Dispersion Relation of a Ferrofluid Layer of Any Thickness and Viscosity in a Normal Magnetic Field; Asymptotic Regimes

We have calculated the general dispersion relationship for surface waves on a ferrofluid layer of any thickness and viscosity, under the influence of a uniform vertical magnetic field. The amplification of these waves can induce an instability called peaks instability (Rosensweig instability). The expression of the dispersion relationship requires that the critical magnetic field and the critical wavenumber of the instability depend on the thickness of the ferrofluid layer. The dispersion relationship has been simplified into four asymptotic regimes: thick or thin layer and viscous or inertial behaviour. The corresponding critical values are presented. We show that a typical parameter of the ferrofluid enables one to know in which regime, viscous or inertial, the ferrofluid will be near the onset of instability.Comment: 21 pages, 6 eps figures, Latex, to be published in Journal de Physique I

A Temporal Map in Geostationary Orbit: The Cover Etching on the EchoStar XVI Artifact

Geostationary satellites are unique among orbital spacecraft in that they experience no appreciable atmospheric drag. After concluding their respective missions, geostationary spacecraft remain in orbit virtually in perpetuity. As such, they represent some of human civilization's longest lasting artifacts. With this in mind, the EchoStar XVI satellite, to be launched in fall 2012, will play host to a time capsule intended as a message for the deep future. Inspired in part by the Pioneer Plaque and Voyager Golden Records, the EchoStar XVI Artifact is a pair of gold-plated aluminum jackets housing a small silicon disc containing one hundred photographs. The Cover Etching, the subject of this paper, is etched onto one of the two jackets. It is a temporal map consisting of a star chart, pulsar timings, and other information describing the epoch from which EchoStar XVI came. The pulsar sample consists of 13 rapidly rotating objects, 5 of which are especially stable, having spin periods < 10 ms and extremely small spindown rates. In this paper, we discuss our approach to the time map etched onto the cover and the scientific data shown on it; and we speculate on the uses that future scientists may have for its data. The other portions of the EchoStar XVI Artifact will be discussed elsewhere.Comment: Accepted for publication in Astronomical Journa

Exomoon habitability constrained by energy flux and orbital stability

Detecting massive satellites of extrasolar planets has now become feasible, which led naturally to questions about their habitability. In a previous study we presented constraints on the habitability of moons from stellar and planetary illumination as well as from tidal heating. Here I refine our model by including the effect of eclipses on the orbit-averaged illumination. Moons in low-mass stellar systems must orbit their planet very closely to remain bound, which puts them at risk of strong tidal heating. I first describe the effect of eclipses on stellar illumination of satellites. Then I calculate the orbit-averaged energy flux including illumination from the planet and tidal heating. Habitability is defined by a scaling relation at which a moon loses its water by the runaway greenhouse process. As a working hypothesis, orbital stability is assumed if the moon's orbital period is less than 1/9 of the planet's orbital period. Due to eclipses, a satellite in a close orbit can experience a reduction in orbit-averaged stellar flux by up to about 6%. The smaller the semi-major axis and the lower the inclination of the moon's orbit, the stronger the reduction. I find a lower mass limit of ~0.2M_sun for exomoon host stars to avoid the runaway greenhouse effect. Precise estimates depend on the satellite's orbital eccentricity. Deleterious effects on exomoon habitability may occur up to ~0.5M_sun. Although the habitable zone lies close to low-mass stars, which allows for many transits of planet-moon binaries within a given observation cycle, resources should not be spent to trace habitable satellites around them. Gravitational perturbations by the star, another planet, or another satellite induce eccentricities that likely make any moon uninhabitable. Estimates for individual systems require dynamical simulations that include perturbations among all bodies and tidal heating in the satellite.Comment: 4 pages, 2 figures, accepted by A&

Oscillations in the Habitable Zone around Alpha Centauri B

The Alpha Centauri AB system is an attractive one for radial velocity observations to detect potential exoplanets. The high metallicity of both Alpha Centauri A and B suggest that they could have possessed circumstellar discs capable of forming planets. As the closest star system to the Sun, with well over a century of accurate astrometric measurements (and Alpha Centauri B exhibiting low chromospheric activity) high precision surveys of Alpha Centauri B's potential exoplanetary system are possible with relatively cheap instrumentation. Authors studying habitability in this system typically adopt habitable zones (HZs) based on global radiative balance models that neglect the radiative perturbations of Alpha Centauri A. We investigate the habitability of planets around Alpha Centauri B using 1D latitudinal energy balance models (LEBMs), which fully incorporate the presence of Alpha Centauri A as a means of astronomically forcing terrestrial planet climates. We find that the extent of the HZ is relatively unchanged by the presence of Alpha Centauri A, but there are variations in fractional habitability for planets orbiting at the boundaries of the zone due to Alpha Centauri A, even in the case of zero eccentricity. Temperature oscillations of a few K can be observed at all planetary orbits, the strength of which varies with the planet's ocean fraction and obliquity.Comment: 10 pages, 9 figures, accepted for publication in MNRA

Habitable Climates: The Influence of Obliquity

Extrasolar terrestrial planets with the potential to host life might have large obliquities or be subject to strong obliquity variations. We revisit the habitability of oblique planets with an energy balance climate model (EBM) allowing for dynamical transitions to ice-covered snowball states as a result of ice-albedo feedback. Despite the great simplicity of our EBM, it captures reasonably well the seasonal cycle of global energetic fluxes at Earth's surface. It also performs satisfactorily against a full-physics climate model of a highly oblique Earth-like planet, in an unusual regime of circulation dominated by heat transport from the poles to the equator. Climates on oblique terrestrial planets can violate global radiative balance through much of their seasonal cycle, which limits the usefulness of simple radiative equilibrium arguments. High obliquity planets have severe climates, with large amplitude seasonal variations, but they are not necessarily more prone to global snowball transitions than low obliquity planets. We find that terrestrial planets with massive CO2 atmospheres, typically expected in the outer regions of habitable zones, can also be subject to such dynamical snowball transitions. Some of the snowball climates investigated for CO2-rich atmospheres experience partial atmospheric collapse. Since long-term CO2 atmospheric build-up acts as a climatic thermostat for habitable planets, partial CO2 collapse could limit the habitability of such planets. A terrestrial planet's habitability may thus depend sensitively on its short-term climatic stability.Comment: Minor changes, references added. 34 pages, 13 figures, accepted by Ap

Tidal Venuses: Triggering a Climate Catastrophe via Tidal Heating

Traditionally stellar radiation has been the only heat source considered capable of determining global climate on long timescales. Here we show that terrestrial exoplanets orbiting low-mass stars may be tidally heated at high enough levels to induce a runaway greenhouse for a long enough duration for all the hydrogen to escape. Without hydrogen, the planet no longer has water and cannot support life. We call these planets "Tidal Venuses," and the phenomenon a "tidal greenhouse." Tidal effects also circularize the orbit, which decreases tidal heating. Hence, some planets may form with large eccentricity, with its accompanying large tidal heating, and lose their water, but eventually settle into nearly circular orbits (i.e. with negligible tidal heating) in the habitable zone (HZ). However, these planets are not habitable as past tidal heating desiccated them, and hence should not be ranked highly for detailed follow-up observations aimed at detecting biosignatures. Planets orbiting stars with masses <0.3 solar masses may be in danger of desiccation via tidal heating. We apply these concepts to Gl 667C c, a ~4.5 Earth-mass planet orbiting a 0.3 solar mass star at 0.12 AU. We find that it probably did not lose its water via tidal heating as orbital stability is unlikely for the high eccentricities required for the tidal greenhouse. As the inner edge of the HZ is defined by the onset of a runaway or moist greenhouse powered by radiation, our results represent a fundamental revision to the HZ for non-circular orbits. In the appendices we review a) the moist and runaway greenhouses, b) hydrogen escape, c) stellar mass-radius and mass-luminosity relations, d) terrestrial planet mass-radius relations, and e) linear tidal theories. [abridged]Comment: 59 pages, 11 figures, accepted to Astrobiology. New version includes an appendix on the water loss timescal

Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity

In this paper, we present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut model, valid at any order in eccentricity, obliquity and spin. We demonstrate, both analytically and numerically, that, except if the system was formed with a nearly circular orbit (e<0.2), solving consistently the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal models truncated at second order in eccentricity, as done in all previous studies, lead to erroneous tidal evolutions. As a consequence, tidal energy dissipation rates are severely underestimated in all these calculations and the characteristic timescales for the various orbital parameters evolutions can be wrong by up to three orders in magnitude. Based on these complete, consistent calculations, we revisit the viability of the tidal heating hypothesis to explain the anomalously large radius of transiting giant planets. We show that, even though tidal dissipation does provide a substantial contribution to the planet's heat budget and can explain some of the moderately bloated hot-Jupiters, this mechanism can not explain alone the properties of the most inflated objects, including HD 209458b. Indeed, solving the complete tidal equations shows that enhanced tidal dissipation and thus orbit circularization occur too early during the planet's evolution to provide enough extra energy at the present epoch. In that case another mechanisms, such as stellar irradiation induced surface winds dissipating in the planet's tidal bulges, or inefficient convection in the planet's interior must be invoked, together with tidal dissipation, to provide all the pieces of the abnormally large exoplanet puzzle.Comment: 14 pages, 10 figures, Accepted for publication in Astronomy and Astrophysics

Tidal effects on brown dwarfs: Application to the eclipsing binary 2MASSJ05352184-0546085 - The anomalous temperature reversal in the context of tidal heating

2MASSJ05352184-0546085 (2M0535-05) is the only known eclipsing brown dwarf (BD) binary, and so may serve as an important benchmark for models of BD formation and evolution. However, theoretical predictions of the system's properties seem inconsistent with observations: i. The more massive (primary) component is observed to be cooler than the less massive (secondary) one. ii. The secondary is more luminous (by roughly 10^{24} W) than expected. We study the impact of tidal heating to the energy budget of both components. We also compare various plausible tidal models to determine a range of predicted properties. We apply two versions of two different, well-known models for tidal interaction, respectively, (i.) the 'constant-phase-lag' model and (ii.) the 'constant-time-lag' model, and incorporate the predicted tidal heating into a model of BD structure. We find that the contribution of heat from tides in 2M0535-05 alone may only be large enough to account for the discrepancies between observation and theory in an unlikely region of the parameter space. The tidal quality factor of BDs, Q_{BD}, would have to be 10^{3.5} and the secondary needs a spin-orbit misalignment greater than 50 degrees. However, tidal synchronization time scales for 2M0535-05 restrict the tidal dissipation function Q_{BD} to values greater than 10^{4.5} and rule out intense tidal heating in 2M0535-05. We provide the first constraint on Q_{BD}. Tidal heating alone is unlikely to be responsible for the surprising temperature reversal within 2M0535-05. But an evolutionary embedment of tidal effects and a coupled treatment with the structural evolution of the BDs is necessary to corroborate or refute this result.Comment: accepted by AandA January 2010, 18 pages, 13 figures, 1 tabl

Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates corrections in the theory of tidal despinning and libration damping. We prove that when the inclination is low and phase lags are linear in frequency, the Kaula series is equivalent to a corrected version of the MacDonald method. The correction to MacDonald's approach would be to set the phase lag of the integral bulge proportional to the instantaneous frequency. The equivalence of descriptions gets violated by a nonlinear frequency-dependence of the lag. We explain that both the MacDonald- and Darwin-torque-based derivations of the popular formula for the tidal despinning rate are limited to low inclinations and to the phase lags being linear in frequency. The Darwin-torque-based derivation, though, is general enough to accommodate both a finite inclination and the actual rheology. Although rheologies with Q scaling as the frequency to a positive power make the torque diverge at a zero frequency, this reveals not the impossible nature of the rheology, but a flaw in mathematics, i.e., a common misassumption that damping merely provides lags to the terms of the Fourier series for the tidal potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the magnitudes of the terms, too, get changed. Reinstating of this detail tames the infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial text overlap with arXiv:0712.105

Effect of the stellar spin history on the tidal evolution of close-in planets

We investigate how the evolution of the stellar spin rate affects, and is affected by, planets in close orbits, via star-planet tidal interactions. To do this, we used a standard equilibrium tidal model to compute the orbital evolution of single planets orbiting both Sun-like stars and 0.1 M\odot M-dwarfs. We tested two stellar spin evolution profiles, one with fast initial rotation (P=1.2 day) and one with slow initial rotation (P=8 day). We tested the effect of varying the stellar and planetary dissipation and the planet's mass and initial orbital radius. Conclusions: Tidal evolution allows to differentiate the early behaviors of extremely close-in planets orbiting either a rapidly rotating star or a slowly rotating star. The early spin-up of the star allows the close-in planets around fast rotators to survive the early evolution. For planets around M-dwarfs, surviving the early evolution means surviving on Gyr timescales whereas for Sun-like stars the spin-down brings about late mergers of Jupiter planets. In light of this study, we can say that differentiating between one spin evolution from another given the present position of planets can be very tricky. Unless we can observe some markers of former evolution it is nearly impossible to distinguish the two very different spin profiles, let alone intermediate spin profiles. Though some conclusions can still be drawn from statistical distributions of planets around fully convective M-dwarfs. However, if the tidal evolution brings about a merger late in its history it can also entail a noticeable acceleration of the star in late ages, so that it is possible to have old stars that spin rapidly. This raises the question of better constraining the age of stars