Trends in Atmospheric Properties of Neptune-Size Exoplanets

Precise atmospheric observations have been made for a growing sample of warm Neptunes. Here we investigate the correlations between these observations and a large number of system parameters to show that, at 95% confidence, the amplitude of a warm Neptune's spectral features in transmission correlates with either its equilibrium temperature (T_eq) or its bulk H/He mass fraction (f_HHe) --- in addition to the standard kT/mg scaling. These correlations could indicate either more optically-thick, photochemically-produced hazes at lower T_eq and/or higher-metallicity atmospheres for planets with smaller radii and lower f_HHe. %Since hazes must exist in some of these planets, we favor the former explanation. We derive an analytic relation to estimate the observing time needed with JWST/NIRISS to confidently distinguish a nominal gas giant's transmission spectrum from a flat line. Using this tool, we show that these possible atmospheric trends could reduce the number of expected TESS planets accessible to JWST spectroscopy by up to a factor of eight. Additional observations of a larger sample of planets are required to confirm these trends in atmospheric properties as a function of planet or system quantities. If these trends can be confidently identified, the community will be well-positioned to prioritize new targets for atmospheric study and eventually break the complex degeneracies between atmospheric chemistry, composition, and cloud properties.


INTRODUCTION
Short-period planets with sizes of 2 − 6 R ⊕ (hereafter, "warm Neptunes") are a ubiquitous outcome of planet formation. They occur around > 25% of all stars and comprise a distinct, gas-rich population separate from smaller, terrestrial super-Earths (e.g., Buchhave et al. 2014;Fulton et al. 2017). Understanding this population is therefore critical for building a comprehensive theory of planet formation and linking the larger gas giants to the smaller terrestrial planets. The existence of the intermediate-sized planets raises many questions: what stunts their growth and prevents them from reaching Jupiter proportions (Pollack et al. 1996;Lambrechts et al. 2014;Lee & Chiang 2016), or alternatively what whittles down their younger bulk to the smaller bodies seen today (Owen & Wu 2013;Jin & Mordasini 2017)? Where did they form in their solar systems? Why does our solar system lack planets in this size range? One powerful approach to answering these questions is to determine these planets' bulk composition -their core masses and the metallicity and chemistry of their outer envelopes. These properties provide a record of the planets' origins that can be compared to formation models.
Planet formation models predict two broad trends in atmospheric composition for warm Neptunes. One is compositional diversity, ranging from H 2 O-rich "super-Ganymedes" to puffy H/He envelopes (Elkins-Tanton & Seager 2008;Fortney et al. 2013). Hints of this diversity appear in the mass-radius diagram for Neptunemass planets, which shows a factor of three scatter in density (Weiss & Marcy 2014). Warm Neptunes likely have some hydrogen in their atmospheres (Wolfgang & Lopez 2015;Rogers 2015); however, there is a strong degeneracy between core mass and envelope metallicity (M/H) that prevents an exact determination of warm Neptunes' bulk makeup from mass and radius measurements alone (Figueira et al. 2009;Miller-Ricci & Fortney 2010;Rogers et al. 2011).
Another qualitative prediction is that the atmospheres of smaller planets should be more enhanced in metals than Jupiter-size planets (e.g. Fortney et al. 2013;Venturini et al. 2016). Infalling planetesimals can ablate and pollute the atmosphere (e.g Pinhas et al. 2016;Mordasini et al. 2016), so all else being equal, metal enrichment of the envelope will be more pronounced for lower-mass planets, because they have less gas to dilute. Indeed, the metal enrichment of the Solar System gaseous planets (e.g., Karkoschka & Tomasko 2011;Luszcz-Cook & de Pater 2013;Guillot & Gautier 2014) reveals a striking trend of increasing M/H with decreasing planet mass that extends to massive hot Jupiters (Kreidberg et al. 2014). Observations of lower-mass ex-oplanets are broadly consistent with these trends, but the uncertainties are much larger (Moses et al. 2013;Fraine et al. 2014;Morley et al. 2017;Wakeford et al. 2017).
There has been extensive observational study of the handful of warm Neptunes that are accessible targets for atmospheric characterization with current facilities, but so far the results defy easy explanation. Some planets exhibit spectral features from water (Fraine et al. 2014;Wakeford et al. 2017), whereas others have flat, featureless spectra (e.g. Kreidberg et al. 2014;Knutson et al. 2014a). In most cases, the featureless spectra could either be caused by a high mean molecular weight atmospheric composition, or high altitude clouds or hazes. Even in cases where features are detected, the features are lower in amplitude than expected for a cloud-free solar composition atmospheres (Fraine et al. 2014;Wakeford et al. 2017;Fu et al. 2017).
In this paper, we explore possible explanations for the ensemble of warm Neptune observations. We hope to identify trends in these planets' atmospheric properties to provide forward guidance for future studies, especially in light of the imminent detection and characterization efforts from the TESS, CHEOPS, and JWST missions (Broeg et al. 2013;Ricker et al. 2014). We note that several previous studies have also investigated trends in exoplanet transmission spectra (Stevenson 2016;Heng 2016;Fu et al. 2017); however, these efforts focused mainly on hot Jupiters, whose atmospheres may differ substantially from those of warm Neptunes. We also note that the sample size of warm Neptunes is small, and that previous attempts to classify exoplanet atmospheres have not always held up as the sample size increased or as measurements improved (e.g., Hansen & Barman 2007;Fortney et al. 2008;Knutson et al. 2010;Madhusudhan et al. 2011). Nevertheless, we aim to present a useful framework for discussing atmospheric trends as the sample size grows. In Sec. 2 we present the sample and observational data used. We then describe our analysis of these atmospheric measurements in Sec. 3 and 4, discuss the implications for the TESS+JWST sample in Sec. 5, and we conclude in Sec. 6.

PLANETS AND OBSERVATIONS
For the purposes of this paper, we restrict ourselves to planets with sizes 2 < R P /R ⊕ < 6, which are distinct from the smaller, presumably rock-dominated super-Earths (Fulton et al. 2017) and yet have bulk H/He mass fractions of < 50% (Lopez & Fortney 2014). We also restrict our analysis to planets with T eq < 2000 K, since small planets at these high temperatures can be significantly sculpted by atmospheric mass loss (Owen & Wu 2013). Note that both these criteria exclude 55 Cnc e, whose bulk makeup may be consistent with little or no volatile elements (Demory et al. 2016); even if this planet has an atmosphere (Ridden-Harper et al. 2016;Tsiaras et al. 2016) it is highly irradiated and likely of a fundamentally different character than those in our final sample.
Several warm Neptunes satisfying our criteria have been observed from a variety of facilities, including both broadband photometry and spectroscopy, at low and high spectral resolution, from the ground and from space, at wavelengths from the UV to the mid-IR. This is an extremely heterogeneous data set. One concern with trying to combine such observations is that stellar variability can introduce an arbitrary offset between observations taken at different epochs (e.g., Knutson et al. 2011;Fraine et al. 2014) and a host star's non-uniform surface brightness can introduce significant slopes, especially at shorter wavelengths (McCullough et al. 2014;Oshagh et al. 2014). Different assumptions about fitting system parameters and instrument systematics can also introduce bias in absolute transit depth measurements (Stevenson et al. 2014).
For these reasons we further restrict our analysis to those planets observed with a single spectroscopic instrument, HST's Wide Field Camera 3 (WFC3), and a single grism (the near-infrared G141). Our final sample of six planets is described in Table 1, and spans radii from 2-6 R ⊕ and temperatures from 500-1000 K.

ANALYSIS
Ultimately, we hope that atmospheric observations of exoplanets will provide useful measurements of elemental and molecular abundances, atmospheric metal enrichment and chemistry, cloud composition and particle size distribution. Beyond that, we hope to elucidate underlying trends in the ensemble properties of planetary atmospheres and learn how these are influenced by bulk planetary, stellar, and/or orbital parameters: radius, mass, irradiation, etc. However, the complex interplay of all these factors -along with atmospheric models that do not yet encapsulate all necessary processes -means that achieving this goal is an extremely complicated task.
For now we consider a simpler question: under what conditions do the atmospheres of warm Neptunes show detectable spectral features in transit? This is a lowerorder question than those enumerated above, but detecting spectral features is a necessary first step toward these more ambitious goals. For this purpose our choice of WFC3/G141 observations is ideal, since a single species -H 2 O-dominates the expected opacity at these wave-  lengths. Although CH 4 , HCN, and other species absorb in the G141 bandpass, none of these have been reported in our sample.
To facilitate comparison of the WFC3/G141 measurements of our diverse targets, we place all the spectra on the same scale. A fundamental unit in transmission spectroscopy is the atmospheric scale height H = k B T eq /µg, where g is the planet's surface gravity. Here µ is the mean molecular weight, 2.3 amu for a H-dominated atmosphere with Solar abundances and increasing only slowly for M/H up to ∼ 100× Solar (where µ = 3.05 amu); beyond this, µ rises increasingly quickly with increasing M/H. We therefore initially assume µ = 2.3 for all our sample and calculate H HHe , the scale height assuming a low atmospheric metallicity. If any of our targets have highly enriched atmospheres, H < H HHe and the true signal amplitude would be a larger number of scale heights. We plot the normalized WFC3/G141 measurements in Fig. 1. One conclusion is immediately apparent: not all small, cool exoplanets have flat spectra.
To estimate the amplitude of H2O absorption, we fit a template spectrum S t normalized to unit amplitude. Using weighted linear least squares, we fit the observed spectrum S o = a 1 + a 2 λ + a 3 S t , where λ is the wavelength in microns, and the a i are constants. The tem- plate comes from a carbon-free atmospheric model of GJ 1214b, described by Crossfield et al. (2011). When the template is convolved to a resolution of 600, approximately 6.7 scale heights separate the peak at 1.4 µm from the trough at 1.25 µm 1 . The resulting scaled bestfit models are plotted over the measurements in Fig. 1, and the H 2 O feature amplitudes are listed in Table 1. We then investigate whether the amplitude of H 2 O absorption in these planets' spectra could be explained by various planetary and system parameters. We investigated planetary R P , M P , ρ p , g, T eq , and bulk H/He mass fraction (f HHe ; from Lopez & Fortney 2014), stellar T ef f , and predicted FUV and XUV irradiation (from France et al. 2016). We then simply investigate which of these quantities correlates with our measured amplitude for the H 2 O feature, both by computing the Pearson correlation coefficient r and associated chance probability p, and by fitting a linear relation and comparing the resulting χ 2 . Table 2 summarizes how a variety system properties correlate with the detectability of atmospheric features in warm Neptunes. Two properties stand out as better predictors than the others. The first is T eq , which gives the lowest χ 2 and the second-highest r (with p = 4%). The second possibility is the pair R P and f HHe (which both have p < 5%). We note that R P and f HHe are expected to be tightly correlated for planets of this type (Lopez & Fortney 2014). Since f HHe is more physically  Fig. 1, along with the best-fit linear trend (red dashed line). This correlation suggests that smaller planets (with lower fHHe) might have higher-metallicity atmospheres.

RESULTS
linked to atmospheric composition and is directly connected to the observable atmosphere probed by transmission spectroscopy, we henceforth consider only f HHe along with T eq . The correlation plots for these two parameters are shown in Fig. 2 and 3, respectively, and the implications for each are discussed below.  Fig. 1, along with the best-fit linear trend (red dashed line). This correlation suggests that hazes might become more significant for planets with Teq 850 K. The correlation between H 2 O feature scale height and f HHe is shown in Fig. 2. The higher the hydrogen/helium mass fraction, the larger the features tend to be. One possible interpretation for this trend is that atmospheres with smaller H/He envelopes have higher metallicity (and thus the true scale height H is less than our predicted scale height H HHe ). This interpretation agrees with predictions from planet formation models that smaller envelopes are more polluted by infalling planetesimals (Fortney et al. 2013;Venturini et al. 2016).

A correlation with H/He mass fraction
If the amplitude of features depends solely on atmospheric metallicity, we can use the observed spectra to put a lower limit on the atmospheres' mean molecular mass. We assume that the feature amplitude is linearly proportional to µ and that HAT-P-11b and HAT-P-26b, our two largest planets, have µ = 2.3 amu (though neither planet's spectrum is consistent with a Solarmetallicity, cloud-free atmosphere). Under this assumption GJ 3470b, GJ 436b, and GJ 1214b would have µ equal to 8 ± 2, 10 +9 −4 , and 61 +63 −24 , respectively. Excluding non-physical negative values, HD 97658b would have µ > 3.0 at 99.7% confidence, consistent with previous analyses (Knutson et al. 2014b).
The derived values for GJ 3470b and GJ 436b are plausible; however, the transmission spectrum of GJ 1214b is so flat that it requires a higher metallicity composition than is expected for any volatile species (Kreidberg et al. 2014;Morley et al. 2015). Furthermore, we confirm that the data for GJ 1214b statistically justify a perfectly flat spectrum, rather than inclusion of a H 2 O signature; indeed, our simplistic H 2 O-only analysis finds µ > 22 with 99.7% confidence. Therefore the only explanation for these data is a high-altitude condensate blocking the transmission of stellar flux. This result may therefore point toward a correlation between transmission spectral amplitude and planetary equilibrium temperature rather than µ, as described next.

A correlation with equilibrium temperature
The correlation between H 2 O feature scale height and T eq is shown in Fig. 3. Instead of invoking higher M/H for the flatter spectra, an increasing particulate density of cloud or haze particles at high altitude could be suppressing features in the spectra, as inferred for GJ 1214b (e.g., Kreidberg et al. 2014).
A plausible route for forming high-altitude aerosols is through photochemical interactions with hydrocarbons (e.g. CH 4 , C 2 H 2 ), producing hazes analogous to those seen on Titan. Morley et al. (2015) modeled the interaction of stellar irradiation and atmospheric metallicity on the amount of high-altitude, high-order hydrocarbons, deemed "soot precursors," and found a strong increase in the high-altitude abundances of these compounds as planetary equilibrium temperature drops over a narrow range from 1100 K to 800 K.
The transition from haze-free to hazy atmospheres at temperatures of 800-1100 K, predicted by Morley et al. (2015), matches the transition observed in Fig. 3 surprisingly well. In this scenario, the warmer HAT-P-11b and HAT-P-26b show strong features in transmission because their atmospheres are too warm to form obscuring photochemical hazes; the other warm Neptunes are below the critical irradiation threshold and so form sufficient haze to block most or all of the expected transmission signature. This trend could be tested by observing additional warm Neptunes across this T eq range, and by more sophisticated modeling of haze formation in this atmospheric regime.
The correlation with T eq could instead indicate something about cloud top pressure instead of total aerosol content, but the data do not seem to bear this out. When considering HST/WFC3 G141 data alone and assuming a Solar-metallicity atmosphere, the top of an opaque cloud deck in these planets' atmospheres lie at pressures of ∼0.1 mbar for GJ1214b (Kreidberg et al. 2014), ∼0.4 mbar for GJ 3470b (Benneke et al., submitted), 1 mbar for HD 97658b (Knutson et al. 2014a), ∼1 mbar for GJ 436b (Knutson et al. 2014b), and ∼100 mbar for HAT-P-11b (Fraine et al. 2014). If all planets had Solar-metallicity, then clouds would seem to sink deeper into the atmosphere with increasing planet temperature -the opposite of what is typically understood to happen in brown dwarf atmospheres (e.g., Lodders 2004). If temperature is related to cloudiness, the connection to photochemical haze production seems more likely.

ATMOSPHERIC CHARACTERIZATION WITH JWST
At present, both our identified trends rely on a small sample of only six planets. This is because just a handful of Neptune-size and smaller planets are feasible targets for atmosphere characterization with current facilities. JWST will revolutionize the study of planets in this size regime, thanks to its larger aperture and broader wavelength coverage, enabling higher signal-to-noise characterization of more spectral features. In addition, the Transiting Exoplanet Survey Satellite (TESS) is predicted to discover hundreds of small planets orbiting bright, nearby stars, which are ideal candidates for atmospheric study (Ricker et al. 2014;Sullivan et al. 2015). In this section, we explore the feasibility of characterizing the atmospheres of the TESS population of warm Neptunes with JWST, based on the possible trends identified above.

Exposure Time Calculator
The amplitude of features in a transmission spectrum is traditionally calculated using the atmospheric scale height and is ∝ HR P /R 2 * (Miller- Ricci et al. 2009). However, for cooler planets with potentially higher metallicities, this relation does not strictly hold. Particularly below 1000 K and for M/H > 100 × solar, the dominant molecular species vary, qualitatively changing the shape and amplitude of absorption features (Moses et al. 2013).
Here we introduce an empirical scaling relation to estimate the observing time needed to make a significant (5σ) detection of features in a JWST transmission spectrum. This relation is based on model planet spectra calculated over a grid of atmospheric temperatures (400 − 1600 K) and metallicities (Z = 1 − 1000× solar), using the open-source radiative transfer code ExoTransmit (Kempton et al. 2016). Our nominal planet has a transit depth of 1% and surface gravity g = 10 m/s 2 , and so is roughly comparable to HAT-P-11b or HAT-P-26b. Our calculation includes opacity from the major absorbing species expected for gaseous planetary atmospheres: H 2 O, CH 4 , CO, CO 2 , and NH 3 , in addition to collisionally-induced H 2 absorption.
We use the PandExo tool ) to simulate JWST observations for the NIRISS instrument in Single Object Slitless Spectroscopy (SOSS) mode. NIRISS/SOSS yields the highest information content for any single JWST instrument/disperser combination (Batalha & Line 2017). For the star, we use a PHOENIX stellar model with a temperature of 4000 K, surface gravity log g = 4.5, and J = 10 mag. We assume the data are photon-noise limited (i.e., there is no noise floor) but the assumed noise floor is not critical, since we find that most TESS targets will orbit stars with J 8 mag.
For each planet in our grid, we calculate how many total hours of observing time (including transit and an equal amount of baseline) are needed to detect features in the transmission spectrum at 5σ confidence on average. We determine the detection significance by simulating a sample of 100 model spectra, binning them to a resolution of λ/∆ λ ∼ 100, and calculating the reduced χ 2 values for the spectra compared to a flat line. Based on these results, we fit an analytic model to the observing time in hours, t hr , required to distinguish a spectrum from a featureless flat line at 5σ confidence: where F * is the relative stellar photon flux, 10 −0.4(J−10) , and where R p is the planet radius (×10 7 km), R s is the stellar radius (×10 8 km), and g is the planet's surface gravity (in 10 m s −2 ). The functional form of the above relation is not physically motivated, but it successfully reproduces the exposure time needed to an accuracy of 15% on average over the whole parameter space we consider (T eq = 400-1600 K, M/H = 1-1000).

TESS Yield of JWST-accessible Neptunes
We use this relation to estimate the number of expected TESS planets whose transmission spectra JWST/NIRISS can distinguish from a flat line at ≥ 5σ in five transits. The simulated TESS yield of Sullivan et al. (2015) does not include an assumption for each planet's atmospheric M/H, so we initially make the optimistic (indeed, unrealistic) assumption that M/H = 3 for all planets. We then subsequently assume that the transmission spectral amplitudes of these planets scales linearly with T eq or R P (a proxy for f HHe ) as shown in Figs. 2 and 3. Fig. 4 shows the result of this investigation under these three assumptions.
In the nominal case the expected accessible sample comprises 370 planets with R P < 6R ⊕ , suggesting a large haul of interesting planet targets. However, even under this most favorable case the number of systems amenable to very high-S/N atmospheric measurements is much smaller: it drops to just 30 planets when the bar is raised to 20σ. The 5σ TESS+JWST sample also decreases rapidly once we account for the scalings implied by our analyses. The sample drops by over half, to 154 planets, when the signal decreases linearly with T eq : from full amplitude at 1000 K to featureless at 550 K. If instead transmission amplitude decreases with R P from 6R ⊕ to 2.5R ⊕ (using R P as a proxy for f HHe ), the sample shrinks to just 47 planets. Under this pessimistic assumption, almost no planets with R P 4R ⊕ are accessible even after observing five transits with JWST/NIRISS; this is because (by construction) the amplitude of transmission features rapidly decreases for these smaller planets.
In all of these simulations TESS identifies warm Neptunes with a range of properties, from those observable in just a few JWST transits to those requiring many, many transits to plausibly detect any atmospheric signatures (see Fig. 4). Until we understand the atmospheric processes dominating these planets, the best targets for detecting features in transmission spectroscopy will be warmer planets with larger f HHe and R P .

CONCLUSIONS
We have identified two possible trends in the transmission spectra of warm Neptunes, both at > 95% confidence. As shown in Figs. 2 and 3, the amplitude of H 2 O absorption at 1.4 µm increases with both T eq and f HHe (or equivalently, R P ) for the 2-6 R ⊕ , 500-1000 K planets in Table 1. The scaling with f HHe could indicate that smaller planets have higher-metallicity at-mospheres, but at least for GJ 1214b we know that increased M/H cannot explain the observations: aerosols must be involved (Kreidberg et al. 2014). Presumably both metallicity and aerosol production both play a role, though the relative contribution of each effect remains undetermined.
The trends we have identified remain tentative due to our small sample size. The two key parameters of T eq and f HHe are largely degenerate in our halfdozen planets. Aside from the more poorly characterized HD 97658b, our coolest planet (GJ 1214b) is also the smallest, and the largest and most H/He-rich planet (HAT-P-26b) is also the hottest. Obtaining transmission spectra of cool yet puffy Neptunes (such as HD 3167c; Vanderburg et al. 2016b;Christiansen et al. 2017) and/or hotter yet lower-f HHe planets (such as HIP 41378b; Vanderburg et al. 2016a) will be essential if we are to break this degeneracy and truly determine the key factors controlling these planets' atmospheres. Additional measurements for planets with less precise transmission spectra (such as HD 97658b) would also help with this effort.
We also estimated the number and type of warm Neptunes to be discovered by TESS that will also be accessible to JWST transmission spectroscopy. Fig. 4 shows that under the common, optimistic assumption of cloudfree conditions, JWST/NIRISS could distinguish atmospheric features in ∼370 warm Neptunes by observing ≤5 transits of each. But experience shows that the true accessible yield will be lower: just ∼150 if feature amplitude scales with T eq , and only ∼50 if it scales with R P or f HHe . Until the physical mechanism(s) underlying these trends can be identified, the most promising warm Neptunes for transmission spectroscopy are those with R P 4R ⊕ and T eq 850 K. Of course, such observations cannot alone reveal the nature of the trends discussed here; for that, a larger and more diverse planetary population must be explored.
Until TESS and JWST arrive, more progress can be made by observing additional warm Neptunes in transit, both with HST and with ground-based spectroscopy. Transit surveys continue to identify new targets, and scheduled or pending observations of planets such as WASP-107 (GO-14915, PI Kreidberg), Kepler-51 (GO-14218, PI Berta-Thompson), K2's warm Neptunes (GO-15333, PIs Crossfield & Kreidberg), and others will help reveal the trends in atmospheric properties of Neptunesize exoplanets.
We thank Eliza Kempton, Ruth Murray-Clay, and David Sing for productive discussions and encouragement. We also thank the organizers of the 2017 Disks  Figure 4. Expected TESS planets accessible to JWST/NIRISS transmission spectroscopy. Large points are those TESS planets for which NIRISS could distinguish spectral features from a flat line at 5σ in ≤ 5 transits. Small points show the rest of the expected TESS sample (from Sullivan et al. 2015). Left: The nominal case as modeled by ExoTransmit; the indicated JWST+TESS sample comprises 370 planets smaller than 6R⊕. Center: Assuming that the amplitudes of transmission spectra decrease linearly with Teq as shown in Fig. 3; in this case, the sample drops to 154 planets. Right: Assuming that transmission amplitude decreases linearly with RP (a proxy for fHHe) as shown in Fig. 2; in this case, the sample drops to just 47 planets smaller than 6R⊕.
and Planets conference at Ringberg for motivating us to consider these issues in more depth, and our referee for careful attention that improved the quality of this work.