1.2. El campo académico-universitario
1.2.2. Especies de capital y de poder en el campo académico-universitario
As outlined above, C/O ratios of ⇠ 1 can lead to inversions in atmospheres with high enough effective temperature, if the stellar host is of K spectral type or earlier. The reason for the inversions to occur for these spectral types is that an appreciable amount of stellar flux is received from the star in the optical wavelength regime. This means that the alkali lines, and the pseudo-continuum contribution of the alkali line wings, will become very effective in absorbing the stellar irradiation. At the same time, close to C/O = 1, most of the oxygen and carbon is locked up in CO, leading to low H2O, CH4and HCN abundances and, hence, low opacities.
The combined effect of the effective absorption of the strong irradiation and a decreased ability of the atmospheric gas to cool, because of too little CH4, H2O, and HCN leads to the inversion in the atmospheres. In the simple analytic model introduced for the atmospheres in Section 2.2.1, this would mean that the IR opacity decreases, such that increases (cf. Figure2.2).
The absorption of the stellar light as a function of depth can be seen in Figure4.2, where I plotted the P –T structure of a log(g) = 3, [Fe/H] = 1, Te↵ = 2250 K, C/O = 0.95 atmosphere of a planet in orbit around a G5 star, as well as the local stellar flux at the pressure levels 3.47 ⇥ 10 5, 9.07 ⇥ 10 3and 1.27 ⇥ 10 1 bar in the atmosphere. Also a plot of the logarithm of the (rescaled) opacity log() is shown in the figure, for each pressure level. The respective pressure levels are indicated by red points in the P –T structure.
110 Chapter 4. The theoretical properties of hot jupiters
FIGURE4.2: Left panel: P –T -structure of a log(g) = 3, [Fe/H] = 1, Te↵= 2250 K, C/O = 0.95 atmosphere of a planet in orbit around a G5 star. Right panels: Local stel- lar flux (red solid line) at the three pressure levels at 3.47 ⇥ 10 5(top panel), 9.07 ⇥ 10 3(middle panel) and 1.27 ⇥ 10 1bar (bottom panel) in the atmosphere. The local opacity log() for each layer is shown as a gray solid line (rescaled). The respective pressure levels are indicated by a red circle, square and diamond in the P –T structure. Figure adapted fromMollière et al.(2015).
FIGURE4.3: Mass fractions of CH4(thin solid red line), H2O (dashed blue line), HCN (dotted green line) and CO (thick solid black line) as a function of the C/O ratio for a log(g) = 3, [Fe/H] = 1 atmosphere of a planet in orbit around a G5 star at a pressure level of 9.07 ⇥ 10 3bar. The top panel shows the mass fractions for a planet with Te↵= 1750 K while the bottom panel shows the mass fractions for a planet with Te↵= 2250 K. Figure adapted fromMollière
et al.(2015).
Figure4.2 nicely shows how the alkali pseudo-continuum absorbs the full stellar flux in its wavelength domain at the position of the inversion: At the highest pressure shown in the spectral plots (3.47 ⇥ 10 5 bar) the stellar flux is still completely unaffected by any absorption effects: the atmosphere is still optically thin at all wavelengths (except for right at the core of the alkali lines). At the hottest point in the temperature inversion (at 9.07 ⇥ 10 3 bar) one can see that the alkali wings have already started to absorb non-negligible amounts of energy, and just after the inversion (at 1.27 ⇥ 10 1 bar) the stellar flux in the alkali wings has been completely absorbed. Interestingly, the inversions obtained in this calculations, due to alkali heating, seem to abide by the rule that the tropopause5 should
commonly be found at ⇠ 0.1 bar for a wide variety of possible atmospheres (Robinson & Catling 2014).
As can be seen in the stellar flux spectrum at the highest pressure, the absorption of the stellar light outside of the alkali wings is rather sluggish, showing the importance of the alkali wings in the formation of the inversion.
As mentioned above, in a small region of C/O ratios around 1, the atmosphere’s ability to efficiently radiate away the absorbed stellar light decreases due to the involved chemistry. This can be seen well by looking at Figure4.3, which shows the CH4, H2O, HCN, and CO mass fractions in a log(g) = 3, [Fe/H] = 1 atmosphere of a planet in orbit around a G5 star as a function of C/O at a pressure level of 9.07 ⇥ 10 3 bar, i.e. close to the pressure where the inversion temperature, if an inversion occurs, is maximal. Two cases for planets with Te↵ = 1750 K and Te↵ = 2250 K are shown and I carried out 100 self-consistent atmospheric calculations for both cases with C/O going from 0.35 to 1.4 in equidistant steps.
One sees that for the Te↵ = 2250 K case, at C/O = 0.95, the H2O abundance has already decreased by 4 orders of magnitude when compared to the lowest C/O values, while the
CH4 abundance is still more than 2 magnitudes smaller than its highest abundance at the highest C/O values. Further, also HCN has not yet risen to a high enough abundance to take over the cooling. The C/O = 0.95 point at Te↵ = 2250 K is thus very close to the aforemen- tioned point of minimum IR opacity, leading to the inversions seen in my results for all host spectral types except M5. For higher C/O ratios the IR opacity, and the atmosphere’s ability to cool, increases, such that no inversions are observed anymore, mainly because HCN takes over the cooling.
FIGURE4.4: Emission spectra as a function of host star spectral type for a Te↵= 1750 K, log(g) = 3, [Fe/H] = 1 planet with C/O = 0.55 (upper panel) and C/O = 1.05 (lower panel). The spectra are shown for a F5 (blue lines), G5 (purple lines), K5 (red lines) and M5 (orange lines) host star. The colored bars indicate the position of the absorption maxima of vari- ous species. The black line shows the blackbody flux at the atmosphere’s effective temperature. Figure taken fromMollière et al.(2015).
For the particular case of Te↵ = 1750 K in Figure 4.1 the situa- tion must be different, as there is no inversion present in the atmo- sphere. The reason for this can be seen in the panel for Te↵ = 1750 K in Figure4.3: for this atmosphere the transition from water-rich to methane-rich atmospheres occurs much quicker as a function of C/O than it does for the Te↵= 2250 case. The methane mass fraction jumps from 10 8 to 10 5 at C/O = 0.93 and the HCN mass fraction jumps from 10 6to 10 4and no extended region of low water, methane and HCN abundance is seen. In con- clusion, this atmosphere can cool
more efficiently. Further, as this atmosphere is cooler, the overall CH4content is higher than in the hotter case. This is expected to occur and has been studied before both in equilib- rium and disequilibrium chemical networks (see, e.g.,Moses et al. 2013), showing that CH4 becomes less abundant as the temperature increases in carbon-rich atmospheres.