THERMAL PHASES OF EARTH-LIKE PLANETS: ESTIMATING THERMAL INERTIA FROM ECCENTRICITY, OBLIQUITY, AND DIURNAL FORCING

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 3x 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 (similar to 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.