19 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
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
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
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