Effects of extreme obliquity variations on the habitability of exoplanets

Abstract

We explore the impact of obliquity variations on planetary habitability in hypothetical systems with high mutual inclination. We show that large-amplitude, high-frequency obliquity oscillations on Earth-like exoplanets can suppress the ice-albedo feedback, increasing the outer edge of the habitable zone. We restricted our exploration to hypothetical systems consisting of a solar-mass star, an Earth-mass planet at 1 AU, and 1 or 2 larger planets. We verified that these systems are stable for 10(8) years with N-body simulations and calculated the obliquity variations induced by the orbital evolution of the Earth-mass planet and a torque from the host star. We ran a simplified energy balance model on the terrestrial planet to assess surface temperature and ice coverage on the planet's surface, and we calculated differences in the outer edge of the habitable zone for planets with rapid obliquity variations. For each hypothetical system, we calculated the outer edge of habitability for two conditions: (1) the full evolution of the planetary spin and orbit and (2) the eccentricity and obliquity fixed at their average values. We recovered previous results that higher values of fixed obliquity and eccentricity expand the habitable zone, but we also found that obliquity oscillations further expand habitable orbits in all cases. Terrestrial planets near the outer edge of the habitable zone may be more likely to support life in systems that induce rapid obliquity oscillations as opposed to fixed-spin planets. Such planets may be the easiest to directly characterize with space-borne telescopes.

FIG. 1.

A simplified schematic illustrating how the evolution of the inclination leads to an evolution in obliquity. As the inclination of the orbit increases, the spin axis continues to point at a fixed position in space, causing the angle between the spin axis and the fundamental plane to increase. In this figure, the inclination changes in such a way that the obliquity goes from a starting value of 23.5 degrees to 0 degrees. (Color graphics available online at www.liebertonline.com/ast)

FIG. 2.

Orbital-rotational results for System 1, Baseline, the Earth-like comparison system. The left column shows the variations of eccentricity, inclination, and longitude of ascending node; the right column shows the variations of the argument of perihelion, obliquity, and precession rates.

FIG. 3.

Orbital-rotational results for System 2. The left column shows the variations of eccentricity, inclination, and longitude of ascending node; the right column shows the variations of the argument of perihelion, obliquity, and precession rates.

FIG. 4.

Orbital-rotational results for System 3. The left column shows the variations of eccentricity, inclination, and longitude of ascending node; the right column shows the variations of the argument of perihelion, obliquity, and precession rates.

FIG. 5.

Orbital-rotational results for System 4. The left column shows the variations of eccentricity, inclination, and longitude of ascending node; the right column shows the variations of the argument of perihelion, obliquity, and precession rates.

FIG. 6.

Orbital-rotational results for System 5. The left column shows the variations of eccentricity, inclination, and longitude of ascending node; the right column shows the variations of the argument of perihelion, obliquity, and precession rates.

FIG. 7.

Orbital-rotational results for System 6. The left column shows the variations of eccentricity, inclination, and longitude of ascending node; the right column shows the variations of the argument of perihelion, obliquity, and precession rates.

FIG. 8.

Orbital-rotational results for System 7. The left column shows the variations of eccentricity, inclination, and longitude of ascending node; the right column shows the variations of the argument of perihelion, obliquity, and precession rates.

FIG. 9.

Baseline climate models for an Earth-like planet with ψ=25, e=0.0 (top); ψ=25, e=0.15 (middle); and ψ=90, e=0.0 (bottom). The discontinuities are caused by the change in albedo between an ice/snow-covered and ice-free surface.

FIG. 10.

The temperature habitability index (THI, left column), the ice habitability index (IHI, middle column), and the mean global temperature (right column) for seven systems listed in Section 3. From top to bottom: System 1 (Baseline) through System 7.

FIG. 11.

A visualization for the HZ enhancement factors from Table 4. The height of the bars is the HZ enhancement factor, E_S, for the complete simulations. The green box shows the fraction of that enhancement due to the variability of the system, E_V.

FIG. 12.

A comparison of how the eccentricity and obliquity impact the calculated outer edge of the HZ as determined by the temperature habitability index for the baseline opacity of 0.095. The top panels show the eccentricity (left) and obliquity (right) for the variable runs. The bottom panels show the same for the static cases. The error bars for the simulations represent the standard deviation in the eccentricity and the obliquity. Note there is little correlation with eccentricity but a strong correlation between obliquity and the outer edge of the HZ. When the variability in the runs is removed, the outer edge moves inward in all but four cases (see Table 4). Values for the linear fits are given in Table 5. (Color graphics available online at www.liebertonline.com/ast)