One of the most basic conclusions from early secondary eclipse detections, as noted by Seager & Deming [2010], was the confirmation that ‘hot’ Jupiters were indeed hot. Predictions of temperatures for these planets exceeded 1000 K, in agreement with the brightness temperatures derived from infra-red secondary eclipse observations [e.g. see Cowan & Agol, 2011, Table 1]. Early theoretical models also highlighted that the dominant energy source for hot Jupiters would be the irradiating flux (rather than energy released through gravitational contraction) and that this would significantly alter the temperature structure and emergent spectra compared with isolated planets [Seager & Sasselov, 1998].
These early theoretical studies also suggested that silicate clouds on the most highly irradiated planets could increase albedos significantly [e.g. Sudarsky et al., 2000]. However, this is not supported by the significant amounts of infra- red flux detected in secondary eclipse observations. Stronger evidence comes from direct measurements of the geometric albedo, through optical secondary eclipse and phase curve detections. For example, Rowe et al. [2008] found that for HD 209458b Ag,M OST <0.08 at 1σ (where the MOST bandpass is 400−700 nm). The authors argue thatAB<0.12, ruling out the possibility of reflective clouds. Other examples
Figure 1.13: 4.5µm phase curve for HD 189733b, taken usingSpitzer’s IRAC instru-
ment [Knutson et al., 2012]. The eclipse signals for the planet are clear and have a depth of 0.18 %, while the phase curve has an amplitude of 0.09 %, implying a modest day-night temperature contrast of 260 K. Note that the troughs and peaks of the phase curve model are not centred on φ= 0 and 0.5, which Knutson et al. [2012] interpret as evidence of a strong equatorial jet.
of planets with low albedo include TrES-2b, Kepler-5b and Kepler-6b. However, recent results have uncovered planets that buck this trend, for example Kepler-7b for whichAg = 0.35±0.02 in the Kepler bandpass, with high altitude silicate clouds being a possible explanation [Demory et al., 2011].
The level of day-side thermal emission for hot Jupiter planets is not only given by the opacity sources (which set the albedo), but also the efficiency with which the irradiating energy is transported from the (permanent) day-side to the night-side of the planet. Theoretically this contrast is often described in terms of two competing processes: re-radiation of the incident stellar energy, which supports the day-night contrast, and redistribution of the energy (by advection) to the planet’s night-side, which suppresses the contrast [Fortney et al., 2008].
Information on this efficiency can be derived from thermal phase curves by measuring the planet’s day-night flux contrast. Large contrasts suggest a poor heat redistribution efficiency and vice versa. Examples of large contrasts have been found for WASP-18b [Maxted et al., 2013] and WASP-12b [Cowan et al., 2012], with the value for WASP-12b being particularly extreme at ∆T4.5µm≃1900 K. More modest
measurements for the planet HD 189733b [see Figure 1.13; Knutson et al., 2012]. The flux maxima and minima in the HD 189733b phase curves were found to be sig- nificantly offset from their expectations (φ= 0.5 andφ= 0, respectively) consistent with the advection of the longitudinal temperature structure by a super-rotating equatorial jet (supporting the inference of significant advection from the day-night contrast). These phase curve results show that, even amongst these handful of plan- ets, there is diversity in the global atmospheric properties of hot Jupiters - another example of the diversity being seen in the exoplanet population.
A greater body of observations exists for infra-red secondary eclipse detec- tions than exists for optical secondary eclipse and thermal phase curve observations. The number of hot Jupiter planets that have had at least one such detection cur- rently8 stands at over 40. Many of these have been taken with Spitzer’s IRAC instrument in various combinations of the photometric bands this instrument offers (centred on 3.6, 4.5, 5.8 and 8.0µm). Making use of this larger sample, Cowan & Agol
[2011] carried out a statistical analysis of possible albedo and redistribution efficien- cies of 24 planets. From secondary eclipse measurements, estimates of the day-side effective temperature (Td) of each planet were derived and used to constrain the
Bond albedo (AB) and redistribution efficiency using the parameterisation:
Td=T0(1−AB)1/4 2 3 − 5 12ε 1/4 , (1.11) whereT0= q R⋆
a Teff is the equilibrium temperature of the planet’s sub-stellar point (a measure of the irradiating flux), and Teff is the stellar effective temperature. ε
describes the extent to which heat is redistributed from the day- to night-side of the planet. It can take values 06ε61, where ε= 1 describes the fully redistributed case (i.e. no day-night contrast - the planet emits isotropically), whileε= 0 is for no redistribution (i.e. instantaneous re-radiation).
For a given estimate of Td/T0, AB and εare degenerate (equation 1.11), so
unique estimates of these quantities cannot be made. However, from the ensemble of 24 planets Cowan & Agol [2011] note interesting trends in the data. They find that low Bond albedo values are favoured (typicallyAB<0.35), which is an independent
confirmation of the conclusions from reflected light measurements. They also find that the most highly irradiated planets have uniformly highTd/T0 values, suggesting
they have both low albedos and low redistribution efficiencies (see Figure 1.14). On the other hand, less highly irradiated planets show a variety of albedos and/or redistribution efficiencies. This trend is found to qualitatively agree with the fact
Figure 1.14: Day-side effective temperature estimates, normalised to the equilibrium temperature of the planet’s sub-stellar point (Td/T0), plotted against the irradiation
level of the planet. The solid red line represents the maximum day-side effective temperature, where the planet absorbs all of the incident stellar flux and re-radiates it without redistribution. More weakly irradiated planets show a range of Td/T0,
while the most highly irradiated planets (Tε=0 >2400 K) tend to have high Td/T0
values, implying both lowAB and εvalues. Figure from Cowan & Agol [2011].
that the time-scale for radiative processes on these planets is expected to be a stronger inverse function of temperature than the advective time-scales [Cowan & Agol, 2011]. Subsequent infra-red observations, including some of the phase curve studies highlighted earlier, have supported this trend.