Viscoelastic Models of Tidally Heated Exomoons

Tidal heating of exomoons may play a key role in their habitability, since the elevated temperature can melt the ice on the body even without significant solar radiation. The possibility of life is intensely studied on Solar System moons such as Europa or Enceladus, where the surface ice layer covers tidally heated water ocean. Tidal forces may be even stronger in extrasolar systems, depending on the properties of the moon and its orbit. For studying the tidally heated surface temperature of exomoons, we used a viscoelastic model for the first time. This model is more realistic than the widely used, so-called fixed Q models, because it takes into account the temperature dependency of the tidal heat flux, and the melting of the inner material. With the use of this model we introduced the circumplanetary Tidal Temperate Zone (TTZ), that strongly depends on the orbital period of the moon, and less on its radius. We compared the results with the fixed Q model and investigated the statistical volume of the TTZ using both models. We have found that the viscoelastic model predicts 2.8 times more exomoons in the TTZ with orbital periods between 0.1 and 3.5 days than the fixed Q model for plausible distributions of physical and orbital parameters. The viscoelastic model gives more promising results in terms of habitability, because the inner melting of the body moderates the surface temperature, acting like a thermostat.Comment: accepted for publication in Ap

The Effect of Multiple Heat Sources on Exomoon Habitable Zones

With dozens of Jovian and super-Jovian exoplanets known to orbit their host stars in or near the stellar habitable zones, it has recently been suggested that moons the size of Mars could offer abundant surface habitats beyond the solar system. Several searches for such exomoons are now underway, and the exquisite astronomical data quality of upcoming space missions and ground-based extremely large telescopes could make the detection and characterization of exomoons possible in the near future. Here we explore the effects of tidal heating on the potential of Mars- to Earth-sized satellites to host liquid surface water, and we compare the tidal heating rates predicted by tidal equilibrium model and a viscoelastic model. In addition to tidal heating, we consider stellar radiation, planetary illumination and thermal heat from the planet. However, the effects of a possible moon atmosphere are neglected. We map the circumplanetary habitable zone for different stellar distances in specific star-planet-satellite configurations, and determine those regions where tidal heating dominates over stellar radiation. We find that the `thermostat effect' of the viscoelastic model is significant not just at large distances from the star, but also in the stellar habitable zone, where stellar radiation is prevalent. We also find that tidal heating of Mars-sized moons with eccentricities between 0.001 and 0.01 is the dominant energy source beyond 3--5 AU from a Sun-like star and beyond 0.4--0.6 AU from an M3 dwarf star. The latter would be easier to detect (if they exist), but their orbital stability might be under jeopardy due to the gravitational perturbations from the star.Comment: accepted for publication in A&A, 8 pages, 4 figure

Legendrian and transverse twist knots

In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the $m(5_2)$ knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least $n$ different Legendrian representatives with maximal Thurston--Bennequin number of the twist knot $K_{-2n}$ with crossing number $2n+1$. In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that $K_{-2n}$ has exactly $\lceil\frac{n^2}2\rceil$ Legendrian representatives with maximal Thurston--Bennequin number, and $\lceil\frac{n}{2}\rceil$ transverse representatives with maximal self-linking number. Our techniques include convex surface theory, Legendrian ruling invariants, and Heegaard Floer homology.Comment: 27 pages, v3: added figure, other minor changes, to appear in JEM

Interior Structures and Tidal Heating in the TRAPPIST-1 Planets

With seven planets, the TRAPPIST-1 system has the largest number of exoplanets discovered in a single system so far. The system is of astrobiological interest, because three of its planets orbit in the habitable zone of the ultracool M dwarf. Assuming the planets are composed of non-compressible iron, rock, and H$_2$O, we determine possible interior structures for each planet. To determine how much tidal heat may be dissipated within each planet, we construct a tidal heat generation model using a single uniform viscosity and rigidity for each planet based on the planet's composition. With the exception of TRAPPIST-1c, all seven of the planets have densities low enough to indicate the presence of significant H$_2$O in some form. Planets b and c experience enough heating from planetary tides to maintain magma oceans in their rock mantles; planet c may have eruptions of silicate magma on its surface, which may be detectable with next-generation instrumentation. Tidal heat fluxes on planets d, e, and f are lower, but are still twenty times higher than Earth's mean heat flow. Planets d and e are the most likely to be habitable. Planet d avoids the runaway greenhouse state if its albedo is $\gtrsim$ 0.3. Determining the planet's masses within $\sim0.1$ to 0.5 Earth masses would confirm or rule out the presence of H$_2$O and/or iron in each planet, and permit detailed models of heat production and transport in each planet. Understanding the geodynamics of ice-rich planets f, g, and h requires more sophisticated modeling that can self-consistently balance heat production and transport in both rock and ice layers.Comment: 34 pages, 3 tables, 4 figures. Accepted for publication in Astronomy & Astrophysics -- final version including corrections made in proof stag

Possibility for albedo estimation of exomoons: Why should we care about M dwarfs?

Occultation light curves of exomoons may give information on their albedo and hence indicate the presence of ice cover on the surface. Icy moons might have subsurface oceans thus these may potentially be habitable. The objective of our paper is to determine whether next generation telescopes will be capable of albedo estimations for icy exomoons using their occultation light curves. The success of the measurements depends on the depth of the moon's occultation in the light curve and on the sensitivity of the used instruments. We applied simple calculations for different stellar masses in the V and J photometric bands, and compared the flux drop caused by the moon's occultation and the estimated photon noise of next generation missions with 5 $\sigma$ confidence. We found that albedo estimation by this method is not feasible for moons of solar-like stars, but small M dwarfs are better candidates for such measurements. Our calculations in the J photometric band show that E-ELT MICADO's photon noise is just about 4 ppm greater than the flux difference caused by a 2 Earth-radii icy satellite in a circular orbit at the snowline of an 0.1 stellar mass star. However, considering only photon noise underestimates the real expected noise, because other noise sources, such as CCD read-out and dark signal become significant in the near infrared measurements. Hence we conclude that occultation measurements with next generation missions are far too challenging, even in the case of large, icy moons at the snowline of small M dwarfs. We also discuss the role of the parameters that were neglected in the calculations, e.g. inclination, eccentricity, orbiting direction of the moon. We predict that the first albedo estimations of exomoons will probably be made for large icy moons around the snowline of M4 -- M9 type main sequence stars.Comment: 13 pages, 6 figures, accepted for publication in A&