Detectable molecular features above hydrocarbon haze via transmission spectroscopy with JWST: Case studies of GJ 1214b-, GJ 436b-, HD 97658b-, and Kepler-51b-like planets
Yui Kawashima Renyu Hu Masahiro Ikoma



















































Yui Kawashima
y.kawashima@sron.nl

0000-0003-3800-7518]Yui Kawashima
SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
Earth-Life Science Institute, Tokyo Institute of Technology 2-12-1-IE-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan


Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
Division of Geological and Planetary Sciences, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA


Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan















Some of the exoplanets so far observed show featureless or flat transmission spectra, possibly indicating the existence of clouds and/or haze in their atmospheres. 
Thanks to its large aperture size and broad wavelength coverage, JWST is expected to enable detailed investigation of exoplanet atmospheres, which could provide important constraints on the atmospheric composition obscured by clouds/haze.
Here, we use four warm (≲ 1000 K) planets suitable for atmospheric characterization via transmission spectroscopy, GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b, as examples to explore molecular absorption features detectable by JWST even in the existence of hydrocarbon haze in the atmospheres. We simulate photochemistry, the growth of hydrocarbon haze particles, and transmission spectra for the atmospheres of these four planets.

Among the planetary parameters considered, super-Earths with hazy, relatively hydrogen-rich atmospheres are mostly expected to produce detectable molecular absorption features such as a quite prominent CH_4 feature at 3.3 μm even for the extreme case of the most efficient production of photochemical haze.



For a planet that has extremely low gravity, such as Kepler-51b, haze particles grow significantly large in the upper atmosphere due to the small sedimentation velocity, resulting in the featureless or flat transmission spectrum in a wide wavelength range.
This investigation shows that the transmission spectra with muted features measured by HST in most cases do not preclude strong features at the longer wavelengths accessible by JWST.
























§ INTRODUCTION
 

Transmission spectra of close-in exoplanets observed so far are somewhat diverse <cit.>.


There are some studies that explored such diversity by examining the correlation between the observed amplitude of absorption features and the planetary properties 
<cit.>.

They all reached the conclusion that molecular absorption features are less pronounced in transmission spectra for lower equilibrium temperature although other planetary properties may affect such a correlation.

One explanation for this correlation is existence of photochemically-produced hydrocarbon haze obscuring the molecular features in the atmospheres of cooler planets <cit.>, because its primary source CH_4 exists only at such low temperatures (≲ 1000 K) <cit.>. 






Among stars hosting currently observable warm (≲ 1000 K) low-mass planets, GJ 1214, GJ 436, and HD 97658 are the only three host stars whose UV emission spectra have been observed <cit.>. 
Also, high-precision transmission spectra for their planets were observed with HST <cit.>.
They all show flat or featureless transmission spectra between 1.1 and 1.7 μ m, possibly indicating the existence of haze in the atmospheres. Since the knowledge of host-star's UV spectrum is essential for the modeling of hydrocarbon haze 
<cit.>, the above three planets serve as the most promising targets to understand the nature of haze in exoplanet atmospheres.
In addition, Kepler-51b is attracting attention as a favorable target for atmospheric characterization via transmission spectroscopy due to its extremely low density and large atmospheric scale height <cit.>.
In terms of haze science, this planet is also an interesting target because the sedimentation velocity of the particles in the atmosphere is expected to be quite low due to its low gravity, which allows particle growth in the upper atmosphere and mute features in the transmission spectrum.
Recently, <cit.> investigated the effect of dusty outflows for Kepler-51b and 51d and showed that the existence of small dust of a fixed size at high altitudes could flatten the transmission spectra.


Currently, the number of exoplanets suitable for atmospheric characterization is still small due to the lack of bright targets and sufficient observational precision. Fortunately, 
TESS <cit.> 
is expected to detect a great number of transiting exoplanets around nearby stars bright enough for atmospheric characterization. Also, 
JWST <cit.> 
will enable high-precision transmission spectroscopy thanks to its large diameter, and also enable the spectroscopy at longer wavelengths than HST with its suite of spectroscopy instruments up to 12 μm, with photometry up to 28.5 μm <cit.>.

In this Letter, we use the above four favorable planets, GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b, as examples and explore molecular absorption features detectable by JWST in the existence of hydrocarbon haze in their atmospheres.
Planets similar in size to GJ 1214b and HD 97658b have been shown to be abundant <cit.>, indicating more planets in this size range will be found by TESS and will be the primary targets for atmospheric characterization by JWST <cit.>.
We describe the models in <ref>, and show the results in <ref>. We 

discuss several effects to be examined in <ref> and conclude this Letter in <ref>




§ METHOD
 
We model transmission spectra of an atmosphere with hydrocarbon haze using the photochemical, particle growth, and transmission spectrum models of <cit.> as follows:
We first perform photochemical calculations to derive the steady-state, distribution of gaseous species. Our reaction rate list is the reduced vesion of <cit.> and we include the reverse reactions in the same way as <cit.>.

Then we assume that the production rate of haze monomers at each altitude as the sum of the photodissociation rates of the major hydrocarbons in our photochemical model, CH_4, HCN, and C_2H_2, as an upper limit for the monomer production rate since this approach effectively assumes 100% conversion efficiency from the photodissociation of these hydrocarbons to haze monomers.

With this assumption, we derive the steady-state distribution of haze particles by the particle growth calculations.
Finally, we model transmission spectra of the atmospheres with the obtained distributions of haze particles and gaseous species.

For the details of each of the three models, see <cit.>.

As for the UV spectra of the host stars GJ 1214, GJ 436, and HD 97658, we use the data constructed by the MUSCLES Treasury Survey <cit.>.



As for Kepler-51 whose UV spectrum has not been observed, 
because of its similar properties to the Sun,

we use the solar spectrum from <cit.>[http://vpl.astro.washington.edu/spectra/stellar/other_stars.htm].


The setting for the atmospheres is as follows.
We assume that the elemental abudance ratios of the atmospheric gas are the solar system ones, which we take from Table 2 of <cit.>.

For the temperature-pressure profile, we use the analytical formula of Eq. (29) of <cit.>.
We choose the values of the parameters, namely, the intrinsic temperature T_int, irradiation temperature T_irr, averaged opacity in the optical k_v and that in the infrared k_th, so as to match the temperature-pressure profiles from <cit.> (the version with the solar metallicity and efficient dayside-to-nightside heat redistribution) for GJ 1214b and from <cit.> (their solar-metallicity version) for GJ 436b. 

As for HD 97658b and Kepler-51b, we adopt the same parameter values 
as the case of GJ 1214b except for T_irr, which 
we calculate 
with Eq. (1) of <cit.>.


We adopt the lower-boundary pressure of 1000 bar for photochemical calculation, 
while 10 bar in particle growth and transmission spectrum calculations.

For the calculations of photochemistry and particle growth, we choose the values of the reference radius equivalent to 1000 bar so as to roughly match the observed transit radii 
for a clear solar-composition atmosphere. 
Only for Kepler-51b, we use different values of the 1000-bar radius for two cases of the hazy and clear atmospheres. 
This is because with the same 1000-bar radius as in the clear atmosphere case, we would obtain too large transit radii for the hazy atmosphere to be consistent with the observed depth due to its extremely low gravity.
When calculating the transmission spectra, we find the appropriate value of 10-bar radius that minimizes the reduced χ^2 value in comparison between the theoretical and observed transit depths. We consider the observed transmission spectra of <cit.>, <cit.>, <cit.> for GJ 1214b, GJ 436b, and HD 97658b, respectively, and the observed radius of Kepler-51b from <cit.>. 
For the calculation of theoretical transit depth for each observed data point, we consider the transmission curve of the filter used in the observation, taking those data 
from the SVO Filter Profile Service[http://svo2.cab.inta-csic.es/theory/fps/] <cit.>.

The parameters and their values we use are listed in Table <ref>.



llll
Model parameters and their values used in the simulations 

Parameter     Description     Value     Reference 


Common parameters 

K_zz     Eddy diffusion coefficient     1.00 × 10^7 cm^2 s^-1     

s_1     Monomer radius     1.00 × 10^-3 μm     

ρ_p     Particle internal density     1.00 g cm^-3     
 GJ 1214b 

R_s     Host star radius     0.201 R_⊙     <cit.> 

M_p     Planet mass     6.26 M_⊕     <cit.> 

R_1000 _bar     1000-bar radius     2.07 R_⊕     

a     Semi-major axis     0.0148 AU     <cit.> 

d     Distance     14.6 pc     <cit.> 
 
T_int     Intrinsic temperature     120 K     

T_irr     Irradiation temperature     790 K     

k_v     Averaged opacity in the optical     10^-4.1 cm^2 g^-1     

k_th     Averaged opacity in the infrared     10^-2.7 cm^2 g^-1     
 GJ 436b 

R_s     Host star radius     0.464 R_⊙     <cit.> 

M_p     Planet mass     23.2 M_⊕     <cit.> 

R_1000 _bar     1000-bar radius     3.758 R_⊕     

a     Semi-major axis     0.02872 AU     <cit.> 

d     Distance     10.1 pc     <cit.> 
 
T_int     Intrinsic temperature     170 K     

T_irr     Irradiation temperature     860 K     

k_v     Averaged opacity in the optical     10^-3.6 cm^2 g^-1     

k_th     Averaged opacity in the infrared     10^-2.3 cm^2 g^-1     
 HD 97658b 

R_s     Host star radius     0.703 R_⊙     <cit.> 

M_p     Planet mass     7.86 M_⊕     <cit.> 

R_1000 _bar     1000-bar radius     1.943 R_⊕     

a     Semi-major axis     0.0796 AU     <cit.> 

d     Distance     21.1 pc     <cit.> 
 
T_int     Intrinsic temperature     120 K     

T_irr     Irradiation temperature     1037 K     

k_v     Averaged opacity in the optical     10^-4.1 cm^2 g^-1     

k_th     Averaged opacity in the infrared     10^-2.7 cm^2 g^-1     
 Kepler-51b 


R_s     Host star radius     0.940 R_⊙     NASA Exoplanet Archivea 

M_p     Planet mass     2.1 M_⊕     <cit.> 

R_1000 _bar     1000-bar radius     1.8 R_⊕b     

a     Semi-major axis     0.2514 AU     <cit.> 

T_int     Intrinsic temperature     120 K     

T_irr     Irradiation temperature     793 K     

k_v     Averaged opacity in the optical     10^-4.1 cm^2 g^-1     

k_th     Averaged opacity in the infrared     10^-2.7 cm^2 g^-1     

ahttps://exoplanetarchive.ipac.caltech.edu
bWe use the value of 2.3 R_⊕ for the clear atmosphere case



















§ RESULTS
 
Figure <ref> shows the transmission spectrum models for atmospheres with and without haze for the cases of GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b.




We calculate the deviation in transit depth caused by n H_ref at a reference pressure level, R_ref, as 2 n R_ref H_ref / R_s^2 <cit.>, where H_ref is the atmospheric scale height at R_ref.
The reference pressures are taken to be 10^-4 bar for GJ 1214b, GJ 436b, and HD 97658b, and 10^-6 bar for Kepler-51b, which roughly correspond to the pressure-levels of the transit radii.


Note that the transmission spectrum models for clear atmospheres are also calculated with the distribution of gaseous species 
from photochemical calculations.






A number of spectral features are produced by molecules above the optically-thick photochemical haze.

These features are generally ≲ 2 atmospheric scale heights for GJ 1214b- and GJ 436b-like planets, and ≲ 1 for HD 97658b-like planets, while ≲ 6 for the cases of clear atmospheres. As photodissociation is the driver for haze formation, this finding is general for exoplanets having solar composition atmospheres under similar levels of UV irradiation.






Considering a precision of ∼25 ppm expected to be achieved by JWST <cit.> and a spectral resolution of R = 100, we find detectable absorption features with the upper-limit production rate of haze monomers for each planet as listed in Table <ref>.





lll
Detectable absorption features by JWST

Planet Type    
Molecules    
Wavelength [μm] 


GJ 1214b     H_2O     1.4, 1.8, 1.9, 2.6, 2.7, 5.0, 5.2, 6.5, 6.6, 7.2 

     CH_4     1.7, 2.3, 3.2, 3.3, 3.4, 3.6, 7.4, 7.7, 8.2, 8.3 

     NH_3     3.0, 6.2, 8.9-11.8 

     HCN     3.0 

     CO_2     4.2 
 GJ 436b     CH_4     2.3, 3.3, 7.7 

     NH_3     10.4, 10.7 
 HD 97658b     -     - 
 Kepler-51b     H_2O     2.6, 2.7, 5.2 

     CO_2     4.3 

     CO     4.6





Some molecular absorption features will be detectable for a planet like GJ 1214b, due to lower incoming UV flux, namely lower monomer production rate, and larger planet-to-star radius ratio.

For the planet GJ 1214b itself, however, the 1.4 μm H_2O feature was not detected by <cit.> at the precision of ∼ 25 ppm.
While <cit.> demonstrated that their haze formation efficiency parameters of ≳ 10% could match the observed flatness of <cit.> for 50 × Solar atmosphere, by considering particle growth, we have confirmed that our 1, 10, 100, 1000 × Solar atmospheres all fail to become as flat as the observation even adopting the maximum monomer production rates <cit.>, possibly indicating extremely high metallicity, and/or aggregate haze particles <cit.>, and/or coexistence of haze and other aerosols (see also discussion in <ref>).

The message here is that a GJ 1214b-like planet having solar composition atmospheres and similar UV environment will be particularly suitable for future atmospheric characterization.
For the case of HD 97658b, all the features in the wavelength range 
are undetectable due to the higher incoming UV flux, namely higher monomer production rate, and smaller planet-to-star radius ratio.

Among the detectable molecules, it is promising that several features of CH_4, which is a key indicator of haze formation, remains detectable even in the existence of haze for GJ 1214b- and GJ 436b-like planets, especially for its 3.3 μm feature.
Note that this strong 3.3 μm CH_4 feature has been detected in the solar occultation spectrum of cooler celestial bodies in our solar system such as Saturn <cit.> and Titan <cit.>.
In the spectrum for Kepler-51b, the CH_4 features are invisible, because CH_4 is photodissociated and virtually absent above a thick haze layer at the low pressures of ∼ 10^-6 bar.







In the case of Kepler-51b, the transmission spectrum model for the atmosphere with haze is quite featureless due to the existence of large haze particles in the upper atmosphere, 

unlike in the other three cases.
However, distinct absorption features of CO_2 and CO

are detectable due to their larger abundances in the upper atmosphere.

This comes from its extremely low gravity, which makes an optical depth for a given pressure much larger

and thus both the photodissociation rate of CH_4 and resultant production flux of atomic carbon much smaller. 
This very small production flux of C allows effective conversion of C into CO/CO_2 by reaction between H_2O, while C remains abundant and CO/CO_2 less abundant for the other planet cases.





















In Figure <ref>, we plot the calculated vertical profiles of haze properties for the typical super-Earth gravity case of (a) HD 97658b and the extremely low gravity case of (b) Kepler-51b. 
In the case of HD 97658b, in the upper atmosphere (≲ 10^-6 bar), particles grow little because sedimentation occurs faster than collisional growth. 

Collisional growth occurs significantly from the pressure level of ∼ 10^-6 bar on and results in haze particles with the average radius of ∼ 3-4 μm at the lower boundary of 10 bar. 

On the other hand, in the case of Kepler-51b, it is demonstrated that haze particles grow much larger in the upper atmosphere (∼ 0.1 μm at ∼ 10^-6 bar) and results in the particles of as large as ∼ 100 μm at 10 bar. This is because particles can become large via collisional growth even in the upper atmosphere, instead of falling downward rapidly, due to the small sedimentation velocity from low gravity.
Note that although the monomer production rate for Kepler-51b is ∼ 2 times higher than that for HD 97658b, the effect of the extremely low gravity turns out to make a much greater contribution to such a difference between those two spectra than that of high monomer production rate. Trends of vertical profiles for GJ 1214b and GJ 436b are similar to that of HD 97658b but with slightly smaller haze mass density because of the smaller monomer production rates <cit.>.







§ DISCUSSION
 





In this study, we have assumed maximum production rate of haze monomers in order to explore the detectable features at the worst case for solar composition atmospheres. 


As for the eddy diffusion coefficient, the molecular absorption features become more prominent for the larger value because of the efficient downward transport of haze particles, while remaining similar for the smaller value <cit.>.



In order to briefly assess the effect of metallicity and C/O ratio, in Figure <ref>, we show the transmission spectrum models for the cases of different metallicity and C/O ratio for GJ 1214b. One realizes that more absorption features become detectable for the case of 100 × Solar atmosphere because of the smaller monomer production rate due to an enhanced photon-shielding effect by other molecules, while some features at relatively long wavelengths become undetectable due to smaller atmospheric scale height <cit.>. On the other hand, the effect of the C/O ratio is relatively small and among the detectable features for the solar composition atmosphere, H_2O features at 1.8, 5.0, 5.2, and 7.2 μm, CO_2 features at 4.2 μm, and NH_3 features at 6.2 μm become undetectable due to the slightly higher monomer production rate <cit.>.








Besides hydrocarbon haze, the existence of other aerosols can mute spectral features in transmission: condensation clouds such as KCl, ZnS, K_2SO_4, ZnO, and graphite clouds in the temperature range of interest in this study (≲ 1000 K) <cit.> and photochemical haze made of sulfur species <cit.>.



In outflowing atmospheres, while having little effect on 
the profiles of pressure and density, the velocity of the outward flow may affect the sedimentation of small particles.

The sedimentation velocity of haze particles are much faster than the outward velocity, which we estimate with the isothermal Parker solution <cit.> for simplicity, for all the cases except Kepler-51b, whereas we have confirmed that in the case of Kepler-51b, the sedimentation velocity of the volume-averaged-size particles are smaller than the outward velocity for the region of the pressures lower than 1.3 × 10^-7 bar. However, since the dominant monomer production region is below this pressure-level, 
the flow would have little impact on our results. The detailed consideration of this effect is beyond the scope of this study.

Also, as for 
extended atmospheres like Kepler-51b's, the effect of the tidal potential may affect the hydrostatic structure of the atmosphere. By using Eq. (12) of <cit.>, we have confirmed that the gravitational potential at the optically thick radius at 1.0 × 10^-6 bar, which is 9% of its Hill radius, would decrease to 86% due to the tidal potential and thus do not have significant impact on our results.






§ CONCLUSIONS
 
In this study, we have used four warm (≲ 1000 K) planets suitable for atmospheric characterization via transmission spectroscopy, GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b, as examples and explored molecular absorption features detectable by JWST even in the existence of hydrocarbon haze in their atmospheres. 


Using the 
models of <cit.>, we have simulated photochemistry, the growth of hydrocarbon haze particles, and transmission spectra for the atmospheres of these four planets.

We have found
that among the planetary parameters considered, super-Earths with hazy, relatively hydrogen-rich atmospheres are mostly expected to produce detectable molecular absorption features such as a quite prominent CH_4 feature at 3.3 μm even for the extreme case of the most efficient production of photochemical haze.








The sizes of those features correspond to 1∼2 atmospheric scale heights; while they are substantially smaller than a haze-free atmosphere, those features would be detectable with at precision expected for JWST.
Especially, planets with higher gravity, lower UV irradiation, and higher temperature are more suitable <cit.>.
Slight disagreement between our synthetic spectrum and very flat one observed for GJ 1214b, however, implies the importance of additional confounding effects. 

We have also demonstrated that in the case of extremely low gravity planet, Kepler-51b, haze particles grow significantly large in the upper atmosphere due to the small sedimentation velocity, resulting in the featureless or flat transmission spectrum in a wide wavelength range.

In summary, various molecular absorption features are expected to be detectable for relatively hydrogen-rich atmospheres even in the existence of hydrocarbon haze 
with JWST, given its high precision and long-wavelength capabilities.
We thus suggest that the transmission spectra with muted features measured by 
HST in most cases do not preclude strong features at the longer wavelengths accessible by JWST.





We thank the anonymous referee for his/her careful reading and constructive comments, which helped us improve this letter greatly.
The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
Y.K. thanks the travel support of JPL's Science Visitor and Colloquium Program.
Y.K. is supported by the Grant-in-Aid for JSPS Fellow (JSPS KAKENHI No.15J08463), Leading Graduate Course for Frontiers of Mathematical Sciences and Physics, Grant-in-Aid for Scientific Research (A) (JSPS KAKENHI No.15H02065), and the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement 776403.
R.H. is supported by NASA Grant No. 80NM0018F0612.
M.I. is supported by JSPS KAKENHI No. 18H05439 and Core-to-Core Program International Network of Planetary Sciences.
This work has made use of the MUSCLES Treasury Survey High-Level Science Products (doi:10.17909/T9DG6F) and the SVO Filter Profile Service (http://svo2.cab.inta-csic.es/theory/fps/) supported from the Spanish MINECO through grant AyA2014-55216.

































































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