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. 2013 Mar;13(3):225-50.
doi: 10.1089/ast.2012.0851.

Tidal Venuses: triggering a climate catastrophe via tidal heating

Rory Barnes  1 , Kristina Mullins, Colin Goldblatt, Victoria S Meadows, James F Kasting, René Heller
Affiliations

Tidal Venuses: triggering a climate catastrophe via tidal heating

Rory Barnes et al. Astrobiology. 2013 Mar.

Abstract

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. We simulated the evolution of hypothetical planetary systems in a quasi-continuous parameter distribution and found that we could constrain the history of the system by statistical arguments. Planets orbiting stars with masses<0.3 MSun may be in danger of desiccation via tidal heating. We have applied these concepts to Gl 667C c, a ∼4.5 MEarth planet orbiting a 0.3 MSun star at 0.12 AU. We found 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 noncircular 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.

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Figures

FIG. 1.
FIG. 1.
Comparison of HZ boundaries for different planetary masses and desiccating greenhouses. The shaded regions represent the IHZ boundaries from Selsis et al. (2007): dark gray assumes no cloud coverage, medium gray 50%, and light gray 100%, and assuming a 1 MEarth planet. The black curves represent the runaway greenhouse limit from Pierrehumbert (2011), with a planetary albedo of 0.49. The solid curve is for a 30 MEarth planet, dashed for a 0.3 MEarth planet. For these calculations we used the stellar mass-radius relationship from Bayless and Orosz (2006), the mass-luminosity relationship from Reid and Hawley (2000), and the terrestrial mass-radius relationship from Sotin et al. (2007).
FIG. 2.
FIG. 2.
Parameter space of the Tidal Venus. The top left panel is a 0.1 MSun star, top right 0.15 MSun, bottom left 0.2 MSun, and bottom right 0.25 MSun. The grayscale represents the Selsis et al. (2007) IHZ boundaries: from lightest to darkest gray, the cloud coverage is 100%, 50%, and 0%, respectively. The colored curves mark where Ftide=Fcrit. Red curves assume the CTL model, blue the CPL. Solid curves assume the Pierrehumbert (2011) runaway greenhouse model and dotted the dry world model of Abe et al. (2011). Thick lines are for a 10 MEarth planet and thin for 1 MEarth. Tidal Venuses lie to the left of these curves.
FIG. 3.
FIG. 3.
Evolution of a 10 MEarth planet orbiting a 0.1 MSun star with an initial orbit of a=0.04 AU, e=0.3. Top: semimajor axis evolution. Top middle: eccentricity evolution. Middle: insolation evolution. Bottom middle: tidal heat flux evolution. Bottom: total surface heat flux (insolation+tidal).
FIG. 4.
FIG. 4.
Orbits of hypothetical planets around M dwarfs after tdes. The top left panel is a 0.1 MSun star, top right 0.15 MSun, bottom left 0.2 MSun, and bottom right 0.25 MSun. The grayscale represents the Selsis et al. (2007) IHZ boundaries with the same format as Fig. 2. For reference, the red and blue curves show the tidal greenhouse limit for a 2.5 MEarth planet with Qp=10 (CPL model, blue curve) or τp=640 s (CTL model, red curve). Contours denote levels of constant probability density (for densities 50%, 90%, and 99% of the peak value) for the initial orbit of the planet: solid corresponds to the CPL model (compare to blue curve), dashed to CTL (compare to red curve). In the bottom two panels there has been negligible orbital evolution for either tidal model.
FIG. 5.
FIG. 5.
Comparison of the IHZ to the tidal greenhouse limits for Gl 667C c, in a similar format as Fig. 2. Here the thin lines correspond to a 4.5 MEarth planet and thick to 9 MEarth. The vertical black lines correspond to the uncertainty in eccentricity of c and d (the latter's existence remains uncertain). The dashed, black curve represents where c's and b's orbits cross; hence the region to the left is dynamically unstable.
FIG. A1.
FIG. A1.
Surface flux required to trigger a runaway greenhouse (Fcrit) as a function of planet mass. The solid line is the relation for wet planets from Pierrehumbert (2011), and the cross is the limit from Abe et al. (2011) for a dry planet.
FIG. A2.
FIG. A2.
IHZ boundaries for different combinations of mass-radius and mass-luminosity relations and using the three different cloud cover IHZ limits from Selsis et al. (2007). Except for the inner edge near M*=0.2 MSun, the effective temperature does not affect the boundaries (note the numerous curves that are visible). Six combinations are plotted, but most are invisible as they are on top of each other. At low M*, the more interior IHZ limits assume the RH00 mass-luminosity relationship; see Appendix C.
FIG. B1.
FIG. B1.
Desiccation timescale for an Earth-like planet orbiting a 0.1 MSun star as a function of the fraction of the luminosity in the XUV and the efficiency of converting that energy into escaping particles. Contour lines are log10(tdes/yr). The planet initially has the same water mass fraction as the Earth and a semimajor axis of 0.03 AU.
FIG. C1.
FIG. C1.
Scaling relations for M dwarfs. Top: Mass-radius relations. Black curves are empirical relations: solid from BO06, dashed from RH00, and dotted from GS99. Red curves are theoretical curves from B98: solid assumes [Fe/H]=0, dashed [Fe/H]=™0.5. Bottom: Mass-luminosity relations. Black curves are empirical relations: solid from RH00 and dotted from S07. Red curves are theoretical curves from B98: solid assumes [Fe/H]=0, dashed [Fe/H]=™0.5.
FIG. D1.
FIG. D1.
Mass-radius relationships for terrestrial planets of varying compositions. Solid curves assume a roughly Earth-like composition, dashed are all silicates, dotted are at least half water, and dot-dashed are pure iron. Black correspond to Fortney et al. (2007), red to Sotin et al. (2007), blue to Grasset et al. (2009), green to Valencia et al. (2007), and orange to Seager et al. (2007).
FIG. E1.
FIG. E1.
Comparison of the equilibrium spin periods in the CPL framework. The solid line is the value predicted by our model, Eqs. E1–E4, the dashed is the “continuous” model of Goldreich (1966).
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References

    1. Abe Y. Matsui T. Evolution of an impact generated H2O–CO2 atmosphere and formation of a hot proto-ocean on Earth. Journal of Atmospheric Sciences. 1988;45:3081–3101.
    1. Abe Y. Abe-Ouchi A. Sleep N.H. Zahnle K.J. Habitable zone limits for dry planets. Astrobiology. 2011;11:443–460. - PubMed
    1. Adams E.R. López-Morales M. Elliot J.L. Seager S. Osip D.J. Transit timing variation analysis of OGLE-TR-132b with seven new transits. Astrophys J. 2011;728 doi: 10.1088/0004-637X/728/2/125. - DOI
    1. Agol E. Transit surveys for Earths in the habitable zones of white dwarfs. Astrophys J. 2011;731:L31.
    1. Aksnes K. Franklin F.A. Secular acceleration of Io derived from mutual satellite events. Astron J. 2001;122:2734–2739.

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