An outline of Atmospheric Circulation and Composition of GJ 1214 b (Menou, 2011)

The so-called “super-earth” (i.e. a planet heavier than Earth, but lighter than Neptune) GJ 1214 b is an interesting planet. Its mass ($6.5\pm0.9$ $M_{\rm{earth}}$) and radius ($2.65\pm 0.11$ $R_{\rm{earth}}$) do not allow us to deduce a single model about the composition of the planet. Instead, several models could give the same observations of the mass and radius. We have written about research on the transmission spectrum of GJ 1214 b before, which may shed some light on the atmospheric composition.

Menou (2011) has conducted numerical investigations using a General Circulation Model (a GCM called IGCM3). They used the dual-band approximation, treating the incoming radiation from the star and the outgoing long-wave radiation as two broad bands, with a single opacity for each band. The use of a single value of opacity for a wide band is called the gray gas approximation – in reality, the opacity of a gas, alone or in an atmospheric mixture, will be strongly sensitive to frequency.

They investigate three atmospheric models:

1. a pure water atmosphere,
2. an atmosphere with composition similar to the solar composition, and
3. an atmosphere with 30 times solar composition, or “supersolar” composition.

These three models allow two comparisons to be made:

• A pure water atmosphere and a supersolar atmosphere have similar opacity, but very different mean molecular weights (18 v/s 3.3).
• A super-solar atmosphere and a solar atmosphere have similar molecular weight (3.3 and 2.2), but the super-solar atmosphere has a much higher opacity than the solar atmosphere.

All three models show broad superrotating equatorial jets (which have been found in many studies using GCMs in the past), and the poles are much colder than the equator due to the strong zonal circulation.

The following Figure shows the pressure-temperature profile for the water model at several points in the atmosphere. Each profile tells us how the temperature varies vertically above a certain point on the planet’s photosphere (the vertical axis is labelled in pressure, as pressure goes down monotonically with altitude).

Notice how the East terminator is warmer than the substellar point. This is similar to the results from the observed phase curve for HD 189733b, where Knutson et al. (2007) found that the hottest point is advected East of the substellar point. The poles are noticeably colder.

The following Figure shows the “phase-variation” of the planet, which tells us how bright the planet should look during its orbit. Zero phase, on the left, and phase = 1.0, refer to the transit, while phase=0.5 refers to the eclipse of the planet, i.e. the planet is behind the star.

Once again, we can see the phase shift of the hottest point, eastwards of the substellar point, due to the eastward superrotation.

The increased opacity when going from solar to super-solar composition decreases the radiative timescale about seven fold, but keeps the advection timescale the same. This causes the day side of the planet to warm up faster than it can transport heat to the night side.

Increasing the mean molecular weight from the super-solar composition to a pure water atmosphere increases the amplitude of the phase variation by decreasing the radiative timescale fivefold, and keeping the advection timescale constant, again warming the planet up faster than it can transport heat to the night side.

The techniques used in this study could be used in the future for other super-earths, and would shed light on the different effects of opacity and mean molecular weight on the observable phase curve.

Share.