Figure 1: Artist’s impression of a habitable planet.
A previous study by Yang et al. (2013) showed that tidally-locked terrestrial planets around red dwarf stars can remain habitable at much closer distances to their host stars than previously thought due to a stabilizing cloud feedback mechanism. Strong convection drives the formation of water clouds that can cover most of the planet’s dayside, increasing the planet’s reflectivity and keeping the planet cool. In a more recent study by Yang et al. (2014), the focus shifts towards terrestrial planets around Sun-like stars, especially those near the inner edge of the habitable zone (HZ). The study examines the influence of planetary rotation on habitability.
A planet’s rotation rate determines its atmospheric circulation by establishing the strength of the Coriolis effect and the length of day. For a fast rotation rate, the Coriolis effect is strong and atmospheric circulation is organised into latitudinal bands, like on Earth - Hadley cell, Ferrel cell and Polar cell (Figure 2). Also, the short length of day due to fast rotation results in small surface temperature differences between day and night.
Figure 2: The three-cell model of atmospheric circulation on Earth. From Equator to Pole - Hadley cell, Ferrel cell and Polar cell. Source: Pearson Prentice Hall.
For a slow rotation rate, the Coriolis effect is weak and the Hadley cells can extend globally. If the rotation rate is slow enough, the dayside can become much warmer than the nightside, leading to atmospheric circulation characterised by ascending air masses on the warm dayside and descending air masses on the cold nightside.
Using 3D atmospheric general circulation models (GCMs), Yang et al. (2014) examined, for an Earth-analogue, rotation periods ranging from 12 hours to 365 days. In the 3D GCMs, the stellar flux is increased until the mean surface temperature reaches ~310 K, which is roughly when a runaway greenhouse effect begins to occur and the planet becomes too hot for habitability.
Rotation rate determines the atmospheric circulation, which in turn influences the spatial distribution of clouds on a planet. Clouds can reflect a great deal of incoming stellar flux back into space. In doing so, clouds play a vital role in regulating the planet’s surface temperature and hence, the planet’s habitability. For example, greater cloud coverage increases the planet’s reflectivity and keeps the planet cool.
The 3D GCMs revealed that for a given stellar flux, the surface temperature of rapidly rotating planets is much higher than that of slowly rotating planets. This is especially true for planets near the warm, inner edge of the HZ. The Earth, considered a rapidly rotating planet in this study, has high cloud coverage in the tropics due to the intertropical convergence zone (ITCZ) associated with the ascending air masses of the Hadley cells. These tropical clouds have the largest influence on Earth’s albedo (i.e. Earth’s reflectivity) because the tropics receive the highest amount of stellar flux.
If the stellar flux is increased for a rapidly rotating planet, the equator-to-polar temperature gradient decreases, weakening the Hadley cells, reducing tropical cloud coverage and decreases the planet’s albedo. The end result is more warming of the planet. This drives a positive feedback where the increase in stellar flux eventually leads to a runaway greenhouse effect, creating temperatures too hot for habitability.
For slowly rotating planets, the atmospheric circulation consists of Hadley cells that extend globally. This is unlike fast rotating planets whose atmospheric circulation is organised into latitudinal bands. On a slowly rotating planet, the substellar point (i.e. spot on the planet’s surface where the planet’s host star is “directly overhead”) moves slowly across the planet’s surface. Around the substellar point, convection leads to the formation of clouds that can cover much of the planet’s dayside. These clouds allow the planet to reflect incoming stellar flux, keeping the planet cool.
When stellar flux is increased for a slowly rotating planet, convection becomes stronger due to more heating of the planet’s dayside. This leads to the formation of yet more clouds, allowing the planet to reflect away more incoming stellar flux and creates a negative feedback that stabilizes the climate from overheating. As a result, the inner edge of the HZ for slowly rotating planets can be much closer to the host star than for rapidly rotating planets.
Figure 3: Dependence of planetary climate on rotation period for planets orbiting a Sun-like star. (a) and (b): Global-mean surface temperature (TS) and planetary albedo as a function of rotation period for a given stellar flux. The surface heat capacity (D) is equivalent to 50m of water. (c) and (d): Global-mean surface temperature (TS) and planetary albedo as a function of stellar flux for a given rotation period with D of 50 m. Source: Yang et al. (2014).
Figure 4: Differences in clouds and atmospheric circulation between rapidly (left) and slowly (right) rotating planets. Source: Yang et al. (2014).
Figure 5: Habitable zone boundaries as a function of stellar type and planetary rotation rate for a 1D radiative-convective model and for the 3D GCM. Blue line: outer edge of the HZ (Kopparapu et al. 2013); green line: inner edge of the HZ (Kopparapu et al. 2013); black line: inner edge of the habitable zone for rapidly rotating planets in this study; red line: inner edge of the habitable zone for slowly rotating planets in this study (rotation period of 128 days for G-type and F-type stars, and tidally-locked with an orbit of 60 days for M-type and K-type stars); gray line: the tidal-locking radius. Source: Yang et al. (2014).
Using the 3D GCMs, Yang et al. (2014) also examined a Venus-analogue with Venus’ orbital characteristics, but with Earth’s atmosphere. The results suggest that such a planet could be habitable, even though it receives a higher stellar flux of 2610 W/m^2 versus 1360 W/m^2 that Earth gets from the Sun. It would imply that when Venus went through a runaway greenhouse to become the hellish, inhospitable place it now is, it must have had a higher rotation rate at that time.
Figure 6: The climate of a planet with modern Earth’s atmosphere and continental configuration, but in Venus’ orbit and with Venus’ (slow) rotation rate. (a): Time series of global-mean surface temperature (TS) simulated for Venus’ rotation rate (slowly rotating, black), Earth’s rotation rate (rapidly rotating, green) and Venus’ rotation rate with clouds artificially set to zero (slowly rotating, no clouds, red). The planet quickly tends toward a runaway greenhouse if it is rapidly rotating or has no clouds, but is habitable if it is slowly rotating. (b): Global-mean TS and vertically-integrated ocean temperature (Tocn) in a coupled ocean-atmosphere simulation using Venus’ rotation rate. (c-e): maps of TS, planetary albedo and thermal emission to space averaged over 1 day in the simulation. The black dot in (c-e) is the transient substellar point, which moves eastward around the planet with a period of 117 days. Source: Yang et al. (2014).
- Yang et al. (2013), “Stabilizing Cloud Feedback Dramatically Expands the Habitable Zone of Tidally Locked Planets”, arXiv:1307.0515 [astro-ph.EP]
- Yang et al. (2014), “Strong Dependence of the Inner Edge of the Habitable Zone on Planetary Rotation Rate”, arXiv:1404.4992 [astro-ph.EP]
- Kopparapu et al. (2013), “Habitable Zones Around Main-Sequence Stars: New Estimates”, arXiv:1301.6674 [astro-ph.EP]