Thermal Phases of Earth-Like Planets: Estimating Thermal Inertia From Eccentricity, Obliquity, and Diurnal Forcing

Abstract

In order to understand the climate on terrestrial planets orbiting nearby Sun-like stars, one would like to know their thermal inertia. We use a global climate model to simulate the thermal phase variations of Earth analogs and test whether these data could distinguish between planets with different heat storage and heat transport characteristics. In particular, we consider a temperate climate with polar ice caps (like the modern Earth) and a snowball state where the oceans are globally covered in ice. We first quantitatively study the periodic radiative forcing from, and climatic response to, rotation, obliquity, and eccentricity. Orbital eccentricity and seasonal changes in albedo cause variations in the global-mean absorbed flux. The responses of the two climates to these global seasons indicate that the temperate planet has 3× the bulk heat capacity of the snowball planet due to the presence of liquid water oceans. The obliquity seasons in the temperate simulation are weaker than one would expect based on thermal inertia alone; this is due to cross-equatorial oceanic and atmospheric energy transport. Thermal inertia and cross-equatorial heat transport have qualitatively different effects on obliquity seasons, insofar as heat transport tends to reduce seasonal amplitude without inducing a phase lag. For an Earth-like planet, however, this effect is masked by the mixing of signals from low thermal inertia regions (sea ice and land) with that from high thermal inertia regions (oceans), which also produces a damped response with small phase lag. We then simulate thermal light curves as they would appear to a high-contrast imaging mission (TPF-I/Darwin). In order of importance to the present simulations, which use modern-Earth orbital parameters, the three drivers of thermal phase variations are (1) obliquity seasons, (2) diurnal cycle, and (3) global seasons. Obliquity seasons are the dominant source of phase variations for most viewing angles. A pole-on observer would measure peak-to-trough amplitudes of 13% and 47% for the temperate and snowball climates, respectively. Diurnal heating is important for equatorial observers (∼5% phase variations), because the obliquity effects cancel to first order from that vantage. Finally, we compare the prospects of optical versus thermal direct imaging missions for constraining the climate on exoplanets and conclude that while zero-and one-dimensional models are best served by thermal measurements, second-order models accounting for seasons and planetary thermal inertia would require both optical and thermal observations.

Demarcating Circulation Regimes of Synchronously Rotating Terrestrial Planets within the Habitable Zone

“…Thermal phase curves have been proposed as a relatively simple method for observing and characterizing terrestrial extrasolar planets (e.g., Cowan et al (2012)). Thermal phase curves show the disk-integrated thermal flux emitted by a planet as seen by the observer as a function of the planet's position in its orbit around the host star.…”

Climate variations on Earth-like circumbinary planets

“…We then use the model as a basis to discuss more complex aspects of the climate response to periodic forcings. Similar types of models have been used to describe thermally heated slab-oceans28293031. The model equations are introduced and solved in the methods section.…”

ORBITAL PHASE VARIATIONS OF THE ECCENTRIC GIANT PLANET HAT-P-2b

“…Thermal phase variations probe the diurnal cycle, T (Φ). A tidally locked planet has a one-to-one correspondence between local stellar zenith angle and longitude (e.g., φ = Φ), but phase maps can be made regardless of rotation rate (e.g., for Earth; Cowan et al 2012b).…”