Capital simbólico y especies de capital

In this Section I discuss important physical processes which govern the atmospheres of hot jupiters, and assess how well the version of petitCODE, used inMollière et al.(2015), was suited to describe them.

Chemistry

As summarized in Section3.4.1, petitCODE uses a chemical equilibrium model for obtaining molecular and atomic abundances, where in Mollière et al. (2015) we still used the CEA code, and switched to my self-written Gibbs minimizer inMollière et al.(2017, this study is described in Chapter5).

The knowledge of the abundances is fundamental for constructing the atmospheric opac- ities. As summarized in Section2.3.2, there are different regions in hot jupiter atmospheres, in which different chemical assumptions are fulfilled: usually the equilibrium abundances of the planet’s hot regions (dayside vs. nightside, deep atmosphere vs. upper atmosphere) dominate the cool regions, if the mixing processes in the horizontal or vertical direction are fast enough.

As explained in Section2.3.2, planets with equilibrium temperatures above 1000 1500 K should not be affected by non-equilibrium effects too much. This may change if photochem- ical reactions produce hazes, but the temperatures of hot jupiters are too high for the usually assumed photochemical haze species to be stable (see ‘Open Question’3, Section1.5). Be- cause the grid of model atmospheres I describe here goes down to atmospheric effective temperatures of 1000 K, the lowest temperature atmospheres in the grid may have needed non-equilibrium chemistry for a correct abundance computation. This should be kept in mind for deductions made with the cool grid models.

The following elemental species were assumed for the model calculations: H, He, C, N, O, Na, Mg, Al, Si, P, S, Cl, K, Ca, Ti, V, Fe and Ni. Based onSeager et al.(2000) I considered the following reaction products: e , H, He, C, N, O, Na, Mg, Al, Si, P, S, K, Ca, Ti, Fe, Ni, H2, CO, OH, SH, N2, O2, SiO, TiO, SiS, H2O, C2, CH, CN, CS, SiC, NH, SiH, NO, SN, SiN, SO, S2, C2H, HCN, C2H2, CH4, AlH, AlOH, Al2O, CaOH, MgH, MgOH, VO, VO2, PH3, CO2, TiO2, Si2C, SiO2, FeO, NH2, NH3, CH2, CH3, H2S, KOH, NaOH, NaCl, KCl, H+_{, H , Na}+_, K+_{, Fe (condensed), Al2O3 (condensed), MgSiO3 (condensed), SiC (condensed).}

The choice of condensed species is motivated by Seager et al. (2000); Sudarsky et al.

(2003). Additionally, I also added SiC as a condensable species, to account for condensation of C in atmospheres with a high C/O ratio, as has also been suggested bySeager et al.(2005).

Clouds

Clouds appear to be widespread in all planetary atmospheres (see ‘Open Question’3, Sec- tion1.5). The most commonly stated evidence for clouds or hazes in hot jupiter atmospheres is the fact that the transmission spectra of many of these objects show no or only weak fea- tures at optical wavelengths (see the ‘Transit spectroscopy’ part of Section1.4.1). A promi- nent example for such a planet, which appears to be cloudy in transmission, is HD 189733b, featuring a nearly flat transmission spectrum at optical wavelengths, except for the alkali line cores (e.g.Sing et al. 2011).

Assessing the influence of clouds on the P –T structure and emission spectra of hot jupiters is not an easy task.2 _{In the case of HD 189733b, which shows a nearly featureless}

optical transmission spectrum,Barstow et al.(2014) find that the temperature structure they retrieve, using the planet’s emission spectrum, is insensitive to whether or not a cloud model is included (they use various MgSiO3models). At the same time many of their cloud model setups are able to reproduce HD 189733b’s transmission spectrum. This indicates that for hot jupiters, at least for HD 189733b, the treatment of clouds is important for the appearance of the planet’s transmission spectrum, but not so much for the actual absorption of the bulk of the stellar light in the deeper layers of the dayside atmosphere. In this case the influence of clouds on the P –T structure and the emission spectrum would be minor. The reason why such situations can arise is straightforward to see: in Equation1.11it was derived that the slant optical depth for a stellar ray of light is set by a length scale ⇠ pRPlHP, whereas for the emission, which leaves the planet ⇠vertically, it is of the order of ⇠ HP. Due to this, the slant optical depths of possible cloud species can be ⇠35-90 times larger than the verti- cal optical depth (Fortney 2005). This is in agreement with the work byFortney et al.(2008), who find that clouds have a minor effect on their self-consistently calculated PT-profiles and emission spectra of hot jupiters, and therefore neglect clouds.

The Mollière et al.(2015) grid did not yet consider the formation of clouds. However, from the previous discussion I concluded that it may be permissible to neglect clouds, as long as only emission spectra are calculated. However, as pointed out byFortney (2005), in cases of high metallicity planets the effects of clouds may become important, especially if appreciable amounts of silicate, iron or corundum condensates can form. This has to be stressed in light of the fact that hot jupiters seem to be most prevalent in stellar systems of high metallicity (Fischer & Valenti 2005).

Because I neglected clouds, I further concluded that the omission of scattering in the

Mollière et al.(2015) grid was not introducing too large an error, thus no strong scattering contribution to the opacity in the NIR and MIR is to be expected. In addition, the reported optical albedos of hot jupiters are very low, in the low single digit percentage range, as

106 Chapter 4. The theoretical properties of hot jupiters

Te↵ (K) Te↵ [Fe/H] (dex) [Fe/H] C/O C/O SpT SpT log(g) log(g) 1000–2500 250 -0.5–2.0 0.5 0.35–1.4 0.1(a) _{M5–F5 “1”}(b) _{2.3–5 1.0}(a) TABLE4.1: Grid range and step size of theMollière et al.(2015) grid. Footnotes: (a): more finely or coarser spaced regions may exist, see Section4.2.2. (b): spectral types are stepped by “one” spectral type, with the associated temperature being 3000, 4345, 5570, and 6560 K for M5, K5, G5, and F5, respectively.

summarized by Madhusudhan et al. (2014c). Absorption appears much more important than scattering in these objects. Exceptionally cloudy hot jupiters may exist, however, such as Kepler 7b, having a geometric albedo of 0.32 ± 0.03 (Demory et al. 2011). In general, if scattering was important, then it would cause the incoming stellar radiation to traverse, on average, a somewhat longer distance through the atmosphere before reaching a certain pressure level (because it will carry out a random walk). Hence, the photons will on average be absorbed at lower pressures (higher altitudes), if they are not scattered back to space before. This will result in the deeper atmospheric regions to be cooler, also see Section2.2.1.

Horizontal winds

Based on GCM simulations and theoretical considerations, winds are expected to be present on hot jupiters, driven by the temperature contrasts between the day and nightside, and the polar and equatorial regions (see summary in Section2.1.1). In Section2.1.1I already mentioned that the higher the effective temperature of a hot jupiter, the less efficient the transport of energy by wind becomes (Perez-Becker & Showman 2013; Komacek & Show- man 2016;Komacek et al. 2017). For “cool” planets with effective temperatures of ⇠ 1000 K redistribution of energy may be quite efficient unless the planet has a mass of a few Jupiter masses or more (Kammer et al. 2015).

As summarized in Section3.1.1 (and Figure 3.1 therein) petitCODE has three possible ways to treat the distribution of the incident stellar light across the atmosphere, to at least partially accommodate the effect of heat redistribution by winds: (a) global averaging, and (b) dayside averaging (or (c), no wind transport of energy). For the grid presented inMol- lière et al.(2015), which goes from atmospheres at temperatures of 1000 to 2500 K (see Sec- tion4.2.2), I decided to consider a dayside-averaged case for the stellar irradiation as a com- promise between of the two limiting cases (a) and (c).

A fourth way would be to use a redistribution parameter for the incident stellar irra- diation which adds a fraction of the absorbed stellar energy to the night side internal tem- perature and decreases the amount of light to be absorbed on the dayside (Burrows et al. 2006). Other possibilities include the mimicking of planetary winds by assuming that the atmosphere carries out a rigid body rotation, and to follow a vertical atmospheric structure as it rotates around the planet, while modeling its time-dependent cooling (Iro et al. 2005).