87 research outputs found
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
Square root and division elimination in PVS
International audienceIn this paper we present a new strategy for PVS that imple- ments a square root and division elimination in order to use automatic arithmetic strategies that were not able to deal with these operations in the ﰁrst place. This strategy relies on a PVS formalization of the square root and division elimination and deep embedding of PVS expressions inside PVS. Therefore using computational reﰂection and symbolic com- putation we are able to automatically transform expressions into division and square root free ones before using these decision procedures
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
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
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
The role of chaotic resonances in the solar system
Our understanding of the Solar System has been revolutionized over the past
decade by the finding that the orbits of the planets are inherently chaotic. In
extreme cases, chaotic motions can change the relative positions of the planets
around stars, and even eject a planet from a system. Moreover, the spin axis of
a planet-Earth's spin axis regulates our seasons-may evolve chaotically, with
adverse effects on the climates of otherwise biologically interesting planets.
Some of the recently discovered extrasolar planetary systems contain multiple
planets, and it is likely that some of these are chaotic as well.Comment: 28 pages, 9 figure
Needle & knot : binder boilerplate tied up
To lighten the burden of programming language mechanization, many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages.
This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its meta-theory constructively guarantees the coverage of a considerable amount of binder boilerplate for well-formed specifications, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in COQ and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems.
Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables
The co-administration of quetiapine or placebo to cognitive-behavior therapy in treatment refractory depression: A preliminary trial
A seven-planet resonant chain in TRAPPIST-1
The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star1. At least seven planets similar to Earth in radius were previously found to transit this host star2. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost transiting planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations3 and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 R⊕ and an equilibrium temperature of 169 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf
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