Transmission spectroscopy relies on the light of the star being blocked by the thin annulus of the planet’s atmosphere. A separate and complementary set of techniques relies on the emitted thermal flux of the planet itself; these are the secondary eclipse and thermal phase curve measurements. Because these photons are directly emitted by the planet itself, these methods give an insight into the thermal structure and heat transport within the planetary atmosphere.
Analogous to the primary transit, the thermal flux of the planet can be blocked out as it passes behind the star. Note that the presence of a primary transit does not necessarily mean that a secondary transit will occur, and vice versa, due to non-zero eccentricities. Approximating both the star and the planet as black body radiators, the expected occultation signal is
δF F = Rp R∗ 2B λ(Tp) Bλ(T∗) (1.28) where Bλ is the Planck function, and Tp and T∗ are the equilibrium temperatures
of the planet and the star, respectively.
A diagram of this expected contrast ratio against J band magnitude is shown in Figure 1.15. In contrast to the optical transmission spectroscopy diagram shown in Figure 1.11, HD 209458b and particularly HD 189733b have significantly stronger signals than any other exoplanet. However, the absolute signal strengths are typi- cally higher than found in transmission spectroscopy for all planets.
The thermal emission of an exoplanet was detected for the first time using
Spitzer for TrES-1b by Charbonneau et al. (2005) and for HD 209458 by Deming et al. (2005).
A carbon rich chemistry was inferred for WASP-12b by Madhusudhan et al. (2011), by combining J H and K data from ground based observatories withSpitzer
data of the secondary eclipse. Their analysis suggested a deep carbon monoxide signature in the dayside spectrum, but very low, or no absorption from water. Their atmospheric recovery suggested a scenario where the carbon to oxygen ratio was greater than 1, whereas C/O is only 0.54 in the Sun (Asplund, 2005). Studies of planetary debris on white dwarfs suggest that such C/O ratios are uncommon
(Wilson et al., 2016). More recent results from Kreidberg et al. (2015) do detect a very significant water signal in the atmosphere of WASP-12b, and with a new method of atmospheric fitting, they showed that C/O ratios>1 were ruled out at greater than 3σ significance by these new data. For the time being, carbon planets, while in principle very interesting objects, have no observational evidence of their existence.
As well as the secondary eclipse, if the thermal emission is not emitted evenly from the planet’s surface (and due to the tidal locking, the extreme flux contrast be- tween the two hemispheres makes this seem unlikely), there will be a thermal phase curve, as the orbit of the planet changes the portion of the emitting surface that is observed from the Earth, transitioning from being almost entirely the permanent night side close to the primary transit, to almost entirely the day side close to the secondary transit.
The first detection of a planet’s thermal phase curve was made by Harrington et al. (2006) using theSpitzer space telescope. The 24 micrometer light curve forν
Andromedae b showed that there was indeed a variation in flux between the day and the night side, indicating that the timescale for heat transport was comparable to the radiative timescale in the atmosphere. Other hot Jupiters show less significant flux differences between the day and night sides of the planet (e.g. Cowan et al., 2007; Zellem et al., 2014), with indications that the heat transport efficiency may be proportional to the planet’s irradiation level.
Knutson et al. (2007a, 2009) found that the maxima of the thermal phase curve of HD 189733b was significantly offset from the secondary eclipse time, and were able to construct a longitudinal map of the brightness temperature of the planet (see Figure 1.16). They found that the brightest point of the planet’s atmosphere was offset from the substellar point by approximately 30 degrees. This was inter- preted as evidence of strong equatorial winds blowing around the equator of the planet, with speeds of up to 10 km s−1 which was an early prediction of General Circulation Models of hot Jupiters (Showman and Guillot, 2002). The equatorial jet is a natural consequence in highly irradiated, tidally locked atmospheres, and is caused by planetary scale Rossby waves interacting with the day to night flow caused by the extreme temperature contrast between the two hemispheres (Showman and Polvani, 2011).
It was predicted that these strong winds would also imprint signatures on the transmission spectra, through Doppler shifting the transmission lines (Showman et al., 2013; Miller-Ricci Kempton and Rauscher, 2012). In addition to an equatorial jet, these models predicted an average blue shift to the planet’s atmosphere from
4 6 8 10 12 14 16 J magnitude 1.0 0.01 0.0001 Eclipse Signal (p ercent) HD 209458 b HD 189733 b 55 Cnc e
Figure 1.15: A plot of J magnitude against the expected thermal eclipse signal for transiting planets. Planets detected through radial velocity are in pink, through ground based transit in blue, and space based transit in yellow. Planets with radii smaller than 0.1 RJ are plotted as triangles. Several important exoplanets are
labeled, exquisite phase curves of a super Earth recently (Demory et al., 2016a), (Demory et al., 2016b). The signal sizes are significantly larger than transmission spectroscopy (though the systematics inSpitzer more than make up for it), also not that unlike in transmission spectroscopy, HD 189733b is significantly better than any other target.
Figure 1.16: The Spitzer lightcurve and inferred temperature distribution of HD189733b from Knutson et al. (2007a). The hottest point of the atmosphere is clearly offset from the substellar point, indicating planetary winds.
a polar wind. Measuring these wind speeds directly through transmission spec- troscopy, instead of indirectly with thermal phase curves, in principle allows direct constraints on theories of heat transport in planets to be made.
Redfield et al. (2008) found a very high average blueshift in the signal of sodium in HD 189733b, though they suspected that this was a systematic effect due the unphysicaly high velocity, which was significantly higher than the speed of sound. In Chapter 5 I will show that this was likely caused by not accounting the the Rossiter-Mclaughlin effect on the stellar absorption lines. Using high dispersion spectroscopy, Snellen et al. (2010) was able to measure the average windspeed of HD 209458b, and found that there was an average blueshift of 2±1 km s−1. In Chap- ter 5 I find a very similar average wind velocity in the atmosphere of HD 189733b, 1.9+0−0..76 km s−1, but I will also show that with high dispersion spectroscopy it is possible to spatially resolve the atmosphere. This allows direct measurements of wind speeds on the two limbs of the planet, and is no longer limited to being a sin- gle velocity for the whole planet. Refinement of this technique, and application to other exoplanets, will enable tests of the predictions of heat transport in exoplanet atmospheres.