Directly imaged exoplanets in reflected starlight. The importance of knowing the planet radius
Authors: Carrión-González Óscar , García Muñoz Antonio , Cabrera Juan , Csizmadia Szilárd , Santos Nuno C. , Rauer Heike 
Published: October 2020

AbstractDirect-imaging observations of exoplanets in reflected starlight are expected to be available this decade. This will improve our knowledge about cold and temperate exoplanets and their atmospheres. Current theoretical efforts related to such planets aim to understand the effects that planet and atmospheric properties have on the spectra to be measured. This will help predict the science outcome of direct-imaging missions and identify the key needs for models used in the interpretarion of future measurements. In this work, we have investigated the information contained in reflected-light exoplanetary spectra and the role played by the planet radius in the atmospheric characterization.IntroductionLong-period exoplanets are a population that remains substantially unexplored because of the biases introduced by the technology currently available. These planets have small transit probabilities due to their large orbital distances and hence the direct-imaging technique will be key to analyse their atmospheres. Space missions such as NGRST (formerly WFIRST), LUVOIR or HabEx will allow us to study this population of long-period exoplanets, providing a more complete picture of exoplanet diversity.ModelWe set up an atmospheric model with hydrogen and helium as the main components. We include methane, in a volume-mixing-ratio fCH4, as the only absorbing gaseous species. We add a cloud layer, described by its optical thickness (&#964;c), its geometrical extension and the position of the cloud top. The aerosols are modelled by their single-scattering albedo and their effective radius, which determines the scattering phase function through Mie theory. This model is motivated by previous modelling of the atmospheres of Solar System gas giants. Apart from the six atmospheric parameters, we include the planet radius (Rp) as another model parameter. We apply our analysis to a particular target, Barnard's Star b candidate super-Earth[1], although our conclusions are generally planet-independent.RetrievalWe built a grid of ~300,000 synthetic reflected-light spectra for a range of possible atmospheric configurations. The spectra were computed at phase angle &#945;=0&#186; (that is, with the exoplanet fully illuminated). The wavelength interval under study is 500-900 nm and the spectral resolution, R~125-225. The multiple-scattering radiative-transfer problem was solved with a previously validated code[2].Observations were simulated by adding wavelength-independent noise at S/N=10. Three atmospheric configurations were considered to simulate observations and carry out retrievals: a cloud-free one (&#964;c=0.05), one with a thin-cloud (&#964;c=1.0) and one with a thick-cloud (&#964;c=20.0). We developed an MCMC-based retrieval package achieving a continuous sampling of the parameter space by interpolating within the pre-computed grid of spectra.The retrievals were carried out for cases where the planet radius was either known (and hence there were only 6 free parameters) or completely unconstrained (7 free parameters). We also analysed intermediate scenarios in which estimates of Rp with different uncertainties were assumed.ResultsThe retrievals of atmospheric properties degrade as the uncertainties in the value of Rp increase. Indeed, the correlations between model parameters triggered by adding Rp as a free parameter make it challenging to distinguish between cloudy- and cloud-free atmospheres. Fig. 1 shows that, even if the atmosphere contains a thick-cloud, the evidence for the cloud disappears as the uncertainties in Rp grow. When the planet radius is a priori unconstrained, the retrieval of &#964;c shows a nearly-flat posterior probability distribution. This indicates that the evidence is equal for both thick clouds or cloud-free atmospheres. On the other hand, if Rp is known we can generally distinguish between cloudy or cloud-free atmospheres in all of the scenarios analysed in this work. The retrieval results for other parameters such as the methane abundance also improve if the planet radius is known.Fig. 1 also shows that a priori estimates on the value of Rp improve the retrievals. This result encourages the development of synergies between direct-imaging and other techniques in order to reduce the uncertainties in the mass and radius of long-period exoplanets.Besides, we find that, if Rp is completely unconstrained, direct-imaging observations can constrain its value to within a factor of ~2 for all the cases explored. This might help start addressing the bulk composition of an exoplanet.Several works have addressed the possible science return of future direct-imaging observations[3]-[5]. Since the exoplanets observed in direct-imaging will generally lack a measurement of Rp, we conclude that this parameter will play an important role in the retrievals and therefore should be included in this type of retrieval exercises.References[1]&#160;Ribas et al. (2018), Nature, 563, 365[2] Garc&#237;a Mu&#241;oz &amp; Mills (2015), A&amp;A, 573, A72[3] Lupu et al. (2016), AJ, 152, 217[4] Nayak et al. (2017), PASP, 129, 973[5] Damiano &amp; Hu (2019), AJ, 159, 175&#160;