Strategies for Constraining the Atmospheres of Temperate Terrestrial Planets with JWST

When using JWST to probe exoplanet atmospheres with high-precision time-series observations, the precision expected for each observing mode depends on the stellar energy distribution (SED) of the parent star. We first compute the potential systematic noise sources from each instrument mode using PandExo, described in Batalha et al. (2017). PandExo relies on the JWST Exposure Time Calculator engine Pandeia (Pontoppidan et al. 2016) to compute throughputs, realistic point spread functions and other instrumental effects. Both PandExo and Pandeia generally agree with the instrument team’s individual noise simulators to better than 10% (Batalha et al. 2017).

First, we compute simulations for each time-series spectroscopy mode, using the standard readout patterns offered in Cycle 1. Then, we explore the expected performance for readout patterns and observing strategies that have been proposed. We bin all of our calculations to a resolving power of R = 100 to facilitate direct comparisons between different instruments (later discussed in Section 3.1). Lastly, we use a T = 2550 K, M/H = 0.4, and log g = 4.0 Phoenix stellar model (Husser et al. 2013) for all of the calculations in this work because we are using TRAPPIST-1 as a case study.

Extensive theoretical work has been done to assess the climate, habitability, composition, and detectability of the planets that transit TRAPPIST-1 (Barstow & Irwin 2016; Bolmont et al. 2017; Dong et al. 2018; Morley et al. 2017; Turbet et al. 2017; Unterborn et al. 2017; Wolf 2017). Nevertheless, a model capable of predicting, a priori, the atmospheric composition of these planets from the few known parameters (mass, radius, orbital properties) does not exist. Therefore, many of the predictions of the atmospheric composition of these planets are grounded in Solar System science. For example, Morley et al. (2017) created an extensive grid of both primary and secondary transit spectra using the elemental ratios of Earth, Titan, and Venus with different incident flux levels, surface pressures, and albedos for each planet in their study.

Due to the complexity and quantity of unknown parameters, here we do not aim to produce chemically consistent spectra in composition or temperature–pressure. Instead, in order to obtain estimates for constraints that we might expect from a variety of atmospheres, we explore nine simple chemical prescriptions for each planet. This allows us to assess the impact of the quality and spectral coverage of JWST data on how well atmospheric parameters can be constrained. Our transmission and emission model is described in Line et al. (2013), Greene et al. (2016), Line & Parmentier (2016), and Batalha & Line (2017).

All nine of the chemical scenarios considered here are composed of a combination of H₂O, CO₂, N₂, and CH₄, based on the dominant molecules in the atmospheres of rocky Solar System bodies and also the dominant molecules in the Morley et al. (2017) grid. The main difference between the nine scenarios is the background gas: either H₂O-rich, N₂-rich or CO₂-rich. After the background gas, the three remaining species are added in equal quantities at trace levels (1%, 0.01% and 0.0001%). Adding the gases in equal quantities allows any inability to detect a spectral feature to be attributed to data precision, spectral coverage, or masking by the dominant gas. All compositions are uniform with altitude.

For each planet we explore temperature–pressure profiles, which we assume can be fully described by a 1D profile. For our 1D profiles we use a five-parameter double-gray analytic formula (Guillot 2010; Line et al. 2013), which for weakly irradiated systems approximates to , where p and T_z are the height-dependent pressure and temperature, respectively. Using this scaling, we explore surface temperatures consistent with the full range of potential values given an Earth-like composition, and a range of pressures and Bond albedos from Morley et al. (2017). This range is particularly important in the analysis of emission spectra. We use a surface temperature of 200 and 400 K to set the our pessimistic and optimistic atmospheric constraints in emission, respectively.

Clouds mute or mask the atmospheric features in transmission spectra (e.g., Kreidberg et al. 2014; Sing et al. 2016). For terrestrial planets, the models of the cloud-microphysics for Earth (e.g., Albrecht 1989; Tinsley 2000), Venus (e.g., Knollenberg & Hunten 1980; Allen & Crawford 1984), and Titan (e.g., McKay et al. 2001; Rannou et al. 2006) have all been guided by observations. For exoplanets, a general cloud model does not yet exist. Therefore, we use a gray opacity source at two different pressures levels (0.01 and 0.1 bars) to set our optimistic and pessimistic cases. Optimistically, we assume observations would be limited by the tropopause of the planet, located at 0.1 bars in the Solar System planets (Robinson & Catling 2014). Pessimistically, we assume observations would be limited by the formation of high-altitude clouds in slowly rotating habitable zone planets (Kopparapu et al. 2017). For emission, we do not include the presence of clouds because their reduced optical depths have less of an impact on the spectrum (Fortney 2005).

Batalha & Line (2017) detailed our information content methodology. We describe the relevant sections here. The information content is a quantity that describes how the state of knowledge of a system has increased (relative to the prior) by making a measurement (Shannon 2001; Line et al. 2012). Here, we are specifically interested in the posterior covariance matrices, , which describe the uncertainties on each of the state vector parameters. We assume that our atmospheric state is described by T, , , , , and . T is the temperature above the tropopause that we set to planet’s T_eq, ξ_i is the concentration of the ith gas, and ×R_p is a factor to account for the radius arbitrarily set at 10 bars. can be computed as

where K is the Jacobian matrix, which describes the model sensitivity, is the a priori covariance matrix, and is the error covariance matrix. We assume that the observer has no prior information so that . This ensures that our calculations are driven by the model sensitivity and the JWST data, not the prior.

JWST nondestructively reads charge in a pixel as it accumulates during an integration. Each integration begins with a reset frame, during which pixels in the subarray are reset one at a time. For time-series science, each downlinked group consists of one frame, the result of reading each pixel once. The first frame after a reset will usually be used to establish a zero point, or bias level. Subsequent frames will be read as accumulated science photons. The efficiency of an observation is then =, where n is the number of groups. If the bias level is known a priori, then efficiency is . The MIRI detectors are somewhat more efficient at small n because they can read then reset pixels in a single frame time.

For bright targets near the saturation point of the instrument, this readout pattern becomes inefficient. The opaque lines in Figure 1 show our results for the expected spectral precision for each mode as a function of J-magnitude at key wavelengths (H₂O at 1.4 μm and 2.5 μm, CH₄ at 3.3 μm, CO/CO₂ at ∼4.5 μm).

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Each opaque curve follows the expected photon-limited relationship until the lower limit in magnitude, where the detectors begin to approach saturation. This flattening out in precision is the result of decreasing the groups within an integration for brighter targets, which decreases the observing efficiency to 33% for the brightest targets. The transparent lines in Figure 1 show the expected spectral precision if JWST had 100% observing efficiency at all magnitudes within the saturation limits of the instrument. For temperate terrestrial planets, which require very high spectral precision, we need to determine strategies to increase this observing efficiency for targets near the saturation limits of a given mode.

Therefore, high-efficiency readout patterns are under investigation for NIRISS and NIRSpec, shown in Figure 2. Each of the three columns in Figure 2 shows what takes place during a single pixel’s read and/or reset. As stated above, a full group is the result of clocking through all of the pixels one time. The top panel is the currently supported readout pattern, and the bottom two panels show potential enhancements. In the Read-Reset and Read pattern, the position of the reset frame is moved to take place directly after an individual pixel is read (middle panel). Reading each pixel immediately before the reset measures all accumulated charge and yields 100% efficiency, only if the reset level is known. If the reset level is not known, the Read-Reset-Read readout pattern would have to be implemented to yield ∼100% efficiency (bottom panel).

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If these new readout patterns get implemented, it will greatly increase the efficiency of targets near the saturation limits of specific high-precision time-series modes. However, these enhanced readout patterns are not currently slated to be available for observations in JWST’s Cycle 1. TRAPPIST-1, J = 11.3, saturates the NIRSpec Prism after the third group. Therefore, an observation with no saturation leads to observing efficiency across the entire detector. Using the NIRSpec Prism is advantageous because it yields a 1–5 μm spectrum in a single transit. For targets not accessible with the Prism, observers will have to decide if they want to split up observations between modes to yield an entire 1–5 μm spectrum, or use all of their time in a single observing mode.

One additional caveat with the NIRSpec Prism, shown in Figure 1, is its decrease in precision toward longer wavelengths. At wavelengths less than 2.5 μm, the NIRSpec Prism attains higher spectral precision than other available instruments at identical 2MASS J. The NIRSpec Prism becomes less favorable at higher wavelengths though, because the stellar SED dramatically drops off, causing read noise to dominate over photon noise, and because the efficiency of the observation is limited by saturation at the shorter wavelengths.

To combat both of these sources of decreased precision, we propose an observing strategy to partially saturate the detector. JWST acquires sampled up the ramp data and will return a data product for every single group within the integration. Therefore, unless the observation is saturated at the end of the second group, a variable number of groups can be used to extract the full wavelength space, regardless of saturation.

Figure 3 shows the spectral precision of this variable group observing strategy (orange) versus a non-saturated PandExo run with three groups (blue) for the TRAPPIST-1 system. In this particular phase space (targets with low-efficiency observations), this proposed strategy has the potential to increase the precision at longer wavelengths by a factor of 2 for the NIRSpec Prism. Note, this observing strategy has not yet been formally introduced into the PandExo package.

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In order to obtain emission spectroscopy of cool planets, observations in the mid-infrared (IR) using MIRI LRS, will be required. There are currently no plans to increase the observing efficiency of MIRI LRS near the saturation limit. There are other ways to increase observing efficiency that are not specific to the exoplanet case. Although, because the MIRI detectors are readout more efficiently than the near-infrared (NIR) detectors, this is less problematic (see Figure 1). One caveat of MIRI is that observations become background limited past J = 10, seen by the gray photon-limited line in the MIRI LRS panel of Figure 1. Therefore, TRAPPIST-1 is not an ideal target to study emission spectroscopy of terrestrial exoplanets, and it will be especially important for TESS to detect planets with J < 10 to optimize observations with MIRI LRS.

The relationship between the uncertainties on the retrieved parameters and the number of transmission spectra needed are similar for each planet in the TRAPPIST-1 system. The differences between planets are driven by differences in temperature and gravity, which set the strength of the molecular features through the scale height = kT/μg. We choose TRAPPIST-1f to illustrate our results. TRAPPIST-1f is the outermost habitable zone planet (219 K), and has a gravity similar to that of Earth (8.33 m s⁻²).

Figure 4 shows the expected uncertainty on the atmospheric parameters of TRAPPIST-1f after each transit, if it were observed with NIRSpec Prism’s partial saturation strategy in transmission. The upper and lower bound of the curve is set by the pessimistic (P = 0.01 bar) and optimistic (P = 0.1 bar) specifications for the gray cloud top pressure, respectively. When there is no information content in the observation, the uncertainty approaches the prior (12 dex for abundances and 1000 K for temperatures). We do not show the results for detecting N₂ because it is void of molecular features unless temperatures are very high (Schwieterman et al. 2016). Therefore, it cannot be directly detected or constrained.

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Temperature is difficult to constrain in transmission spectroscopy, regardless of atmospheric composition. Meaningful constraints (<±50 K) are only achievable with 10+ transits. For abundances, in all of our cases, the dominant absorber is constrained by the 10th transit. Therefore, for the TRAPPIST-1 system, if no atmospheric signals are detected by the 10th transit, it is unlikely that coadding more would reveal new information. However, if the dominant absorber is detected by the 10th transit, additional observations could reveal trace gases in the atmosphere at the 0.01% level.

Our results demonstrate the high potential that the NIRSpec Prism has for detecting a wide variety of molecular features. H₂O has dominant absorption features from 1 to 2 μm, CH₄ has dominant absorption features from 3 to 4 μm, and CO₂ has dominant absorption features from 4 to 5 μm. In Cycle 1, it is important to survey this entire parameter space. For targets too bright to be accessible with NIRSpec Prism, observations with a combined NIRISS SOSS and NIRSpec G395H observation yield higher information content results, despite the lower precision that comes from splitting time between two modes.

For emission we also show the case of TRAPPIST-1f. Figure 5 shows the constraints on the atmospheric state vector parameters. Emission spectroscopy is more sensitive to the atmospheric temperature structure than transmission spectroscopy. However, the uncertainties on temperature for emission spectroscopy (Figure 5) are comparable to that of transit transmission (Figure 4). This is because the JWST MIRI LRS data does not have sufficient precision to detect the small signal that comes from the emission of temperate planets at 5–12 μm. The constraints on abundances are also highly driven by the prior (12 dex). No molecules are constrained within 1 dex for less than 50 transits. Detecting molecular features in emission spectroscopy of truly temperate exoplanets will be very difficult with JWST's MIRI LRS. This conclusion is also supported by the analysis of Morley et al. (2017), which suggests photometry of temperate planets as an alternative to emission spectroscopy.

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