interior of Io is thought to be a key driver of ongoing volcanic activity although it does not maintain a permanent magma ocean (Park et al. 2024;Peale et al. 1979;Segatz et al. 1988;Matsuyama et al. 2022). Time-varying tides within Io are induced by its eccentric orbit around Jupiter, enabled by gravitational interactions with its sister moons Europa and Ganymede. ...
... The radiation-tide-rheology feedback mechanism modelled in this work is different to the negative feedback between tidal heating and mantle convection proposed to occur within Io and some exoplanets (Segatz et al. 1988;Wienbruch & Spohn 1995;Fischer & Spohn 1990;Moore 2003;Matsuyama et al. 2022;Henning et al. 2009). It is also distinctly different to the 'runaway melting' mechanism proposed by Peale et al. (1979) and Seligman et al. (2024), which works under the assumption of mantle melting from the bottom-up. Zahnle et al. (2015) previously suggested that a thick atmosphere slowed the cooling of the early Earth shortly following the Moonforming impact (Canup & Asphaug 2001). ...
... Continual forcing, such as in the case of mean-motion resonances between planets, acts to sustain orbital eccentricities on long timescales. This interaction is seen in the Galilean satellites (e.g., Peale et al. 1979;Yoder 1979). We model the evolution of these planets under the assumption of orbital steady state, for simplicity. ...
Rocky exoplanets accessible to characterisation often lie on close-in orbits where tidal heating within their interiors is significant, with the L 98-59 planetary system being a prime example. As a long-term energy source for ongoing mantle melting and outgassing, tidal heating has been considered as a way to replenish lost atmospheres on rocky planets around active M-dwarfs. We simulate the early evolution of L 98-59 b, c and d using a time-evolved interior-atmosphere modelling framework, with a self-consistent implementation of tidal heating and redox-controlled outgassing. Emerging from our calculations is a novel self-limiting mechanism between radiative cooling, tidal heating, and mantle rheology, which we term the 'radiation-tide-rheology feedback'. Our coupled modelling yields self-limiting tidal heating estimates that are up to two orders of magnitude lower than previous calculations, and yet are still large enough to enable the extension of primordial magma oceans to Gyr timescales. Comparisons with a semi-analytic model demonstrate that this negative feedback is a robust mechanism which can probe a given planet's initial conditions, atmospheric composition, and interior structure. The orbit and instellation of the sub-Venus L 98-59 b likely place it in a regime where tidal heating has kept the planet molten up to the present day, even if it were to have lost its atmosphere. For c and d, a long-lived magma ocean can be induced by tides only with additional atmospheric regulation of energy transport.
... While tidal forces generally operate to circularize the orbits of short-period planets, non-zero planetary eccentricities can be maintained in tightly packed multi-planet systems through forced eccentricity induced by planet-planet interactions (S. J. Peale et al. 1979; A. C. Barr et al. 2018 Figure 2, the HHZ and dark HHZ around stars of various mass for a 7M⊕, 1.7R⊕ hycean planet with tidal quality factor Q = 2. Here we use an orbital eccentricity e = 0.1 throughout: about the value for the hycean candidate planet K2-18 b, whose location in this parameter space is indicated by the blue dot. ...
Hycean planets -- exoplanets with substantial water ice layers, deep surface oceans, and hydrogen-rich atmospheres -- are thought to be favorable environments for life. Due to a relative paucity of atmospheric greenhouse gases, hycean planets have been thought to have wider habitable zones than Earth-like planets, extending down to a few times 0.001 au for those orbiting M dwarfs. In this Letter, we reconsider the hycean habitable zone accounting for star-planet tidal interaction. We show that for a moderately eccentric hycean planet, the surface temperature contribution from tidal heating truncates the habitable zone at significantly larger orbital radii, and that moderate eccentricity is readily obtained from any massive outer companion in the system. Though few current hycean planet candidates orbit stars of low enough mass for tides to plausibly significantly alter the extent of the habitable zone, this effect will be important to note as more such candidates are identified orbiting M dwarfs. We suggest that tides are a significant factor both for determining the extent of the hycean habitable zone around low-mass stars and for the development of a detectable hycean biosphere.
... By the time in situ measurements were collected by the Plasma Science instrument on board Voyager 1 and provided a rst characterization of the plasma environment (H. S. Bridge et al. 1979;V. R. Eshleman et al. 1979), it had become clear that the main source of this plasma distribution was the intense volcanic activity of Io (e.g., S. J. Peale et al. 1979). Io ejects neutral gas at a rate of about 1 ton s −1 (F. ...
The neutral gases released by the intense volcanic activity of the Jupiter moon Io, once ionized by the Jupiter magnetic environment, give rise to a toroidal plasma distribution known as the Io plasma torus (IPT). Radio signals passing through charged-particle environments such as the IPT are heavily perturbed proportionally to the rate of change of the charged-particle distribution along the path of the radio wave. If not properly calibrated, the IPT may induce significant perturbation on the radiometric tracking link to Earth. The radio tracking signal is the main observable for the Gravity and Radio Science (G/RS) investigation on NASA’s Europa Clipper, whose aim is to measure the gravity field, tidal response, and moment of inertia of Europa, and to precisely reconstruct the trajectory of the probe in support of other scientific investigations. In this work, we quantify the detrimental effects of the IPT on the radiometric observables. We show how these affect the products of the G/RS, and prove the necessity of accurate calibrations. We simulate different calibration strategies to mitigate its net perturbative effect, based on currently available models of the IPT. Considering that these models have been developed with Juno in mind, they are tailored to its orbital geometry and we show that they cannot be easily applied to other geometries. We conclude that, although the model-based calibration strategies can be very effective, further work will be needed to make them applicable to probes with a significantly different orbital geometry such as Europa Clipper or ESA’s JUICE.
... An analogous expression has also been obtained for tidally driven orbital migration and mean motion resonances of the Galilean satellites of Jupiter (Peale et al. 1979;Lin & Papaloizou 1979). The generalized expression for more realistic mutually-evolving planet pair migrating inwards is given by Terquem & Papaloizou (2019), which can be approximated to order-unity as 2 eq = 1 2( + 1) ...
Mean-motion resonances (MMRs) form through convergent disc migration of planet pairs, which may be disrupted by dynamical instabilities after protoplanetary disc (PPD) dispersal. This scenario is supported by recent analysis of TESS data showing that neighboring planet pairs in younger planetary systems are closer to resonance. To study stability of MMRs during migration, we perform hydrodynamical simulations of migrating planet pairs in PPDs, comparing the effect of laminar viscosity and realistic turbulence. We find stable 3:2 resonance capture for terrestrial planet pairs migrating in a moderately massive PPD, insensitive to a range of laminar viscosity (alpha = 0.001 to 0.1). However, realistic turbulence enhances overstability by sustaining higher equilibrium eccentricities and a positive growth rate in libration amplitude, ultimately leading to resonance escape. The equilibrium eccentricity growth rates decrease as planets migrate into tighter and more stable 4:3 and 5:4 MMRs. Our results suggest that active disc turbulence broadens the parameter space for overstability, causing planet pairs to end up in closer-in orbital separations. Libration within MMR typically lead to deviation from exact period ratio |Delta| \sim 0.5%, which alone is insufficient to produce the typical dispersion of |Delta| \sim 1 to 3% in TESS data, suggesting that post migration dynamical processes are needed to further amplify the offset.
... In this scenario, the secular interactions within a multi-planet system launch the innermost planet into an eccentric and inclined orbit. The elevated eccentricity allows the innermost planet to migrate inward via eccentricity tides, with dissipation occurring inside the planet, similar to the case of Io and Jupiter (Peale et al. 1979). Over time, the eccentricity is damped, but the inclined orbit persists due to slower tidal realignment, because it requires the dissipation to occur inside the host star instead of the planet. ...
We report an observation of the Rossiter-McLaughlin (RM) effect of the transiting planet HD 93963 Ac, a mini-Neptune planet orbiting a G0-type star with an orbital period of , accompanied by an inner super-Earth planet with . We observed a full transit of planet c on 2024 May 3rd UT with Keck/KPF. The observed RM effect has an amplitude of and implies a sky-projected obliquity of degrees for HD 93963 Ac. Our dynamical analysis suggests that the two inner planets are likely well aligned with the stellar spin, to within a few degrees, thus allowing both to transit. Along with WASP-47, 55 Cnc, and HD 3167, HD 93963 is the fourth planetary system with an ultra-short-period planet and obliquity measurement(s) of any planet(s) in the system. HD 93963, WASP-47, and 55 Cnc favor largely coplanar orbital architectures, whereas HD 3167 has been reported to have a large mutual inclination (100) between its transiting planets b and c. In this configuration, the probability that both planets transit is low. Moreover, one planet would quickly evolve to be non-transiting due to nodal precession. Future missions such as ESO/PLATO should detect the resulting transit duration variations. We encourage additional obliquity measurements of the HD 3167 system to better constrain its orbital architecture.
... J. Veeder et al. 1994;J. A. Rathbun et al. 2004), believed to drive a runaway melting in the interior and to sustain its extreme volcanism (e.g., S. J. Peale et al. 1979). Small rocky planets at the edge of the magnetic drag may also undergo significant melting and active surface volcanism, which could be detectable by the James Webb Space Telescope (e.g., D. Z. Seligman et al. 2024). ...
Short-period planets provide ideal laboratories for testing star–planet interaction. Planets that are smaller than ∼2 R ⊕ are considered to be largely rocky, either having been stripped of or never having acquired the gaseous envelope. Zooming in on this short-period rocky planet population, clear edges appear in the mass–period and radius–period space. Over ∼0.2–20 days and 0.09–1.42 M ⊙ , the maximum mass of the rocky planets stays below ∼10 M ⊕ with a hint of decrease toward ≲1 day, ≳4 days, and ≲0.45 M ⊙ . In radius–period space, there is a relative deficit of ≲2 R ⊕ planets inside ∼1 day. We demonstrate how the edges in the mass–period space can be explained by a combination of tidal decay and photoevaporation, whereas the rocky planet desert in the radius–period space is a signature of magnetic drag on the planet as it orbits within the stellar magnetic field. Currently observed catastrophically evaporating planets may have started their death spiral from ∼1 day with planets of mass up to ∼0.3 M ⊕ under the magnetic drag. More discoveries and characterization of small planets around mid- to late M and A stars would be welcome to better constrain the stellar parameters critical in shaping the edges of rocky planet population, including their UV radiation history, tidal effects, and magnetic properties.
We present a novel method of constraining volcanic activity on extrasolar terrestrial worlds via characterization of circumstellar plasma tori. Our work generalizes the physics of the Io plasma torus to propose a hypothetical circumstellar plasma torus generated by exoplanetary volcanism. The quasi-steady torus mass is determined by a balance between material injection and ejection rates from volcanic activity and corotating magnetospheric convection, respectively. By estimating the Alfvén surfaces of planet-hosting stars, we calculate the torus mass-removal timescale for a number of exoplanets with properties amenable to plasma torus construction. Assuming a uniform toroidal geometry comparable to Io’s “warm” torus, we calculate quasi-steady torus masses inferable from the optical depth of atomic spectral features in torus-contaminated stellar spectra. The calculated quasi-steady masses can be used to constrain the volcanic outgassing rates of each species detected in the torus, providing quantitative estimates of bulk volcanic activity and interior composition with minimal assumptions. Such insight into the interior state of an exoplanet is otherwise accessible only after destruction via tidal forces. We demonstrate the feasibility of our method by showcasing known exoplanets that are susceptible to tidal heating and could generate readily detectable tori with realistic outgassing rates of order 1 t s ⁻¹ , comparable to the Io plasma torus mass injection rate. This methodology may be applied to stellar spectra measured with ultraviolet instruments with sufficient resolution to detect atomic lines and sensitivity to recover the ultraviolet continuum of GKM dwarf stars. This further motivates the need for ultraviolet instrumentation above Earth’s atmosphere.
Mean-motion resonances (MMRs) form through convergent disc migration of planet pairs, which may be disrupted by dynamical instabilities after protoplanetary disc (PPD) dispersal. This scenario is supported by recent analysis of TESS data showing that neighboring planet pairs in younger planetary systems are closer to resonance. To study stability of MMRs during migration, we perform hydrodynamical simulations of migrating planet pairs in PPDs, comparing the effect of laminar viscosity and realistic turbulence. We find stable 3:2 resonance capture for terrestrial planet pairs migrating in a moderately massive PPD, insensitive to a range of laminar viscosity (α = 10−3 − 10−1). However, realistic turbulence enhances overstability by sustaining higher equilibrium eccentricities and a positive growth rate in libration amplitude, ultimately leading to resonance escape. The equilibrium eccentricity growth rates decrease as planets migrate into tighter and more stable 4:3 and 5:4 MMRs. Our results suggest that active disc turbulence broadens the parameter space for overstability, causing planet pairs to end up in closer-in orbital separations. Libration within MMR typically lead to deviation from exact period ratio |Δ| ∼ 0.5 %, which alone is insufficient to produce the typical dispersion of |Δ| ∼ 1 − 3 % in TESS data, suggesting that post-migration dynamical processes are needed to further amplify the offset.
We report volcanic changes on Io since the last Galileo (2002) and New Horizons (2007) flybys as observed by NASA’s Juno spacecraft, examining Io’s volcanism down to the local scale (<10 km pixel ⁻¹ ). From 3428 Jovian Infrared Auroral Mapper image frames obtained between 2017 March 21 (PJ5) and 2023 October 15 (PJ55), a catalog of 2305 hot spot detections with temperatures >200 K at 325 individual sites of volcanic activity has been generated. Where possible, hot spot color temperature, emitting area, and power output are calculated. Some prominent areas of volcanic activity first identified or better resolved in Juno data (Tonatiuh, Lei-Kung Fluctus, Volund, Guaraci Fluctus, Seth Patera, and others) are described. We examined their appearance, volcanological and geological settings, observed thermal emission, and evolving behavior, and quantified the changes that have taken place. Volcanic activity at Tonatiuh and Guaraci Fluctus, the sites of newly imaged lava flows, are examined in detail. At Tonatiuh, JunoCam data provide important context; at Guaraci Fluctus, the combination of data from multiple assets yields a comprehensive understanding of the evolution of a specific eruption episode. We further examine different types of active paterae, some possibly containing lava lakes. A group of bright eruptions are identified whose spatial and temporal locations suggest regional clustering. Our estimates of volcanic thermal emission are broadly consistent with previous analyses of spacecraft data. All derived products are available from the Io Geographical Information System database at Arizona State University. Appendix A contains newly approved feature names.
The effects of solid interior convection on the thermal history of the moon are examined. Convective models of lunar evolution are calculated to demonstrate the influence of various viscosities, radioactive heat source distributions and initial temperature profiles and tested by means of a thermal history simulation code. Results indicate that solid convection does not necessarily produce a quasi-steady thermal balance between heat sources and surface losses. The state of the lithosphere is found to be sensitive to the efficiency of heat source redistribution, while that of the convecting interior depends primarily on rheology. Interior viscosities of 10 to the 21st to 10 to the 22nd cm/sec are obtained, along with a central temperature above 1100 C. It is suggested that mare flooding could have been the result of magma production by pressure release melting in the upwelling region of convection cells.
Measurements of the overall heat flux in steady convection have been made in a horizontal layer of dilute aqueous electrolyte. The layer is bounded below by a rigid zero-heat-flux surface and above by a rigid isothermal surface. Joule heating by an alternating current passing horizontally through the layer provides a uniformly distributed volumetric energy source. The Nusselt number at the upper surface is found to be proportional to Ra0[cdot B: small middle dot]227 in the range 1[cdot B: small middle dot]4 [less-than-or-equal] Ra/Rac [less-than-or-equal] 1[cdot B: small middle dot]6 × 109, which covers the laminar, transitional and turbulent flow regimes. Eight discrete transitions in the heat flux are found in this Rayleigh number range. Extrapolation of the heat-transfer correlation to the conduction value of the Nusselt number yields a critical Rayleigh number which is within -6[cdot B: small middle dot]7% of the value given by linearized stability theory. Measurements have been made of the time scales of developing convection after a sudden start of volumetric heating and of decaying convection when volumetric heating is suddenly stopped. In both cases, the steady-state temperature difference across the layer appears to be the controlling physical parameter, with both processes exhibiting the same time scale for a given steady-state temperature difference, or [mid R:]Ra[mid R:] > 100Rac, the time scales for both processes can be represented by Fo [proportional, variant] [mid R:]20 % of the layer in the early stages of flow development for Rayleigh numbers corresponding to turbulent convection. This excess disappears when the average core temperature becomes large enough to permit eddy transport and mixing processes near the upper surface. The steady-state limits in the transient experiments yield heat-transfer data in agreement with the results of the steady-state experiments.
Secular changes brought about by tidal friction in the solar system are reviewed. The presence or absence of specific changes is used to bound the values of Q (the specific dissipation function) appropriate for the planets and satellites. It is shown that the values of Q separate sharply into two groups. Values in the range from 10 to 500 are found for the terrestrial planets and satellites of the major planets. On the other hand, Q for the major planets is always larger than 6 × 104. Estimates of tidal dissipation in the atmospheres of the Jovian planets lead to values of Q which are consistent with those we have calculated on the basis of secular changes in the satellites' orbits. However, it is difficult to reconcile these large Q's with the much smaller values obtained in laboratory tests of solids. Lyttleton's hypothesis that Pluto is an escaped satellite of Neptune is critically examined. Using the Q's we obtain for the major planets and their satellites, we show that any eccentricity that Triton's orbit may have possessed after a near encounter with Pluto would have been subsequently damped, thus accounting for its present near-circular orbit.
The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and non-axisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.
Axisymmetric solutions become unstable to non-axisymmetric perturbations at values of the Rayleigh number that depend on Prandtl number and shell thickness. However, even when stable, axisymmetric solutions are not a preferred solution to the full equations; steady non-axisymmetric solutions are obtained for the same parameter values. Initial conditions determine the characteristics of the finite-amplitude solutions, including, in the cases of non-axisymmetry, whether or not a steady state is achieved. Transitions in horizontal flow structure can occur, accompanied by a transition in functional dependence of heat flux on Rayleigh number. The dominant modes in the solutions are usually the modes most unstable to the onset of convection, but not always.
If Hyperion's radius is near the upper limit of recent estimates, and tidal dissipation in Hyperion is reasonably well represented by a frequency-independent Q ≲ 2–300, finding Hyperion rotating in the 3:2 spin-orbit resonance like Mercury would imply a primordial origin for the Titan-Hyperion 4:3 orbital resonance. Independent of this test, observation of Hyperion's spin rate will place an upper bound on the average tidal effective Q for the satellite as a function of its assumed initial angular velocity.
The structures and thermal evolutions of the large icy-satellites of the outer solar system are considered. It is shown (for bodies comparable in size and mass to the Galilean satellites, having sizeable mass fraction of H2O, and with meteoritic abundances of radioactive materials contained within their silicate fractions) that the crust of solid ice over a liquid mantle predicted by conductive heat-transfer calculations is unstable to large-scale solid-state convection. For appropriate material parameters, convective heat-transfer rates are sufficient to freeze a large liquid mantle on a time scale that is short compared to the lifetime of the body. It is also concluded that the ice layer is convecting at the present time. A reevaluation of previous work, using improved values for material parameters and boundary conditions, reverses earlier conclusions and implies a rigid outer crust with resulting long-term stability of surface features to creep deformation. The combination of a rigid crust with active internal convection presents the additional possibility of surface features that are produced and maintained by dynamic internal processes.
Spectrophotometric observations of the jovian satellite Io on 20 and 21 February 1978 (Universal Time) were made from 1.2 to 5.4 micrometers. Io's brightness at 4.7 to 5.4 micrometers was found to be three to five times greater at an orbital phase angle of 68 degrees than at orbital phase angles of 23 degrees (5.5 hours before the brightening) and 240 degrees (20 hours after the brightening). Since the 5-micrometer albedo of Io is near unity under ordinary conditions, the observed transient phenomenon must have been the result of an emission mechanism. Although several such mechanisms were examined, the actual choice is not clear.
Steady-state thermal models for the large satellites of the outer planets strongly indicate that their interiors are currently maintained at temperatures well above the ice-ammonia eutectic temperature by the decay of long-lived radioisotopes of potassium, uranium, and thorium. The present-day steady-state thermal structure of a representative satellite, J IV (Callisto), is shown to be characterized by the presence of a thin icy crust over a deep liquid mantle, with a dense core of hydrous silicates and iron oxides. Some dynamical consequences of this model are briefly discussed.
The subsolidus convective cooling histories of terrestrial planets evolving from hot initial states are investigated quantitatively. A simple analytic model simulating average heat flux from a vigorously convecting mantle and incorporating a mantle viscosity proportional to mantle temperature and a lithosphere which thickens as the planet cools is employed. Heat flux from the convecting mantle is calculated on the basis of a power law relation between Nusselt number and Rayleigh number. The temperature distribution in the lithosphere is assumed to be linear throughout the cooling history of the planet. Cooling histories have been determined for the earth, Mars, Mercury and the moon and the mantle temperature decreases, mantle viscosity increases and decreases of heat flux to the surface and to the base of the lithosphere and of Nusselt and Rayleigh numbers are illustrated for each planet. It is found that primordial heat can contribute substantially to the present surface heat flux of a planet.