The Pennsylvania State University The Graduate School Eberly College of Science

A SYNERGISTIC APPROACH TO INTERPRETING PLANETARY

ATMOSPHERES

A Dissertation in Astronomy and Astrophysics by Natasha E. Batalha

© 2017 Natasha E. Batalha

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

August 2017 The dissertation of Natasha E. Batalha was reviewed and approved∗ by the following:

Steinn Sigurdsson Professor of Astronomy and Astrophysics Dissertation Co-Advisor, Co-Chair of Committee

James Kasting Professor of Geosciences Dissertation Co-Advisor, Co-Chair of Committee

Jason Wright Professor of Astronomy and Astrophysics

Eric Ford Professor of Astronomy and Astrophysics

Chris Forest Professor of Meteorology

Avi Mandell NASA Goddard Space Flight Center, Research Scientist Special Signatory

Michael Eracleous Professor of Astronomy and Astrophysics Graduate Program Chair

∗Signatures are on file in the Graduate School.

ii Abstract

We will soon have the technological capability to measure the atmospheric compo- sition of temperate Earth-sized planets orbiting nearby stars. Interpreting these atmospheric signals poses a new challenge to planetary science. In contrast to jovian-like atmospheres, whose bulk compositions consist of hydrogen and helium, terrestrial planet atmospheres are likely comprised of high mean molecular weight secondary atmospheres, which have gone through a high degree of evolution. For example, present-day Mars has a frozen surface with a thin tenuous atmosphere, but 4 billion years ago it may have been warmed by a thick greenhouse atmosphere. Several processes contribute to a planet’s atmospheric evolution: stellar evolution, geological processes, atmospheric escape, biology, etc. Each of these individual processes affects the planetary system as a whole and therefore they all must be considered in the modeling of terrestrial planets. In order to demonstrate the intricacies in modeling terrestrial planets, I use early Mars as a case study. I leverage a combination of one-dimensional climate, photochemical and energy balance models in order to create one self-consistent model that closely matches currently available climate data. One-dimensional models can address several processes: the influence of greenhouse gases on heating, the effect of the planet’s geological processes (i.e. volcanoes and the carbonate- silicate cycle) on the atmosphere, the effect of rainfall on atmospheric composition and the stellar irradiance. After demonstrating the number of assumptions required to build a model, I look towards what exactly we can learn from remote observations of temperate Earths and Super Earths. However, unlike in-situ observations from our own solar system, remote sensing techniques need to be developed and understood in order to accurately characterize exo-atmospheres. I describe the models used to create synthetic transit transmis- sion observations, which includes models of transit spectroscopy and instrumental noise. Using these, I lay the framework for an information content-based approach to optimize our observations and maximize the retrievable information from exo- atmospheres. First I test the method on observing strategies of the well-studied,

iii low-mean-molecular weight atmospheres of warm-Neptunes and hot Jupiters. Upon verifying the methodology, I finally address optimal observing strategies for tem- perate, high-mean-molecular weight atmospheres (Earths/super-Earths).

iv Table of Contents

List of Figures ix

List of Tables xviii

Acknowledgments xix

Chapter 1 Understanding and characterizing planetary atmospheres and climates 1 1.1 Remote Observations of Exoplanet Atmospheres ...... 2 1.1.1 Primary Transit Spectroscopy ...... 2 1.1.2 Secondary Transit Spectroscopy ...... 5 1.1.3 Overview of Exoplanet Observations ...... 5 1.1.4 Looking Forward: The James Webb Space Telescope . . . . 6 1.2 Constraining Exoplanet Atmospheres Through Retrievals . . . . . 8 1.2.1 Bayesian Framework in the Context of Atmospheres . . . . . 8 1.2.2 Overview of Retrieval Techniques ...... 10 1.2.3 Challenges to Constraining Atmospheres of Earths and super- Earths ...... 12 1.3 Forward Modeling of Planetary Climates and Atmospheric Compo- sitions ...... 15

Chapter 2 Modeling the Planet System 17 2.1 One-Dimensional Climate Modeling ...... 18 2.1.1 Calculating Radiative Fluxes ...... 19 2.1.2 Treatment of Water Vapor and Clouds ...... 20 2.2 One-Dimensional Photochemical Modeling ...... 21 2.2.1 Model Description ...... 21 2.2.2 Boundary Conditions and Volcanic Outgassing ...... 22

v 2.2.3 The Atmospheric and Global Redox Budgets ...... 23 2.3 Time-dependent Evolution of Atmospheres ...... 27 2.3.1 Energy-Balance Climate Model Description ...... 27 2.3.2 Basic model equations ...... 27 2.3.3 Hydrogen escape ...... 28

Chapter 3 Early Mars: An Application to Modeling the Planet System 30 3.1 Testing the 1D H2-CO2 Greenhouse Hypothesis ...... 30 3.1.1 Possible Sources of Hydrogen on Early Mars ...... 33 3.1.1.1 Volcanic Outgassing ...... 33 3.1.1.2 Serpentinization ...... 38 3.1.1.3 Photochemical Fe Oxidation ...... 40 3.1.2 Early Mars Model Setup ...... 40 3.1.3 Photochemical Results ...... 42 3.1.4 Potential Warming from Other Atmospheric Constituents . . 49 3.1.4.1 CO & CH4 ...... 49 3.1.4.2 SO2 ...... 50 3.1.5 Synergies with Current Observations ...... 51 3.1.5.1 S-MIF Signal Implications ...... 51 3.1.5.2 D/H ratios, hydrogen escape rates, and initial water inventories ...... 52 3.1.5.3 Tests for higher H2 outgassing rates ...... 54 3.1.5.4 Analyses of ancient Martian mantle redox state . . 55 3.1.5.5 Analyses of Fe-oxide rich sedimentary rocks . . . . 56 3.1.6 Conclusion ...... 57 3.2 Climate Cycling Caused by the Carbonate-Silicate Cycle ...... 59 3.2.1 Why climate limit cycles should occur on early Mars but not Earth ...... 59 3.2.1.1 1-D climate model calculations for present Earth . 60 3.2.1.2 The Carbonate-Silicate Cycle ...... 60 3.2.1.3 1-D climate model calculations for early Mars . . . 64 3.2.2 Energy Balance Model Setup ...... 64 3.2.3 Energy Balance Model Results ...... 65 3.2.4 Sensitivity of Models to Input Parameters ...... 67 3.2.4.1 Sensitivity to outgassing rates and ice albedo . . . 67 3.2.4.2 Sensitivity to obliquity ...... 68 3.2.5 Conclusion ...... 68

vi Chapter 4 The Planet System Observed as an Exoplanet 69 4.1 Modeling Transit Transmission Spectra ...... 69 4.2 Instrumental Noise Models ...... 71 4.2.1 Pandeia: Simulating Noise Sources ...... 71 4.2.2 PandExo: Simulating JWST Observations ...... 74 4.2.3 Benchmarking PandExo Performance ...... 79 4.2.3.1 NIRCam ...... 79 4.2.3.2 NIRISS ...... 80 4.2.3.3 NIRSpec ...... 83 4.2.3.4 MIRI ...... 83 4.2.4 PandExo: Simulating HST Observations ...... 85 4.2.5 Conclusion ...... 88

Chapter 5 Retrieving Information from the Spectra of the Planet System 89 5.1 The Information Content of Transit Spectra ...... 89 5.1.1 The Theory of IC Analysis ...... 91 5.1.2 Transit Transmission Spectra Models & their Jacobians . . . 93 5.2 Optimizing Observation Strategies for JWST: Sub-Neptunes−Hot Jupiters ...... 95 5.2.1 Single Observing Mode Analysis ...... 97 5.2.2 Validation of Covariance Matrix Approximation Against a Full Retrieval ...... 99 5.2.3 Two Observing Mode Analysis ...... 101 5.2.4 Multiple Observing Mode Analysis ...... 104 5.2.5 Implications for Planning Observagtions ...... 106 5.2.5.1 Why Two Modes Remain Superior ...... 106 5.2.5.2 Wavelength Coverage Versus Precision ...... 107 5.2.5.3 Saturation of Information ...... 107 5.2.6 Conclusion ...... 108 5.3 Optimizing Observation Strategies for JWST: Earths & Super-Earths 110 5.3.1 Noise models & Observing Strategies ...... 113 5.3.2 Transit Transmission Spectra Models & their Jacobians . . . 117 5.3.3 Information Content Analysis ...... 120 5.3.4 Conclusion ...... 121

Chapter 6 Degeneracies in Transmission Spectroscopy 124 6.1 Theoretical Setup to Investigate Degeneracies ...... 126

vii 6.2 A Comparison of Forward Models ...... 127 6.3 Implications on Future Observations of Small Planets ...... 132

Chapter 7 Conclusions and Future Work 135 7.1 Conclusions ...... 135 7.2 Future Work ...... 137 7.2.1 Connecting Forward Models to Retrievals ...... 137 7.2.2 Preparation for Direct Imaging ...... 139

Appendix A Photochemical Reaction Rates 140

Appendix B Energy Balance Model Parametrization 146

Bibliography 156

viii List of Figures

1.1 A schematic diagram showing the method used for observing tran- siting exoplanets...... 3 1.2 Schematic showing all of the JWST spectroscopy modes as com- pared to HST’s spectroscopy (WFC3) and spectrophotometry (STIS) modes. Color coding shows approximate resolving powers of each mode...... 7 1.3 Figure adapted from [Benneke and Seager, 2012]. The transmission spectra of an atmosphere with three absorbers (H2O, CH4, CO2). Each individual observable within the transmission spectra is labeled. For an atmosphere with n absorbers, there are n+4 total observables. This leads to a total of n + 4 retrievable parameters. The phrase “spectrally inactive gasses” refers to gases such as N2, H2 and He that do not exhibit strong absorption features but that may be the dominant background gas...... 13

2.1 Model and grid setup for the 1-D photochemical model...... 23 2.2 A schematic diagram showing the method used for balancing the ocean-atmosphere system. Φout(Red) is the flux of reductants out- gassed through volcanoes, Φrain(Red/Ox) is the flux of rained-out reductants or oxidants (including surface deposition). ΦOcean(H2) is the flux of H2 back into the atmosphere required to balance the oceanic H2 budget. An excess of reductants, such as H2S, flowing into the ocean leads to an assumed upward flux of H2...... 26 3.1 Temperature-pressure profile (top) and eddy diffusion profile (bot- tom) assumed for the photochemical calculations. The temperature decreases from 273K to 147K at an altitude of 67 km and then is isothermal to the top (200 km altitude). This is consistent with the 5% H2, 95% CO2 3-bar atmosphere from Ramirez et al. [2014]. . . 41

ix 3.2 Mixing ratios of different species in the base case martian atmosphere assuming the (minimal) outgassing rates from Table 3.2. Major constituents are shown in the top left, sulfur species in the top right, nitrogen species in the bottom left, and less abundant hydrocarbons in the lower right...... 45 3.3 Calculation showing the effect of H2 outgassing rate on H2 mixing ratio, along with the different sources of H2 thought to contribute to the overall outgassing rate. The escape rate is assumed to be diffusion-limited, as discussed in the text...... 46 3.4 Calculation showing the effect of sulfur (SO2/H2S) outgassing rate on the atmospheric H2mixing ratio. The blue dashed curve is the H2 mixing ratio under the assumption that H2S reacts to form pyrite, as seems likely. The blue solid curve shows what happens if all of the H2S dissolved in the ocean returns back to the atmosphere as a flux of H2 (less likely)...... 47 3.5 Calculation showing the effect of carbon outgassing rate on the atmospheric H2 mixing ratio. At total carbon outgassing rates > 3×1010 cm−2s−1, the atmosphere goes into CO runaway (see discussion in text)...... 48 3.6 CO volume mixing ratio as a function of assumed deposition velocity. The atmospheric profile in Figure 3.7 was used for all calculations. The loose constraint on deposition velocity prevents us from deter- mining precise values for CO volume mixing ratio...... 49 3.7 1-D photochemical model results showing volume mixing ratio as a function of altitude. This is the base case early Martian atmosphere (Figure 3.1) after adding volcanic outgassing and balancing the redox budget for the combined ocean-atmosphere system. Here we are optimistic, and add in enough H2 outgassing to attain a 5% H2 atmosphere...... 50 3.8 Total removal rate (rainout + surface deposition) for low (top) and high (bottom) cases of sulfur outgassing in an early Martian atmosphere. This shows three quantitatively important pathways that should allow for the preservation of a sulfur isotope MIF signal. 52

x 3.9 The green and red curves represent surface temperatures calculated using a 1D climate model [Kopparapu et al., 2013] for present Earth (green) and early Mars (red) with three different atmospheric compositions and two different surface albedos (0.216 for dry land and ocean, 0.45 for a fully glaciated planet). The solar flux for early Mars is 0.3225 times the flux for present Earth. The brown curve shows the temperature at which the weathering rate balances 0.5 the present terrestrial CO2 outgassing rate, assuming a pCO2 dependence (solutions for Eqn. 3.13 when W/W⊕ = 1). The blue circle shows the location of the present soil pCO2 level. These curves define three regions of climate stability: 1) Warm stability: The surface temperature and weathering rate curves intersect above the freezing point (abiotic Earth) and planets remain permanently de- glaciated 2) Cold Stability: The surface temperature fails to ever rise above the freezing point of water (red dotted early Mars case). Such planets remain permanently glaciated. 3) Limit Cycling: The surface temperature and weathering rate curves intersect below the freezing point, but temperatures above freezing are possible as CO2 and H2 build up (solid/dashed red early Mars case with H2). . . . 61 3.10 The heat map shows the fraction of time within a billion year period when the maximum surface temperature was above freezing (273 K). Panel ’A’, ’B’, and ’C’ show cases where limit cycles are moderate, absent, and rapid, respectively. For reference, the modern CO2 and H2 outgassing rates on present Earth are 7.5 Tmol/year [Jarrard, 2003] and 2.4 Tmol/year [Ramirez et al., 2014, and refs therein], respectively. These rates are scaled down by a factor of 3.5 for Mars to account for its smaller surface area...... 66

4.1 Varying levels (low, medium, high) of pre-computed background flux used within Pandeia for cirrus (dashed) and zodiacal (solid) back- ground contamination. Black curve shows the level used (medium) for all noise simulations in this analysis...... 72 4.2 Subsets of the two dimensional Pandeia detector simulation of a T=4000 K, Fe/H=0.0 and, logg=4.0 stellar SED normalized to a J=10, with 100 seconds of observing time. Color coding shows the electron rate in each pixel. Panel A is simulation of NIRISS SOSS (Order 2 not shown), panel B is a simulation of NIRSpec G395H, panel C is a simulation of NIRCam F444W, and panel D is a simulation of MIRI LRS...... 73

xi 4.3 Three of the most popular PandExo output products. The top panel is the raw planet transmissions spectrum with associated errors. The middle panel is the raw noise and the bottom panel is the out of transit flux rate. Each simulation is for a NIRSpec G395H observation of a T=4000 K, Fe/H=0.0 and logg=4.0 stellar target normalized to a J=10. The single transit observation consists of a 2.7 hour in-transit observation along with a 2.7 out-of-transit baseline observation. In the top panel, the observation is binned to R=200. In the middle and bottom panel, resolving power is left at native resolving power (per pixel), with ten pixels summed in the spatial direction. The gaps seen in all three panels are the result of a gap between the detectors from 3.8172-3.9163 µm...... 78 4.4 Benchmarking results for NIRCam, which show the differences be- tween the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is NIRCam F444W, which was run with one integration both in- and out-of- transit. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MULTIACCUM noise formulation, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively. . 80 4.5 Benchmarking results for NIRISS, which show the differences be- tween the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is NIRISS SOSS, which was run for a 4 hour integration (2 hours in- and 2 hours out-of-transit) with 2 groups per integration. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MUL- TIACCUM noise formulation, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively. Missing points in red depict pixels that have been saturated in PandExo. Likewise, purple diamonds depict pixels that have been saturated in the instrument team’s model...... 81 4.6 2D detector simulation for the NIRISS SOSS observation shown in Figure 4.5. Only the first order is depicted to enable a clear view of the saturated pixels (colored in grey). Color indicates electron rate in e− s−1. The wavelength channels with saturated pixels are flagged by PandExo but usable data may still be extractable from non-saturated regions...... 82

xii 4.7 Benchmarking results for NIRSpec, which show the differences be- tween the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is NIRSpec G395H with the f090lp filter, which was run for a single integration in- and out-of-transit. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MULTIACCUM noise formula- tion, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively...... 84 4.8 Benchmarking results for MIRI, which show the differences between the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is MIRI LRS slitless mode, which was run for a single integration in- and out- of-transit. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MULTIACCUM noise formulation, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively. 85 4.9 Simulated observations of WASP-43b in emission using HST WFC3 G141. For the utilized instrument configuration, the simulated uncertainty is 37.6 ppm and the mean published uncertainty is 36.5±3.5 ppm [Stevenson et al., 2014]. For the same example system, panels B & C display simulated band-integrated light curves with the earliest and latest possible observation start times, respectively, that correspond to the computed minimum and maximum phase values of 0.3071 and 0.3241...... 86

5.1 Eight transmission spectra forward models used for the IC analysis. Each transmission spectrum is computed for a WASP-62 type star with a planet the size and mass of WASP-62 b. Atmospheres were computed assuming chemical equilibrium with the specified temperature (red: 1800 K, blue: 600 K). Each subpanel represents a different combination of C/O and [M/H], as labeled...... 95 5.2 The elements of the Jacobian, described in Chapter 1 Eqn. 1.6, for the T=1800 K transmission spectrum forward models (Zλ) cases shown in Fig 5.1. Each Jacobian is binned to R=100...... 96

xiii 5.3 Loss of information content as a result of the removal of a R=100 element of an observation of a spectrum with a uniform precision of 1 ppm. Each panel contains a different [M/H] and C/O, equivalent to Fig 5.1. Also as with Figure 5.1, red lines are for a simulation of a target with T=1800 K and blue lines are for a simulation of a target with T=600 K. Shaded boxes in bottom panels shows the available transit time spectroscopy modes on board JWST. . . . . 97 5.4 The information content as the precision on a spectrum increases. The colored lines in each panel represents a different observing mode. Each panel represents a different combination of [M/H] and C/O for a T=1800 K (left) or T=600 K (right) target. Noise simulations were not computed for these calculations. Instead, the "error on spectrum" dictates a fixed precision over the wavelength region of the particular observing mode. Transparent lines show, for the same observation mode, the loss in information content with the addition of a grey cloud at 1 millibar...... 98 5.5 Here, ECI is the expected credible interval for the posterior distri- bution of the indicated parameter. The red and blue curves show the derived errors from the IC analysis on the state parameters of interest for an observation with only NIRISS of a planet with 1) T=1800 K, C/O=0.55 and [M/H]=1×Solar, and no cloud and 2) T=600 K, C/O=1 and [M/H]=100×Solar, and no cloud. The ECI on each parameter were calculated using Eqn. 5.8. The top x axis shows IC content (taken from y axis in Figure 5.4). Circles show the expected precision on the parameters as a result of a multinest retrieval scheme. Asterisks show the expected precision the parame- ters as a result of using a multinest retrieval scheme on a combined NIRISS & NIRSpec G395M observation...... 101 5.6 Information content maps (in bits) for the T=1800 K planet cases as shown in Figure 5.1 with the addition of a grey cloud at 1 millibar. Rows are different [M/H]’s and columns are different C/O’s. Information content is measured in bits and the bins used for each color map is shown next to each panel. Note that each panel has a different color scale. Diagonal elements are two transits in one mode. Observation modes which will maximize observers chances of obtaining the true atmospheric state appear as dark squares in all four panels...... 102

xiv 5.7 Information content maps (in bits) for the same planet as shown in Figure 5.1 but with T=600 K and a grey cloud at 1 millibar. Rows are different [M/H]’s and columns are different C/O’s. Information content is measured in bits and the bins used for each color map is shown next to each panel. Note that each panel has a different color scale. Diagonal elements are two transits in one mode. Observation modes which will maximize observers chances of obtaining the true atmospheric state appear as dark squares in all four panels. . . . . 103 5.8 Here we show how the ECI of the state parameters decrease with the addition of more observation modes. Like the others, this is for the planet system WASP-62b with Teq = 1800 K. The lines represent the four combinations of C/O = 1 or 0.55 and [M/H]=1 or 100×Solar. No clouds have been added to these calculations. . . 104 5.9 Here we show how the ECI of the state parameters tightens with the addition of more observation modes. Like the others, this is for the planet system WASP-62b with Teq = 600 K. The lines represent the four combinations of C/O = 1 or 0.55 and [M/H]=1 or 100×Solar. No clouds have been added to these calculations...... 105 5.10 Curves show the relative line strengths of H2O absorption as a function of H2O volume mixing ratio. Line strengths have been normalized so that maximum is 1, which is why the maximum line strength on the y axis is at unity. All atmospheres are composed of a H2-H2O mixture. Each curve is computed for a different grey cloud deck at the pressure level indicated. Figure is adapted from [Kempton et al., 2016]...... 111 5.11 Curves show the noise on the planet spectrum as a function of 2MASS J magnitude at various wavelengths for TRAPPIST-1 (i.e. parent star with T=2550K from Phoenix Stellar Atlas). TRAPPIST- 1’s true magnitude (11.3) is shown as a vertical dashed line. Each simulated observation is composed of 1 hour in-transit and 1 hour out- of-transit. Colored opaque lines are for the RESET-READ-READ mode and transparent lines are for the READ-READ-RESET mode. Colors correspond to the different observing modes, as indicated in the label. All simulations are binned to R=100...... 114

xv 5.12 During data acquisition, JWST acquires sampled up the ramp data at a cadence equal to the frame time of the subarray. The figure shows simulations of the TRAPPIST-1 system with the NIRSpec Prism (SUB512). The first red tick corresponds to the reset frame, followed by 14 groups. The detector simulations show time stamps at each position up the ramp, with the group number labeled in the top left of each simulation. Red, in the detector simulations, corresponds to saturated regions of the detector. Lastly, the variable group data extraction shows the result of summing several thousand integrations (not pictured). The illustrative spectrum is a 100% water composition of TRAPPIST-1f. The number of groups used in the extraction corresponds to the maximum groups before saturation for the corresponding wavelength region...... 116 5.13 A comparison of four different observing strategies to acquire the same 1-5 µm region for TRAPPIST-1. Red, purple, and black are all different strategies for observing with the NIRSpec Prism. The partial saturation strategy (black) is depicted in Figure 5.12. All NIRSpec Prism simulations consist of 25 transits, each of which contain 1 hour of in-transit and 1 hour of out-of transit observing time. NIRISS and NIRSpec G395H simulations consist of 12 and 13 transits, respectively (in order to match the 25 single mode observation with the Prism). All simulations are binned to R=100. 117 5.14 Nine spectral models for TRAPPIST-1f with Teff =219 K and 9 different chemical compositions. Green curves correspond to a H2O background with either 1, 0.01, or 0.0001% of CO2, CH4, and N2. Red curves correspond to an N2 background with either 1, 0.01, or 0.0001% of CO2, CH4, and H2O. And blue curves correspond to a CO2 background with either 1, 0.01, or 0.0001% of N2, CH4, and H2O. All chemical species and temperatures are constant with altitude. Spectra are offset for clarity...... 119 5.15 Errors calculated from information content theory for TRAPPIST- 1f with Teff =219 K and 3 different chemical compositions. Each transit observation consists of a NIRSpec Prism observation with total observation time = 2 ×t14. Green curves correspond to a H2O background with either 0.01% of CO2, CH4, and N2. Red curves correspond to an N2 background with either 0.01% of CO2, CH4, and H2O. And blue curves correspond to a CO2 background with either 0.01% of N2, CH4, and H2O. The transparent lines show the increase in error when the presence of a grey cloud is introduced at 0.01 bar. All observations are binned to R=100...... 120

xvi 5.16 Errors calculated from information content theory for LHS 1140b with Teff =230 K and 3 different chemical compositions. Each transit observation consists of either a combination of NIRISS SOSS and NIRSpec G395H (circles) and only NIRISS SOSS (lines). Green curves correspond to a H2O background with either 0.01% of CO2, CH4, and N2. Red curves correspond to an N2 background with either 0.01% of CO2, CH4, and H2O. And blue curves correspond to a CO2 background with either 0.01% of N2, CH4, and H2O. All observations are binned to R=100...... 122

6.1 Maximum difference between pairs of models binned to the native resolving power of each JWST instrument, without instrumental noise. All models are for a planet with Rp = 1.5 R⊕ and T = 400 K. The color scale is indicated for both a GJ 1214-type host star and a Sun-like star. All model #1’s have a surface gravity of 9.3 m/s2, and all model #2’s have a surface gravity of 20.7 m/s2. For reference, the suggested noise floors are ±20 ppm and ±50 ppm for NIRISS/NIRSpec and MIRI LRS, respectively...... 128 6.2 JWST simulations for NIRISS SOSS (top), NIRSpec G395H (mid- dle), MIRI LRS (bottom) with no noise floor. Each simulation is done for 100 transits in each observing mode. One transit obser- vation consists of 1 hour in-transit and 1 hour out-of-transit. All simulations are for a GJ 1214-type host star with J = 8, for the same planet parameters as in Figure 6.1. The only difference between the simulations is the gravity and metallicity (H2O/H2), indicated in the color legend. All spectra are binned to R = 100. The red error bars represent the proposed ±20 ppm noise floor for NIRISS/NIRSpec and ±50 ppm noise floor for MIRI [Greene et al., 2016]...... 130 6.3 Simulated data for a GJ 1214-type system for the same stellar and planetary parameters as the previous two figures. The two simulations differ in their assumed gravity, metallicity (H2O/H2), indicated in the color legend, and cloud assumptions. In the top panel neither model has clouds. In the bottom panel, the low gravity, high metallicity model has a 10 millibar cloud that reduces the strength of its absorption features. Observations were simulated for NIRISS SOSS with no noise floor and binned to R=100. Top panel observations were simulated with 40 transits (80 hrs). Bottom were simulated with 100 transits (200 hrs). Some error bars are too small to see. The red error bars represent the proposed ±20 ppm noise floor for NIRISS [Greene et al., 2016]...... 131

xvii List of Tables

3.1 Assumed Deposition Velocities at Lower Boundary for Early Mars . 43 3.2 Assumed Total Outgassing Values for Early Mars ...... 44 3.3 H2 Sources and Respective Yields for Early Mars ...... 46 3.4 Parameters for input into EBM ...... 65

4.1 Instrument Modes in PandExo ...... 76

5.1 Instrument modes for IC Analysis ...... 96 5.2 TAPPIST-1 Planet Properties ...... 118

xviii Acknowledgments

When I was entering graduate school a wise woman told me to use my time as graduate student to absorb as much information from others as humanly possible. I’ve tried my hardest to follow this advice and would like to acknowledge those who have significantly impacted this work as a result. Thank you to Avi Mandell for drawing out that first diagram of transmission spectroscopy my sophomore year of undergrad. That internship kickstarted my interest in characterization of exoplanet atmospheres. Thank you to Jason Kalirai for giving me the most solid foundation for my graduate career, for constantly being my advocate, for teaching me the importance of a money plot, and for teaching me how to be a powerful communicator. Thank you to James Kasting for teaching me the intricacies of theoretical models. I learned more planetary science than I ever thought was possible from you. I also learned that models are only as useful as the people who run them because our theoretical results are entirely predicated on the assumptions we make. Thank you to Sonny Harman and Ravi Kopparapu for being my photochemical and climate model tech support. I would still be trying to compile fortran codes, if not for you two. Thank you to all the members of my committee: Jason Wright, for teaching me that "the source function is what the intensity wants to be" and all the other intracies of radiative transfer that I will never forget; Steinn Sigurdsson, for guiding me through the completion of my dissertation and for the quick and succinct emails; Chris Forest, for the many discussions about the differences between modeling exoplanet atmospheres and earth atmospheres and for guiding me through the world of 3D models; and, Eric Ford, for teaching me everything I know about computers: parallel programming, Julia, benchmarking codes, testing codes and much more. Thank you to Mike Line for teaching me the ins and outs of atmospheric retrieval, statistics, information content theory, modeling transit spectra and for restoring my belief that math is everything.

xix Thank you to Megan Barrett and Nicole Aurigemma for teaching me how to drink an IPA. Thank you for the morning eggs with franks, the endless supplies of coffee & guacamole, the delicious wines and cheeses, fat cat & skinny cat (I love you and I hate you), the walks through the golf course, the show at the 2nd, Fridays at Ottos, nachos at Happy Valley, Mad Mex Mondays, and Sam Smith en route to DC. Thank you for the zucchini, the other zucchini, the other zucchini and that other zucchini. Thank you to the town of State College and to our Teaberry Ln neighbors for the 500 dollar noise violation. It taught me that you cannot put a price on good times and good laughs. Thank you to Hannah Wakeford for teaching me how to complete my sentences out loud. Thank you for being an unwavering source of support and advocacy, for answering any and all questions pertaining to graduate school and science and life. And thank you for your continued efforts to try and teach me about pop culture. And lastly, thank you to the Lady Cats of 534. Our D.C. family was truly a remarkable stroke of luck. Thank you for the safe haven away from work, morning coffee (courtesy of Hannah), numerous house parties (around the world ♥), family time in the living room, chaos while making weeknight dinners, tolerating enough of one gross thing for everyone, nights at little miss whiskeys, flower the insufferable dog, the AZ trip and our minivan, and 2 solid years at the walk MS.

xx Dedication

This work is dedicated to the entire Farkle Family: Grandma, Grandpa, Mom, Dad, Nolan, Dimitri and littlest Sophia. For keeping me sane through the highest highs and the lowest lows.

xxi Chapter 1 | Understanding and characteriz- ing planetary atmospheres and climates

The last two decades have seen an exponential growth in the number of extra- solar planets (exoplanets) detected. We now have a large statistical population of planets ranging from hot Jupiters, warm Neptunes, super-Earths and even a handful of Earth-sized planets at habitable temperatures. The most fruitful method of detection has been the transit method, by which planets are discovered when they pass in front of their parent star’s disk and block a fraction of their parent star’s light. To date, over 3000 exoplanets have been discovered using this method, a number which continues to grow. Although we may never gather as much information on these individual planets as we have for Solar System bodies, a large number of exoplanets allows for us to capitalize on planet population studies and puts us in a new era of exoplanet science: that of characterization. Exoplanet characterization strives to decompose the atmospheres of exoplanets by determining key parameters such as bulk composition and temperature distri- bution. Doing so is crucial to understanding the planet’s formation or migration history, energy balance, and atmospheric dynamics. The atmospheric characteri- zation work done thus far, has been mostly on hot Jupiters and warm Neptunes using the Hubble Space Telescope and Spitzer Space Telescope. Hot Jupiter and warm Neptune atmospheres are favorable because their bulk compositions (hydro- gen/helium) and their hot temperatures (T > 1000 K) give them atmospheres with large scale heights.

1 With the upcoming launch of the James Webb Space Telescope (JWST), we are now striving to characterize planets that are smaller and cooler. Characterizing these low-mass, low-temperature, exoplanets presents new challenges that the community has not yet faced. Low-mass planets likely contain secondary atmospheres, which are a product of billions of years of atmospheric escape and volcanic outgassing. Their bulk composition is not known, and their atmospheric chemistry is dominated by non-equilibrium process such as photochemistry and vertical mixing. This is because the timescales for equilibrium chemical reactions are much slower than the timescales for atmospheric mixing. And while some of these processes have been studied intensively in Solar System and Earth science, we have not yet had the data necessary to study them in exoplanetary atmospheres. In order to adequately prepare for the upcoming launch of JWST and the future observations of terrestrial planets, we must start to bridge these two facets of research. Here I explore the pieces needed to observe (§1.1), constrain (§1.2) and model (§1.3) the atmospheres of cool low-mass exoplanets.

1.1 Remote Observations of Exoplanet Atmospheres

Observing exoplanet atmospheres can be done indirectly via transmission spec- troscopy or directly via direct imaging. Direct imaging, however, is currently only possible for large, extremely hot young planets at wide separations. This is because it is difficult to block out the light of the parent star without also blocking out the planet. For perspective, the contrast ratio (i.e brightness difference) between Earth and the Sun is about 10 billion at visible wavelengths. The technology needed to suppress this starlight is currently in development for WFIRST, a space-based mission without a definitive launch date. Therefore, the following discussion is limited to transmission spectroscopy techniques, which will be performed with JWST 1. Direct imaging is revisited in Chapter 6, Future Work.

1.1.1 Primary Transit Spectroscopy

Transmission spectroscopy relies on the planet transiting through the disk of the parent star (Figure 1.1). When the planet passes in front of the star, some of the

1JWST does have direct imaging capabilities

2 T2 λ2: High atmospheric absorption

Secondary Altitude T1 λ1: Low atmospheric Planet Temp absorption Primary T1 > T2 Fp,day @ λ1 > Fp,day @ λ2

Flux F∗ + Fp,day,λ

λ1: Low atmospheric absorption F∗ Rp,λ1

Rp,λ2 λ1: High atmospheric absorption F∗ + Fp,night 2 Rp,λ F ∗ (1 − 2 ( R∗

Figure 1.1. A schematic diagram showing the method used for observing transiting exoplanets. radiation from the star is transmitted through the planet’s upper atmosphere. If molecular absorbers are present, the planet radius becomes wavelength dependent. This is because absorbers increase the opacity of the atmosphere and cause the planet’s effective radius to appear larger to the observer. In order to calculate the exact signal, the altitude of the atmosphere at any given wavelength can be derived [Seager and Sasselov, 2000, Burrows et al., 2001, Brown, 2001, Fortney, 2005]. Accurate atmospheric models account for variations in temperature, pressure and composition with altitude, and then numerically integrate the equations of radiative transfer to obtain a full primary transit transmission spectrum. In Chapter 4, these methods are detailed in our model description. However, first-order equations are shown here to gain an intuition for the parameters that can be retrieved from primary transit transmission spectra.

From Des Etangs et al. [2008], the effective planet radius, Rp,λ as seen in Figure

1.1, can be approximated as Rp(λ) = Rp + z(τ = τeq), where τeq is the optical depth needed to produce an equivalent opaque disk and z is the height above the fixed

3 radius Rp. In this formulation, z(λ) is

s N ! Pz=0 2πRp X z(λ) = H ln ξiσλ,i (1.1) τeq kT µg i

where ξi and σi are the mixing ratios and cross sections of the atmospheric absorbers,

T is the temperature for an isothermal atmosphere, H is the scale height, and Pz=0 is the reference pressure at “zero” altitude. The goal of a retrieval is to obtain T ,

P , ξi, and µ.

Assuming that z(λ) (from here on referred to as zλ) is much smaller than Rp, 2 the eclipse depth ((Rp/R∗) in Figure 1.1) can be approximated as

2 Rp + zλ  αλ = (1.2) R∗

Differentiating Eqn. 1.2 with respect to wavelength, λ, yields an equation which shows what parameters are sensitive to changes in wavelength and therefore, retrievable. In the case of a single absorber, this is

dαλ 2Rp d ln(σλ) = 2 H (1.3) dλ R∗ dλ

Cross sections are highly wavelength dependent, making molecular detections relatively trivial. However, note the loss of the dependency on mixing ratio, ξ. This alludes to the difficulty (or impossibility) in accurately measuring abundances if only a single absorption feature is detected. In reality, detailed atmospheric models (explored in Chapter 4) are used to accurately portray transmission spectra. These are needed because cross sections

(σλ) are dependent on pressure and temperature, mixing ratios might affect the mean molecular weight (and therefore, scale height), and scattering/clouds introduce additional wavelength dependencies. However, valuable insight can be gained by looking at this toy model, which will become important when discussing retrievals in §1.2.

4 1.1.2 Secondary Transit Spectroscopy

By observing the planet before it passes behind the stellar disk, a secondary transit spectrum can be obtained (Figure 1.1). If the star and the planet were approximated as a blackbody, the decrease in brightness because of the planet transiting behind the star could be expressed as

2 Rp  Bλ(Tp) δocc(λ) = (1.4) R∗ Bλ(T∗) where Bλ(T ) is the Planck function. In reality, there are strong deviations from the blackbody spectrum as a result of altitude-dependent molecular absorbers and atmospheric temperatures. Tp in 1.4 is effectively the temperature where the optical depth is unity. If the planet were isothermal, secndary transit spectroscopy would yield blackbody at all wavelengths. If altitude dependent temperature variations were present, those variations would be probed as the optical depth of unity surface increase and decreased (see 1.1). Therefore, secondary transit spectra constrains not only information on the brightness temperature of the planet, but also the atmospheric composition of the planet. As a result, a nice synergy exists between primary transit and secondary transit transmission spectra. The former probes the limb of the planet atmosphere and the latter probes the day side hemisphere.

1.1.3 Overview of Exoplanet Observations

Although neither was designed for exoplanet observations, the HST and Spitzer have made significant strides in the field of exoplanet characterization. Alkali metals were the first chemical species discovered in the atmosphere of hot Jupiter HD 209458b using HST’s Space Telescope Imaging Spectrograph (STIS, 0.3-1 µm) [Charbonneau et al., 2002]. Since then, however, further studies have showed that detecting alkali metals (among other molecules) is difficult because of strong scattering hazes that block spectral features short of 1 µm [Pont et al., 2013, Dragomir et al., 2015]. HST’s other instrument, Wide Field Camera 3 (WFC3), has also yielded fruitful detections of water vapor in the primary transit spectra of hot Jupiter atmospheres [Wakeford et al., 2013, Mandell et al., 2013, Huitson et al., 2013, Deming et al., 2013] and one warm Neptune [Fraine et al., 2014] at 1.4µm. Most recently, a large

5 HST program was combined with the two Spitzer data points around 4.5µm to create 10 of the most complete exoplanet transit transmission spectra to date [Sing et al., 2016]. These 10 spectra show varying magnitudes of water absorption. Some water features are highly muted, while others are missing entirely. The authors point out that this is a result of complex and diverse cloud features, which were further explored in [Wakeford et al., 2017]. In fact, because of prevalence of clouds in the observations of transmission spectra, they have become an active area of focus. For example, one of the most heavily studied exoplanets, GJ 1214 b, exhibits a complete absence of spectral features, despite high precision measurements, likely a result of cloud coverage [Kreidberg et al., 2014b]. Along with the detections listed above, several claims have been made, which were later disputed. For example, the detection of: methane in HD 189733b [Swain et al., 2008], a temperature inversion in HD 209458b [Knutson et al., 2008], disequilibrium chemistry in GJ 436b [Stevenson et al., 2010], and a high C/O ratio in WASP 12b [Madhusudhan, 2012] have all been disputed or disproved [Beaulieu et al., 2011, Zellem et al., 2014, Morley et al., 2016, Crossfield et al., 2012, respectively]. These studies could have been victims of incorrect data reduction schemes or previously unknown systematics. However, the disagreements are likely a product of the assumptions that went into interpreting the data, also referred to as spectral retrievals. For example, some retrieval schemes place constraints on chemistry based on plausibility arguments (i.e. equilibrium chemistry) [Madhusudhan et al., 2011], while others do not [Line et al., 2014]. All of these subtleties, explored in §1.2, are crucial to gaining accurate insights into planetary atmospheres.

1.1.4 Looking Forward: The James Webb Space Telescope

Beyond HST and Spitzer, JWST is equipped with a 6.5-meter primary mirror and four visible to mid-IR instruments (NIRCam, NIRISS, NIRSpec, MIRI) that span 0.6-28 µm with low and medium resolution modes, which has the potential for ground-breaking exoplanet science. Figure 1.2 shows all of the available spectroscopy modes on board JWST, as compared to HST. In preparation for JWST’s launch in October of 2018, several new studies have focused on characterizing the observatory’s expected performance.

6 Wavelength Coverage and Resolution

0.3 1 2 3 4 5 10 Res. μm 30

HST STIS WFC3 100 500 NIRISS SOSS 1000 Prism NIRSpec G140 G235 G395 2000

NIRCam F322W2 F444W 3000

MIRI LRS 4000

Figure 1.2. Schematic showing all of the JWST spectroscopy modes as compared to HST’s spectroscopy (WFC3) and spectrophotometry (STIS) modes. Color coding shows approximate resolving powers of each mode.

Greene et al. [2007] were among the first to baseline the performance of JWST’s primary imaging instrument, NIRCam, with regards to exoplanet science. They found that with 1000 seconds of integration time, R=500 spectra of Jupiter-sized exoplanets in primary transit and secondary eclipse will be attainable with signal- to-noise ratios (SNRs) ranging from SNR∼5 for faint (J magnitude of 10) G2V stars and up to SNR∼90 for bright (J magnitude of 5) G2V stars. Deming et al. [2009] created a sensitivity model for NIRSpec and MIRI, and predicted that JWST will be able to measure temperature and absorption of CO2 and H2O in 1-4 habitable Earth-like planets discovered by the Transiting Exoplanet Survey Satellite (TESS). Since then, many have sought to baseline the performance of JWST using independent sensitivity models [Kaltenegger and Traub, 2009, Charles Beichman et al., 2014, Batalha et al., 2015, Cowan et al., 2015, Barstow et al., 2015, Barstow and Irwin, 2016, Greene et al., 2016, Mordasini et al., 2016, Mollière et al., 2016, Howe et al., 2017]. For example, Batalha et al. [2015] reported that primary transit spectroscopy with NIRSpec of 1-10 M , 400-1000 K planets orbiting M dwarfs would result in high SNR spectra if the planets were within ∼50 pc and if 25 transits were co-added. These results were based on noise simulations which included spacecraft jitter, drift, flat field errors and background noise. In reality, exoplanet observations

7 with JWST could suffer from other systematics as well. Barstow et al. [2015] explored these effects by including time varying astrophysical and instrumental systematics in their observational simulations. Greene et al. [2016] used a retrieval algorithm (see §1.2) with an independent noise simulator for NIRISS, NIRCam, and MIRI in order to determine what atmospheric properties could be retrieved from a hot Jupiter, warm Neptune, warm sub-Neptune and cool super-Earth. All of these were pivotal to our knowledge and understanding of the functionality of JWST observing modes and all of these relied on simulating noise sources. With just over one year left until launch, it is imperative that the exoplanet community begins to digest and integrate these studies into their observing plans and strategies. In order to encourage this and to allow all members of the community access to HST and JWST simulations, Chapter 4 presents an open source python package for creating observation simulations of all observatory-supported time-series spectroscopy modes.

1.2 Constraining Exoplanet Atmospheres Through Re- trievals

After obtaining transit transmission spectra, the next step is to constrain the atmospheric parameters. Using a Bayesian framework to constrain atmospheric properties from remote observations has been done for several years in Solar System and Earth science [Chahine, 1968, Rodgers, 1976, Twomey et al., 1977, Rodgers, 2000]. The goal is to obtain the posterior probability distribution for model parameters given a set of observations. Several pipelines have been developed to do this for exoplanet atmospheres. What follows is a revision of the Bayesian framework, an overview of retrieval techniques and outstanding problems.

1.2.1 Bayesian Framework in the Context of Atmospheres

The model parameters, which define the atmospheric state, are just a vector, x, of length n, that is usually composed of gas mixing ratios, temperature at each atmospheric level, and any other atmospheric parameters pertinent to the model. If there were no noise, the model (F(x)), the state vector (x) and the observations (y), would simply be related by y = F(x). For exoplanet atmospheres, y is usually

8 the eclipse depth as a function of wavelength, analogous to Eqn 1.2, and the state vector, x, can be composed of temperature, pressure, mixing ratios, etc. However, since the state vector is not known a priori, F(x) can be expanded around an initial guess for the true state, xa using one step of a Taylor series

dF y ∼= F(x ) + (x − x ). (1.5) a dx a xa

The derivative of F(x) with respect to the state vector is referred to as the Jacobian matrix, K, which describes how sensitive the model is to perturbations in each state vector parameter at each wavelength position. It is an m × n matrix given by

∂Fi(x) Kij = (1.6) ∂xj

th th Fi is the measurement in the i wavelength position and xj is the j state vector parameter. Lastly, in order to solve for the true state, Equation 1.5 can be inverted to yield −1 x = xa + K (y − F(xa)) (1.7)

However, the initial assumption that y = F(x) is not entirely valid because real data are never completely free of noise. In order to deal with this problem, a Bayesian framework is used. The relevant equations of Bayesian statistics can be found in Rodgers [2000]. Only the most pertinent equations are shown here. Bayes theorem [Bayes et al., 1763] states that the posterior distribution function, p(x|y), is

p(x)p(y|x) p(x|y) = . (1.8) R p(x)p(y|x)dx

The posterior distribution function describes the probability that a certain state, x, exists given a set of measurements, y. p(x) is the prior probability distribution, which describes the a priori knowledge of the true state before the measurement is taken. And p(y|x) is the likelihood function, which is the probability of a set of measurements, given a model and known values of the state. Next, assuming that both the probability distribution of the prior and the error on the measurements are Gaussian, the likelihood function and the prior become

9 proportional to − 1 (y−Kx)T S −1(y−Kx) p(y|x) ∝ e 2 e (1.9)

− 1 (x−x )T S −1(x−x ) p(x) ∝ e 2 a a a (1.10)

where Se and Sa are the m × m measurement error and n × n prior covariance

matrices, respectively. We assume that Sa is a diagonal matrix and it defines the prior state of knowledge, e.g., the uncertainties on the atmospheric state

vector parameters before we make a measurement. Se defines the error on each measurement and is only diagonal if there are no correlations between measurements. Finally, if we replace Eqns 1.9 & 1.10 back into the original Bayes theorem Eqn. 1.8, the posterior probability function can be rewritten as

P (x|y) ∝ e−0.5J(x) (1.11)

where the cost function, J(x) is

T −1 T −1 J(x) = (y − Kx) Se (y − Kx) + (x − xa) Sa (x − xa) (1.12)

The first term in the cost function describes the data’s contribution to the state of knowledge (“chi-squared”) and the second describes the contribution from the prior. When deriving the most likely state, x, the goal is to maximize P (x|y) or minimize the cost function, J(x).

1.2.2 Overview of Retrieval Techniques

In deriving Eqn. 1.11, we have assumed a linearized model and a Gaussian posterior. Often however, models are highly non-linear. In these cases Kx is usually replaced with F(x) in the cost function [Line et al., 2012]. Here we explore the techniques that exist to maximize the posterior probability function for linear and non linear models. The simplest and fastest technique is optimal estimation (OE), which has been most commonly used in Earth/Solar System science [e.g. Rodgers, 1976, 2000, Kuai et al., 2013, Irwin et al., 2008b], but has also been applied to exoplanet science [Line et al., 2012, 2013b]. Optimal estimation involves using an iterative scheme (e.g. Levenberg-Marquardt [Line et al., 2012], Newton’s Method [Irwin et al., 2008a,

10 Line et al., 2013b]), where a new state vector is only selected when a lower cost function is discovered. Unfortunately, OE methods only tend to converge with high resolution, high S/N data, and they make the assumption that the posterior is Gaussian. Recently there has been a rise of high performance parallel computing, which has led to another technique to adequately sample parameter space, called the Markov Chain Monte Carlo (MCMC) method. MCMC methods do not make assumptions about the shape of the posterior, and instead evaluate the posterior millions of times over a broad parameter space. Because the available data with HST and Spitzer has suffered heavily from low resolution and low S/N, the MCMC method has been most widely used [Madhusudhan et al., 2011, Benneke and Seager, 2012, Benneke and Seager, 2013, Line et al., 2013b, 2014, de Wit and Seager, 2013, Waldmann et al., 2015]. In some cases, constraints on the abundance of water have been derived [Line et al., 2014, Madhusudhan et al., 2014, Kreidberg et al., 2014b] because of a strong detection of water absorption at 1.4µm. This is contradictory to the discussion in §1.1.1, Eqn. 1.3. It was shown there that if only a single absorber is observed, the eclipse depth differentiated with respect to wavelength yields a function that is independent of mixing ratio. So then, how has it been possible to obtain viable constraints? Herein lies the subtlety of retrieving properties of exoplanet atmospheres. Because Line et al. [2014], Madhusudhan et al. [2014], Kreidberg et al. [2014b] observed hot Jupiters, the background composition of the atmosphere was known to be a combination of H2/He. Therefore, we can re-derive Eqn. 1.3 for the case of two absorbers: water and H2/He. In this case, the eclipse depth, differentiated with respect to wavelength is

dα 2R 1 d ln σ ξ σ d ln σ ! λ = p H λ,1 + 2 λ,2 λ,2 (1.13) 2 ξ2σλ,2 dλ R∗ 1 + dλ ξ1σλ,1 dλ ξ1σλ,1 where ξi are the mixing ratios and σi are the cross sections. If other dependencies are not present (i.e. pressure dependencies on cross sections), only the ratio of mixing ratios can be constrained from the sole detection of a water absorption feature [Benneke and Seager, 2012, Line and Parmentier, 2016]. With the ratio though, an absolute mixing ratio can technically be derived because the sum of all

11 the atmospheric constituents must be unity. Therefore, the water mixing ratio is

ξH2O = 1 − ξH2/He. (1.14)

In reality though, this is only a lower limit. In some cases, researchers also attempted

to constrain CH4, CO and CO2 along with H2O [Kreidberg et al., 2014b]. Not surprisingly, no significant constraints could be placed. With the upcoming launch of JWST, observations of a wide variety of planet- types will be obtained, not just Jupiters and Neptunes. In fact, out of the thousands of planet candidates discovered by Kepler [Mullally et al., 2015], 80% of them have

radii <3R⊕. Additionally, occurrence rate studies verify that this high frequency is not merely an observational bias [Dressing and Charbonneau, 2013, Petigura et al., 2013, Morton and Swift, 2014, Silburt et al., 2015]. This means that several of the planets discovered by missions such as the TESS and the Habitable Zone

Planet Finder (HPF) will be planets with R=1-1.5R⊕ and M=1-10M⊕ . This, along with the push towards characterizing Earth 2.0, makes Earths and super-Earths of great interest in the upcoming decade. However, this presents a particularly strong challenge when it comes to uniquely constraining their atmospheric conditions.

1.2.3 Challenges to Constraining Atmospheres of Earths and super-Earths

“Low-mass planets” is an inherently broad phrase, as it encompasses anything

from 1-1.5R⊕ and 1-10M⊕ [Weiss and Marcy, 2014, Rogers, 2015]. Low-mass planets could be rocky, icy, or they could have large H-He envelopes. The implied atmospheric composition that accompanies each type of planet spans a wide range. This poses a challenge for retrieving atmospheric properties because: 1) the mean molecular weight, µ, is completely unconstrained (remember, in the case of Jupiters,

µ ∼ 2.3), 2) diatomic background gases H2 and N2, referred to as spectrally inactive gases, do not exhibit broad band absorption features in the near-infrared and, 3) most low-mass planets do not have precise mass measurements. To remedy 1) and 2), studies have sought to find ways to uniquely constrain the atmospheres of low-mass planets. Benneke and Seager [2012] outline each of the spectral observables needed to do so, shown in Figure 1.3 (adapted from Fig. 3 in Benneke and Seager [2012]). They conclude that a unique constraint of mixing

12 ratios as well as the background gases can be achieved if at least one absorption feature per absorber, and the slope and strength of the Rayleigh scattering signature are all measured. They emphasize that it will not be possible to tell whether or not a species is the main or minor atmospheric constituent, without the detection of a Rayleigh slope, short of 1 µm, which would help to constrain the absolute pressure at depth.

Transit depth of abundances Relative n=3 for H2O, CO2, CH4 Feature Shape absorber #1

Rel. Transit depth of 1) n absolute Transit absorber #n mixing Depth DCO2 } ratios Mean Mean molecular Rayleigh 2) 2 mixing scattering slope ratios of mass spectrally DH20 Slope Feature Shape inactive gases Rel. Transit Depth 3) planetary Relative Transit Depth RelativeTransit DCH4 } radius

DRayl Depth offset of 4) cloud top Dmin Rayleigh slope pressure 0.5 1.0 2.0 3.0 4.0 5.0 Sum of mixing Wavelength (μm) ratios is 1 Lowest transit depth

n+4 n+4 observables retrievable parameters

Figure 1.3. Figure adapted from [Benneke and Seager, 2012]. The transmission spectra of an atmosphere with three absorbers (H2O, CH4, CO2). Each individual observable within the transmission spectra is labeled. For an atmosphere with n absorbers, there are n + 4 total observables. This leads to a total of n + 4 retrievable parameters. The phrase “spectrally inactive gasses” refers to gases such as N2, H2 and He that do not exhibit strong absorption features but that may be the dominant background gas.

To add to this complexity, these results assume that accurate planet masses have already been obtained, which might not necessarily be the case. Masses are unobtainable via Kepler’s transit method. Even though they can be calculated from transit timing variations (TTVs; e.g., Agol et al. [2005], Holman and Murray [2005], Ford et al. [2011], Lissauer et al. [2011, 2013]; Carter et al. [2012], Jontof-Hutter et al. [2014, 2016], Masuda [2014]) and radial velocity measurements (RV; e.g.,

13 Batalha et al. [2011], Howard et al. [2013], Weiss et al. [2013], Dressing et al. [2015]), these methods have only yielded masses for a fraction of the low-mass systems to date because they required large numbers of observing hours. In the interest of bypassing resource-intensive RVs/TTVs to determine exoplanet masses, a technique for determining the mass of a transiting exoplanet from atmospheric observations alone – via its transmission spectrum – was proposed by de Wit and Seager [2013]. This method, termed MassSpec, relies on accurate determinations of atmospheric temperature, T , mean molecular weight (MMW), µ, 2 kT kT Rp and scale height, H = µg , because Mp = µGH . They conclude that their technique is able to constrain the masses of super-Earth and Earth-sized planets using future telescopes, such as JWST. More specifically, they conclude that 200 hours of in-transit observing time spread across three arbitrary modes (NIRSpec G140M, NIRSpec G235M and NIRSpec G395M), could result in an accurate/unique constraint of atmospheric constituents, temperature and mass of a super-Earth around an M1V star at 15 pc. This conclusion is contradictory to the results of Benneke and Seager [2012], as the combination of JWST’s three NIRSpec grisms does not contain the wavelength coverage necessary to measure a Rayleigh slope. One additional subtlety of de Wit and Seager [2013] is that because observations of transiting exoplanets require both in-transit and out-of-transit measurements, their estimate of 200 hours is too small by at least a factor of 2 (typical HST observations usually consist of a baseline that is at least the duration of the transit Wakeford et al. [e.g. 2013], Kreidberg et al. [e.g. 2014b]). 400 hours is a lot of time to devote to even the most interesting of systems. For context, the largest HST proposals have been for WASP-43 and GJ 1214 with 91.5 and 90 hours, respectively. It is not clear exactly how many hours will be devoted to any target, or exoplanets, in general. Regardless, interest in small temperate targets is not likely to subside. Therefore, in order to maximize our chances of accurately retrieving atmospheric parameters from low-mass (and other) planets, Chapter 5 explores how observations with JWST can be optimized to yield the most precise/accurate constraints on key atmospheric parameters with the least amount of observing time. And, Chapter 6 explores to what degree poor mass constraints will hinder our ability to constrain atmospheric parameters. Both Chapters 5 & 6 leverage the JWST noise models and the transit transmission model described in Chapter 4.

14 1.3 Forward Modeling of Planetary Climates and At- mospheric Compositions

Beyond retrievals, chemical and climate forward models will be crucial for under- standing the underlying physical processes that drive exoplanetary atmospheres. The range of theoretical models that have been created in this phase space is incred- ibly diverse and is founded in several decades of literature and model development. Recently, Madhusudhan et al. [2016] reviewed the status of chemical modeling efforts for exoplanetary atmospheres in all the discovered classes of planets: hot Jupiters, ice giants, super-Earths and Earths. Chemical models range in complexity from chemical equilibrium for the deep layers of hot Jupiters to Earth-centric one- dimensional photochemical models. As a general rule of thumb, one-dimensional model complexity increases with decreasing temperatures. This is because as the temperature decreases, the timescale for chemical reactions becomes slower than the timescales for other atmospheric processes, such as mixing or photolysis. On one side of the spectrum, for the purposes of matching low resolution, low S/N HST observations of hot Jupiters to models, the assumption of chemical equilibrium has been commonly used [Burrows and Sharp, 1999, Moses et al., 2011, Venot et al., 2012, Kreidberg et al., 2015]. Chemical equilibrium is calculated by minimizing the Gibbs free energy of the system and is only dependent on temperature, pressure and elemental abundances. Because of the speed at which these forward models can be computed, chemical equilibrium models have been folded into various retrieval schemes (remember MCMC schemes often taken ∼ 106 model runs) [e.g. Madhusudhan et al., 2011, Kreidberg et al., 2015]. Even for hot Jupiters, though, chemical equilibrium is not valid in certain layers of the atmosphere. For example, in the cooler upper atmosphere, chemical reactions become slower than some dynamical processes such as advection, diffusion or turbulence [Showman et al., 2009]. Also, because hot Jupiters are highly irradiated, molecules originating in the deep atmosphere are photodissociated to produce radicals upon being transported upward. These radicals then react to create different molecular species [Moses et al., 2011]. Nevertheless, equilibrium acts as a good starting point in this regime. On the other side of the spectrum, photochemical models rooted in Earth-science

15 were created to study the terrestrial Solar System planets (e.g. Earth [Yung and McElroy, 1979, Kasting and Donahue, 1980, Kasting et al., 1983]; Mars [Kasting, 1991, Nair et al., 1994]; Venus [Yung and DeMore, 1982, Kasting and Pollack, 1983]; Titan [Yung et al., 1984]). These photochemical models all include gravity, irradition, photolysis, lightning, rainout, parametrized vertical transport, and upper & lower boundary conditions (e.g. volcanic outgassing as a lower boundary flux). Unlike equilibrium models, which rely on a few input parameters and which pro- duce solutions rapidly, photochemical models require several dozen input parameters and an “initial guess”, which must be close to the correct solution. The combination of these two necessities make it highly non-trivial to wrap self-consistent chemical models of terrestrial-like planets at low temperatures within a retrieval scheme. Some authors have created photochemical models, which are more general than those developed by Kasting. Hu and Seager [2014] developed a photochemistry- thermochemistry kinetic-transport model for studying the compositions of super- Earths and mini Neptunes. In this framework, the model computes not only the trace gases, but also the abundances of the major background gases. This model, however, has also not yet been paired within a retrieval framework, most likely because the adequate data are not available. With the upcoming launch of JWST, transit transmission spectra of cool, terrestrial planets may be obtained. Once we have them, the question of how to reliably constrain parameters from forward models becomes more interesting. The goals of this dissertation are to: 1) explore each forward model piece-by-piece, starting with the climate model, then photochemistry, and lastly the energy balance model (Chapter 2), 2) apply these models to a early Mars, whose atmospheric composition is largely unknown (Chapter 3), 3) leverage knowledge gained by doing so, to determine the best strategies for observing exoplanets in the JWST era (Chapters 4 and 5), 4) investigate other complications that could hinder our determination of the atmospheric state of exoplanets (Chapter 6). Lastly, we discuss on how more complex forward models can eventually be coupled to retrieval schemes and be used for exoplanet research, in Chapter 7.

16 Chapter 2 | Modeling the Planet System

The models outlined in this chapter have been in development for several decades. My specific contributions to the models were in the form of updates, improvements, and several bug fixes. For the photochemical model I:

• Updated reaction rates

• Added nitrogen chemistry, removed hydrocarbon chemistry

• Created a working martian model from earth starting conditions

• Implemented a mechanism to handle global redox budgets

• Several bug fixes

Then, I used the photochemical model to explore the atmospheric chemistry of early Mars (Chapter 3.1). Specifically, I was interested in determining whether or not a 5% H2, 95% CO2 atmosphere was chemically consistent with a 273 K, 3 bar atmosphere. The resutlts of the paper are published in Batalha et al. 2015 (see Chapter 3 for full reference). For the climate code, I:

• Derived CO cross sections

• Updated CO2–H2 and CH4–H2 absorption cross sections

• Several bug fixes

17 Then, I used the climate model to run several thousand calculations over a wide parameter space in pressure, hydrogen mixing ratio, temperature, pressure, surface albedo and zenith angle. Doing so, allowed us to parameterize the code for the energy balance model. The results of the paper are published in Batalha et al. 2016 (see Chapter 3 for full reference). For the energy balance model I:

• Created valid Mars EBM from Earth EBM

• Added the dependence of hydrogen on pCO2

• Added radiative transfer calculations for early Mars parameterizations

Then, I used the energy balance model to determine whether or not a hydrogen- carbon dioxide atmosphere is climatically stably on early Mars. This required

adding the dependece of hydrogen on the partial pressure of CO2 and making sure the carbonate-silicate cycle weathering was accounted for in the model. The results are published in Batalha et al. 2016. All of these models are grounded in Earth sience and validated for present Earth and present Mars. Therefore, the further away from “Earth-like” we get, the harder it is to verify the solutions. In doing our simulations we make several analogies between preset Earth and early Mars. This assumption is grounded in in situ measurements of the martian surface. For exoplanets, where this data is not available, it will be difficult to use these same forward models to create self-consistent models. I discuss this further in Chapter 7 & 8. Below, I briefly describe the methodology of each model.

2.1 One-Dimensional Climate Modeling

To investigate the planet’s globally average surface temperature, we use a one- dimensional (in altitude) radiative-convective model. One-dimensional models do not account for differences in latitude or longitude. For latitude-dependent temperature information, we use the energy balance model (Section 2.3). The one-dimensional climate model solves the energy-conservation equation:

∂T (p, t) g ∂F (p) = − (2.1) ∂t cp ∂p

18 where g is gravity, cp is the specific heat at constant pressure, T (p, t) is the vertical temperature profile, p is the pressure, and F (p) is the globally averaged total radiative flux at each pressure (where positive flux corresponds to a downward flux). The flux, F (p), is usually split into two parts:

F (p) = Fs(p) + FIR(p) (2.2)

Where FS is the visible stellar flux and FIR is the thermal-infrared flux. In our models, both of these terms are integrated over both wavelength and zenith angle. To solve Eqn. 2.1 we use a first order time difference technique, where the temperatures are calculated at the midpoints of the layers and the fluxes are computed at the layer boundaries.

2.1.1 Calculating Radiative Fluxes

Although there are several different methods to approximate radiative fluxes, we use the delta 2-stream method based on Toon et al. [1989], along with the delta-scaling of Joseph et al. [1976], when particles are involved. The basic principle of the two stream method is to approximate integrations of diffuse radiation over an upward and downward hemisphere as a single stream of radiation in each direction at some average zenith angle. Then, the scaling [Joseph et al., 1976] is specifically used to better approximate the forward scattering by particles. The most difficult part of the calculation is accounting for the absorption of the gaseous species contained in the atmosphere. Some radiative transfer models use a line-by-line technique, where the individual vibration-rotation lines of each molecule are resolved and adjusted to account for line broadening at different altitudes (using a Voigt profile). Although this method results in high accuracy, a single calculation can often take anywhere from 10 minutes to a couple hours to complete. In our climate model, we have to perform several of these calculations and a line-by-line technique is not possible. Instead, we use a broadband approximation where the thermal-infrared is divided into 55 spectral bands between 0.7-500 µm and the solar spectrum is divided into 38 intervals between 0.25-4.5 µm. Within each of these sections, the absorption by each gas is parametrized using correlated-k coefficients [Kato et al., 1999]. In this

PN −kiP scheme, the broadband transmission is parametrized as T = i=1 αie where

19 the weights, αi, are Gaussian and the absorption coefficients, ki are derived by binning the line-by-line coefficients. These coefficients were most recently updated in Kopparapu et al. [2013] using HITRAN 2008 for CO2 and HITEMP (2010) for

H2O. Although I do not explore warming from other gases, a description of how they are included can be found in the Supplementary Info of [Ramirez et al., 2014].

2.1.2 Treatment of Water Vapor and Clouds

It is important to (as much as possible) self-consistently model water vapor since it is a powerful greenhouse gas. However, this is difficult in 1D radiative-convective models, which lack spatial resolution and therefore an accurate treatment of the hydrologic cycle. In order to rectify this, we follow the Manabe and Wetherald [1967] approach in the troposphere. That is, we assume a fixed vertical distribution of relative humidity of the form:

Q(z) − 0.02 RH(z) = (2.3) 1 − 0.02 where RH is the relative humidity and Q(z) = p(z)/pg is the ratio of the ambient pressure at altitude z to the surface pressure, pg. As this distribution is derived for modern Earth, it is not valid for any planet atmosphere which differs greatly in surface pressure or temperature. For example, for early Mars, we use RH =1, not because it is realistic, but because it allows us to calculate an upper limit on surface temperature. Another factor to consider when modeling the water vapor in a planetary atmosphere is the tropopause cold trap. In the upper layers of the tropopause, the air is cold and the saturation vapor pressure is low, water vapor condenses to form clouds and the stratosphere is, as a result, dry. For modern Earth [i.e. Manabe and Wetherald, 1967], we simulate this process by finding the altitude where the water mixing ratio is no less than 4 ppmv and assuming a constant water mixing ratio of 4 ppmv above this point. For other cases, e.g. early Mars, we assume a saturated tropopause and therefore that the saturation mixing ratio of water is fH2O = psat(T )/p(z). This way, fsat reaches a minimum at the top of the troposphere. Above that point, we assume the water mixing ratio is constant at that minimum value. The last process to consider is the effect of clouds. There is no reliable way

20 to parametrize clouds in a 1-D model, which makes them difficult to include. For modern Earth, some authors have derived a statistical ensemble of cloud heights, optical properties and cloud coverage but these only work for modern Earth [Goldblatt and Zahnle, 2010]. Instead, we adjust the surface albedo of the planet to replicate the effect of clouds. For Earth, this means adjusting the surface albedo to replicate the observed mean temperature of 288 K. Goldblatt and Zahnle [2010] compared models using the albedo adjust technique and the statistical ensemble technique. They concluded that adjusting the surface albedo leads to an overestimation of greenhouse warning. Despite being aware of these potential problems, a better (i.e. accurate, general, and computationally fast) solution has not yet emerged, without going to three dimensions. Therefore, we continue to employ the albedo adjustment method in this work.

2.2 One-Dimensional Photochemical Modeling

2.2.1 Model Description

To investigate the theoretical composition of terrestrial planet atmospheres, we use a 1-D (in altitude), horizontally averaged photochemical model. Horizontally averaged models make use of the fact that variations in atmospheric composition with altitude are much more pronounced than those with latitude/longitude. This is because in non-tidally locked systems, vertical transport is slower than horizontal transport and because the depth that UV photons will penetrate depends on the atmospheric composition at each altitude layer. The model, originally developed by [Kasting et al., 1979], has been most recently updated by [Domagal-Goldman et al., 2011]. The model solves the coupled continuity and flux equations for multiple atmo- spheric species using an implicit, reverse Euler integration technique. The standard continuity equation is: ∂n ∂Φ i = P − l n − i (2.4) ∂t i i i ∂z and the standard flux equation is

! ∂fi 1 ∂ni 1 1 + αT i ∂T Φi = −Kn − Dini + + (2.5) ∂z ni ∂z Hi T ∂z

21 −3 where t is time, z is altitude, ni is number density of species i (molecules cm ), −3 −1 Pi is chemical production rate (molecules cm s ), li is chemical loss frequency −1 s , Φ is flux of species i, fi=ni/n is the mixing ratio of species i, K is the eddy 2 −1 diffusion coefficient (cm s ), n is the total number density, Di is the diffusion coefficient between species i and the background atmosphere, Hi is the scale height of species i, and αT i is the thermal diffusion coefficient of species i with respect to the background atmosphere. By converting to mixing ratio units and using the ideal gas law, equation 2.4 can be converted to:

" # ∂fi 1 ∂ ∂fi Pi = (K + Di)n + Hinfi + − lifi (2.6) ∂t n ∂z ∂z n where ! 1 1 αT i ∂T Hi ≡ Di − + (2.7) Hi Ha T ∂z This equation is the set of partial differential equations for the mixing ratios of each species that are tracked in the model. Furthermore, these partial differential equations can be converted to to a set of ordinary differential equations (ODEs) using a finite difference approximation. There are several versions of this model. The model used here (for early Mars) does not include higher hydrocarbon chemistry (alkenes, alkynes, alkanes longer than C2). Instead, the model includes 29 long-lived species and 16 short-lived species involved in 215 reactions (see Appendix A). In addition to the 45 species, the Mars model consists of 100 plane parallel layers spaced by 2 km in altitude, allowing it to calculate species profiles up to 200 km. With 100 layers and 45 species, the model solves 45 × 100 = 4500 ODEs.

2.2.2 Boundary Conditions and Volcanic Outgassing

Boundary conditions are required at both the top and bottom of the model grid. At the lower boundary species can either be set to a constant mixing ratio, a constant flux or a constant deposition velocity. The deposition velocity is limited to a value between 0 and 1 cm/s and is specifically for species that are chemical removed at the surface or for species that are soluble such as SO2 and H2S. Upper boundary conditions are treated similarly. Most species are given fluxes of zero at the top. H and H2 are an exception and are set equal to the diffusion

22 typically flux =0 (except H/H2) 200 km

f j+1 Φ j+1/2 i i f j Φ j -1/2 i i f j -1 i 20 km outgassing region lower troposphere ∆z 0 km constant flux, mixing ratio or dep. vel.

Figure 2.1. Model and grid setup for the 1-D photochemical model.

limited value (see following section). O2 is also treated differently because above the model grid (200 km) it is photodissociated. Therefore, atomic O is given a constant downward flux of twice the upward flux of O2. Similarly, CO2 photolysis also occurs above the model grid. Therefore, CO and O are also given downward fluxes.

2.2.3 The Atmospheric and Global Redox Budgets

All atmospheres must be in approximate redox balance over sufficiently long time scales; otherwise, their oxidation state would change during the time frame of interest. Earth for example, is slowly oxidizing over thousands of years. In order to create a self-consistent theoretical chemical model, redox must balance on the timescale of the model run. Otherwise, the model would never converge. For an

H2−rich atmosphere, ’long’ means time scales of tens to hundreds of thousands of years [Kasting, 2013]. Both an atmospheric redox budget and a global redox budget can be computed [e.g. Kasting and Canfield, 2012, Kasting, 2013]. The global redox budget is defined as the redox budget of the combined atmosphere-ocean system. This is the budget that is considered in models of the modern Earth’s redox balance

23 [e.g. Holland, 2002, 2009]. To balance the atmospheric redox budget, we assume that the sources of reducing power to the atmosphere are volcanic outgassing, Φout(Red), and rainout/surface deposition of oxidizing species, Φrain(Oxi). The sources of oxidizing power are rainout of reduced species, Φrain(Red), and the escape of hydrogen to space,

Φesc(H2). Given these definitions, a balanced atmospheric redox budget should obey the following relationship:

Φout(Red) + Φrain(Oxi) = Φesc(H2) + ΦRain(Red) (2.8)

Typically, our atmospheric photochemical model balances the redox budget to about 1 part in 107. The escape rate of hydrogen is given by the diffusion-limited expression [Walker, 1977].

bi fT (H2) ∼ bifT (H2) Φesc(H2) = = (2.9) Ha 1 + fT (H2) Ha

Here, bi is the weighted molecular diffusion coefficient for H and H2 in air, H (=kT/mg) is the scale height (at T 160K, bi = 1.6 × 1013cm−2s−1) and f (H ) a Ha T 2 is the total hydrogen volume mixing ratio: fT (H2) = f(H2) + 0.5f(H) + f(H2O) +

2f(CH4) + ..., expressed in units of H2 molecules. Realistic models must also balance the redox budget of the combined atmosphere- ocean system. Kasting [2013] refers to this as the global redox budget. His expression for this budget is as follows:

ΦOut(Red) + ΦOW +Φburial(CaSO4) + Φburial(F e3O4) = (2.10) Φesc(H2) + 2Φburial(CH2O) + 5Φburial(F eS2)

Here, ΦOW represents oxidative weathering of the continents and seafloor, and

Φburial(i) is the burial rate of species i.H2O, CO2,N2, and SO2 are taken as redox neutral species in this formulation. The global redox balance takes into account processes occurring at the ocean- sediment interface, e.g., burial of organic carbon and pyrite. If we assume, as a starting point, that nothing is happening at that interface, and if oxidative

24 weathering is neglected, then the global redox budget simplifies to

Φout(Red) = Φesc(H2) (2.11) i.e., volcanic outgassing of reduced gases must be balanced by escape of hydrogen to space. Inserting this equation back into Eqn. 2.8 implies that

Φrain(Oxi) = Φrain(Red) (2.12) that is, the rainout rate of oxidants from the photochemical model must equal the rainout rate of reductants. Or, to think of this in a different way, if no redox reactions are happening on the seafloor, the rate of transfer of oxidants from the atmosphere to the ocean must equal the rate of transfer of reductants. We will start from this simplifying assumption and then add seafloor processes as we proceed. In practice, a photochemical model will not satisfy Eqs. 2.11-2.12 on its own. Rather, the photochemical modeler must make decisions about how to deal with any imbalance. Although previous models have typically not considered the ocean- atmosphere balance [Segura et al., 2003, Tian et al., 2010], two more recent models have done so [Domagal-Goldman et al., 2014, Tian et al., 2014]. Domagal-Goldman et al. [2014] did this by wrapping the photochemical code in a separate script that repeatedly ran the model, changing the boundary conditions between simulations, until the model satisfied the above equations for a specified value of Φrain(Oxi) -

Φrain(Red) to within a determined tolerance level. We used the simpler procedure previously employed by Tian et al. [2014]. In all of our simulations, we found that Φrain(Oxi) - Φrain(Red) was < 0, that is, the rainout rate of reductants exceeded that of oxidants. So, we let H2 flow back from the ocean into the atmosphere at a rate equal to that of the difference between the rained out reductants and oxidants. Without this assumption, H2 would flow back into the planet (without any physical justification), and we might therefore underestimate the atmospheric H2 concentration. The global redox budget is illustrated in Figure 2.2. By following this methodology, we essentially assume that dissolved reductants and oxidants react with each other in solution in such a way as to yield H2, and that the organic carbon burial rate is essentially zero. This may not always be the case, and we must be conscious of that in our analysis. For example, if the burial

25 ΦESC(H2)

ΦOUT(Red)

Φrain(Ox)%–!Φrain(Red) ΦOcean(H2)""=""Φrain(Red)&#!Φrain(Oxi)&&

OCEAN!

! Figure 2.2. A schematic diagram showing the method used for balancing the ocean- atmosphere system. Φout(Red) is the flux of reductants outgassed through volcanoes, Φrain(Red/Ox) is the flux of rained-out reductants or oxidants (including surface depo- sition). ΦOcean(H2) is the flux of H2 back into the atmosphere required to balance the oceanic H2 budget. An excess of reductants, such as H2S, flowing into the ocean leads to an assumed upward flux of H2. rate of organic carbon or other reduced species exceeded the sum of the burial rate of oxidized species and the rate of oxidative weathering, our assumptions would not apply, and atmospheric H2 concentrations would decrease.

If all of the H2 in the atmosphere came directly from volcanic outgassing, Eq.

2.9 and 2.11 taken together show that in order to have 5% H2, the minimum H2 concentration needed to sustain a warm early Mars, the outgassing rate of H2 must be at least 8×1011 cm−2s−1. If an appreciable fraction of the atmospheric hydrogen is in some other form, e.g., CH4, then the total hydrogen outgassing rate would need to be correspondingly higher because the main greenhouse warming is coming from just the H2.

This approach allows us to consider the various sources of H2, including both outgassing terms and terms at the ocean-sediment interface. We outline these sources below. First, we consider contributions to Φout(Red) from outgassed H2, S, and CH4. Then, we consider the contributions to Φrain(Oxi)- Φrain(Red) (assumed > 0) from serpentinization and burial of iron oxides.

26 2.3 Time-dependent Evolution of Atmospheres

2.3.1 Energy-Balance Climate Model Description

Our EBM, like the one parameterized by Menou, was originally created by Williams and Kasting [Williams and Kasting, 1997]. We updated this EBM with new radiative transfer parameterizations from our 1-D climate model for Mars (Chapter 3.1). Details concerning the EBM are included in the following sections and the parameterizations are included in Appendix B. In addition to calculating surface temperature as a function of latitude, our

EBM simulates geochemical cycles of the greenhouse gases, CO2 and H2. The CO2 cycle was described in the previous section. The only difference is that silicate weathering occurs at a range of different temperatures corresponding to different latitude bands. These individual rates are combined in an area-weighted manner to yield the global weathering rate. The atmospheric H2 concentration is determined by balancing volcanic outgassing with diffusion-limited escape to space. Escape slows down as the atmosphere becomes denser; thus, the concentrations of H2 and

CO2 are positively correlated. The outgassing rates of H2 and CO2 are treated as free parameters in the modeling exercise.

2.3.2 Basic model equations

Our EBM calculates the meridionally averaged temperature as a function of latitude and time according to

∂T 1 ∂ ∂T ! C = S¯(1 − α) − F + D cos θ (2.13) ∂t OLR cos θ ∂θ ∂θ

Here, θ is latitude and t is time. S¯ = S × q(θ) is the diurnally averaged solar flux, which accounts for seasonal changes in the solar flux (S) at each latitude band due to seasonal changes. C is the effective heat capacity of the surface, which includes the ocean. It is calculated by the procedure described in Williams and Kasting [1997], Fairén et al. [2012]. D, the diffusion coefficient, accounts for the energy transport across latitude bands. It is scaled so as to reproduce the correct equator-to-pole temperature gradient for a present-day Earth [Fairén et al., 2012]

27 and depends on changes in surface pressure, atmospheric mass and heat capacity, and rotation rate. The original radiative transfer parameterizations, from Williams and Kasting [1997], were replaced for this study with new parameterizations based on the 1-D model of Kopparapu et al. [2013]. Over 40,000 calculations with the 1-D model were used to investigate the dependence of radiative fluxes on different parameters. The outgoing long wave flux, FOLR, was calculated as a 4th-order polynomial in surface pressure, surface temperature, and volume mixing ratio of

H2. The top-of-atmosphere albedo, α, (which is related to the absorbed solar flux) was split into two 3rd-order polynomials. One is for surface temperatures less than 250 K and the other is for surface temperatures between 250 K and 350 K. Both fits are calculated as a function of zenith angle, surface pressure, surface temperature, H2 volume mixing ratio and surface albedo. Both the OLR and albedo parameterizations assume early Mars’ solar constant and Mars’ radius. They also assume an H2O-H2-CO2 atmosphere. All of the parameterizations are included in Appendix B. Surface albedo is calculated at each latitude band as a weighted sum of unfrozen land, unfrozen ocean, and fractional ice coverage. Unfrozen land is given a fixed albedo of 0.216, while the ocean albedo is allowed to vary, depending on solar zenith angle. H2O ice is given a fixed albedo of 0.45, consistent with slightly dirty ice.

The CO2 ice albedo is given a fixed value of 0.35, but is only used when CO2 is condensing onto the surface [Warren et al., 1990]. If the partial pressure of CO2 exceeds the saturation vapor pressure at the corresponding surface temperature, we assume it condenses on the surface as dry ice over the water ice. We also do not let the surface temperature fall below the saturation temperature of CO2. If it does fall below, we bring the temperature up to the saturation temperature. Similar behavior is observed during winter above the martian polar caps today.

2.3.3 Hydrogen escape

As mentioned previously, molecular hydrogen (H2) is required to bring the early martian surface temperature above freezing. We assume that escape of H2 is diffusion limited [Walker, 1977] and obeys the equation:

bi fH2 Φesc(H2) = (2.14) Ha 1 + fH2

28 Here, bi = 5×1011 cm−2s−1 for early Mars [de Pater and Lissauer, 2001]. For each Ha time step, the escape rate of H2 is calculated. We then increment the column density of H2 according to:

dn (H ) col 2 = φ (H ) − φ (H ) (2.15) dτ out 2 esc 2

Here, φout(H2) is the volcanic outgassing rate of H2 per unit area. The column density of CO2 is related to its time varying partial pressure via

ncol(CO2) = pCO2/(g × mCO2 ) (2.16)

Here, g is gravitational acceleration and mCO2 is the molecular mass of carbon dioxide. After each time step, the mixing ratio of hydrogen is recalculated from the column density of H2 and CO2:

fH2 = nH2 /(ncol(CO2) + nH2 ) (2.17)

Because nCO2 is proportional to pCO2, a decrease in the CO2 partial pressure will lead to an increase in the H2 mixing ratio, and hence to an increase in the H2 escape rate, following eq. 2.14.

29 Chapter 3 | Early Mars: An Application to Modeling the Planet System

Material in this chapter is published in:

Batalha, Natasha, et al. “Testing the early Mars H2-CO2 greenhouse hypothesis with a 1-D photochemical model.” Icarus 258 (2015): 337-349.

Batalha, Natasha E., et al. “Climate cycling on early Mars caused by the carbonate- silicate cycle.” Earth and Planetary Science Letters 455 (2016): 7-13.

3.1 Testing the 1D H2-CO2 Greenhouse Hypothesis

Observations of the Martian surface reveal complex valley networks that can only be explained by running water in the distant past [Irwin et al., 2008b, Grott et al., 2013]. Analyses of crater morphologies [Fassett and Head, 2008] suggest that this water was present circa 3.8 Ga. Further support for the warm early Mars hypothesis has been provided just recently by new data obtained by the Mars Curiosity Rover. Deposits at Gale Crater have been interpreted as being formed in a potentially habitable fluvio-lacustrine environment [Grotzinger et al., 2014], and the rover has observed stacked sediments at Mt. Sharp in Gale Crater which suggest the presence of a lake that lasted a million years or more. This implies prolonged warm conditions and a relatively Earth-like hydrologic cycle 1. New estimates for the global equivalent early martian water reservoir have recently been

1http://mars.jpl.nasa.gov/msl/news/whatsnew/index.cfm?FuseAction=ShowNews&NewsID=1761

30 calculated to be 137 m, and this may only be a lower limit (see Section 3.1.5.2) [Villanueva et al., 2015]. That said, exactly how Mars was able to maintain an environment suitable for liquid water remains an open question, as modelers have been mostly unsuccessful at recreating these types of warm and wet conditions in their simulations. Some authors have argued that sporadic impacts during the Late Heavy Bom- bardment may have generated steam atmospheres and that the ensuing rainfall (about 600 m total planet wide during that entire period) carved the valley net- works [Segura et al., 2002, 2008, 2012]. This hypothesis seems unlikely because the amount of water required to form the valley networks is higher than that by at least three orders of magnitude, according to estimates made using terrestrial hydrologic models [Hoke et al., 2011, Ramirez et al., 2014]. Extending the duration of these warm, impact-induced atmospheres is theoretically possible if cirrus clouds provide strong warming [Urata and Toon, 2013]; however, doing so requires high fractional cloud cover almost everywhere, and so it would be nice to see this prediction verified by independent calculations. Wordsworth et al. [2013] propose transient warming episodes caused by repeated volcanic or impact episodes, but they also find that achieving the necessary erosion rates remains challenging. Kite et al. [2013] invoke the idea that liquid water was the product of seasonal warming episodes, specifically at the equator. For seasonal melting to occur, though, there still must have been a source of precipitation and the energy to power it, so this mechanism does not resolve the issue of where the water originally came from. Most recently, Halevy and

Head [2014] argued that early Mars was transiently warmed by SO2 emitted during intense episodes of volcanic activity and that daytime surface temperatures at low latitudes (and low planetary obliquity) may have been high enough to result in rainfall. Their 1-D climate model may overestimate temperatures near the subsolar point, though, as it does not include horizontal heat transport. We discuss their hypothesis further in Section 6.1.2 below. The late Noachian-early Hesperian period (∼3.8-3.6 Ga) was also characterized by substantial weathering, as evidenced by the global distribution of phyllosilicates (e.g. clays). Although phyllosilicate formation requires long-term contact between igneous rocks and liquid water [Poulet et al., 2005, Carter et al., 2013], some investigators suggest that this process could occur in the subsurface [Ehlmann et al., 2009, Meunier et al., 2012]. Hydrothermal systems could accomplish this,

31 in principle; however, they require recharging with water, and it is unclear how this could happen if the surface was cold and dry. Other authors have argued that widespread surface clay formation is suggestive of a warmer and wetter past climate [Loizeau et al., 2010, Noe Dobrea et al., 2010, Gaudin et al., 2011, Le Deit et al., 2012, Carter et al., 2013], opposing the claim that valley network formation was the product of short climatic warming episodes [Poulet et al., 2005]. An alternative to the cold Mars hypotheses is the notion that early Mars ex- hibited a relatively long period of warmth characterized by a dense atmosphere dominated by greenhouse gases. Early work suggested that this could be accom- plished [Pollack et al., 1987] with only CO2 and H2O as greenhouse gases; however, these authors erred by neglecting condensation of CO2. Subsequent climate mod- elers [Kasting, 1991, Tian et al., 2010, Wordsworth et al., 2010, Forget et al.,

2013, Wordsworth et al., 2013] have been unable to warm early Mars when CO2 condensation is included in their simulations. However, Ramirez et al. [2014] were successful in creating above-freezing temperatures when CO2-H2 collision-induced absorption effects were included in their calculations. A 5% H2 atmosphere with a ∼

3-bar 95% CO2 component produced 273 K surface temperatures, and models with

10-20% H2 produced temperatures above 290 K. The dense, CO2-rich atmospheres required in this and other warm early Mars models have often been criticized on the grounds that they should have left extensive carbonate sediments on the surface, none of which has been observed. But the rain falling from a 3-bar CO2 atmosphere would have had a pH of 3.7 or less [Kasting, 2010], which would almost certainly have dissolved any such rocks, allowing the carbonate to be redeposited on the subsurface. Carbonates have occasionally been detected at the bottoms of fresh craters [Michalski and Niles, 2010] but most craters are likely filled with dust, and so it is not obvious that the carbonates should always show up in this type of observation. While the Ramirez et al. [2014] work found a combination of greenhouse gases that could explain a warm and wet early Mars, the feasibility of that combination has not yet been demonstrated. A 5% H2 atmosphere requires a total hydrogen 11 −2 −1 outgassing rate of 8×10 H2 molecules cm s , if hydrogen escapes at the diffusion- limited rate (see Section 2 below). Ramirez et al. [2014] made estimates of H2 outgassing rates on early Mars that came within a factor of 2 of this value. This factor of 2, they argued, could be recovered if hydrogen escaped from early Mars at

32 less than the diffusion-limited rate. However, the knowledge of the escape rate of H from the martian atmosphere is poorly constrained. Part of the problem is that we do not know how water-rich early Mars might have been. Data concerning the volatile content of the martian crust have been obtained from meteorite [Kurokawa et al., 2014] and in situ [Mahaffy et al., 2015] analyses, but they still leave an order of magnitude uncertainty in the global near-surface water inventory prior to 4 Ga.

While a higher escape rate could be offset by a higher volcanic H2 outgassing rate or by supplementing volcanic H2 with other H2 sources, this idea has not been previously explored.

In this paper, we test the plausibility of the high-H2 hypothesis of Ramirez et al. [2014] by using a photochemical code to study whether such an atmosphere would be sustainable over geological timescales. We do this by carefully maintaining the redox balance of each simulation, looking for self-consistent atmospheres that could maintain liquid water at the planet’s surface. These simulations allow us to infer the volcanic fluxes required to maintain the high H2 levels needed to keep early Mars warm. We also consider the potential climatic effects of species other than CO2,H2O, and H2- specifically CO, CH4, SO2, and H2S. Finally, we consider whether the H2 greenhouse hypothesis might be tested using Mars rover, orbiter, and meteorite data.

3.1.1 Possible Sources of Hydrogen on Early Mars

3.1.1.1 Volcanic Outgassing

The term ’outgassing’ refers to release of gases from magma. Volcanic outgassing rates on early Mars have frequently been estimated by looking at surface igneous rocks, evaluating their ages, and making assumptions about the volatile content of the lava from which they formed [e.g. Greeley and Schneid, 1991, Grott et al., 2011, Craddock and Greeley, 2009]. Grott et al. [2011] estimated that 0.25 bars of CO2 and 5-15 m of H2O were outgassed on Mars during the interval 3.7-4.1

Ga. The corresponding implied outgassing rates are 0.06 Tmol/yr for CO2 and 0.3

Tmol/yr for H2O. By comparison, the estimated outgassing rates for CO2 and H2O on modern Earth are 7.5 Tmol/yr and 102 Tmol/yr, respectively [Jarrard, 2003]. Even taking into account the 4 times larger surface area of Earth, the implied per unit area martian outgassing rates are 25-100 times smaller. Such outgassing rates

33 are almost certainly too small to maintain a warm, dense atmosphere, leading some to conclude that the martian atmosphere has always been thin and cold [Forget et al., 2013, Wordsworth et al., 2013, Grott et al., 2013], except, perhaps in the aftermath of repeated explosive eruptions [Wordsworth et al., 2013] or giant impacts [Segura et al., 2002]. However, these outgassing estimates for early Mars are potentially underesti- mated, because they ignore the effects of volatile recycling. For example, Earth’s relatively high outgassing rates result from volatile recycling between the crust and the mantle, not from juvenile degassing. Much higher outgassing rates could be expected on early Mars if the planet experienced plate tectonics and associated element recycling. Heat flow on early Mars is thought to have been comparable to that on modern Earth [Montési and Zuber, 2003], so some authors have postulated that outgassing rates of major volatiles may also have been similar [Ramirez et al., 2014, Halevy and Head, 2014]. Evidence for past tectonic activity incudes Mars Global Surveyor data of an alternating polarity in the remanent magnetic field, inferred to be evidence for sea-floor spreading [Connerney et al., 1999], and major faults associated with these crustal variations. Magnetic polarity patterns deduced by Connerney et al. [1999] are Noachian in age, but Sleep [1994] suggests that plate tectonics extended at least through the early Hesperian. Along these same lines, Anguita et al. [2001] discuss how plate tectonics better explains the observed tectonic regime in the early Hesperian than do other hypotheses. No consensus has been reached on this topic, however; for example, Grott et al. [2013] have argued that crust-mantle recycling never occurred on Mars because plate tectonics never got started. Although the notion that plate tectonics may have operated on early

Mars remains controversial, it is required to support the thick, H2-rich atmospheres proposed by Ramirez et al. [2014]. Therefore, we assume here that Mars did recycle volatiles and that the overall efficiency of recycling was comparable to that on modern Earth. Future exploration of Mars will reveal whether this assumption is correct. We also consider other sources of hydrogen from oxidation of crustal ferrous iron and from photochemical oxidation of other reduced gases.

H2 : Differences in the composition of volatiles outgassed on Mars compared to Earth should result from the different oxidation states of their respective mantles. Earth’s upper mantle is thought to have an average oxygen fugacity, fO2 , near that of the

34 QFM (quartz-fayalite-magnetite) synthetic buffer. At typical surface outgassing ∼ −8.5 conditions (1,450 K, 5 bar pressure), this yields fO2 = 10 [Frost et al., 1991,

Ramirez et al., 2014]. Given this value for fO2 , the H2:H2O ratio, R, in the gas that is released can be calculated from the expression:

P K !0.5 H2 ≡ R = 1 (3.1) PH2O fO2

−12 Here, PH2 and PH2O are the partial pressures of the two gases, and K1 (=1.80×10 atm) is the equilibrium constant for the reaction: 2H2O→2H2+O2 [Ramirez et al.,

2014]. Plugging K1 and the terrestrial mantle into Eqn. 3.1 gives an H2:H2O ratio of 0.024. This yields a terrestrial H2 outgassing flux of ∼2.4 Tmol/yr, when multiplied by the terrestrial H2O subaerial outgassing rate of 100 Tmol/yr, or ∼3.7×1011 cm−2s−1 [Jarrard, 2003]. (On Earth, the conversion from geochemical to atmospheric science units is 1 Tmol/yr = 3.74×109 cm−2s−1.) The terrestrial 10 −2 −1 H2 outgassing rate is therefore of the order of 1×10 cm s , with a factor of 2 or more uncertainty in either direction [Holland, 2009]. Mars’ oxygen fugacity is thought to be at least 3 log units lower than Earth’s, near ∼ IW+1 [Grott et al., 2011]. IW is the iron-wüstite buffer, which has an fO2 about 4 log units below QFM. Based on this observation, Ramirez et al.

[2014] calculated that Mars could have outgassed H2 at up to 40 times the rate of Earth: 40×1010 cm−2s−1 = 4×1011 cm−2s−1. This estimate included a 50 percent contribution from H2S, which was assumed to be oxidized to SO2 by atmospheric photochemistry, according to

H2S + 2H2O → SO2 + 3H2 (3.2)

We demonstrate in the next section that this assumption may be unfounded, and so outgassing of H2S may not have added much H2to Mars’ atmosphere. That said, terrestrial H2 outgassing estimates are uncertain by about a factor of 2 or more, and the early Martian mantle could have had an oxygen fugacity near IW-1 [Warren and Kallemeyn, 1996]. The latter factor alone could have approximately doubled the estimated H2 outgassing rate [Ramirez et al., 2014]. Thus, an H2 outgassing rate of 8×1011 cm−2s−1 is not implausible; it just requires slightly more optimistic assumptions than have hitherto been adopted. Specifically, this higher outgassing

35 rate is highly dependent on the estimate of the redox state of the ancient Martian mantle, and is the single largest source of uncertainty in our estimates of Martian

H2outgassing rates. This highlights the importance of future measurements that might reduce the uncertainties in that quantity. Sulfur: Several hundred millibar to as much as 1 bar of sulfur may have been outgassed via juvenile degassing throughout Martian history [Craddock and Greeley, 2009]. This leads to a sulfur outgassing rate of at most 6×106 cm−2s−1, if we assume it was outgassed over a period of ∼1 billion years. As with other estimates of juvenile degassing, this small outgassing rate is not enough to maintain a warm, dense atmosphere on early Mars. On Earth, volcanic sulfur comes from three main sources: arc volcanism, hotspot volcanism, and submarine volcanism.

Direct satellite measurements of arc volcanism yield SO2 outgassing rates of 0.2-0.3 Tmol/yr (equivalent to ∼(0.7-1.1)×109 cm−2s−1 via the conversion above)

[Halmer et al., 2002]. These numbers probably underestimate the total SO2 out- gassing rate, as they only measure the SO2 outgassed through explosive volcanism.

Instead, if we combine the ratio of total sulfur to H2O in arc volcanism (∼0.01 in Fig 6, Holland [2002]) and the ratio of H2O to CO2 (∼30 in Fig 6, Holland

[2002]), then the rate of SO2 outgassing on modern Earth should be ∼0.8 Tmol/yr, assuming a CO2 outgassing rate from arc volcanism of ∼2.5 Tmol/yr [Jarrard, 2003]. Hotspot volcanism, such as that which occurs in Hawaii, also contributes to sulfur outgassing. Although hotspot outgassing rates are difficult to accurately determine, the observed ratio of SO2/CO2 is ∼0.5 [Walker, 1977, Table 5.5]. Therefore, if the release rate of carbon from hotspot volcanism on Earth is 2 Tmol/yr [Jarrard,

2003], the corresponding release rate of SO2 should be ∼1 Tmol/yr. This leads to 9 −2 −1 a total subaerial SO2 outgassing rate of 1.8 Tmol/yr or ∼6.7×10 cm s .

Sulfur is also outgassed as H2S during submarine volcanism. Holland [2002] averaged measurements of H2S concentrations in hot, axial vent fluids, 3-80 mmol/kg

[Von Damm, 1995, 2000], to estimate dissolved H2S concentrations of 7 mmol/kg. By combining this value with estimates for the total emergent water flux, ∼5×1013 kg/yr, we can convert the H2S concentration to an H2S outgassing rate of 0.35 Tmol/yr, or ∼1.3×109 cm−2s−1.

Gaillard and Scaillet [2009] show that on Mars, H2S and SO2 should be outgassed

36 at approximately the same rate for a mantle redox state near IW. Therefore, we 9 2 −1 use an outgassing rate of 5×10 cm s for both SO2 and H2S, which is roughly in agreement with the values above. We note parenthetically that Halevy and Head

[2014] assumed that all sulfur outgassed on early Mars was in the form of SO2. Carbon: On modern Earth carbon is outgassed as CO2 at a rate of ∼7.5 Tmol/yr (2.8×1010 cm2s−1) [Jarrard, 2003]. We expect that carbon outgassing should have also been a major contributor to the early martian atmosphere. A recent study by Wetzel et al. [2013] showed that carbon should be stored in different forms in planetary mantles, depending on the oxygen fugacity, fO2 . At fO2 values above IW-0.55, carbon is stored as carbonate in the melt and would be outgassed as CO2. At fO2 values below IW-0.55, carbon is stored as iron carbonyl, Fe(CO)5, and as CH4, and would be outgassed as CO and CH4. Wetzel et al. [2013] calculated that initial solidification of a 50 km-thick crust should lead to outgassing of 1.3 bar CH4 and

1 bar CO at low fO2 or to 11.7 bar of CO2 at higher fO2 . The higher pressure of the outgassed CO2 atmosphere is caused by a factor of two increase in carbon solubility in melts at fO2 > IW-0.55, along with the higher molecular weight of

CO2 compared to CO and CH4. Assuming this gets released over ∼1 billion years, 6 2 −1 we derive a lower bound estimate for carbon outgassing of 6×10 cm s at low fO2 or about twice that value at higher fO2 . As pointed out earlier, juvenile outgassing rates are always relatively small.

A low rate of carbon outgassing may not be an issue for the CO2 content of the early martian atmosphere because the CO2 removal rate from silicate weathering depends on temperature. At low surface temperatures, liquid water would not be present and so CO2 would not be lost by this process. 11.7 bar of CO2, or even half that amount, is more than adequate for the greenhouse atmospheres postulated here. CO2 could also have been lost by solar wind interactions, as happens today, but such loss might have been precluded if Mars had a magnetic field at this time. We assume that the early martian atmosphere was not being rapidly stripped away in this manner. Here, we are interested in whether outgassing of carbon in reduced form could have provided an additional source of H2. Outgassing rates do matter in this case because hydrogen is always being lost to space, regardless of the presence or absence of a magnetic field. At low mantle fO2 values, outgassing of the reduced gases CO

37 and CH4 could have contributed to the atmospheric H2 budget. The outgassing rate computed from initial crustal solidification would not have been high enough

to supply an appreciable amount of additional H2. To obtain a higher estimate,

consistent with our estimate for direct H2 outgassing above, we used modern Earth

carbon outgassing estimates (Jarrard 2003) and assumed that mantle fO2 was <

IW-0.55 and that CO and CH4 were released in the 1:1.3 ratio calculated by Wetzel et al. [2013] This yields outgassing rates of 2×1010 cm−2s−1 and 8×109 cm−2s−1

for CH4 and CO, respectively. If all of the CH4 was oxidized to CO2 following the stoichiometry

CH4 + 2H2O → CO2 + 4H2 (3.3)

the equivalent H2 production rate should have been 4 times the CH4 outgassing 10 −2 −1 rate, or 8×10 cm s . This is about 1/10th the H2 flux needed to sustain a warm

H2-CO2 greenhouse atmosphere. CO outgassing is less important as a source of H2,

as its outgassing rate is lower and its stoichiometric coefficient for H2 production,

assuming oxidation to CO2, is only unity

CO + H2O → CO2 + H2. (3.4)

3.1.1.2 Serpentinization

A second possible source of hydrogen to Mars’ early atmosphere is serpentinization. This process differs from volcanic outgassing in that it occurs at relatively low temperatures, 500-600 K, whereas outgassing from magmas occurs at the melt temperature of ∼1450 K. Serpentinization occurs when warm water interacts with ultramafic (Mg- and Fe-rich) basalts. Ferrous iron contained in the basalts is excluded from the serpentine alteration products, and so it forms magnetite,

releasing H2 in the process

3F eO + H2O → F e3O4 + H2. (3.5)

Evidence for serpentinization on Mars exists in the form of ultramafic rocks discov- ered on the Martian surface. Olivine concentrations of 10-20% have been detected both by the Thermal Emission Spectrometer [Koeppen and Hamilton, 2008] and in SNCs [e.g. McSween et al., 2006]. Moreover, the Mars Reconnaissance Orbiter (MRO) has detected serpentine itself from orbit [Ehlmann et al., 2009].

38 Serpentinization is a minor source of hydrogen to Earth’s current atmosphere, 9 −2 −1 accounting for ∼0.4 Tmol H2/yr, or 1.5×10 cm s [Sleep, 2005, Kasting, 2013].

For this process to have made an important contribution to the early martian H2 budget, it would have needed to occur 10-100 times faster than it does on Earth today. That sounds daunting, but it may be possible. Most oceanic basalts today are not prone to serpentinization because the terrestrial seafloor is predominantly mafic, not ultramafic. Ultramafic rocks, e.g., peridotites, are found deep within the seafloor and are exposed to hydrothermal circulation within slow-spreading ridges such as the Mid-Atlantic Ridge. Earth’s upper mantle should have been hotter in the past; hence, the degree of partial melting during seafloor creation should have been higher, and the seafloor itself should have been more mafic, or even ultramafic. Similarly, if Mars’ upper mantle was originally hot, and if seafloor was being generated there as it is here on Earth, interaction of ultramafic rocks with water may have been commonplace, as well.

One can make a crude estimate of the H2 flux that might have been generated by this process by drawing an analogy to seafloor oxidation on Earth today. The rate at which ferric iron is generated and carried away by seafloor spreading today is about 21×103 kg/s, or 1.2×1013 mol/yr [Lécuyer and Ricard, 1999]. Most of this ferric iron is produced by sulfate reduction, not by serpentinization. But if the oceanic crust were more ultramafic, and if this same amount of ferric iron were generated by serpentinization, then according to reaction 3.5 it would produce 1 mole of H2 for every 2 moles of ferric iron (because Fe3O4 contains two atoms of ferric iron), 10 −2 −1 and so the corresponding H2flux would be 6 Tmol/yr, or 2.2×10 cm s . That is roughly 10% of the volcanic H2 outgassing rate estimated by Ramirez et al. [2014] for early Mars with a mantle fO2 near IW+1. So, unless martian seafloor was serpentinizing much faster than terrestrial seafloor gets oxidized today, this process would have been a relatively minor term in the martian H2budget. When we do the estimate this way, serpentinization appears to be a relatively minor source of H2.

Other authors however, have made more generous estimates of H2 production from this process, as high as 35 Tmol/yr (on Mars), or 4×1011 cm−2s−1 [Chassefière et al., 2014], about half the flux needed to sustain a 5% H2 mixing ratio. So we should not rule out serpentinization as an important source of hydrogen on early Mars.

39 3.1.1.3 Photochemical Fe Oxidation

On Earth, Fe oxidation by way of UV irradiation of surface waters could have also been a source of H2and could have contributed to the deposition of banded iron-formations (BIFs) [Braterman et al., 1983]. Additionally, Hurowitz et al. [2010] showed that the sedimentary rocks found at Meridiani Planum on Mars were formed in the presence of acidic surface waters and that Fe oxidation may have played a role in maintaining that high acidity. This mechanism could potentially have produced large amounts of gaseous H2. Still, it is uncertain how much of the martian surface 5 was producing H2 in this manner, as Meridiani Planum has an area of ∼2×10 km2, only ∼0.1% the total surface area of Mars [Hurowitz et al., 2010]. To get around this problem, we once again make an analogy to early Earth.

Kasting [2013] estimated H2 production rates from deposition of BIFs on the 10 Archean Earth. His estimates ranged from (0.2-25) Tmol(H2)/yr, or (0.7-9)×10 cm−2s−1. But the higher end of this range is an extremely generous upper bound which would require dissolved Fe+2 concentrations in vent fluids that were hundreds of times higher than those in modern terrestrial hydrothermal systems. Even with those assumptions, this mechanism would likely have been only a minor source of

H2on early Mars. Despite its apparent lack of importance, we parametrize these potential effects below, because of their possible relationship to sedimentary layers on Mars, including the hematite beds on Mount Sharp in Gale Crater.

3.1.2 Early Mars Model Setup

To investigate how fast volcanic gases such as H2S and CH4 would be converted into

H2, we used the 1-D (in altitude), horizontally averaged photochemical model that solves the coupled continuity and flux equations for multiple atmospheric species using an implicit, reverse Euler integration technique. This model is described in detail in Chapter 2.1. We begin by assuming that Mars was wet and warm with a surface temperature of 273 K. These parameters were chosen to be consistent with a temperature- pressure profile derived by Ramirez et al. [2014] for a 3-bar, 5% H2, 95% CO2 atmosphere. This assumed composition ignores the possible presence of higher amounts of N2 in the early martian atmosphere, which can be inferred from the high 15 14 measured N/ N ratio today [Fox, 1993]. Higher N2 should not greatly affect the

40 climate; indeed, N2 can substitute for CO2 to create pressure-induced absorption by H2 [Ramirez et al., 2014, Fig. 2]. Whether our assumed composition is an accurate representation of the early martian atmosphere depends, of course, on the validity of the Ramirez et al. [2014] hypothesis. However, the point of this study is to see if such an atmosphere is sustainable, so the use of it here is consistent with that goal. This means atmospheres that do not reproduce the Ramirez et al.

[2014] H2 concentrations have an inconsistent temperature profile; however any simulations that could maintain such an atmosphere would be self-consistent. The temperature is assumed to decrease from 273 K at the surface to 147 K at an altitude of 67 km, following a moist H2O adiabat in the lower troposphere (0-20 km) and a moist CO2 adiabat above that (20-120 km). Above 67 km, the atmosphere is assumed to be isothermal up to 200 km altitude, consistent with the assumed lack of oxygen and ozone. Several reaction rates are positively correlated with temperature (i.e. an increase in temperature causes an increase in the rate of a reaction). In the case of water vapor, a 10 K increase in temperature doubles the water vapor volume-mixing ratio. H2, however, is less affected (1% increase) by this same change in temperature. Figure 3.1 shows this temperature profile along with the eddy diffusion profile. At the top of the atmosphere, CH4, H and H2 are

−10 10 200

150

100 Altitude (km)

Pressure (bars) 50

0 10

4 5 150 200 250 10 10 Mean temperature (K) Eddy Diffusion (cm2s−1)

Figure 3.1. Temperature-pressure profile (top) and eddy diffusion profile (bottom) assumed for the photochemical calculations. The temperature decreases from 273K to 147K at an altitude of 67 km and then is isothermal to the top (200 km altitude). This is consistent with the 5% H2, 95% CO2 3-bar atmosphere from Ramirez et al. [2014]. assumed to diffuse upward at the diffusion-limited velocity Walker [1977], while CO

41 and O are given constant downward fluxes that balance photolysis of CO2 above the top layer of our model. All other species are assigned a flux of zero at the top of the atmosphere, implying that nothing else is escaping besides hydrogen. This assumption is consistent with the presence of a magnetic field to prevent solar wind stripping and with hydrodynamic escape rates for heavy species that were slower than those calculated by [Tian et al., 2009](whose escape model did not include

appreciable concentrations of H2).

At the lower boundary, every species except for H2 was given a constant

deposition velocity. (As stated in Chapter 2.1, H2 was assigned a constant upward flux at the lower boundary to ensure redox balance.) This accounts for their reaction with surface rocks and any ocean that might have been present. Table 3.1 lists the assumed deposition velocities for each species. Our results are insensitive to most of these deposition velocities, with the notable exception of CO. In most of our simulations, the CO deposition velocity is fixed at 10−8 cm s−1, the value derived for an abiotic early Earth [Kharecha et al., 2005]. The assumption here is that dissolved CO equilibrates with formate, but that a small percentage of that formate is photochemically converted to acetate and is lost from the atmosphere-ocean system. This implies that there is a small, but finite, burial flux of organic carbon (as acetate). Sensitivity tests, described below, were performed to determine the effect of varying the CO deposition velocity.

Six different gases, H2, CO, CH4, NH3, SO2, and H2S, were assumed to have

sources from volcanic outgassing. CO2 has a volcanic source, as well, but the CO2 mixing ratio is fixed in our model at 0.95. The other 5% of the atmosphere is

assumed to consist of N2. When H2 builds up to appreciable concentrations in

the model, it displaces CO2. Volcanic fluxes for the base case and final model are listed in Table 3.2. These fluxes were distributed over the lowest 20 km of the troposphere, leaving the bottom boundary of the model free to simulate atmosphere-ocean exchange.

3.1.3 Photochemical Results

The photochemical profiles of major constituents, sulfur species, nitrogen species and hydrocarbon species in the base case model are shown in Figure 3.2. The base case was modeled with the outgassing rates shown in Table 2. With these relatively

42 Table 3.1. Assumed Deposition Velocities at Lower Boundary for Early Mars Species Deposition Velocity (cm/s) O 1 O2 0 H2O 0 H 1 OH 1 HO2 1 H2O2 0.2 CO 1× 10−8 HCO 1 H2CO 0.1 CH4 0 CH3 1 −5 C2H6 1×10 NO 3×10−4 −3 NO2 3×10 HNO 1 H2S 0.015 HS 3×10−3 S 1 HSO 1 SO 3×10−4 SO2 1 NH3 0 NH2 0 N 0 N2H4 0 N2H3 0 H2SO4 0.2

low rates the base case was dominated by CO2 (95%) and N2 (5%). H2and CO were both in the 0.1% range, while CH4 and H2S were trace gases at 0.3 ppmv and 0.1 ppbv, respectively. Next, we increased H2, sulfur (SO2/H2S), and carbon (CO/CH4) outgassing to test whether or not the reducing species would effectively convert to

H2. Figure 3.3 shows the effect of increasing H2 outgassing on the H2 mixing ratio. As one would expect based on Eqs. [2] and [4], this produced a linear relationship.

But Figure 3.3 also shows the possible increase in atmospheric H2 from the H2

43 Table 3.2. Assumed Total Outgassing Values for Early Mars

Outgassing Base Case 5% H2 Case Molecule (cm2s−1) (cm2s−1) 10 11 H2 1×10 8×10 9 9 SO2 5.4×10 5.4×10 9 9 H2S 5.4×10 5.4×10 6 10 CH4 5×10 1.9×10 CO 0.0 8×109 5 5 NH3 1.7×10 1.7×10

sources discussed in Section 3, namely, ferrous iron oxidation and serpentinization.

In order to get up to 5% H2 by this mechanism, the net H2 sources would need to be ∼80 times larger than the modern terrestrial H2 outgassing rate. We can get about half of this hydrogen from direct volcanic outgassing of H2 if the mantle fO2 was near IW-1. Serpentinization is also a significant H2 source (see Table 3.3).

BIF deposition could contribute smaller amounts of H2. If serpentinization was not as efficient as assumed here, then either volcanic outgassing rates must have been higher than we have assumed, or hydrogen escape must have been slower in order to reach the required 5% atmospheric H2. We then returned to a negligible

H2 outgassing rate and varied only the sulfur outgassing, keeping SO2 and H2S outgassing rate in a 1:1 ratio. If the H2S is directly converted to H2 we would also expect a linear relationship between the outgassing rate and f(H2). Instead, we found that this relationship depended on what chemistry was assumed to be occurring in the ocean. If H2S was converted to H2 and SO2 in solution, then the stoichiometry is given by Eq. [7], and our models produce the linear relationship shown by the blue solid curve in Figure 5. By analogy with early Earth, however, it seems more likely that H2S would have reacted with dissolved ferrous iron to form pyrite, FeS2. The redox reaction in this case can be written as

2H2S + F eO → F eS2 + H2O + H2. (3.6)

Based on this stoichiometry, 0.5 mole of H2 should be generated for each mole of H2S outgassed. This yields the blue dashed curve in Figure 3.4, which has a more gradual rise in the H2 mixing ratio, as compared to the solid curve (∼1/6th the solid line). We conclude that H2S outgassing was at best a minor source of

44 120 120 ! 120 100 100100 O 80 H HSO 8080 2 CO H S 2 CH O 2 2 CO 4 2 60 N SO2 6060 CH N 2 2 4 2 CO SO 40 CO H 40 Altitude (km) 40 2 20 H O 20 20 2H O 2 HS −5 0 −15 −10 −4 10 −3 10 10−2 −1 10 0 120 10 10 10 10 10 120 Mixing Ratio (v/v) 100 120 100 NO NO O2 2 100 H 8080 C2H 2 6 CO 80 N H CO 2 60 CH 2 2 60 4 HCO CO HNO 60

Altitude (km) 4040 CH 40 3 20 H O 20 2 NH 20 3 −4 −15 −3 −10 −2 −1 0 −15 −10 10 10 10 10 10 10 10 10 10 Mixing Ratio (v/v) Mixing Ratio (v/v) Mixing Ratio (v/v)

Figure 3.2. Mixing ratios of different species in the base case martian atmosphere assuming the (minimal) outgassing rates from Table 3.2. Major constituents are shown in the top left, sulfur species in the top right, nitrogen species in the bottom left, and less abundant hydrocarbons in the lower right.

atmospheric H2. 9 −2 −1 Additionally, we find that at terrestrial SO2 outgassing rates (5.4×10 cm s ),

H2S becomes the dominant sulfur species: its concentration was ∼0.1 ppbv (solid curve in figure 3.4), while SO2 was a factor of 2-3 lower. Halevy and Head (2014) argue that Mars could have rapidly outgassed SO2 over brief intervals at rates that were a few thousand times higher than modern Earth (∼1012 cm−2s−1), leading to

10 ppmv SO2. If SO2 outgassing rates were at those levels, then so were the rates of

H2S, and the early martian atmosphere would have been even more highly reducing. We repeated this process for carbon outgassing, with the results shown in figure

3.5. On early Mars, carbon would have been outgassed as a combination of CH4 and CO, in the ratios discussed in Chapter 3.1.2. As with sulfur, it is theoretically possible that some of this outgassed carbon could have been deposited in reduced

45 5

4 Lower bound Upper bound serpentinization serpentinization 3 or aditional outgassing Fe oxidation

Mixing Ratio (v/v) Volcanic outgassing

2 2

1 Percent H

0 0 1 2 3 4 5 6 7 8 H Outgassing Rate (x1011) (cm−2s−1) 2

Figure 3.3. Calculation showing the effect of H2 outgassing rate on H2 mixing ratio, along with the different sources of H2 thought to contribute to the overall outgassing rate. The escape rate is assumed to be diffusion-limited, as discussed in the text.

Table 3.3. H2 Sources and Respective Yields for Early Mars

H2 Source H2 yield lower limit H2 yield upper limit Value in 5% H2 model [×1010 cm−2s−1][×1010 cm−2s−1][×1010 cm−2s−1] H2 20 40 40 S (SO2 + H2S) 0.25 3.0 0.25 CH4 0.0012 8 8 Serpentinization 0.15 40 20 Fe-oxide burial 0.7 9 9 Total 21 100 77

form in sediments. (This is represented by the term Φburial(CH2O) in eq. [3].) But formation of organic carbon on Earth is almost entirely biological; thus, for an abiotic early Mars, this term would probably have been small. It seems more likely that both CH4 and CO were converted to CO2 and H2, following the stoichiometry of eqs. [8] and [9]. Therefore, carbon outgassing could have made a significant contribution to the H2 concentration in the early Martian atmosphere, raising it to as high as 0.4%. But it would not have pushed the H2 mixing ratio above 5% unless total carbon outgassing rates on early Mars were substantially higher than those on modern Earth. When the carbon outgassing rate was high, the CO volume mixing ratio reached

46 −2 10

−4 10 H (no pyrite formation) 2

H (with pyrite 2 formation) Surficial −6 6 modern Mixing Ratio (v/v) 10 SO (x 10 ) Submarine 2 Earth modern SO Earth 2 H S outgassing 2 rate H S (x 106) outgassing 2 rate −8 10 7 8 9 10 11 10 10 10 10 10 Outgassing rate (cm−2 s−1)

Figure 3.4. Calculation showing the effect of sulfur (SO2/H2S) outgassing rate on the atmospheric H2mixing ratio. The blue dashed curve is the H2 mixing ratio under the assumption that H2S reacts to form pyrite, as seems likely. The blue solid curve shows what happens if all of the H2S dissolved in the ocean returns back to the atmosphere as a flux of H2 (less likely).

9%, and the model atmosphere entered a regime referred to as "CO runaway" [Zahnle, 1986, Kasting et al., 1983]. The primary sink for CO in this situation is the flux of CO into the ocean. Because little is understood about the rate at which CO will decompose in solution, it is difficult to accurately constrain the CO deposition velocity. As a result, different authors employ different values. Kharecha et al. [2005] derived an abiotic CO deposition velocity of 10−9-10−8 cm s−1, based the assumption that dissolved CO equilibrates with formate, but that a small percentage of the formate is photochemically converted to acetate and is lost from the atmosphere-ocean system. If CO-consuming bacteria were present in the ocean, holding the dissolved CO concentration near zero, the CO deposition velocity would have been much higher, ∼1.2×10−4 cm s−1. Tian et al. [2014] simply logarithmically averaged these biotic and abiotic deposition velocities. There is no obvious physical justification for this assumption. Figure 3.6 shows a linear correlation between CO deposition velocity and CO volume mixing ratio. The loose constraint on this lower boundary condition makes it difficult to rule out the possibility of a CO-dominated

47 −2 10

−4 10 H (no organic matter deposition) 2 H (with organic matter deposition) 2 modern −6 CO Earth 10 carbon Mixing Ratio (v/v) outgassing CH 4 −8 10

6 7 8 9 10 11 10 10 10 10 10 10 Carbon Outgassing (cm−2 s−1)

Figure 3.5. Calculation showing the effect of carbon outgassing rate on the atmospheric 10 −2 −1 H2 mixing ratio. At total carbon outgassing rates > 3×10 cm s , the atmosphere goes into CO runaway (see discussion in text). atmosphere. In the limiting case where the deposition into the surface is not a sink for CO (CO deposition velocity = 0), the model atmosphere contains ∼50% CO by volume. More work on the behavior of CO in solution is needed to constrain these possibilities. Finally, figure 3.7 shows profiles of major atmospheric species after adding volcanic outgassing in the amounts shown in the Table 3.2. Table 3.3 shows a breakdown of the outgassing sources contributing to 5% H2compared to their upper and lower limits. In order to determine what would be required to maintain the H2 greenhouse proposed by Ramirez et al. (2014), we simply assumed that the various outgassed fluxes add up to the required value. For this atmosphere, CO constituted ∼9% (by volume) of this atmosphere, and the CH4 mixing ratio was just under 2000 ppmv. Surprisingly, this large amount of CH4 has little effect on the climate (see discussion below). Based on the discussion above, all but a small fraction of the H2 in this atmosphere must have come from direct H2 sources, such as H2 outgassing, ferrous iron oxidation, and serpentinization.

48 0 10

−1 10

−2 10

−3 10 CO Mixing Ratio (v/v)

−4 10 −10 −9 −8 −7 −6 10 10 10 10 10 CO Deposition Velocity (cm s−1)

Figure 3.6. CO volume mixing ratio as a function of assumed deposition velocity. The atmospheric profile in Figure 3.7 was used for all calculations. The loose constraint on deposition velocity prevents us from determining precise values for CO volume mixing ratio.

3.1.4 Potential Warming from Other Atmospheric Constituents

3.1.4.1 CO & CH4

A 3-bar, CO2-dominated atmosphere with 5% H2 could have warmed the early Martian surface. But our high-outgassing atmosphere also contained almost 2000 ppmv of CH4, which is considered to be a strong greenhouse gas, along with ∼10% CO. CO has an absorption band in the 5µm region, far into the Wien tail of a blackbody with an effective temperature 235 K. Therefore, despite its high concentration, the effect of CO on climate is limited to pressure-broadening of gaseous absorption by other species and Rayleigh scattering of incident solar radiation. (We tested this just to make sure by deriving k-coefficients for CO and including it in our climate model. The effect was negligible.)

Methane’s effect on climate in a dense, CO2-dominated martian paleoatmosphere has previously been explored [Ramirez et al., 2014, Byrne and Goldblatt, 2014]. Both groups find little to no warming from CH4. Methane has a strong absorption band at 7.7 µm that is important in warming Earth’s climate. However, near-infrared absorption of incoming solar radiation by CH4 in the upper atmosphere produces stratospheric inversions that counteract this greenhouse warming. This stratospheric warming is particularly pronounced when new CH4 absorption coefficients derived

49 120

100 O H 80 2 2 CO N 2 60 CH 2 4 CO

Altitude (km) 40

20 H O 2

−4 −3 −2 −1 0 10 10 10 10 10 Mixing Ratio (v/v)

Figure 3.7. 1-D photochemical model results showing volume mixing ratio as a function of altitude. This is the base case early Martian atmosphere (Figure 3.1) after adding volcanic outgassing and balancing the redox budget for the combined ocean-atmosphere system. Here we are optimistic, and add in enough H2 outgassing to attain a 5% H2 atmosphere. from the HITRAN2012 database are used [Byrne and Goldblatt, 2014]. Collision- induced absorption (CIA) from N2-CH4 interactions is significant in the 200-400 cm−1 region. However, because the strong water vapor pure rotation band also absorbs in that same region (200-400 cm−1), the warm atmosphere would be opaque at those wavelengths and CIA does little to help sustain this [Buser et al., 2004,

Ramirez et al., 2014]. As a result, the additional warming produced by CH4 in this atmospheres modeled here should be negligible. An important caveat is our explicit assumption that CO2 broadening of CH4 is no more efficient than broadening by N2.

During the time of this writing, experimental data for CO2-CH4 CIA interactions were unavailable. Recently, Wordsworth et al. [2017] derived these coefficients and showed that this is a powerful source of warming. Therefore, we are currently working on redoing these calculations.

3.1.4.2SO 2

As mentioned earlier, Halevy and Head [2014] suggested that warm periods lasting

10-100 years could have been produced by short, episodic bursts of SO2. Specifically, 10 they assumed long-term globally averaged SO2 outgassing rates on the order of 10

50 cm−2s−1, with outgassing events on the order of 1012 cm−2s−1 every 1,000-10,000

years. This leads to SO2 concentrations ranging from 0.5-2 ppmv in their model. By

comparison, our assumed SO2 outgassing rate for both the base-case and high-H2 models is 5.4×109 cm−2s−1 (Table 3.2), or just over half that of Halevy and Head

(2014), but our calculated SO2 concentrations are ∼3 orders of magnitude smaller. The difference is caused by our assumption that early Mars was wet and warm and that an ocean-or at least several large seas-was present at its surface. Both rainout and surface deposition are therefore important loss processes in our model,

whereas the (much longer) lifetime of SO2 in the Halevy and Head model is set by

its rate of photochemical oxidation to H2SO4. Their model would predict smaller,

shorter-lived temperature increases if rainout and surface deposition of SO2 were included.

We note that sporadic, high-volume input of SO2, as suggested by Halevy and

Head, should have been accompanied by high-volume input of H2. This should not

have had a great impact on the atmospheric H2 concentration, however, because

the lifetime of H2 in one of our high-H2 atmospheres is close to half a million years.

(This can be readily calculated by dividing the column mixing ratio of H2 by the diffusion-limited escape rate given by eq. [2].) In the Halevy and Head model, slow outgassing during the long periods of relative quiescence dominates the total

volatile input, and the same should be true of H2. 100 years of H2 outgassing at

100 times the normal rate would have increased atmospheric H2 concentrations by only a few percent. So, a spiky volcanic outgassing history for early Mars would not alter our hypothesis to any great extent.

3.1.5 Synergies with Current Observations

3.1.5.1 S-MIF Signal Implications

A concern with the proposed H2-dominated atmosphere is that it would have eliminated the oxidized sulfur exit channels, and thereby have precluded any sulfur mass independent fractionation (MIF) from being recorded in the rock record. This signal can be measured as ∆33S, the deviation of the 33S/32S ratio from the fractionation line defined by 34S and 32S. A recent analysis of 40 Martian meteorites reveals sulfur isotopes indicative of mass-independent fractionation (MIF) in a variety of protolithic ages - ALH 84001, the nakhlites, Chassigny and six shergottites

51 [Franz et al., 2014]. The only way to preserve such a S-MIF signal is if sulfur is distributed amongst two or more different species as they rain out of the atmosphere [Pavlov and Kasting, 2002]. Our simulations predict sulfur would have exited the

atmosphere in at least three different exit channels, HSO, SO2,H2S (see Figure

3.8) even with 5% H2. This suggests that an atmosphere containing 5% H2 could still produce and record a measureable S-MIF signal. ) − 1

s 10

− 2 10 S outgassing = 109 cm−2s−1

5 10

0 10 SO H2SO4 HSO HS SO2 H2S Total deposition flux (cm ) − 1

s 10

− 2 10 S outgassing = 1010cm−2s−1

5 10

0 10 SO H2SO4 HSO HS SO2 H2S Total deposition flux (cm

Figure 3.8. Total removal rate (rainout + surface deposition) for low (top) and high (bottom) cases of sulfur outgassing in an early Martian atmosphere. This shows three quantitatively important pathways that should allow for the preservation of a sulfur isotope MIF signal.

3.1.5.2 D/H ratios, hydrogen escape rates, and initial water inventories

The recent paper by Villanueva et al. [2015] provides additional support for the idea that early Mars was warm and wet. These authors looked at deuterium/hydrogen (D/H) ratios in various water vapor masses across the martian surface and estimated an average enrichment of ∼8 for their source regions (martian ice) relative to

terrestrial seawater. When combined with an estimated modern H2O inventory of 21 m GEL (global equivalent layer) in the polar layered deposits, an estimated initial D/H enrichment of 1.275 relative to seawater, and an assumed fractionation

52 factor, f = 0.02, for escape of D relative to H, this yields a global equivalent water layer of 137 m for early Mars. The relevant mathematical relation is

M I !1/(1−f) p = c (3.7) Mc Ip

Here, Mp and Mc are the ancient and current water reservoir sizes, respectively and Ip and Ic are the ancient and current D/H ratios. 137 m of water may sound like a lot, but in reality it is just a lower bound because the assumed fractionation factor, from Krasnopolsky et al. [1998], is only appropriate for the modern (highly tenuous) martian upper atmosphere in which nonthermal hydrogen escape processes predominate. If the early martian atmosphere was rich in H2, as postulated here, hydrogen escape would have been hydrodynamic, and D would have been dragged off along with H, thereby increasing the fractionation factor, f. We can estimate f if we assume that H2 was escaping at 11 −2 −1 the rate of 8×10 cm s required to maintain a 5% H2 atmosphere. We assume here that hydrodynamic escape was efficient enough to keep up with the diffusion limit. The fractionation factor for hydrodynamic escape is given by [Hunten et al., 1987, Eqn. 17] F /X m − m f = 2 2 = c 2 (3.8) F1/X1 mc − m1 Our notation is slightly different from Hunten et al., and our fractionation factor, 1 f, is related to their factor, y, by f = 1+y . (The y notation is convenient for isotopes of heavy elements that differ in mass by only a small percentage, where f notation is preferred for isotopes of light elements like hydrogen that have large mass differences.) Here, F1 , X1, and m1 are the escape rate, mixing ratio, and molecular mass of the lighter species (H2), F2, X2, and m2 are the equivalent quantities for the heavier species (HD), and mc is the crossover mass, given by [Hunten et al., 1987, Eqn. 16]

kT F1 mc = m1 + (3.9) bgX1

Here, k is Boltzmann’s constant, T is temperature, X1 is the mole fraction of ∼ 2 19 −1 −1 H2 (=1), g (= 373 cm s ) is gravity, and b (=1.76×10 cm s ) is the diffusion constant between H2 and HD [Banks and Kockarts, 1973, Eqn. 15.29]. We can

53 simplify this expression by dividing through by the mass of a hydrogen atom, mH , and letting HH = kT/mH g be the scale height of atomic hydrogen. Then, in atomic mass units, eq. (3.9) becomes

F1 Mc = M1 + (3.10) b/HH

∼ 7 ∼ 11 −2 −1 If we take T = 160 K, then HH = 3.5×10 cm and b/HH = 5 × 10 cm s . For 11 −2 −1 ∼ ∼ F1 = 8×10 cm s , we get Mc = 3.6 amu, and from eq. (3.8), f = 0.4. Then, if we take the other parameters to be the same as those assumed by Villanueva et al. (2015), Eq. (3.7) yields an initial water inventory of ∼450 m, or over three times their published estimate. Higher hydrogen escape fluxes would increase this value even further, following the nonlinear relationships expressed by eqs. (3.7-3.9). We conclude that high measured D/H ratios on present Mars are consistent with a relatively deep global ocean and an H2-rich atmosphere on early Mars. They do not require it, however, as these same high D/H ratios can be produced by loss of lesser amounts of water by mechanisms involving lower fractionation factors.

3.1.5.3 Tests for higher H2 outgassing rates

As discussed above, a 5% H2 atmosphere is possible if H2 outgassing rates on 11 −2 −1 ancient Mars were 8×10 H2 molecules cm s ; however, the assumed outgassing 11 −2 −1 rates in our standard simulations only provide ∼5×10 H2 molecules cm s , if serpentinization did not generate significant H2. If Mars’ early atmosphere was hydrogen-rich, at least one of our estimated H2 outgassing sources must be too low, or else H2 must have escaped at less than the diffusion-limited rate. The escape rate can, in principle, be investigated by constructing sophisticated theoretical models of hydrodynamic escape. This remains as work to be done. Some empirical tests of hydrogen outgassing and escape rates may be possible, either using rover measurements or by analyses of samples returned from the Martian surface. For exampled, Curiosity has already made a significant impact on D/H ratio measurements. D/H was measured in a ∼3-billion-year-old [Farley et al., 2014] mudstone at 3.0 times the ratio in standard mean ocean water [Mahaffy et al., 2015]. This value is half the D/H ratio of present Mars’ atmosphere, which is consistent with continued escape of hydrogen throughout Mars’ history. By making similar measurements as Curiosity moves up-section in Gale Crater, and comparing these

54 measurements to existing measurements of Martian meteorites, a history of martian D/H ratios can be constructed, and from this some information regarding the H escape rate can be inferred. Of course, getting detailed information is complicated because the fractionation between D and H during escape depends on both the rate and mechanism of the escape process. More robust tests are outlined briefly below.

3.1.5.4 Analyses of ancient Martian mantle redox state

The single greatest source of uncertainty in our H2 outgassing budgets is our knowledge of the redox state of the ancient martian mantle. The majority of martian meteorites have a mantle oxygen fugacity near IW+1. But if even part of the story we have outlined here is true, then the redox state of the martian mantle must have evolved with time as H2O was subducted and hydrogen was outgassed as H2, leaving oxygen behind. Other authors, too, have postulated that the redox state of the martian mantle evolved over time [Righter et al., 2008]. An initial redox state of IW-1, or lower, is consistent with a more reducing composition during core formation and with the low measured fO2 of ALH 84001 [Warren and Kallemeyn,

1996, Steele et al., 2012]. The fO2 for ALH 84001 is closer to IW-1, a value that would provide a half the H2 flux needed to maintain a 5% H2 atmosphere, given Earth-like outgassing rates. So, even at this point, our model requires twice Earth outgassing rates (or slower H2 escape). As the mantle fO2 increased, even higher outgassing rates would have been needed to maintain 5% H2. Thus, the end of the warm wet period could have been brought about either by declining outgassing rates or by progressive mantle oxidation. Such an evolution of mantle redox state would be broadly consistent with other assumptions in our conceptual model. Deposition of oxidized iron in BIFs and subsequent subduction of these sediments would have deposited additional O in the mantle. We should note that a similar process of progressive mantle oxidation has been suggested for early Earth [Kasting, 1993] and it has been shown that the mantle redox increased by 0.5-1 log units during the Archean [Aulbach and Stagno, 2016, Nicklas et al., 2016]. The proposed oxidation process involves disproportionation of ferrous iron at high pressures in Earth’s lower mantle-a process that might not have occurred on a smaller planet. If the martian mantle started out with an fO2 near IW, then small additions of oxygen could conceivably have oxidized it more significantly over time. Indeed, the observed spread in fO2 values of martian

55 meteorites up to values approaching QFM suggests that mantle oxidation did occur [Stanley et al., 2011]. We take this as indirect support for our hypothesis. That said, the existing data do not allow us to draw firm conclusions about the early redox evolution of the martian mantle. The only measurement of redox state during this early phase of the planet’s history comes from analyses of ALH 84001.

Given the large spread in measured fO2 values of younger materials, this leaves great uncertainties in the redox state at that time. Ideally, one would like to have a suite of redox measurements at multiple points in martian history, to account for the spread in the data and to constrain the temporal evolution. This is not feasible in the near future, but could happen over the coming decades with an extensive sample return campaign. In the meantime, contextual information on this period of martian history could be obtained from Curiosity, ExoMars, and the Mars 2020 lander. Such contextual information on the early surface evolution of Mars is one of the main goals of the Curiosity mission. Curiosity has already dated sedimentary rocks on the martian surface [Farley et al., 2014], placing an age on the deposition of the lacustrine sediments in Gale Crater [Grotzinger et al., 2014]. Making subsequent time-stamped measurements would help place the rest of the results from Curiosity in an absolute historical context that could be compared to future mantle redox measurements. This context would be augmented by qualitative estimates of the redox state of mantle-derived materials. These can be made through this measurement of the relative abundances of redox-sensitive trace elements such as Fe, for example with MSL’s ChemCam. Similar instrumentation was present on the MER rovers, and planned for future rovers, so it may be possible to stitch together this history, albeit without the quantitative dating capabilities of Curiosity.

3.1.5.5 Analyses of Fe-oxide rich sedimentary rocks

Contextual information on the co-evolution of the Martian atmosphere and mantle may also come through analyses of ancient Fe-oxide rich layers. Although we do not expect a huge H2 outgassing contribution from Fe-oxide deposition, the presence of

Fe-oxide rich sedimentary layers is consistent with an H2-rich atmosphere. Such layers have an analog in the banded iron-formations (BIFs) on ancient Earth. These are thought to have required an anoxic deep ocean so that ferrous iron could

56 be transported over long distances to upwelling regions where the BIFs formed [Holland, 1973]. Therefore, charting and dating the presence/absence of such layers could provide critical information on the long-term evolution of the redox state of the surface, just as the presence/absence of BIF’s has had a huge impact on our assessment of the redox history of Earth’s surface [Walker, 1985]. By measuring the deposition rates of the Fe-oxides, it would also be possible to estimate the H2 outgassing rate they could have provided, both locally and, by extrapolation, globally. The Fe concentration of the samples can be measured, and the deposition times can in theory be calculated by dating the sedimentary layers on Mars [Farley et al., 2014]. However, the uncertainties of the dating measurements (± 0.35 Ga) are significantly longer than the timescales of deposition, and many of the concentration measurements will be qualitative in nature. Further, extrapolation will be difficult unless the size of the lake above the floor of Gale Crater can be estimated and compared to estimates of the contemporaneous global reservoir. That said, even qualitative information on the Fe-oxide deposition rate and its evolution over time would be useful. This could lead to order-of-magnitude inferences on the Fe flux from the subsurface, and the rate at which the mantle was being oxidized through Fe-oxide burial.

3.1.6 Conclusion

• Early Mars could have been warmed by a thick CO2-H2 greenhouse atmo- sphere.

• Photochemical modeling is used to study conversion of reduced volcanic gases

to H2.

• Getting the minimum H2 requires high outgassing or additional hydrogen sources.

• Oxidation of iron by serpentinization can help boost atmospheric H2 concen- tration.

• The Curiosity Rover could test the H2-CO2 greenhouse hypothesis in a variety of ways.

57 Despite the fact that a prolonged, millions of years or more, warm and wet early Mars is consistent with new data from the MSL mission, models have just only recently been able to reproduce warm climates. The only published mechanism that was successful in inducing a stable warm climate for extended periods is the greenhouse effect of a CO2-H2 atmosphere. About 3 bar of CO2 and 5% or more H2 is required to produce global mean surface temperatures above freezing.

Maintaining H2 at this level is challenging but does not appear to be out of the question.

Using photochemical models, we found that direct volcanic outgassing of H2 from a highly reduced early martian mantle was probably the largest source of H2. Recycling of volatiles between the surface and the interior, as happens on Earth because of plate tectonics, would likely have been needed to provide this H2, as rates of juvenile outgassing are small. Additionally, we found that H2 could have been provided by photochemical oxidation of outgassed CH4 and H2S and by processes such as serpentinization and deposition of banded iron-formations. However, none of these sources are sufficient unless: (i) the ancient martian mantle was significantly more reduced than today, (ii) volcanic outgassing rates were substantially higher than those on modern Earth or (iii) hydrogen escaped to space more slowly than the diffusion limit. Some combination of these three mechanisms could also work.

Recycling of water through the mantle followed by outgassing of H2 should have oxidized the mantle over time. Such oxidation is consistent with the observed spread in fO2 values of SNC meteorites from as low as IW-1 up to near QFM.

Additional tests of the H2 greenhouse hypothesis may be provided by MSL and by future missions. MSL itself could look for evidence of banded iron-formations and changes in D/H ratios that might indicate hydrogen loss, as well as providing qualitative and contextual information on the redox evolution of the martian mantle. Future sample return missions could look for quantitative evidence of secular mantle oxidation over time. Improved numerical models of hydrodynamic escape could shed light on the escape rate of H over time. Additional 3-D climate modeling work would also be useful to better constrain the amounts of rainfall and surface runoff that could have been maintained by this model and by its competitors, and compare these results to the lacustrine and fluvial deposits in Gale Crater and across the planet.

58 3.2 Climate Cycling Caused by the Carbonate-Silicate Cycle

All of these theories of martian valley formation have overlooked a phenomenon that has been suggested to be important for early Earth, as well as for planets orbiting near the outer edge of their star’s habitable zone. Planets on which the CO2 outgassing rate is small [Tajika, 2003], or for which stellar insolation is low [Menou, 2015], are predicted to undergo repeated cycles of global glaciation/deglaciation as a consequence of the dependence of the CO2 removal rate on temperature and CO2 partial pressure, pCO2. These ’limit cycles’ occur because when the planet is in a glaciated state, CO2 consumption by silicate weathering cannot keep pace with CO2 outgassing from volcanoes. Atmospheric CO2 builds up and increases the planet’s surface temperature until it is able to deglaciate. But once the planet is ice-free,

CO2 outgassing cannot keep pace with consumption by weathering, so the planet falls back into global glaciation, and the cycle repeats. Such limit cycling does not occur on modern Earth because the solar flux is sufficiently high that weathering can balance outgassing at relatively low atmospheric pCO2 (Fig. 1). Furthermore, on an inhabited planet like Earth, soil pCO2 is decoupled from atmospheric pCO2 by the activities of vascular plants [Berner, 1992]. Here we show that on a poorly illuminated early Mars, the high pCO2 values required for climatic warmth could have induced rapid weathering, perhaps triggering limit cycles.

3.2.1 Why climate limit cycles should occur on early Mars but not Earth

To begin, we looked at terrestrial and martian climates on a global scale using a 1-D climate model coupled to a simple model of silicate weathering. Some important differences between our weathering model and that of [Menou, 2015] are discussed below. Below, we perform a more complex set of coupled climate/weathering rate calculations using an energy-balance climate model similar to that used by Menou, but with significant updates.

59 3.2.1.1 1-D climate model calculations for present Earth

Our 1-D climate model is extensively described in Chapter 2.2, so only a brief summary will be given here. We use the two-stream approximation to treat radiative transfer and assume that the net emitted infrared flux is equal to the net absorbed solar flux in each layer in the stratosphere. Convection in the troposphere is parameterized by assuming a moist CO2 or H2O adiabatic lapse rate, following [Kasting, 1991]. Clouds are not included explicitly in our 1D model, but their effect on climate is simulated by adjusting the surface albedo, as. For Earth, the actual surface albedo is ∼0.1 or below, but we use a value of 0.31. This allows the model to reproduce the present mean surface temperature of 288 K, given present solar insolation and −4 present (or preindustrial) pCO2, 3×10 bar. This calculation is shown by the point labeled ’Present Earth’ in Fig. 3.9. As pCO2 is increased, the surface temperature increases along the green curve. Our model predicts about 10 K of warming per factor of 10 increase in CO2, or 3 K per CO2 doubling, which is near the middle of the 1.5-4.5 K range predicted using more complicated 3-D climate models [Change, 2013]. We have done 1-D climate model calculations for early Mars, as well. Before discussing those, though, we describe the other part of our coupled model, namely, the dependence of pCO2 on surface temperature via weathering.

3.2.1.2 The Carbonate-Silicate Cycle pCO2 is a function of surface temperature by way of its participation in the carbonate-silicate cycle (Menou, 2015; Tajika, 2003). We modeled the time- dependent mass exchange of CO2 with the crust in a manner similar to that of Menou: d (pCO ) = V − W (3.11) dt 2

Here, pCO2 is the partial pressure of CO2 in bar, V is the volcanic outgassing of CO2 (in bar/Gyr), and W is the rate at which CO2 gets removed via rock weathering. These outgassing units are non-standard and can lead to confusion.

Menou took the CO2 outgassing rate for Earth to be 7 bar/Gyr. We can convert this rate to geochemists’ units of Tmol/yr (1012 mol/yr) using the relationship:

Ps = Mcol × g (3.12)

60 Figure 3.9. The green and red curves represent surface temperatures calculated using a 1D climate model [Kopparapu et al., 2013] for present Earth (green) and early Mars (red) with three different atmospheric compositions and two different surface albedos (0.216 for dry land and ocean, 0.45 for a fully glaciated planet). The solar flux for early Mars is 0.3225 times the flux for present Earth. The brown curve shows the temperature at which the weathering rate balances the present terrestrial CO2 outgassing rate, assuming 0.5 a pCO2 dependence (solutions for Eqn. 3.13 when W/W⊕ = 1). The blue circle shows the location of the present soil pCO2 level. These curves define three regions of climate stability: 1) Warm stability: The surface temperature and weathering rate curves intersect above the freezing point (abiotic Earth) and planets remain permanently de-glaciated 2) Cold Stability: The surface temperature fails to ever rise above the freezing point of water (red dotted early Mars case). Such planets remain permanently glaciated. 3) Limit Cycling: The surface temperature and weathering rate curves intersect below the freezing point, but temperatures above freezing are possible as CO2 and H2 build up (solid/dashed red early Mars case with H2).

Here, Ps is surface pressure, Mcol = column mass, and g = gravitational acceleration. Calculating the column mass for a 1-bar atmosphere, multiplying by the surface 5 area of the Earth, and converting to moles yields the relationship: 1 bar CO2 =10 20 Pa CO2 = 1.18×10 moles. Using this conversion factor, Menou’s outgassing rate comes out to be 0.83 Tmol/yr. This is about a factor of 10 lower than the estimates for the terrestrial CO2 outgassing rate, ∼7.5 Tmol/yr [Gerlach, 2011, Jarrard, 2003, and refs therein].

61 The relationship between pCO2 and CO2 atmospheric mass is different on Mars because gravity and surface area are both lower by a factor of 3.6 (for gravity) to 3.5 (for surface area). These factors offset each other, so the result is: 1 bar CO2 is ∼= 1.18×1020 moles (0.75) = 8.85×1019 mol. Ramirez et al. (2014) have suggested that outgassing rates per unit area on early Mars might be similar to those on present Earth based on the fact that heat flow per unit area is thought to be similar on the two planets [Zuber et al., 2000]. Halevy and Head (2014) make similar assumptions. If so, the global outgassing rate on early Mars would be scaled by surface area relative to Earth, yielding 7.5 Tmol/yr (0.28) ∼= 2.1 Tmol/yr ∼= 24 bar/Gyr. In the calculations that follow, we have let the CO2 outgassing rate be a free parameter, and we have varied its value from 0.8-4.5 Tmol/yr, spanning the region of parameter space near the modern terrestrial value. As pointed out earlier, in order for outgassing rates on early Mars to be comparable to those on modern Earth, the initial volatile inventory must have been large, and volatiles must have been recycled between the crust and the mantle. According to eq. 3.11, the silicate weathering rate, W, must balance the volcanic outgassing rate, V, when the system is in steady state. Following Berner (1994), we write the weathering rate as:

W pCO !β 2 kact(Tsurf −288) 0.65 = e [1 + krun(Tsurf − 288)] (3.13) W⊕ p⊕

This equation was formulated for the (biotic) modern Earth and, so, must be scaled −1 to a presumably abiotic early Mars. The parameter kact = 0.09 K is an activation −1 energy, and krun = 0.045 K is a runoff efficiency factor. W⊕ and p⊕ are the weathering rate and effective CO2 partial pressure on modern Earth (see discussion below). Extending our analogy between the outgassing on early Mars and the outgassing on present Earth, we assume that W⊕ = V⊕ = 2.1 Tmol/year for Tsurf = 288 K.

The parameter, β, dictates the dependence of the weathering rate on pCO2. The value of β is uncertain, even when weathering is not influenced by biology. Values of β between 0 and 1 are theoretically possible, depending on whether one has open or closed system weathering [Berner, 1992]. Walker [1985] assumed β = 0.3 based on laboratory experiments by Lagache [1976]. If the weathering rate is proportional to the dissolved [H+] in groundwater, then β should be equal to 0.5.

62 We assumed β = 0.5 in all of our calculations. −4 The parameter p⊕ is complicated. Menou used p⊕ = 3.3×10 bar, which is approximately the preindustrial atmospheric value. But weathering occurs in

soils, and soil pCO2 on Earth is 10-100 times higher than atmospheric pCO2 as a consequence of root respiration by vascular plants [Kump et al., 2004]. Here,

we take the geometric mean of these two values and assume that soil pCO2 is 30

times atmospheric pCO2. When combined with an assumed β value of 0.5, this implies that land plants accelerate silicate weathering by a factor of 300.5 ∼= 5.5. By comparison, Berner and Kothavala [2001] assumed that weathering on the pre- land-plant Earth was slower by a factor of 0.15, implying that land plants enhance weathering by a factor of (1/0.15) ∼= 6.7. Given the large uncertainties in this process, the agreement between these estimates is pretty good. We should note that

biological influences on weathering are not limited to enhancing soil pCO2. Plants also produce organic acids that are more effective than carbonic acid at dissolving rocks. Consequently, some authors [e.g. Schwartzman and Volk, 1989] have argued that land plants accelerate silicate weathering by as much as a factor of 1000. We follow Berner and adopt a more conservative estimate, but we acknowledge that significant uncertainty remains as to exactly how much weathering is affected by the biota.

Following this reasoning, we set p⊕ =0.01 bar in eq. 3.13, consistent with the

current soil pCO2 value. This implies that W/W⊕ = 1 at the point (pCO2,Tsurf ) = (0.01 bar, 288 K). This point is shown as a blue circle along the weathering rate curve in Fig. 3.9. Also shown at the intersection of the weathering rate curve and the (green) greenhouse-warming curve is a point labeled ’Abiotic Earth’. This represents the

(pCO2,Tsurf ) values that the Earth would be expected to achieve if life were

suddenly eliminated. It is calculated as follows: With β = 0.5, reducing pCO2 from 0.01 bar to 3.3×10−4 bar reduces the weathering rate by a factor of 300.5 ∼= 5.5. That’s how much the weathering rate would decrease if life were instantaneously

eliminated. Both Tsurf and pCO2 would then gradually increase until the weathering ∼ rate went back up to its original value. This happens at (pCO2,Tsurf ) = (0.002 bar, 295 K). Thus, our model predicts that present Earth would be about 7 degrees warmer if land plants were to suddenly disappear.

63 3.2.1.3 1-D climate model calculations for early Mars

This brings us, finally, to Mars. For Mars, a surface albedo, as, of 0.216 allows the model to reproduce the present mean surface temperature of 218 K, given the present martian solar flux (0.43 times that of Earth), along with a fully saturated, 95% CO2, 5% N2, 6-mbar atmosphere (calculations not shown). The model was then run with this same value of as for early martian conditions (3.8 Gyr ago) when the solar luminosity was 75 percent of present (3.9, red dotted curve). Not surprisingly, the calculated mean surface temperature never reaches the freezing point of water, regardless of how much CO2 is added. Instead, it turns over and begins decreasing at pCO2 > ∼3 bar. This result is expected, as virtually all climate models predict that early Mars could not have been warmed to the freezing point by a CO2-H2O atmosphere.

We can produce warmer surface temperatures by adding H2 to the early martian atmosphere, following Ramirez et al. (2014). Ramirez et al. showed that above- freezing surface temperatures for early Mars are attainable with as little as 3 bar of

CO2 and a 5% mixing ratio of H2 (red dashed curve, Fig.3.9). A 3-bar atmosphere is within the initial inventory estimated earlier for a volatile-rich early Mars. As can be seen from the figure, however, this curve intersects the weathering rate curve below the freezing point of water. As pointed out above, this implies that no stable steady state is possible. Instead, the climate should oscillate between cold, globally glaciated conditions and warmer, ice-free conditions.

H2 mixing ratios exceeding 5% are needed to produce warm climates in our EBM simulations, described below, because the planet needs to be able to deglaciate, starting from a state with a frozen surface and high albedo. For the red solid curve in Fig. 3.9, as = 0.45 which is consistent with a frozen surface. In this case, ∼20%

H2 is needed to deglaciate the planet. The intersection of this red curve with the weathering rate curve is again below the freezing point of water, indicating that limit cycles should still occur. We explore these limit cycles quantitatively in the next section, using a more complicated climate model.

3.2.2 Energy Balance Model Setup

1-D climate model calculations are useful for determining when climate limit cycles should occur. To explore these cycles, though, it is appropriate to use an energy-

64 balance climate model (EBM) similar to those used by Tajika [2003], Menou [2015], Haqq-Misra et al. [2016] because EBMs can simulate ice-albedo feedback. Menou’s model was actually a zero-dimensional parameterization of an EBM. Below we describe our own, 1-D (in latitude) EBM and how we used it to look at early martian climate cycles. The EBM is described in Chapter 2.3. In essence it calculates the meridionally averaged temperature as a function of latitude and time. Table 3.4 shows that numerous parameters are included within an EBM

Table 3.4. Parameters for input into EBM Model Parameters Value or range of values used Eccentricity 0 Obliquity 25-50◦ Surface Pressure 3 bars Ocean coverage 20% Geography Northern ocean Solar constant relative to present Mars 0.75 CO2 outgassing rate 2.1 Tmol/yr 12 12 −2 −1 H2 outgassing rate 1 ×10 -4.5×10 cm s Ground albedo 0.216 H2O ice albedo 0.38-0.66 CO2 ice albedo 0.35 β 0.5 kact 0.09

3.2.3 Energy Balance Model Results

To explore the effect of limit cycles on early martian climate, we performed over 30 calculations with the EBM, using CO2 outgassing rate and H2 outgassing rate as free parameters. The results are summarized in Fig. 3.10. The bottom panel shows the fraction of time within a billion year period when at least one latitude band was above freezing (273 K). When the H2 outgassing rate is <∼400 Tmol/year, cycling does not occur because there is not enough greenhouse warming to deglaciate the frozen planet. This rate is over 150 times higher than the H2 outgassing rate on modern Earth, but is not out of line for a tectonically active early Mars with a

65 highly reduced mantle [Chassefière et al., 2014]. This rate could be reduced if hydrogen escaped at less than the diffusion limit. The CO2 outgassing rates studied ranged from 0.8 Tmol/yr up to about 4.5 Tmol/yr. (The equivalent modern Earth rate, when adjusted for the difference in planet surface area, is 2.1 Tmol/yr). Low

CO2 outgassing rates create low-frequency cycles. High H2 outgassing rates decrease the length of the warm phase of each individual cycle. Panel ’A’ shows typical cycling behavior for moderate H2 outgassing rates and low CO2 outgassing rates. Limit cycles provide warm periods lasting up to 5-10 Myr, separated by long (160 Myr) periods of below-freezing temperatures. Panel ’B’ shows what happens when outgassing rates are too low to induce cycling. Panel ’C’ shows a case in which cycling is occurring at such high frequency that the planet is warm nearly 50% of the time. Our favored region of parameter space to approximate the actual climate

Figure 3.10. The heat map shows the fraction of time within a billion year period when the maximum surface temperature was above freezing (273 K). Panel ’A’, ’B’, and ’C’ show cases where limit cycles are moderate, absent, and rapid, respectively. For reference, the modern CO2 and H2 outgassing rates on present Earth are 7.5 Tmol/year [Jarrard, 2003] and 2.4 Tmol/year [Ramirez et al., 2014, and refs therein], respectively. These rates are scaled down by a factor of 3.5 for Mars to account for its smaller surface area. of early Mars is in the area of panel ’A’. 10 Myr is an adequate time period to

66 form the larger martian valleys, according to the references mentioned in Chapter. 2.1. And the fact that the surface remains frozen for much longer time periods may help to reconcile our results with those who have favored the ’cold early Mars’ hypothesis.

3.2.4 Sensitivity of Models to Input Parameters

Some of the parameters included in Table 3.4 are not well defined for early Mars, while others have well documented values. An ocean fraction of 20% is consistent with the recent five-year monitoring of atmospheric D/H ratios [Villanueva et al., 2015]. A northern ocean land configuration is consistent with observations of deltas and valleys [Di Achille and Hynek, 2010], as well as observations of the martian topography [Perron et al., 2007]. A present day martian obliquity of 25◦ was chosen for most runs but we also explored cases where obliquity was chaotically varying from 25-50◦ (see discussion below) [Touma and Wisdom, 1993].

3.2.4.1 Sensitivity to outgassing rates and ice albedo

The parameters that are less well documented are CO2 and H2 outgassing rates and

H2O ice albedo. Getting constraints on outgassing rates is challenging. Estimates made by looking at the igneous rocks and making assumptions about the volatile content of the initial lava from which they formed are universally too low to produce a warm early martian climate (Chapter 3.1). Some type of volatile recycling mechanism, such as plate tectonics, is required to do this. As discussed in the main text, high H2 outgassing rates are expected because of Mars’ highly reduced mantle and the presence of ultramafic rock on its surface [Chassefière et al., 2014]. Ice albedo is a critical parameter in our model. Fig. 3.10 shows one case where 18%

H2 is needed to sustain climate cycles. This value can be lowered by decreasing the water ice albedo. Dirtier ice would increase the amount of absorbed solar radiation.

High ice albedos encourage limit cycling but require high concentrations of CO2 and

H2 to deglaciate. Very low ice albedos (< 0.36) disrupt the limit cycling behavior. In most of our simulations, we keep the water ice albedo fixed at a relatively high value of 0.45 and vary H2 and CO2 outgassing rates. Doing so produces the heat map shown in Fig. 3.10.

67 3.2.4.2 Sensitivity to obliquity

The martian climate is also sensitive to obliquity, which is thought to have varied chaotically throughout Mars’ lifetime [Laskar et al., 2004]. We looked at this by changing the assumed obliquity from 25◦ to 50◦ in the EBM. The effects of obliquity interact with the assumed continental distribution. High obliquity causes more incident solar radiation at the poles and less at the equator. With our specification of a northern ocean, high obliquity increases the frequency of cycles, but not the length of each individual cycle. This admittedly does not exhaust the list of possible combinations of obliquity and geography. However, on the basis of this experiment, we infer that higher obliquity would have encouraged limit cycling rather than inhibiting it. We also did a second simulation in which the obliquity was allowed to cycle repeatedly between 25◦ and 50◦ for 1 Gyr. The limit cycles were found to occur at the frequency corresponding to the higher obliquity state. Our specified value of 25◦ is thus conservative; higher values would lead to even more pronounced limit cycling behavior.

3.2.5 Conclusion

The duration of the warm periods caused by limit cycles is comparable to that needed to form the larger martian valleys, 106-107 yrs [Hoke et al., 2011]. The length and the frequency of cycling behavior depend on the assumed CO2/H2 outgassing rates and on the planet’s obliquity. For higher outgassing rates, the length of each warm phase decreases but their frequency increases. Smaller outgassing rates give longer, more widely spaced warm periods, which may be more consistent with the timescales needed for valley formation. If this type of climate cycling was indeed occurring on early Mars, then both the warm and the cold early Mars hypotheses are partly correct. MSL and future Mars missions may be able to test this hypothesis by refining the time scales for valley and lake formation and by determining whether multiple warming events took place.

68 Chapter 4 | The Planet System Observed as an Exoplanet

Material in this chapter is published in: Batalha, Natasha E., & Line, Michael, “Information Content Analysis for Selection of Optimal JWST Observing Modes for Transiting Exoplanet Atmospheres” Astro- nomical Journal Volume 153.4 (2017)151

Batalha, Natasha E., et al. “PandExo: A Community Tool for Transiting Ex- oplanet Science with JWST & HST.” Publications of the Astronomical Society of the Pacific 129.976 (2017): 064501.

4.1 Modeling Transit Transmission Spectra

We use the chemically-consistent transit transmission approach described in Kreid- berg et al. [2015]. Given the temperature-pressure profile of the atmosphere and the elemental abundances parametrized with metallicity, [M/H], and C/O, the model first computes the thermochemical equilibrium molecular mixing ratios (and mean molecular weight) using the publicly available Chemical Equilibrium with Applications code (CEA, McBride and Gordon [1996])1. Chemical equilibrium assumes no change in the number densities of atoms and assumes the system is closed (i.e. no escape processes). Then, by minimizing the Gibbs Free energy, the number density of each species can be determined.

1https://www.grc.nasa.gov/WWW/CEAWeb/

69 It is this way that the thermochemically derived opacity relevant mixing ratio profiles (H2O, CH4, CO, CO2, NH3,H2S, C2H2, HCN, TiO, VO, Na, K, FeH, H2, He) are created. Combined with the temperature profile, cloud and haze proprieties, and planet bulk parameters (10 bar radius, stellar radius, planetary gravity), they are all then fed into a transit transmission spectrum model (Line et al. [2013a], Greene et al. [2016], Line and Parmentier [2016]). The model divides the layers of the planet into annuli and then computes the slant optical depth along each tangent line. The slant transmittance is computed by integrating

Z zmax δF (k) 1  −τ(z,k) = 2 2π(Rp + z) 1 − exp dz (4.1) F (k) 2πRs 0 where Rp and Rs are the radii of the planet and star, respectively, z is the height above the occulting disk, τ is the optical depth, k is the wavenumber [Brown, 2001]. The total opacity is calculated using the Freedman et al. [2008, 2014] opacity database. Each spectrum is to computed at the wavelength-dependent eclipse depth at the appropriate instrument spectral resolving power. For cloudy simulations, we assume a hard gray cloud top pressure set to be a user defined pressure level, below which the transmittance is set to zero and use the “Rayleigh Haze" power law parameterization [Des Etangs et al., 2008] to describe hazes. This simplistic treatment of clouds and hazes is motivated by WFC3+STIS observations [Kreidberg et al., 2014a, Knutson et al., 2014, Sing et al., 2016], in which simple gray cloud top pressures, and power law parameterizations are sufficient to fit the data. Additionally, more complex cloud model parameterizations are not suitably motivated by the data and our generally poor understanding of the very complex coupled, 3D-dynamical-radiative-microphysics in non-Earth-like planets [e.g. Lee et al., 2015].

70 4.2 Instrumental Noise Models

4.2.1 Pandeia: Simulating Noise Sources

The source code for STScI’s exposure time calculator, named Pandeia, was recently released to the observing community 2. Although Pandeia supports all officially- supported observing modes, we limit our discussion to the modes that will be useful for exoplanet transit spectroscopy. Pandeia is a hybrid instrument simulator. It simulates observations using a three-dimensional, pixel-based approach but its ultimate goal is to provide the user with accurate predictions of SNRs for specific observing scenarios. Therefore, it does not fully simulate the entire field of view of the instrument, and it does not include optical field distortion, intra-pixel response variations, other detector systematic noise, or the effects of spacecraft jitter and drift. Pandeia does include accurate and up-to-date estimates for background noise, point-spread-functions (PSFs), instrument throughputs and optical paths, saturation levels, ramp noise, correlated read noise, flat field errors and data extraction for all the JWST instruments. We briefly describe Pandeia below, but a full description can be found in Pontoppidan et al. [2016]. For each calculation, a three dimensional cube is created with spatial and spectral dimensions. Astronomical scenes are modeled by specifying a spectral energy distribution along these two dimensions. In the case of transit spectroscopy, this is always a stellar spectrum or star+planet spectrum placed at the center of the optical axis and normalized at a specific reference wavelength (see §3). After the scene is created, Pandeia uses pre-calculated low, medium and high background cases adopted from Glasse et al. [2015]. For the calculations in this analysis we employ the “medium” background case shown in Figure 4.1. After the background is added, Pandeia convolves each plane in the three- dimensional astronomical scene with the unique, two dimensional PSF for the instrument mode being simulated. All PSFs are calculated using WebbPSF, which is described in Perrin [2011]. For spectroscopy modes (except NIRISS), Pandeia assumes that the PSF profile is independent of spatial location. The inclusion of the PSFs can be seen in Pandeia’s 2-dimensional simulations of the detector 2http://jwst.etc.stsci.edu

71 Zodiacal Cirrus 10.0 high medium (Default in PandExo) low 1.0

Background (MJy/sr) Background 0.1 1 2 3 4 56 7 8 9 10 Wavelength (µm)

Figure 4.1. Varying levels (low, medium, high) of pre-computed background flux used within Pandeia for cirrus (dashed) and zodiacal (solid) background contamination. Black curve shows the level used (medium) for all noise simulations in this analysis.

(Figure 4.2). All JWST exoplanet time series spectroscopy modes will acquire sampled-up-the-ramp data at a constant cadence of one frame [Rauscher et al., 2007]. A frame is a unit of data that results from sequentially clocking and digitizing all pixels in the rectangular area of an SCA. The time it takes to read out one

frame (tf ) depends on the observation mode or, more specifically, on the subarray size. In JWST terminology, a group is a number (n) of consecutively read frames with no intervening resets. For all exoplanet time series modes, there is one frame per group. An integration is composed of a reset of the detector followed by a series of non-destructively sampled groups (n = # groups per integration). The time it takes to reset the detector in between integrations is equivalent to the frame time,

tf . The measured signal can be calculated in two ways. The first, referred to as

72 A 60 20 (pixel) Spatial 0 500 1000 1500 2000 20 B 15 10 (pixel) Spatial 0 1000 2000 3000 4000 C 30 20 (pixel) Spatial 0 400 800 1200

35 D 25 (pixel) Spatial 0 100 200 300 400 Dispersion (pixel)

Figure 4.2. Subsets of the two dimensional Pandeia detector simulation of a T=4000 K, Fe/H=0.0 and, logg=4.0 stellar SED normalized to a J=10, with 100 seconds of observing time. Color coding shows the electron rate in each pixel. Panel A is simulation of NIRISS SOSS (Order 2 not shown), panel B is a simulation of NIRSpec G395H, panel C is a simulation of NIRCam F444W, and panel D is a simulation of MIRI LRS.

MULTIACCUM, is the standard procedure within Pandeia. It computes the final signal by fitting each point up the ramp. The second, referred to as Last-Minus-First (LMF) is the standard procedure within PandExo. In this procedure, the final signal within an integration is equal to the final readout value minus the first readout value. We describe MULTIACCUM below and describe LMF in §3, where we also discuss differences between the two methods. In the MULTIACCUM procedure, correlations between the number of groups and the number of averaged frames per group are considered when computing the individual noise on a single pixel;. Pandeia calculates the total noise via the

73 formulation in Rauscher et al. [2007]:

12(n − 1) 6(n2 + 1) σ2 = σ2 + (n − 1)t f tot mn(n + 1) read 5n(n + 1) g (4.2) 2(m2 − 1)(n − 1) − t f mn(n + 1) f

where m is the number of frames per group (for transit time series m = 1), n is the

number of groups, σread is the read noise per frame, tg is the time per group, f is the electron rate calculated from the astronomical scene cube (e−1s−1pixel−1) and

tf is the time per frame.

The read noise, σread, is calculated by considering the effects of correlated noise. It is well-known that both the near-infrared H2RG detectors and the mid-infrared detectors are affected by correlated noise. Therefore, regardless of the amount of incident light on the detector, the read noise in one pixel will depend on the read noise in other pixels. This effect becomes even larger in the fast-read direction and ignoring it would lead to an underestimation of the noise. The greatest consequence of adding correlated noise is that the error propagation must be handled with a covariance matrix and the noise in each pixel cannot simply be added in quadrature sum.

4.2.2 PandExo: Simulating JWST Observations

Our JWST transit simulator tool, called PandExo, is built around the core capa- bilities of Pandeia’s throughput calculations. Pandeia is packaged as a Python package that is called by PandExo, and therefore any updates to Pandeia, by STScI, will automatically be incorporated into PandExo. In addition to the observatory

inputs required for Pandeia, PandExo requires a stellar SED model (F∗,λ, taken from Phoenix Stellar Atlas [Husser et al., 2013]), an apparent magnitude, a planet

spectrum (primary or secondary), the transit duration (T14), the fraction of time spent observing in-transit versus out-of-transit, the number of transits, the desired exposure level considered to be the saturation limit (% full well), and a user-defined noise floor.

Using the star and planet models, an out-of-transit (F∗,λ) and in-transit model 2 (F∗,λ(1 − (Rp,λ/R∗) ) for primary transit or (Fp,λ + F∗) for secondary transits) is calculated. PandExo does not create full light curve models with an ingress and

74 egress. Likewise, it does not include the effects of time-varying stellar noise. Doing so would require frame-by-frame simulations and would be too computationally demanding for a community tool. We leave an in-depth analysis of these effects for a future paper and treat the transit as a box model. With the out-of-transit spectrum, PandExo calls Pandeia to create a 2D simu- lated image of the flux on the detector with n = 2 (minimum number of groups required for an observation). Then, PandExo calculates the maximum number of groups allowed in an integration before the pixel on the detector receiving the highest flux reaches the user-defined saturation limit. Determining how many groups per integration is a crucial step within PandExo because it sets the observing efficiency, also known as the duty cycle, where:

n − 1 eff = (4.3) n + 1

The above equation is exact for the near-IR detectors, but MIRI is more efficient. MIRI reads pixels in two rows and then resets the two rows before going on to the next two rows. This dramatically shortens the dead time between the last read and reset (the denominator is only a little more than n and little less than n + 1. Therefore, while this is formula is exact for the near-IR instruments, MIRI is somewhat more efficient at small n and so in that regime, PandExo values for MIRI may be slightly conservative. After the timing information is calculated, PandExo uses Pandeia to compute two simulated extracted spectral rates (e−s−1): one for the out-of-transit component and one for the in-transit component. As discussed in §2, Pandeia returns (among − −1 other products) a 1D extracted flux rate (Fin,λ,Fout,λ in e s ).

If there are ni,in integrations taken in, and ni,out integrations taken out of transit, the pure shot noise can be easily calculated from those fluxes via:

2 σshot = Fin,λtg(n − 1)ni,in + Fout,λtg(n − 1)ni,out (4.4)

One important correction that is made to Fin/out,λ from Pandeia, is the contribution from quantum yield. Quantum yield is the number of charge carriers generated per interacting photon [Janesick, 2011]. It ultimately has the effect of increasing the electron rate and by default, the saturation rate, of the detectors by a factor of ∼1.8 at 0.5 µm, dropping to a factor of ∼1.0 at 1.9 µm (for the nir-IR detectors)

75 Table 4.1. Instrument Modes in PandExo

Instrument Filter Wavelength Range Resolving Power RN (µm) e−/frame NIRISS SOSS – 0.6–2.8 700 11.55 NIRSpec Prism Clear 0.7–5 100 16.8 NIRSpec G140M/H F070LP 0.7–1.27 1000/2700 16.8 NIRSpec G140M/H F100LP 0.97–1.89 1000/2700 16.8 NIRSpec G235M/H F170LP 1.70–3.0 1000/2700 16.8 NIRSpec G395M/H F290LP 2.9–5 1000/2700 16.8 NIRCam Grism F322W2 2.5–4.0 1500 10.96 NIRCam Grism F444W 3.9–5.0 1650 10.96 MIRI LRS – 5.0–14 100 32.6 WFC3 G102 – 0.84–1.13 210 20.0 WFC3 G141 – 1.12–1.65 130 20.0

[Pontoppidan et al., 2016]. In Pandeia, this is added to the extracted flux product and corrected for in the noise product. In PandExo, we divide Pandeia’s extracted 2 flux by the quantum yield before computing σshot. Then, to compute the total noise, we must add in the contributions from the background and the read noise. The background signal, Fbkg, is directly computed from Pandeia. The contribution from the read noise is:

2 2 σread = 2RN npix(ni,in + ni,out) (4.5) where RN is the total contribution of read noise in electrons (see Table 1), npix is the number of extracted pixels. The factor of two comes from the fact that Pandeia’s RN values (Table 1) are given in units of e−/frame. Since we are subtracting the last frame from the first, we must account for both frames. The total noise, calculated for the in-transit and out-of-transit data separately, is then

2 2 2 2 σtot = σshot + σbkg + σread. (4.6)

This traditional formulation does not assume any correlations between the number of groups. The total number of electrons collected and the associated noise is simply computed by subtracting the first group from the last group, LMF.

76 Again, in Pandeia’s MULTIACCUM formulation (Eqn. 1) all the groups in the data are used to fit a slope. The first group has tg ∗ Fout electrons, the second as 2tg ∗ Fout electrons, etc. And although each of these groups has a separate photon noise component, the noise is correlated between all of them. Therefore, the MULTIACCUM method will only be equivalent to the LMF method in the case where the flux rate, F , is much larger than the expected read noise and n = 2. In this limit Eqn 1 simplifies to:

2 σtot,MULT I ≈ tg(Finni,in + Foutni,out) (4.7)

The number of groups will be 2 in the cases where the magnitude of the target is very close to the saturation limit of the instrument mode, which will be the case for a small number of exoplanet targets. In these cases, the MULTIACCUM method and the LMF method will yield similar results, barring small correlated noise contributions from the MULTIACCUM method. However, in cases where the magnitude of the target is at least ∼ 1 magnitude greater than the saturation limit of the instrument mode, n will be much larger than 2 and the flux rate will still be much larger than the expected read noise. In this limit, the MULTIACCUM formulation simplifies to:

6 σ2 ≈ t n(F n + F n ) (4.8) tot,MULT I 5 g in i,in out i,out and the uncertainty calculated using the MULTIACCUM method will be a factor 6 ∼ 5 greater than the LMF method. To reconcile these two different noise formulations, PandExo has the capability to derive the noise using either method by simply changing a key word in the input file. However, the default noise calculation is the simplified LMF method. The final simulated transmission (−) and emission (+) spectra combines these and adds a random noise component via the equation:

Nin,λ q 2 2 zλ = 1 ± + σprop × N(µ, σ ) (4.9) Nout,λ where Nout/in,λ is the total number of photons collected out-of- and in-transit and N(µ, σ2) is a standard normal distribution with a mean µ = 0 and variance σ2 = 1.

77 The 1σ propagated error on the final spectrum, σprop is:

!2 !2 2 2 ni,out 2 ni,outNin,λ σprop = σin + σout 2 (4.10) ni,inNout,λ ni,inNout,λ

Greene et al. [2016] argue that a systematic noise floor might inhibit JWST 800

400 CH 4

0 (ppm) -400 CO Rel. Tran. Depth Depth Tran. Rel.

700 500

Noise (ppm) 300 gap between detectors 2500 /s)

- 1500 Flux Flux (e 500

3 3.5 4 4.5 5 Wavelength ( μm)

Figure 4.3. Three of the most popular PandExo output products. The top panel is the raw planet transmissions spectrum with associated errors. The middle panel is the raw noise and the bottom panel is the out of transit flux rate. Each simulation is for a NIRSpec G395H observation of a T=4000 K, Fe/H=0.0 and logg=4.0 stellar target normalized to a J=10. The single transit observation consists of a 2.7 hour in-transit observation along with a 2.7 out-of-transit baseline observation. In the top panel, the observation is binned to R=200. In the middle and bottom panel, resolving power is left at native resolving power (per pixel), with ten pixels summed in the spatial direction. The gaps seen in all three panels are the result of a gap between the detectors from 3.8172-3.9163 µm. observations to get below 20 ppm, 30 ppm, and 50 ppm, for NIRISS SOSS, NIRCam

78 grism, and MIRI LRS, respectively. This argument was based on of a comparison of the lowest noise achieved with an HST WFC3 G141 observations [Kreidberg et al., 2014b] for the NIR instruments and the lowest noise achieved with a Spitzer Si:As observation [Knutson et al., 2009] for MIRI. However, as with the actual effective saturation limit, the noise floor (σf,λ) will not be known until after commissioning and Early Release Science [Stevenson et al., 2016]. Therefore we do not adopt these same noise floors and leave it up to the observer to input their own. In contrast to Greene et al. [2016], noise floors are not added to σprop,λ in quadrature.

Instead, PandExo sets σprop,λ(σprop,λ < σf,λ) = σf,λ. This is done solely to increase the transparency of the calculation. The major final PandExo products are shown in Figure 4.3.

4.2.3 Benchmarking PandExo Performance

In the absence of JWST observations, we test the accuracy of PandExo against each instrument team’s independently written noise simulators. Each of the instrument teams used the LMF noise formulation. For completeness we show the LMF (always in blue) and the MULTIACCUM noise derivations (always in red) as well as the pure shot noise (always dashed lines). The following calculations are also all done using a stellar SED from the Phoenix Stellar Database [Husser et al., 2013] with T=4000 K, Fe/H=0.0 and, logg=4.0 normalized to a J=8, a model of WASP-12b in transmission from Madhusudhan et al. [2014], and ni,in = ni,out. The results of the comparisons are shown in Figure 4.4, 4.5, 4.6, and 4.8, and discussed in the following sections.

4.2.3.1 NIRCam

To benchmark NIRCam, we used the NIRCam F444W grism mode in conjunction with the SUBGRISM64 subarray (tg=0.34 secs). The results are shown in Figure 4.4. For a target with J=8, we selected n = 55 groups to optimize the duty cycle without saturating the detectors (eff=0.96) and ran the simulation for a single integration in transit and a single integration out of transit. Because of the high number of groups, 6 PandExo MULTIACCUM, as expected, is a factor of ∼ 5 higher than PandExo LMF (see discussion in §3) and PandExo LMF, as expected, matches within 10% with the instrument team’s results.

79 3500 Inst.Team PandExo LMF /int]) - PandExo MULTI 3000

2500

2000 λ = 30.0 ∆λ (Out of Transit Variance [e Variance Transit of (Out √ 1500 4 4.2 4.4 4.6 4.8 5.0 Wavelength ( μm)

Figure 4.4. Benchmarking results for NIRCam, which show the differences between the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is NIRCam F444W, which was run with one integration both in- and out-of-transit. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MULTIACCUM noise formulation, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively.

NIRCam is also slitless. While PandExo does not directly incorporate position angles to prevent overlapping spectra, it is important to consider this when planning observations.

4.2.3.2 NIRISS

To benchmark NIRISS, we used the NIRISS SOSS mode in conjunction with the

SUBSTRIP256 subarray (tg=5.491 secs). The results are shown in Figure 4.5. For

80 8E+04 Inst.Team PandExo LMF /2hrs]) - PandExo MULTI 7E+04 Inst. * QY

6E+04

5E+04

4E+04 λ = 30.0 ∆λ (Out of Transit Variance [e Variance Transit of (Out √ 1 1.5 2 2.5 Wavelength ( μm)

Figure 4.5. Benchmarking results for NIRISS, which show the differences between the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is NIRISS SOSS, which was run for a 4 hour integration (2 hours in- and 2 hours out-of-transit) with 2 groups per integration. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MULTIACCUM noise formulation, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively. Missing points in red depict pixels that have been saturated in PandExo. Likewise, purple diamonds depict pixels that have been saturated in the instrument team’s model. a target with J=8, only the minimum number of groups, n = 2, is possible. And even so, this results in a partial saturation of pixels at the peak of the stellar SED. NIRISS simulations were computed with a 2 hour observation in transit, and 2 hour baseline observation out of transit. Because n = 2, the MULTIACCUM (red) approximately follows the PandExo

81 LMF (blue). The omitted points in the red curve, and the purple diamonds represent saturated pixels in PandExo and the instrument team’s simulator, respectively. Both teams are saturating identical pixels.

80

70

60

50

Spatial (pixel) Spatial 40

30

500 1000 1500 2000 Dispersion (pixel)

Figure 4.6. 2D detector simulation for the NIRISS SOSS observation shown in Figure 4.5. Only the first order is depicted to enable a clear view of the saturated pixels (colored in grey). Color indicates electron rate in e− s−1. The wavelength channels with saturated pixels are flagged by PandExo but usable data may still be extractable from non-saturated regions.

PandExo produces 2-dimensional simulations of detector images and of the saturation profiles. Figure 4.6 shows the exact pixels that saturated, colored in gray. Because of NIRISS’ widely sampled PSF (23 pixels), it is likely still possible to extract a spectrum by excluding saturated pixels (a decision the observer must make). Ultimately though, if an observation only contains 2 groups, PandExo marks every wavelength bin which contains at least one saturated pixel as completely saturated, regardless of whether or not it may be possible to extract unsaturated data from that bin. PandExo will then produce the following warning statement: “There are [INSERT # OF PIXELS] saturated pixels at the end of the first group. These pixels cannot be recovered.” The NIRISS team also alerts users by flagging

82 each pixel considering saturated. By adding in these obvious warnings, users will know they are in a region of parameter space where they will, to some degree, encounter saturated pixels. An important limitation with NIRISS is contamination by field stars because it is slitless. It is crucial to run the instrument team’s contamination tool to select observing position angles and dates that minimize spectral trace contamination. It complements the instrument team’s 1D simulator 3 used for comparison with PandExo.

4.2.3.3 NIRSpec

To benchmark NIRSpec, the G395M/F290LP grism/filter was used with the the

32x2048 subarray (tg = 0.90156 secs). The results are shown in Figure 4.7. For the benchmarking, we did not optimize the duty cycle and instead selected n = 2 with a single integration out-of-transit and a single integration in-transit. The instrument team’s simulator, described in Nielsen et al. [2016], can either implement the LMF noise procedure or the "Last-Minus-Zero" (LMZ) procedure. In this strategy, the observer implements a reset-read-reset scheme with n = 1. Currently in PandExo the number of groups must be n ≥ 2. This requirement is a result of Pandeia’s requirements and will be lifted as soon as Pandeia is updated. Here, we only consider the instrument team’s LMF noise formula. As expected, these match within 10%.

4.2.3.4 MIRI

For MIRI, the LRS slitless mode was used (tg=0.159 secs). Figure 4.8 shows the results. For a J=8 target, we selected n = 10 groups to optimize the duty cycle without saturation (eff=0.81) and ran the simulation for a single integration in tran- sit and a single integration out of transit. Similar to NIRCam, the MULTIACCUM 6 PandExo results are offset by ∼ 5 because n > 2. The PandExo LMF formulation results are in good agreement with the instru- ment team’s simulations. It should be pointed out that the jagged behavior of the noise curve is solely a result of binning (λ/∆λ = 30 creates variable pixels per bin) and not an instrument systematic. Also, in both teams simulations MIRI is slightly

3http://jwst.astro.umontreal.ca/?page_id=401

83 1400 Inst.Team PandExo LMF /int]) - PandExo MULTI 1200

1000

800 λ = 30.0 ∆λ (Out of Transit Variance [e Variance Transit of (Out

√ 600 3 3.5 4 4.5 5 Wavelength ( μm)

Figure 4.7. Benchmarking results for NIRSpec, which show the differences between the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is NIRSpec G395H with the f090lp filter, which was run for a single integration in- and out-of-transit. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MULTIACCUM noise formulation, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively. dominated by read noise and background at long wavelengths (λ > 10µm) for a target with J=8. This adds another high degree of certainty to the correctness of both calculations. MIRI is also technically slitless, but the SLITLESSPRISM subarray is small enough so that overlapping spectra are not a major issue.

84 1600 Inst.Team /int]) - 1400 PandExo LMF PandExo MULTI 1200

1000

800

600

400 λ

(Out of Transit Variance [e Variance Transit of (Out 200 = 30.0

√ ∆λ

6 8 10 12 Wavelength ( μm)

Figure 4.8. Benchmarking results for MIRI, which show the differences between the two PandExo noise formulations and the instrument team’s simulations. The specific observing mode depicted is MIRI LRS slitless mode, which was run for a single integration in- and out-of-transit. In solid black is the instrument team’s noise simulation, which includes all pertinent sources of noise. In solid blue and red is PandExo’s LMF and MULTIACCUM noise formulation, respectively (see discussion in §3). In dashed blue and black is the instrument team’s and PandExo’s calculation for pure shot noise, respectively.

4.2.4 PandExo: Simulating HST Observations

In addition to simulating JWST observations, PandExo can simulate realistic un- certainties for HST/WFC3 transmission and emission spectra, optimize instrument setups, and generate scheduling requirements. Accurate spectrophotometric uncer- tainties are necessary to correctly determine the number of transit/eclipse visits required to obtain a meaningful constraint. The HST/WFC3 implementation of PandExo predicts spectrophotometric un-

85 700 Simulated WASP-43b Spectrum Published WASP-43b Spectrum 600

500

(ppm) 400

Eclipse Depth Eclipse 300

200 A 1.2 1.3 1.4 1.5 1.6 Wavelength ( μm) 1.002 1.002 Earliest Start Time Latest Start Time 1.001 1.001 1.000 1.000 0.999 0.999 0.998 0.998 0.997 0.997

Normalized Flux Normalized 0.996 0.996 B C 0.995 0.995 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 Orbital Phase Orbital Phase

Figure 4.9. Simulated observations of WASP-43b in emission using HST WFC3 G141. For the utilized instrument configuration, the simulated uncertainty is 37.6 ppm and the mean published uncertainty is 36.5±3.5 ppm [Stevenson et al., 2014]. For the same example system, panels B & C display simulated band-integrated light curves with the earliest and latest possible observation start times, respectively, that correspond to the computed minimum and maximum phase values of 0.3071 and 0.3241. certainties for any specified system by first scaling measured flux, variance, and exposure time values from previously-observed systems published in Kreidberg et al. [2014b] and Kreidberg et al. [2014a], then computing the expected rms per spectrophotometric channel per exposure, and finally estimating the transit/eclipse depth error based on the anticipated number of individual valid in- and out-of- transit exposures. The uncertainty estimates depend on the orbital properties of the system, instrument configuration, and observation duration. The code assumes Gaussian-distributed white noise and uniform uncertainties over the G102 and G141 grisms, both of which are consistent with published results [e.g. Kreidberg

86 et al., 2014b,a, Stevenson et al., 2014]. PandExo also recommends an observing strategy (best NSAMP and SAMP-SEQ values) optimized to achieve the highest duty cycle (lowest photon-noise rms) and computes an observation start range in units of orbital phase. These instrument and scheduling requirements are important factors to consider when planning proposals and observations in the Astronomer’s Proposal Tools (APT) and can be tedious to compute/optimize manually for a large number of targets. As inputs, PandExo requires the stellar H-band magnitude, full transit/eclipse duration, number of transits/eclipses, number of spectrophotometric channels, disperser type (G102 or G141), scan direction (forward or round trip), subarray size (GRISM256 or GRISM512), and schedulability (30% for small/medium programs or 100% for large programs). Optional inputs that may be optimized include the number of HST orbits per visit and WFC3’s instrument parameters (NSAMP and SAMP-SEQ). Additional inputs for the scheduling requirement include the orbital parameters (transit/eclipse depth, inclination, separation, eccentricity, longitude of periastron, and period) and the observation start window size (usually 20 – 30 minutes). Accepting a user-provided model transmission/emission spectrum, PandExo will simulate binned spectrophotometric data with realistic uncertainties and plot the results against the supplied model. As an example, Figure 4.9A depicts a model emission spectrum of WASP-43b at secondary eclipse as well as simulated and published WFC3/G141 data. For the utilized instrument configuration, the simu- lated uncertainty is 37.6 ppm and the mean published uncertainty is 36.5±3.5 ppm [Stevenson et al., 2014]. These values are consistent at 0.3σ. For the same example system, Figure 4.9B & C display simulated WFC3 light curves with the earliest and latest possible observation start times, respectively, that correspond to the computed minimum and maximum phase values of 0.3071 and 0.3241, respectively. The actual observations would commence anywhere in between these two extremes. Future work for this noise simulator includes adding functionality for the STIS G430 and G750 grisms, computing wavelength-dependent uncertainties, and exploring more sophisticated calculation methods beyond scaling values from previously-observed systems.

87 4.2.5 Conclusion

• With just under two years left until launch, the community needs a tool to help plan JWST observations

• PandExo allows all members of the community access to simulations

• It creates observation simulations of all observatory-supported time-series spectroscopy modes

• PandExo is verified and tested against other models

We introduced a new open-source Python package, called PandExo, which is used for modeling instrumental noise from each of the exoplanet transit time series exoplanet spectroscopy modes with JWST (NIRISS, NIRCam, NIRSpec and, MIRI LRS) and HST (WFC3). PandExo computes noise with two different noise formulations: 1) subtracting the last group from the first group (LMF method) and 2) independently fitting each group up the ramp (MULTIACCUM method) and accounting for correlated noise. The instrument teams’ calculations are in good agreement with PandExo’s noise calculations employing the LMF method. PandExo currently does not include any photometry modes. However, it is expected to continue evolving as we approach JWST launch date in 2018. PandExo is available for download on github4 and there is an associated github pages with full documentation and tutorials 5. The online interface is also currently available 6.

4https://github.com/natashabatalha/PandExo 5https://natashabatalha.github.io/PandExo 6https://pandexo.science.psu.edu:1111

88 Chapter 5 | Retrieving Information from the Spectra of the Planet System

Material in this chapter is published in: Batalha, Natasha E., & Line, Michael, “Information Content Analysis for Selec- tion of Optimal JWST Observing Modes for Transiting Exoplanet Atmospheres” Astronomical Journal Volume 153.4 (2017) 151

5.1 The Information Content of Transit Spectra

The James Webb Space Telescope (JWST) is equipped with eleven different ob- servation modes across eight different wavelength ranges and six different spectral resolving powers that can all be used for transmission spectroscopy of exoplanets. While several studies have sought to identify what the limits of these modes will be, in terms of exoplanet characterization [Charles Beichman et al., 2014, Barstow et al., 2015, Barstow et al., 2015, Batalha et al., 2015, Greene et al., 2016, Rocchetto et al., 2016], little work has been done to specifically identify which instrument modes or combinations of modes will be most useful for characterizing a diverse range of exoplanetary atmospheres. The most rigorous way of accomplishing this is through atmospheric retrieval, which links atmospheric models to the data in a Bayesian framework [Line et al., 2012, 2013b, 2014, 2015, Madhusudhan, 2012, Benneke and Seager, 2013, Charles Beichman et al., 2014, Waldmann et al., 2015]. For example, Barstow et al. [2015] simulated an observation with NIRSpec prism and MIRI Low Resolution Spectrometer (LRS) for four specific case studies: a hot Jupiter, a hot Neptune, GJ 1214, and Earth. For each observation they

89 performed a full retrieval analysis to determine the prospects for identifying the true atmospheric state of the planet and assessed the possible effects of star spots and stitching on the results. Greene et al. [2016] also simulated the observations of four specific planet archetypes (hot Jupiter, warm Neptune, warm sub-Neptune, cool Super-Earth) in three different combinations of modes: NIRISS Single Object Slitless Spectrograph (SOSS) only, NIRISS+NIRCam, NIRISS+NIRCam+MIRI. They concluded that spectra spanning 1-2.5µm will often provide good constraints on the atmospheric state but that in the case of cloudy or high mean molecular weight atmospheres a 1-11µm spectrum will be necessary. While both of these studies offer insights into the kind of data we will obtain from JWST, they do not yet simulate observations for a diverse instrument phase space for a wide variety of planet types, mainly driven by the computational limits of Markov chain Monte Carlo (or related) methods. Evaluating a wider range of planet types and instrument modes, however, is necessary if we want to be able to optimize our science output with JWST. To solve this problem, we use information content (IC) analysis, commonly used in studies of Earth and Solar System atmospheres. As some Earth examples, Kuai et al. [2010] used IC analysis to determine the 20 best channels from each

CO2 spectral region for retrieving the most precise CO2 abundance measurements obtained with the Orbiting Carbon Observatory. Using the channels selected from their analysis, they were able to achieve precision better than 0.1 ppm. Similarly, Saitoh et al. [2009] demonstrated that separately selecting a subset of the 15-µm

CO2 channels based on IC analysis, yielded the same precision on their retrieved results as the entire 15-µm band. IC analysis has also been used with exoplanet spectra. Line et al. [2012] quantified the increase in information content that comes from an increase in signal to noise and spectral resolving power for an arbitrary wavelength range, 1-3 µm, and for a single planet case. Most recently, Howe et al. [2017] also presented IC analysis as a way to optimize JWST observations with a simple three-parameter model (uniform temperature, uniform metallicity, and opaque cloud deck). They designed 7 different theoretical JWST programs, which range in length from observing a single mode in a single transit to observing nine modes across nine transits. They test these programs on a target list composed of 11 targets all with Teq > 958 K, which were separated into

90 bright (J<8), medium (811) targets. They find that MIRI LRS in slitless mode provides more information than in slit mode. They also found that NIRISS SOSS consistently provides the most information content for a given integration time compared with other observing modes. Finally, they conclude that IC analysis is a powerful technique that can be used for selecting JWST observing modes. Here we expand this analysis to look at a broader range of planet archetypes ranging from Teq=600-1800 K, C/O=0.55-1, [M/H]=1-100×Solar, with no cloud/- grey cloudy/haze (84 planet types), across every possible combination of JWST transit spectroscopy modes. In doing so we answer the following questions:

1. Is there a mode or combination of modes that will provide more information per unit observing time?

2. And, does that differ across different combinations of C/O ratio, [M/H], or temperature?

3. Is it better to sacrifice wavelength coverage across several different modes or to increase the precision of a single mode?

4. Is there a point where the addition of more observing modes stops tightening the constraints on the retrieved model parameters?

5.1.1 The Theory of IC Analysis

The theory of atmospheric retrieval was discussed in Chapter 1.2. We defined the

Jacobian matrix, Kij, which describes how sensitive the model is to perturbations in each state vector parameter at each wavelength position. Here, the jacobians are numerically computed with a centered-finite difference scheme. We assume that an exoplanet transit transmission spectrum can be fully de- scribed with a 4 term state vector: x = [T, C/O, [M/H], ×Rp], where T is the isothermal terminator temperature, C/O is the carbon to oxygen ratio, [M/H] is the log-metallicity relative to solar, and ×Rp is a scaling factor to the reported radius arbitrarily defined at 10 bars. This is almost certainly an overly simplistic description as there are numerous additional processes at play such as atmospheric dynamics, photochemistry, clouds etc. Certainly this analysis can be extended for arbitrary atmospheric descriptions.

91 Then, the information content, measured in bits, quantitatively describes how the state of knowledge (relative to the prior) has increased by making a measurement [Shannon and Weaver, 2002, Line et al., 2012]. It is computed as the reduction in entropy of the probability that an atmospheric state exists given a set of measurements: H = entropy(P (x)) − entropy(P (x|y)) (5.1) where T −1 P (x) ∝ e−0.5(x−xa) Sa (x−xa) (5.2)

P (x|y) ∝ e−0.5J(x) (5.3)

In (4) Sa is a n × n a priori covariance matrix, which defines the prior state of knowledge, e.g., the uncertainties on the atmospheric state vector parameters before we make a measurement. J(x) is the cost function, also defined in Chapter 1.2, which is given by:

T −1 T −1 J(x) = (y − Kx) Se (y − Kx) + (x − xa) Sa (x − xa) (5.4) where Se is the m × m data error covariance matrix. The first term in the cost function describes the data’s contribution to the state of knowledge (“chi-squared") and the second describes the contribution from the prior. Assuming Gaussian probability distributions [Rodgers, 2000] the information content can be written in terms of the posterior and prior covariance matrices:

1 H = ln(|Sˆ−1S |) (5.5) 2 a and ˆ T −1 −1 −1 S = (K Se K + Sa ) (5.6) where Sˆ is the posterior covariance matrix that describes the uncertainties and correlations of the atmospheric state vector parameters after a measurement is made. As an illustrative example relevant to JWST, if we were only interested in deciding between NIRISS, NIRCam, and MIRI to maximize the total retrievable information (let’s say: T, ×Rp, C/O, [M/H]), the goal would be to minimize the elements of Sˆ. Because there will likely be little prior knowledge on these

92 −1 T −1 parameters, Sa << K Se K, the mode covering wavelengths with the greatest sensitivity to each of the state vector parameters (maximum values of K) and the smallest error (minimum values of Se), will have the lowest values of Sˆ. The relative information content from one mode to the next under these assumptions will be largely independent of Sa in Eqn. 5.8. The mode with the highest value for H will yield the most information of the atmospheric state, and would thus be considered the optimal mode.

5.1.2 Transit Transmission Spectra Models & their Jacobians

We use the chemically-consistent transit transmission approach described in Kreid- berg et al. [2015]. Given the temperature-pressure profile of the atmosphere and the elemental abundances parametrized with metallicity, [M/H], and C/O, the model first computes the thermochemical equilibrium molecular mixing ratios (and mean molecular weight) using the publicly available Chemical Equilibrium with Applications code (CEA, McBride and Gordon [1996])1. The thermochemically derived opacity relevant mixing ratio profiles (H2O, CH4, CO, CO2, NH3,H2S,

C2H2, HCN, TiO, VO, Na, K, FeH, H2, He), temperature profile, cloud and haze proprieties, and planet bulk parameters (10 bar radius, stellar radius, planetary gravity) are then fed into a transit transmission spectrum model (Line et al. [2013a], Greene et al. [2016], Line and Parmentier [2016], using the Freedman et al. [2008, 2014] opacity database) to compute the wavelength-dependent eclipse depth at the appropriate instrument spectral resolving power. For cloudy simulations, we assume a hard gray cloud top pressure set to be at the 1 mbar pressure level, below which the transmittance is set to zero and use the “Rayleigh Haze" power law parameterization [Des Etangs et al., 2008] to describe hazes. This simplistic treatment of clouds and hazes is motivated by WFC3+STIS observations [Kreidberg et al., 2014a, Knutson et al., 2014, Sing et al., 2016], in which simple gray cloud top pressures, and power law parameterizations are sufficient to fit the data. Additionally, more complex cloud model parameterizations are not suitably motivated by the data and our generally poor understanding of the very complex coupled, 3D-dynamical-radiative-microphysics in non-Earth-like planets [e.g. Lee et al., 2015]. A 1 mbar pressure level was chosen arbitrarily so that

1https://www.grc.nasa.gov/WWW/CEAWeb/

93 the absorption features as viewed in transmission were muted, but not completely masked, as demonstrated in [Iyer et al., 2016]. While perhaps an overly simplistic cloud model, it still allows us to assess which modes are the most susceptible to a loss of information content because of the presence of clouds. We emphasize that the goal is not to identify the ideal setup for characterizing clouds and hazes, but rather the influence that clouds of some form can have on our ability to extract other useful quantities.

For all initial state vectors, x, we assume a planet radius of R=1.39 RJ and mass of M=0.59 MJ around WASP-62 (Teq=6230.0 K, F7, 1.28 R ). The WASP-62 system was chosen because it was identified as a potential target for the JWST Early Release Science [Stevenson et al., 2016] and because it has a magnitude that does not saturate the instrument modes explored here (J=9.07). Howe et al. [2017], in contrast, did explore ranges in stellar magnitudes and found that the NIRSpec prism, which not explored here, is the best mode for faint sources. We do not explore parameter space in planet radius and mass, because changes in radius will affect the spectrum uniformly in wavelength space and we assume that the mass will be known for planets we observe with JWST. Changing the star will affect the precision of the measurement because of the different SED peaks and the different stellar magnitudes. These effects will be minor compared to the effects that come from changing the planetary atmosphere parameters. Therefore, we fix the stellar type as well. We explore 7 temperatures ranging from Teq = 600-2000 K, 2 C/O ratios (0.55 and 1) and two metallicities (1 and 100×Solar). The ranges in C/O and [M/H] were chosen to represent a diverse set of chemical compositions [Madhusudhan, 2012, Kreidberg et al., 2014b]. In contrast, Howe et al. [2017] is limited to Teq >958 K and do not explore different C/O ratios. We explore three different cloud scenarios: no clouds, grey cloud, and power-law haze. For each of these 84 combinations of planet types, we compute a separate Jacobian. We choose eight representing planet types to display our results: T = 1800 K (Figure 5.1, red) and T = 600 K (Figure 5.1, blue) with C/O=0.55 and 1, and with [M/H]=1×Solar and 100×Solar. Figure 5.2 shows the Jacobian for different C/Os and [M/H]’s at T=1800 K (at a resolving power, R=100). Because each combination of C/O and [M/H] have very different Jacobians, instrument mode selection must be optimized without making assumptions about the atmospheric composition of the planet a priori.

94 C/O ratio 0.55 1

800 1200

800 400 1xSolar 400 0 0 Rel. Trans. Depth (ppm) Rel. Trans.

[M/H] 1200 1500 800 1000

100xSolar 500 400

0

Rel. Trans. Depth (ppm) Rel. Trans. 0 2 4 6 8 10 2 4 6 8 10 Wavelength (um) Wavelength (um) T=600 K T=1800 K

Figure 5.1. Eight transmission spectra forward models used for the IC analysis. Each transmission spectrum is computed for a WASP-62 type star with a planet the size and mass of WASP-62 b. Atmospheres were computed assuming chemical equilibrium with the specified temperature (red: 1800 K, blue: 600 K). Each subpanel represents a different combination of C/O and [M/H], as labeled.

5.2 Optimizing Observation Strategies for JWST: Sub- Neptunes−Hot Jupiters

Before we compute the IC of certain instrument modes, we can predict what wavelength regions are going to hold the most information. This will give us intuition for why certain modes are better suited for constraining atmospheric parameters than others. To do this, we start by computing the IC of a synthetic observation of R=100, assuming a precision of 1 ppm, across the full JWST wavelength region 1-12µm. Then, we sequentially remove each R=100 bin from the spectrum and recompute the IC. Figure 5.3 shows the loss of IC from the removal of each R=100 element for representative temperature-C/O-metallicity combinations. Regardless of temperature and chemistry, the removal of spectral elements near 1-1.5µm and 4-4.5µm always results in the greatest loss of IC. The only mode that contains both of these wavelength regions is the NIRSpec prism. The prism will undoubtedly be widely used for exoplanet spectroscopy however, it has a high saturation limit (J<10.5) and a low spectral resolving power of R∼100. We constrain our future discussion to the modes shown in Table 5.1

95 C/O ratio 0.55 1

20 1.5 15 1.0 ,C/O,T,M/H] p

R 10 1xSolar x [

∂ 0.5 /

5 Z ∂ [M/H] 1.2 3

2

,C/O,T,M/H] 0.8 p R x [ 100xSolar

∂ 1 /

Z 0.4 ∂ 0 2 4 6 8 10 2 4 6 8 10 Wavelength (um) Wavelength (um)

Temperature [M/H] C/O Planet Radius

Figure 5.2. The elements of the Jacobian, described in Chapter 1 Eqn. 1.6, for the T=1800 K transmission spectrum forward models (Zλ) cases shown in Fig 5.1. Each Jacobian is binned to R=100.

Table 5.1. Instrument modes for IC Analysis Instrument Filter Wavelength Range Spectral Resolving Power (µm) NIRISS SOSS 0.6-2.8 400-1400 NIRSpec G140M F070LP 0.9-1.8 600-1400 NIRSpec G235M F170LP 1.70-3.0 600-1400 NIRSpec G395M F290LP 2.9-5 600-1400 NIRCam Grism F322W2 2.5-4.0 1000-1770 NIRCam Grism F444W 3.9-5.0 1770-2200 MIRI LRS 5.0-14 100

because we assume that the observer will usually pick the prism for transmission spectroscopy if their target is dim enough and if a low spectral resolving power is sufficient for retrieving their desired atmospheric parameters. Modes that only contain 1-1.5µm include NIRSpec G140M/H, and NIRISS SOSS. Modes that only contain 4-4.5µm are NIRCam F444, and NIRSpec G395M/H. While this is informative, it does not directly dictate which modes hold the highest IC. Next, we compute, for each individual mode, the increase in information content

96 C/O ratio 0.55 1

0

-0.01

-0.02 1xSolar -0.03 T = 1800 K T = 600 K -0.04

[M/H] 0

-0.01

-0.02 IC (bits) IC (bits)

100xSolar -0.03 NIRSpec Prism NIRSpec Prism g140 g235 g395 g140 g235 g395 -0.04 NIRISS SOSS NIRCam f322 f444 MIRI LRS NIRISS SOSS NIRCam f322 f444 MIRI LRS 2 4 6 8 10 2 4 6 8 10 Wavelength (um) Wavelength (um) Figure 5.3. Loss of information content as a result of the removal of a R=100 element of an observation of a spectrum with a uniform precision of 1 ppm. Each panel contains a different [M/H] and C/O, equivalent to Fig 5.1. Also as with Figure 5.1, red lines are for a simulation of a target with T=1800 K and blue lines are for a simulation of a target with T=600 K. Shaded boxes in bottom panels shows the available transit time spectroscopy modes on board JWST. as a function of increasing signal-to-noise.

5.2.1 Single Observing Mode Analysis

Computing the increase in IC as a function of precision on the planet spectrum will tell us how much information we are losing for each instrument mode as the precision on the spectrum decreases. This decrease is usually the result of less observing time, a dimmer target, stellar variability or instrument systematics/noise floors. For each calculation we assumed there were constant errors across the wavelength range of the instrument mode. This assumption is only used in the section in order to explore the exact relationship between the error on the retrieved parameters and the error on a spectrum. In reality, all JWST instruments will have highly wavelength-dependent throughputs with sharply declining edges. To minimize the effects of this on this particular analysis we do not use the edges of the observation bands where the noise increases sharply. Lastly, the conclusions made in this section are later verified by full noise simulations. Each panel in Figure 5.4 shows this function for a different chemical configuration

97 T=1800 K T=600 K C/O ratio 0.55 1 0.55 1 40 30

35 25 30 20 1xSolar 25 15 20

15 10

[M/H] 40 30

35 25 30 20

IC (bits)25 IC (bits) 100xSolar 15 20

15 10 10 50 100 10 50 100 1050 100 10 50 100 Error on Spectrum (ppm) Error on Spectrum (ppm)

NIRISS: NIRSpec: NIRCam: MIRI: SOSS G140M F322W LRS G235M F444W G395M

Figure 5.4. The information content as the precision on a spectrum increases. The colored lines in each panel represents a different observing mode. Each panel represents a different combination of [M/H] and C/O for a T=1800 K (left) or T=600 K (right) target. Noise simulations were not computed for these calculations. Instead, the "error on spectrum" dictates a fixed precision over the wavelength region of the particular observing mode. Transparent lines show, for the same observation mode, the loss in information content with the addition of a grey cloud at 1 millibar. and temperature. The opaque lines are calculations with no clouds and the transparent lines are calculations with a grey cloud at 1 mbar. Interpreting these plots is done best by picking a fixed IC and looking to see what precision each mode needs in order to attain that level of IC. For example, for 1×Solar, C/O=0.55, the observer needs a high precision of 7 ppm with NIRCam F322 to achieve an IC=25 bits. If the observer were to choose NIRISS SOSS instead, to achieve IC=25 bits, they would only need to achieve a precision of 30 ppm. In all four temperature, chemical configurations, and cloud assumptions, NIRISS SOSS (purple) has the highest IC and NIRCam F322W2, and F444W (green) have

98 the lowest. The simplest way to understand this is by analyzing Figure 5.2. NIRISS SOSS covers a large wavelength space specifically over points that hold a lot of information (strong absorption features). The latter statement is especially important. MIRI LRS, for example, covers an even larger wavelength space but over points that hold less information than those in NIRISS SOSS (weaker absorption features). Because of MIRI LRS’ larger wavelength coverage, it holds the second highest IC content in most temperature/chemistry configurations. We discuss these results further in the §5. Adding in clouds (transparent lines) decreases the total IC of each mode and in some cases, changes their relative ranking. In general, shorter wavelength modes lose more IC because of clouds as opposed to than longer wavelength modes. This is clearly seen in the case of Figure 5.4 T=1800 K, C/O=1 & 1×Solar. NIRSpec G140M/H loses up to ∼10 bits of information with the addition of clouds whereas the other modes only lose ∼5 bits. This is as expected, a grey opacity source will strongly mute absorption features at shorter wavelengths (< 2µm), while longer wavelengths will be less affected. NIRSpec G140M/H covers 1-2 µm. NIRISS SOSS is less susceptible to this loss of IC because of its extended coverage out to 2.8 µm. Although it is useful to compute the IC of each mode for generic mode comparison purposes, it does not directly tell us what the expected credible interval on the posterior distribuition of the desired parameters (T, C/O, [M/H]) will be (hereon refered to as the ECI). For this we can look at the diagonal elements of the matrix Sˆ, Eqn. 5.8, which we show below are an accurate enough description of the parameter uncertainties .

5.2.2 Validation of Covariance Matrix Approximation Against a Full Retrieval

A potential issue in our analysis is the assumption of the Gaussianaity of the posterior, described via the covariance matrix Sˆ (e.g., see Benneke and Seager [2012] for a discussion). Non-gaussianaity can, for instance, happen when a parameter is not constrained other than an upper limit. The covariance matrix approximation within the optimal estimation framework would try to approximate such upper limits with a Gaussian, possibly over, or underestimating the uncertainties. However, here we validate this assumption in our atmospheric parametrization and data

99 regimes by performing full retrievals (e.g., Benneke and Seager [2013], Line et al. [2013b], Waldmann et al. [2015], Line and Parmentier [2016]) using PyMultiNest [Buchner, 2016] on select cases. PyMultiNest is a Pythonic Bayesian inference and visualization for the MultiNest Nested Sampling Algorithm [Feroz et al., 2009] that computes the posterior distribution function. It has been validated accross several disciplines (e.g. X-ray spectral analysis [Buchner et al., 2014]; transit transmission spectral of exoplanets [Kreidberg et al., 2014b]; galactic astronomy [Carton et al., 2017]). The results are summarized in Figure 5.5. The circles in Figure 5.5 show the expected precision on the parameters as a result of the PyMultiNest retrieval described above. They indicate that the covariance matrix estimated error analysis and the full retrieval generally agree for the relevant parameters over a wide range of spectral uncertainties. As an illustrative example, the curves in Figure 5.5 show the relationship between the ECI of the parametrs, the precision on the data, and information content for NIRISS SOSS for the case of T=1800 K, C/O=0.55 & 1×Solar (red) and T=600 K, C/O=1 & 100×Solar (blue). For both cases, a loss in 10 bits of information translates to a factor of ∼10 increase in the ECI on the atmospheric parameters (i.e. for T=1800 K, σT = 4 with 30 bits of IC and σT = 40 with 20 bits of of IC). This result can be readily understood by inspecting Eqn. 5.7. If uncertainties on all parameters decrease by 10, then the diagonal elements of Sˆ decrease by a factor of 100. The determinant of the 4×4 Sˆ matrix then increases by a factor of 108, where one half of the natural log of 108 is 9. As another reference point, an IC difference of ∼3 could correspond to a factor ∼ 2 improvement in the ECI of each of the 4 parameters. Also shown in Figure 5.5 (with asterisks) are PyMultiNest retrievals for the case of an observation with NIRISS SOSS and NIRSpec G395M. This reveals that expanding wavelength coverage to two observation modes results in a lower error than two observations in the same mode. The error on the temperature of a 30ppm observation with NIRISS and NIRSpec G395M (horizontal line) is less than the q error on the temperature of a 30/ (2)ppm (vertical line) observation with only q NIRISS SOSS. Additionally, a factor of (2) improvement in the noise is only valid in the case of little systematic noise. In the §5.2.5.1 we explore this further.

100 Information Content (bits) 32 30 28 26 24 22 20 18 26 24 22 20 18 16

102 2 transits @ 30ppm

1 10 2 modes ECI T (K) T ECI @ 30ppm

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ECI logECI [M/H] 10-2

100

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-2 ECI logECI C/O 10

10 50 100 150 Precision on Spectrum (ppm)

Figure 5.5. Here, ECI is the expected credible interval for the posterior distribution of the indicated parameter. The red and blue curves show the derived errors from the IC analysis on the state parameters of interest for an observation with only NIRISS of a planet with 1) T=1800 K, C/O=0.55 and [M/H]=1×Solar, and no cloud and 2) T=600 K, C/O=1 and [M/H]=100×Solar, and no cloud. The ECI on each parameter were calculated using Eqn. 5.8. The top x axis shows IC content (taken from y axis in Figure 5.4). Circles show the expected precision on the parameters as a result of a multinest retrieval scheme. Asterisks show the expected precision the parameters as a result of using a multinest retrieval scheme on a combined NIRISS & NIRSpec G395M observation.

5.2.3 Two Observing Mode Analysis

Not counting modes with overlapping wavelength space, there are approximately 8!∼40,320 combinations of modes on board JWST for exoplanet spectroscopy alone. In order to narrow down these combinations, we first focus on only two mode comparisons in transmission, for the two temperature cases. Instead of fixing the noise as was done in §5.2, we compute full noise models for a single transit in each mode. The IC maps shown in Figs. 5.6 & 5.7 can be easily interpreted by finding

101 C/O ratio 0.55 1

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lrs lrs niriss niriss g140m g235m g395m f322w f444w g140m g235m g395m f322w f444w Original Mode Original Mode Figure 5.6. Information content maps (in bits) for the T=1800 K planet cases as shown in Figure 5.1 with the addition of a grey cloud at 1 millibar. Rows are different [M/H]’s and columns are different C/O’s. Information content is measured in bits and the bins used for each color map is shown next to each panel. Note that each panel has a different color scale. Diagonal elements are two transits in one mode. Observation modes which will maximize observers chances of obtaining the true atmospheric state appear as dark squares in all four panels. the combination of modes which, regardless of C/O or [M/H], give the highest information content (i.e. common dark regions in all four panels). We only show the maps for the cases where a 1 mbar cloud has been added because for most combination of modes, the cloudy and cloud-free cases are similar. For hotter targets (T=1800 K, Figure 5.6), the combination of NIRISS and NIRSpec G395M/H yields the highest information content regardless of temperature, C/O and [M/H]. Other combinations of modes such as 2 transits with NIRISS SOSS, NIRSpec G140M/H+G395M/H, and NIRSpec G140M/H+G235M/H also yield high IC observations. The combinations with the lowest IC are 2 transits with MIRI LRS, NIRCam F444, or NIRCam F322. The difference between the highest IC combination and

102 C/O ratio 0.55 1

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lrs lrs niriss niriss g140m g235m g395m f322w f444w g140m g235m g395m f322w f444w Original Mode Original Mode

Figure 5.7. Information content maps (in bits) for the same planet as shown in Figure 5.1 but with T=600 K and a grey cloud at 1 millibar. Rows are different [M/H]’s and columns are different C/O’s. Information content is measured in bits and the bins used for each color map is shown next to each panel. Note that each panel has a different color scale. Diagonal elements are two transits in one mode. Observation modes which will maximize observers chances of obtaining the true atmospheric state appear as dark squares in all four panels. the lowest IC combination is ∼4 bits. From Figure 5.5, we can estimate this to be about a factor in ∼3 degradation in the ECI on T, C/O, and [M/H]. Meaning, an observation with NIRISS and NIRSpec G395M/H will help constrain these parameters ∼3 times better than an observation of two transits with MIRI LRS. For cooler targets (T=600 K, Figure 5.7), the results are similar. NIRISS and NIRSpec G395M/H have the highest IC while two transits with MIRI LRS, or NIRCam F444 have the lowest. The difference, in bits, between the highest IC and the lowest IC mode is also ∼4 bits. Therefore, as with the T=1800 K target, it is predicted that this difference will cause a factor in ∼3 degradation in the ECI on T, C/O, and [M/H].

103 logFe/H=2, logC/O=0 T = 1800 K 50 logFe/H=2, logC/O=-0.26 40 logFe/H=0, logC/O=0 30 logFe/H=0, logC/O=-0.26 ECI on T (K) T onECI 20

10

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G140 G140 G140 G140 G140 G140 G140 NIRISS NIRISS NIRISS NIRISS NIRISS NIRISS G235 G235 G235 G235 G235 G395 G395 G395 G395 F322 F322 F322 F444 F444 MIRI-LRS

Figure 5.8. Here we show how the ECI of the state parameters decrease with the addition of more observation modes. Like the others, this is for the planet system WASP-62b with Teq = 1800 K. The lines represent the four combinations of C/O = 1 or 0.55 and [M/H]=1 or 100×Solar. No clouds have been added to these calculations.

5.2.4 Multiple Observing Mode Analysis

Beyond two modes, one could pose the question of whether or not adding a third or fourth mode would help tighten the constraint on the atmospheric state. Three modes (NIRISS, NIRSpec G395M/H, & MIRI LRS) will get you across the entire JWST spectroscopic range, 1-12µm. However, it might be the case that a spectrum from 1-5µm will give you the same constraints as a spectrum from 1-12µm, because of a saturation in information. If this is the case, it might be more beneficial to increase precision in one mode. To test this, we sequentially add a mode and compute the expected errors on each of the state vector parameters. Figs. 5.8 & 5.9 show these results for all chemical configurations and T=1800 K and 600 K, respectively. Starting out, an observation with just NIRSpec G140M/H has

104 log [M/H]=2, logC/O=0 80 T = 600 K log [M/H]=2, logC/O=-0.26 60 log [M/H]=0, logC/O=0 log [M/H]=0, logC/O=-0.26 40 ECI on T (K) T onECI

20

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G140 G140 G140 G140 G140 G140 G140 NIRISS NIRISS NIRISS NIRISS NIRISS NIRISS G235 G235 G235 G235 G235 G395 G395 G395 G395 F322 F322 F322 F444 F444 MIRI-LRS

Figure 5.9. Here we show how the ECI of the state parameters tightens with the addition of more observation modes. Like the others, this is for the planet system WASP-62b with Teq = 600 K. The lines represent the four combinations of C/O = 1 or 0.55 and [M/H]=1 or 100×Solar. No clouds have been added to these calculations. relatively poor constraints (for reference, this is equivalent in wavelength space to an observation with the Hubble Space Telescope’s WFC3). With the addition of NIRISS SOSS, which effectively improves the precision of the 1-1.7µm region and adds the 1.7-2.7µm region, the constraints on T, [M/H] and C/O improve by nearly a factor of 2. Adding an observation with NIRSpec G235M/H does not significantly add any new wavelength space, but effectively increases the precision of the observation in the 1.7-3µm region. This results in only a small improvement of the constraints on the atmospheric state. Next, adding in NIRSpec G395M/H effectively expands the wavelength coverage of the observation out to 5µm and again, in some cases, nearly tightens the constraints of the atmospheric state by a factor of 2. After the addition of NIRSpec G395M/H, adding in NIRCam F322, and F444 does not help because even though

105 the precision of the observation increases in the 3-5µm region, no more wavelength coverage is being added. Lastly, the addition of an observation with MIRI LRS does not result in an improvement in the constraint of the atmospheric state. This is unintuitive because the wavelength region is increased out to 12µm. In this case, we have already maximized the total retrievable information from the combined observation of NIRISS SOSS and NIRSpec G395M/H. These results are similar to those found in Greene et al. [2016]: Adding MIRI LRS did not significantly improve the molecular abundance constraints for transit transmission spectra. However, observing targets in emission with LRS could significantly improve observations of targets with cloudy transmission spectra [Morley et al., 2015]. We further discuss this in §5.2.5.

5.2.5 Implications for Planning Observagtions

5.2.5.1 Why Two Modes Remain Superior

In transmission, regardless of temperature, C/O, [M/H] or presence of a cloud, a combination of NIRISS+NIRSpec G395M/H yields the highest information content. Intuitively this makes sense because the combination of the two give relatively broad (1-5 µm) wavelength coverage, more so than other combinations. These wavelength regions are the locations of the spectrum with the highest rate of change with respect to the state vector parameters (the elements of the Jacobian are the highest, Fig 5.2). This is because these wavelengths cover the prominent absorption features of the metallicity and C/O dependent species (e.g., measuring both oxygen and carbon-bearing compounds). The key 4.5 µm region probes CO and CO2 which are powerful metallicity indicators (e.g., Moses et al. [2012]). NIRCam F322W2 and F444W do not yield high information content results because F444W covers too small of a wavelength region to be useful on its own and

F322W cannot capture the presence or absence of carbon based species (CO2 or CO). If the observer knew a priori that a carbon species would be present, it could help constrain [M/H] and C/O to get high spectral resolving power observations in that region–especially since NIRSpec G395M’s photon-to-electron conversion efficiency starts to drop off after 4µm. Noise simulations will have to be done on a case by case basis to assess this trade off. Because the highest information contents per unit observing time are a result

106 of the broad wavelength coverage and not necessarily the precision, the observer could swap out the combination of NIRISS+G395M/H for the NIRSpec prism. The NIRSpec prism was not explored in this paper because it has a very high saturation limit (J< 10.5). Therefore, some of the best JWST targets will saturate the NIRSpec prism. We conclude that if the target is dim enough, it should be observed with the prism instead of NIRISS SOSS and NIRSpec G395M/H.

5.2.5.2 Wavelength Coverage Versus Precision

We can revisit Eqn. 5.7 to gain analytical insights into the question of increased precision versus wavelength coverage. The information content is related to the −1 measurement error covariance matrix by, H ∝ ln |Se |. If we were to both expand wavelength coverage, by increasing the number of data points in our spectrum to N, and reduce the measurement error by some factor, f, the new information content would go as, H ∝ N ln 1 . A second transit in the same mode would only new f 2√ increase the precision by at most 2, which would increase the IC by ln 2. This would be less in the case of significant systematic noise. According to this simplistic argument, doubling the number of points, could have a larger impact on the total IC. This is shown in Figs. 5.7 and 5.8. When we add a mode in overlapping wavelength space (effectively increasing the precision of the measurement), there is less of a decrease on the overal ECI, as opposed to the decrease in ECI that you get from adding a mode in new wavelength space.

5.2.5.3 Saturation of Information

The argument of improving parameter constraints by increasing wavelength coverage seems to break down for MIRI LRS, shown in Figs. 5.7 and 5.8. In these cases, we are expanding wavelength coverage but are seeing no improvement in the errors on the state vector parameters. This is because the 1-5 µm coverage is already enough to cover the prominent metallicity and C/O sensitive absorbers. If this were always true, MIRI LRS would never be useful, if combined with NIRISS and NIRSpec G395M. However, there are several important key modeling aspects not included in this investigation. Firstly, we have not accounted for disequilibrium chemistry (vertical mixing and photochemistry). This will affect planets below 1200K. As an example, the strong

107 9-12 µm ammonia feature is very sensitive to the strength of vertical mixing, as demonstrated by brown dwarf observations (e.g., Saumon et al. [2006]). Similarly, obtaining a second methane band at 7.6 µm will also provide further leverage on the strength of vertical mixing for planets with a carbon reservoir transitioning between CO and methane. Furthermore, methane derived photochemical products like C2H2,C2H6, and C2H4 all have multiple bands long-wards of 5 µm. These longer wavelengths may be diagnostic of photochemistry (e.g., Moses et al. [2011]). Second, high temperature condensate clouds might exist in super-hot Jupiter atmospheres [Wakeford et al., 2017]. The vibrational-mode absorption features of these condensate clouds are only detectable in the 5-14µm region [Wakeford and Sing, 2015, Mollière et al., 2016]. Shorter wavelengths are only sensitive to the Mie/Rayleigh scattering slopes/magnitudes of these condensates. The composition at these shorter wavelengths is in turn degenerate with the particle sizes. Therefore, if this is true, MIRI LRS will be crucial for understanding cloud properties by uniquely identifying their spectral signatures. Lastly, emission spectroscopy of will rely heavily on MIRI LRS, especially the coolest planets (e.g, Greene et al. [2016]). The IC analysis for emission spectroscopy is currently being explored as future work.

5.2.6 Conclusion

• Information content theory can optimize exoplanet observations

• Observations of exoplanets should usually maximize wavelength coverage

• NIRISS SOSS yields the highest information observations regardless of planet parameters

• Modes that cover 1-5 µm with only 1-2 transits instruments are favorable.

Using a transmission spectra model, we first computed how sensitive the trans- mission spectra of different planetary atmospheres are to small changes in temper- ature, C/O, [M/H], and ×Rp. These sensitivities make up the Jacobian, which allowed us to compute the IC of each spectrum. The IC, measured in bits, de- scribes how the state of knowledge (relative to the prior) has increased by making a measurement. Therefore, we then sought to find observing schemes that were agnostic to unknown a priori knowledge of the atmospheric state.

108 First, using only single mode combinations, we computed the IC content as a function of spectral precision on a spectrum for all the JWST exoplanet spec- troscopy modes within NIRISS, NIRSpec, NIRCam, and MIRI. We also estimated the errors expected on each of the atmospheric state vector parameters by com- puting the posterior covariance matrix. We validated this approach, which makes the assumption of Gaussianity of the posterior, against full Monte Carlo based retrievals. We then extended our IC analysis to combinations of two modes. Finally, we explored the effect of adding more than two modes. Our major conclusions summarized below are true for transmission spectra only: 1. A single observation with NIRISS always yields the highest IC content spectra with the tightest constraints, regardless of temperature, C/O, [M/H], cloud effects, or precision. 2. A single observation with NIRSpec G140M/H is most susceptible to a loss of information via cloud coverage and should generally not be used alone. 3. Generally speaking, expanding wavelength coverage will result in more tightly constrained parameters than observing in the same mode twice. 4. An observation with both NIRISS and NIRSpec G395M/H always yields the highest IC content spectra with the tightest constraints, regardless of temperature, C/O, [M/H], cloud effects, or precision. NIRSpec prism, which covers the same wavelength space, could also be used in lieu of NIRISS and NIRSpec G395M/H, if the target is dim enough, J > 10.5. 5. Observations that use more than two modes should be carefully analyzed because sometimes the addition of a third mode results in no gain of information. In these cases, higher precision (more transits) in the original two modes would be more favorable. JWST is scheduled to launch in 2018 October. After commissioning we will have a much better idea of what the inherent systematics are for each of the exoplanet spectroscopy modes. However, proposals for early release science are due in 2017 August. Therefore, until our knowledge of instruments improves, we can use powerful IC analyses to design optimized observing strategies for future proposals.

109 5.3 Optimizing Observation Strategies for JWST: Earths & Super-Earths

While our previous work focused on a wide range of atmospheric parameter space, it entirely neglected atmospheres with high mean molecular weights. As discussed in Chapter 1, observing Earths and super-Earths are challenging because: 1) the mean molecular weight, µ, is completely unconstrained (assumption of µ ∼ 2.3 is no longer valid), 2) diatomic background gases such as H2 and N2, referred to as spectrally inactive gases, do not exhibit strong vibrational absorption bands and, 3) low-mass planets tend to not have precise mass measurements. Additionally, creating transit transmission spectral models for atmospheres that are entirely unconstrained, and then attempting to postulate whether or not such atmospheres are “detectable” is an interesting problem. For the study of hot low mean molecular weight atmospheres, the assumption of chemical equilibrium allows a wide (and useful) parameter space in chemistry to be explored relatively quickly. This is not possible for temperate, high-mean molecular weight atmospheres that are dominated by photochemistry and vertical mixing. Therefore, exactly what kind of atmosphere to model when determining the “detectability” of low-mass planets is not entirely clear. One technique is to define a detectability criteria and explore a range in temper- ature and bulk composition (usually 100% H2O). For example, Batalha et al. [2015] determined how many transits would be required to detect H2O at a S/N=15 in

100% H2O atmospheres ranging in temperature from 400 K to 1000 K. Because Earth-like planets are of great interest, similar detectability criteria have been es- tablished for gases such as ozone with chemically consistent Earth-like atmospheres. For example, Schwieterman et al. [2016] determined that 10 transits could yield a detection of O3 at S/N=3 in the atmosphere of an Earth-like planet orbiting GJ 876. Water-rich and Earth-like atmospheres offer informative lower and upper limits, respectively, on the amount of time needed to solely detect absorption features. The limits are a result of differences in mean molecular weight (14 for water rich and 28 for Earth-like), which impact the scale height. We emphasize that differences in the specific concentration of the absorbers does not define these limits unless

110 1.0 Cloud free

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0.01 mbar 4e-4 4e-3 4e-2 4e-1 H2O Volume Mixing Ratio

Figure 5.10. Curves show the relative line strengths of H2O absorption as a function of H2O volume mixing ratio. Line strengths have been normalized so that maximum is 1, which is why the maximum line strength on the y axis is at unity. All atmospheres are composed of a H2-H2O mixture. Each curve is computed for a different grey cloud deck at the pressure level indicated. Figure is adapted from [Kempton et al., 2016]. the concentration becomes high enough to impact the mean molecular weight. Figure 5.10 demonstrates this by illustrating line strength as a function of water composition. The line strength begins to decrease at 4×10−3 because there is sufficient water in the atmosphere to increase the mean molecular weight. Simply determining the amount of time needed to detect an absorption feature does not fully capture the difficulties in constraining the properties contained within that feature. Barstow et al. [2015] and Greene et al. [2016] used sophisticated retrieval schemes to explore Earth-like and H2O-rich atmospheres, respectively. Both authors used different tactics, though. Barstow et al. [2015] modeled a fiducial planet system (parent star, planet size, atmosphere, etc), whereas Greene et al. [2016] chose a real planet system (K2-3 b) and gave it a fiducial atmosphere. The former strategy attempts to generally understand the constraints we might expect from low-mass planets, whereas the latter attempts to depict the approximate time needed for a specific target. Here, the goal is to investigate optimal observing strategies for low-mass plan- ets. In order to do so, we choose TRAPPIST-1 and LHS 1140 as a case study. TRAPPIST-1 contains seven Earth-sized planets transiting a 2550 K star at 12.1

111 pc [Gillon et al., 2016, 2017]. At least three of the seven planets are in the nominal “habitable zone” [Kopparapu et al., 2013], giving TRAPPIST-1 a strong potential for interesting comparative planetology studies. Already de Wit et al. [2016] observed TRAPPIST-1 b & c with HST, and ruled out a hydrogen-rich atmosphere for both planets at 10-sigma. Atmospheric observations of LHS 1140b have not been made but are expected soon. With regards to JWST, Barstow and Irwin [2016] discussed the possibility of observing b, c, & d and concluded that if modern-day Earth levels of ozone were present, b’s atmosphere could be detected with 60 transits, and c & d’s atmospheres could be detected with 30 transits each2. While Barstow and Irwin [2016] offer a good starting point for understanding how to most effectively observe habitable Earth-sized planets with JWST, several questions remained unanswered:

1. Are there specific observing strategies that have not yet been approved but that could drastically improve the precision of our observations?

2. When selecting observing modes for small planets, if NIRSpec Prism (1-5µm at R=100) is not available, is it better to devote all available transits to a single mode or split the transits among two modes at the cost of higher noise in each?

3. How will the effect of poor mass constraints inhibit our ability to accurately constrain the atmospheres of super-Earth/Earth-like planets?

In the following, we focus on answering these three outstanding questions. Addition- ally, from the conclusions of Barstow and Irwin [2016] and others [e.g. Kaltenegger and Traub, 2009, Batalha et al., 2015, Greene et al., 2016], it is known that super- Earths/Earth-like atmospheres will require the co-addition of several dozen transit simulations. TRAPPIST-1 and LHS-1140 have a total of 99 and 94 days in JWST’s viewing zone during Cycle 1, respectively. For LHS 1140 b, this corresponds to 3 transit visits per year. For TRAPPIST-1 habitable zone planets, this corresponds to 24, 16 and 10 visits for planets d, e and f. With these observing constraints we can determine exactly what our gains in knowledge will be after each cycle.

2This is slightly misleading as in the paper they point out that 30 and 60 transits, respectively, are needed in both NIRSpec Prism and MIRI LRS. This means that these numbers are too small by a factor of 2.

112 In the following §5.3.1, we look at the expected noise per transit for each system by considering various observing strategies not yet discussed in the literature. Then, in §5.3.2 we describe our modeling scheme. In §5.3.3 we assess the information content of super-Earth/Earth-size planet atmospheres and quantify the expected gain in knowledge as a function of JWST observing cycles.

5.3.1 Noise models & Observing Strategies

The approximate noise expected on each observation is usually dominated by the photon rate from the parent star (Chapter 4, Eqn. 4.14). Therefore, before modeling the transit transmission spectra for individual planets, we can compute the potential noise sources from each instrument mode for TRAPPIST-1. To compute these sources we use PandExo, described in Chapter 4. PandExo relies on Pandeia, Space Telescope Science Institute’s Exposure Time Calculator to compute throughputs, realistic point spread functions and other instrumental effects. Both PandExo and Pandeia have been vetted against all of the instrument team’s individual noise simulators. PandExo first simulates a single 2-dimensional detector image with 2 groups in order to determine the maximum number of groups allowed in a single integration before saturation. For time series spectroscopy a group is composed of a single frame, the result of digitizing all the pixels within the detector’s subarray. Each integration also consists of a reset frame. When the reset frame is taken is dependent on the read mode. Currently, in the Astronomer’s Proposal Tool3 there is one standard read mode for all the instruments. One additional read mode is slated to be available in Cycle 1 and one more is being considered but is still not approved. The three read modes are outlined below:

1. Currently supported: RESET-READ-READ... In this mode the reset frame is taken first, followed by a series of groups. The minimum number of groups allowed in this mode is n = 2 and the groups are related to the duty cycle n−1 (i.e. efficiency) by d = n+1 . Therefore, a bright target would be limited to n = 2 with an efficiency of 33%. As the brightness decreases, the efficiency increases. 3http://www.stsci.edu/hst/proposing/apt

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100 100

Noise on Spectrum (PPM) Noiseon 6 8 10 12 14 6 8 10 12 14 2MASS J 8 μm 1.4 μm 2.5 μm NIRSpec G140H NIRSpec G235H 1000 NIRISS NIRISS NIRSpec Prism NIRSpec Prism

3.3 μm 4.5 μm MIRI LRS NIRSpec G395H 100 NIRSpec G395H NIRCam F322W2 NIRCam F444W NIRSpec Prism

Noise on Spectrum (PPM) Noiseon NIRSpec Prism 7 8 9 10 11 12 13 14 2MASS J

Figure 5.11. Curves show the noise on the planet spectrum as a function of 2MASS J magnitude at various wavelengths for TRAPPIST-1 (i.e. parent star with T=2550K from Phoenix Stellar Atlas). TRAPPIST-1’s true magnitude (11.3) is shown as a vertical dashed line. Each simulated observation is composed of 1 hour in-transit and 1 hour out- of-transit. Colored opaque lines are for the RESET-READ-READ mode and transparent lines are for the READ-READ-RESET mode. Colors correspond to the different observing modes, as indicated in the label. All simulations are binned to R=100.

2. Supported Cycle 1: RESET-READ This mode consists of a single reset frame and a single group, taken in that order. Therefore, the efficiency is fixed at 50%. This mode is specifically designed for bright targets that are not read noise limited. [see Nielsen et al., 2016, for more information]

3. Not yet supported: READ-READ-RESET This mode is similar to the first but the reset frame is taken at the end of the integration. Doing so allows the detector to collect photons while digitizing pixels. It results in 100% efficiency at n = 2.

Previous studies of exoplanet atmospheres have only included the first of these

114 three read modes [e.g. Greene et al., 2016]. For targets that are fainter than the observing mode’s saturation limit, this is a good strategy but for bright targets, this results in relatively higher noise. Figure 5.11 shows the noise levels at R=100 for each mode as a function of 2MASS J magnitude at key wavelengths (H2O at 1.4 µm & 2.5 µm, CH4 at 3.3 µm, CO/CO2 at ∼4.5µm). The opaque lines correspond to the currently-supported mode (#1 in the list), and the transparent lines correspond to the not-yet-supported mode (#3 in the list). For each mode, the noise is roughly log-linear with magnitude until ∼1-2 magnitudes fainter than the saturation limit. Even though NIRSpec Prism’s saturation point is J∼=10.5 and TRAPPIST-1’s magnitude is J=11.3, the lower efficiency of RESET-READ-READ results in ∼100 ppm increase in noise. Figure 5.11 is also useful for comparing mode performance at different wave- lengths. We emphasize though, that these noise simulations do not include noise floors. For example, NIRISS SOSS’ 2nd order contamination might increase the noise at 2.5 µm. The true result of this will not be known until after telescope commissioning and/or Early Release Science. Nevertheless, we can draw useful conclusions from these simulations. At wavelengths less than 2.5 µm, the NIRSpec Prism attains lower noise levels than other available instruments at identical 2MASS J. NIRSpec Prism becomes less favorable at higher wavelengths because the stellar SED begins to drop off and because the efficiency of the observation is limited by saturation at the lower wavelengths. One strategy that has been proposed to combat NIRSpec Prism’s drop in precision at longer wavelengths, is to partially or fully saturate the detector. The process is shown in Figure 5.12 for the TRAPPIST-1 system, which has a peak in SED at 1.3 µm and 1.7 µm. Similar to HST, JWST acquires sampled up the ramp data and returns a data product with every group. Therefore, unless the observation is saturated at the end of the second group, data at every wavelength is in theory, extractable. For example, TRAPPIST-1 saturates the NIRSpec Prism after the third group. 3−1 Therefore, an observation with no saturation leads to 3+1 ∼ 0.50 observing efficiency across the entire detector. If the number of groups is doubled to 6 and the detector 6−1 is overexpose, the efficiency in the non-saturated areas is increased to 6+1 ∼ 0.71 3−1 and the efficiency in the saturated areas to is decreased to 6+1 ∼ 0.29. Saturating

115 1) Data Acquisition 2) Detector Simulations: 3

6

group #: ……3……..6..…8…10………14 8

Integration 10

1 2 3 4 5 Wavelength (μm) 3) Variable Group Data Extraction Groups Used: 14 5 3 7 9 7 9 14 300 0 Depth (ppm) Trans. -300 5 1 2 3 4 5 Wavelength (μm)

Figure 5.12. During data acquisition, JWST acquires sampled up the ramp data at a cadence equal to the frame time of the subarray. The figure shows simulations of the TRAPPIST-1 system with the NIRSpec Prism (SUB512). The first red tick corresponds to the reset frame, followed by 14 groups. The detector simulations show time stamps at each position up the ramp, with the group number labeled in the top left of each simulation. Red, in the detector simulations, corresponds to saturated regions of the detector. Lastly, the variable group data extraction shows the result of summing several thousand integrations (not pictured). The illustrative spectrum is a 100% water composition of TRAPPIST-1f. The number of groups used in the extraction corresponds to the maximum groups before saturation for the corresponding wavelength region. the detector at points with the highest photon rate, allows the precision to be optimized at longer wavelengths at the cost of a decrease in precision at lower wavelengths. Figure 5.13 shows the precision of four different observing strategies used to attain a 1-5 µm spectrum of a TRAPPIST-1 planet, if allocated a total of 25 transits. This means either devoting all 25 transits to the NIRSpec Prism using one of the three techniques previously discussed or, splitting 25 transits between NIRISS SOSS and NIRSpec G395H. Without any sophisticated retrievals, Figure 5.13 suggests the combination of the partial saturation technique and the unsupported read mode with the NIRSpec Prism to be favorable. We emphasize that saturation can become unfavorable if the efficiency at shorter wavelengths becomes so small that the noise

116 Comparison of Observing Strategies for NIRSpec Prism

100 NIRSpec Prism: NIRISS + Reset-Read-Read NIRSpec G395H Read-Read-Reset 80 Partial Saturation + Read-Read-Reset

60

40 Error on Spectrum (ppm) Error on

20

1 2 3 4 5 Wavelength (μm)

Figure 5.13.VariableA comparison group extraction of four different+ new readout observing scheme strategies better to than acquire the same 1-5 µm regiontraditional for TRAPPIST-1. reset-read-read. Red, Partial purple, saturation and black moderately are all different helps strategies for observing withpast the 2.3 NIRSpecmicron. Prism. The partial saturation strategy (black) is depicted in Figure 5.12. All NIRSpec Prism simulations consist of 25 transits, each of which contain 1 hour of in-transit and 1 hour of out-of transit observing time. NIRISS and NIRSpec G395H simulations consist of 12 and 13 transits, respectively (in order to match the 25 single mode observation with the Prism). All simulations are binned to R=100. at lower wavelengths begins to surpass the noise at longer wavelengths. A quick way to ensure this does not occur is to check that

p2 p2 sat ≤ 4µm (5.7) nsat − 1 nnew − 1 where psat is the precision attained at the point of maximum flux before saturation with nsat groups, p4µm is the precision at an arbitrarily long wavelength and nnew is the number of groups chosen to increase efficiency at the longer wavelengths. In

Figure 5.13 we chose nnew = 10 such that Eqn. 5.7 is satisfied.

5.3.2 Transit Transmission Spectra Models & their Jacobians

In order to obtain upper and lower limits of the knowledge gained of each of the planets in the system, we explore three chemical scenarios for each planet, whose properties are given in Table 5.2. All three chemical scenarios are composed of a combination of H2O, CO2,N2 and CH4, which will likely be the dominant gases at the effective temperatures of the TRAPPIST-1 planets and LHS 1140 b. The

117 1 2 1 1 Planet Radius Mass Teff Period T14 [R⊕] [M⊕] [K] [days] [hrs] d 0.772 0.33±0.15 288 4.0 0.82 +0.56 e 0.918 0.24−0.24 251 6.1 0.95 f 1.045 0.36±0.12 219 9.2 1.04 g 1.127 0.56±0.038 198 12.4 1.14 1 Gillon et al. [2017] 2 Wang et al. [2017] Table 5.2. TAPPIST-1 Planet Properties

main difference between the three scenarios is the background gas: either H2O-rich,

N2-rich or CO2-rich. The background gas sets the approximate scale height and therefore the lower (H2O) and upper (CO2) limits of how much knowledge could be gained about each planet by the end of each cycle. Along with the background gas, the three remaining species are added in equal quantities. Even though there have been attempts to generalize the chemistry of terrestrial exoplanet atmospheres in a self-consistent way [Hu et al., 2012], choosing arbitrary quantities for the chemical makeup of exoplanets is a ubiquitous technique when exploring the detectability of atmospheres [Benneke and Seager, 2012, Greene et al., 2016]. To create the transit transmission spectra, we use models described in Chapter 4. Figure 5.14 shows the resultant spectra for TRAPPIST-1f with the three different background gases being considered. For each background gas, the three spectra correspond to different volume mixing ratios for the trace gases (1, 0.01, or 0.0001%). This is to emphasize that the absorption strength of a feature is not correlated with an increase in the mixing ratio of the trace gases. Therefore, for the following analysis, we use a level of 0.01% for all trace gases, approximately an order of magnitude higher than Earth’s present-day CO2 levels. All temperature are assumed to be isothermal and all mixing ratios are assumed to be well-mixed. A transit transmission spectrum at any given pressure level is approximately proportional to the sum of the cross section, σi, for each absorber, i, weighted P by the volume mixing ratio, ξi, i.e. zλ ∝ i σiξi. Because CH4,H2O, and CO2 have similar cross sectional strengths, our choice to have equal volume mixing ratios, guarantees that the trace gas spectral features are all visible (unless masked by absorption of the background gas). Although this assumption could bias our results to be more optimistic, exploring three different background gases will help

118 H2O-rich CO Cycle 1 5 2 400 1% ,CH

0.01% 4 ,N

0.0001% } 2 200 N2-rich CO 2 1% ,CH 4

0.01% ,H

0 2

0.0001%} O

CO2-rich H 2 O,CH Rel. Trans. Depth (ppm) Depth Trans. Rel. -200 1%

0.01% 4 } ,N 0.0001% 2 1 2 3 4 5 Wavelength (μm)

Figure 5.14. Nine spectral models for TRAPPIST-1f with Teff =219 K and 9 different chemical compositions. Green curves correspond to a H2O background with either 1, 0.01, or 0.0001% of CO2, CH4, and N2. Red curves correspond to an N2 background with either 1, 0.01, or 0.0001% of CO2, CH4, and H2O. And blue curves correspond to a CO2 background with either 1, 0.01, or 0.0001% of N2, CH4, and H2O. All chemical species and temperatures are constant with altitude. Spectra are offset for clarity.

to mitigate that optimism. For example, H2O and CH4 spectra features will be muted in the CO2-dominated atmosphere. Clouds are ubiquitous in all Solar System bodies with stable atmospheres and have also been shown to mute or mask the atmospheric features of transiting exoplanets [Kreidberg et al., 2014a, Sing et al., 2016]. In terms of terrestrial-like planets, models of the cloud-microphysics for Earth [e.g. Albrecht, 1989, Tinsley, 2000], Venus [e.g. Knollenberg and Hunten, 1980, Allen and Crawford, 1984], and Titan [e.g. McKay et al., 2001, Rannou et al., 2006] have all yielded fruitful results because of the observations that guided them. However, a general cloud model for exoplanets has not yet been written and therefore, our choice to use a grey opacity source for cloud comes from this lack of knowledge. Therefore, for cases with clouds we use a grey opacity source at 0.01 bars. Lastly, the Jacobians used in the information content study are computed identically to those described in §5.1.1. That is, we use a center-finite differencing method centered about the three different background gases and the different planet cases.

119 esatwt naayi fTAPS-f ih1 rnisprJS cycle. JWST per transits 10 with TRAPPIST-1f, of analysis an with start We fe igetast h nyseai hti ihydie ytepiri the is prior the by driven highly is that scenario only the transit, single a After T prahtepir( e o ouemxn aisad10Kfrtemperatures). would for CO error K for the 100 case detection, and no ratios were mixing there volume If for dex bar. (6 0.01 prior show at the lines cloud approach transparent grey dashed a the for while results atmospheres the cloud-free show the lines for Opaque results mode. the READ-READ-RESET Prism’s planet. NIRSpec each with for observed height system. scale TRAPPIST-1 in the differences in by planet driven each be for will and similar differences parameters be Major retrieved will the transits on of errors number the the T between of relationship use general and the models profile, atmospheric simplistic our of Because Analysis Content Information 5.3.3 R=100. introduced to is cloud binned grey are a observations of All presence the bar. when 0.01 error in at increase the show lines CO transparent a to correspond curves 2 N = an time to observation correspond H total a with to observation correspond Prism NIRSpec a of 5.15. Figure eff iue51 hw h xetderro RPIT1 fe ahccei twere it if cycle each after TRAPPIST-1f on error expected the shows 5.15 Figure 29Kad3dffrn hmclcmoiin.Ec rni bevto consists observation transit Each compositions. chemical different 3 and K =219

Error on log H2O VMR Error on Temp. (K) 10 15 20 25 30 35 0 1 2 3 4 5 0 5 0 2 topee.I te od,frteeamshrcseaisasingle a scenarios atmospheric these for words, other In atmospheres. H roscluae rmifraincnetter o RPIT1 with TRAPPIST-1f for theory content information from calculated Errors 2 O-rich 10 2 Number ofNumber Transits akrudwt ihr00%o CO of 0.01% either with background O 2 akrudwt ihr00%o CO of 0.01% either with background 20 N True K = 219 value 2 2 -rich 30 True = -4 value akrudwt ihr00%o N of 0.01% either with background 40 CO 2 50 -rich 120

Error on log CO2 VMR Error on log CH4 VMR 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0

10 Cycle 1 Number ofNumber Transits 2 2 20 CH , CH , Cycle 2 eff 2 4 4 30 CH , n N and , n H and ,

True = -4 value True = -4 value Cycle 3 × o temperature a for t 14 4 40 n H and ,

re curves Green . Cycle 4 2 2 e curves Red . .Adblue And O.

50 Cycle 5 2 .The O. transit would only yield the detection of all three molecules. Detecting molecules is in stark contrast to constraining their compositions. Trying to constrain the composition within a retrieval scheme would yield errors of ∼ ±1-3 dex for clear atmospheres and ∼ ±2 − 3.5 for cloudy atmospheres. Although surprising, this can be seen in Figure 5.13. If all ten transits were utilized, by the end of JWST Cycle 1, there would be a large, factor of ∼ 3, improvement in all of the composition and temperature constraints. From Cycle 1 to Cycle 2 there is a very slight improvement, even for cloudy cases. After Cycle 2 there is almost no gain in knowledge. In order to verify whether this trend is a product of the atmospheric cases chosen, we decrease the trace gas concentrations to 1 ppm and find a similar pattern. For the cloud-free cases, the minimum noise value is attained by the end of Cycle 2 (20 transits). For the cloudy cases, the same is true except for when the derived errors are entirely driven by the prior. LHS 1140 is too bright to be observed with the NIRSpec Prism. Figure 5.16 compares devoting all transits to NIRISS SOSS (line) versus splitting the available transits between NIRISS SOSS and NIRSpec G395H (circles). Splitting time between NIRISS and NIRSpec G395H results in better constraints on temperature, q CH4, and CO2 despite the noise being ∼ (2)× higher. As expected, NIRISS

SOSS yields modestly better constraints for H2O because the locations of the water bands coincide with its wavelength range. Similar to TRAPPIST-1f, the minimum error on the retrieved parameters is attained at 15 transits which corresponds to the end of Cycle 5. Additionally, despite differences in stellar parameters, planet gravity and planet temperature, the minimum error attained on each individual planet is also similar. That is, we could expect to constrain volume mixing ratios by ∼0.5 dex and temperatures by ∼5 K, for clear cases and ∼1-2 dex and ∼5 K, respectively for cloudy cases.

5.3.4 Conclusion

• Different observing strategies are needed for temperate Earth-sized planets

• Bulk compositions of high mean molecular weight atmospheres are completely unconstrained

• Using a partial saturation with a READ-RESET mode could drastically improve the NIRSpec Prism

121 Figure 5.16. Errors calculated from information content theory for LHS 1140b with Teff =230 K and 3 different chemical compositions. Each transit observation consists of either a combination of NIRISS SOSS and NIRSpec G395H (circles) and only NIRISS SOSS (lines). Green curves correspond to a H2O background with either 0.01% of CO2, CH4, and N2. Red curves correspond to an N2 background with either 0.01% of CO2, CH4, and H2O. And blue curves correspond to a CO2 background with either 0.01% of N2, CH4, and H2O. All observations are binned to R=100.

• For NIRSpec Prism, after ∼20 transits, minimum constraints on model parameters are generally reached

• If the target is too bright for NIRSpec Prism, observations should be split between two other modes at the cost of higher noise

Using a transit transmission code and the PandExo noise model, we simu- lated observations of three different atmospheric scenarios for the LHS 1140 and

TRAPPIST-1 system: H2O dominated, CO2 dominated, and N2 dominated. In each atmospheric scenario we insert three trace gases at the 0.0001, 0.01 and 1% levels (either CH4,H2O, CO2 or N2). Different background gases provides insights into the time needed to constrain the atmospheres of these planets because they have a wide range of mean molecular weights and because in several cases, the

122 ability to constrain one gas is dependent on whether or not is not being blocked by the absorption of another gas. For example, in high CO2 atmospheres, H2O and

CH4 are sometimes not visible above CO2 absorption. The NIRSpec Prism (1-5 µm) offers the best chance at fruitful molecular detections of small planets around stars that are fainter than J∼10.5. However, the Prism often yields high noise data at wavelengths greater than ∼3 µm because the efficiency at longer wavelengths is limited by saturation at the shorter wavelengths and because the SED of the star drops off significantly. In order to rectify this we outlined a strategy for improving the noise at longer wavelengths. In this strategy, the detectors are saturated at the shorter wavelengths in order to increase efficiency at the longer wavelengths. We also introduced a readmode that is currently under investigation by the instrument teams that would increase the efficiency of an observation from 33% for the brightest targets to 100%. Using information content theory we predicted the expected confidence interval of the posterior on key model parameters including volume mixing ratio of H2O,

CH4, and CO2 and temperature. TRAPPIST-1f has 10 observable transits per JWST Cycle. If all 10 transits are observed during Cycle 1, we predict that there would be a factor of ∼ improvement in all of the composition and temperature constraints. The same improvement would not carry over through Cycle 2, with only moderate improvements. Even in the cases of cloudy atmospheres, or cases where trace gas concentrations are at the .0001% level, the minimum error on retrievable parameters is achieved by the end of Cycle 2. Lastly, we look at LHS 1140, which is a good test case for a temperate rocky planet that is not observable with NIRSpec Prism. We show that despite poten- tially higher noise, available transits should be split among modes that maximize wavelength coverage (e.g. the combination of NIRISS SOSS and NIRSpec G395H). In most cases, the higher noise does not have a large impact on the error on the constrained model parameters.

123 Chapter 6 | Degeneracies in Transmission Spec- troscopy

Material in this chapter is published in: Batalha, Natasha E., Eliza M-R. Kempton, and Rostom Mbarek. “Challenges to Constraining Exoplanet Masses via Transmis- sion Spectroscopy.” The Astrophysical Journal Letters, 836.1 (2017).L5

The canonical idea of a “small” planet has dramatically changed in the last decade. Out of the thousands of planet candidates discovered by Kepler [Mullally et al., 2015], nearly 80% of them have radii < 3R⊕. Additionally, occurrence rate studies verify that this high frequency is not merely an observational bias [Dressing and Charbonneau, 2013, Petigura et al., 2013, Morton and Swift, 2014, Silburt et al., 2015]. The next step to understanding this large population of planets is to obtain precise mass measurements necessary to shed light on the bulk composition of these objects. Although these masses are unobtainable via Kepler’s transit method, they can be calculated from transit timing variations (TTVs) [e.g. Lissauer et al., 2011, 2013, Carter et al., 2012, Jontof-Hutter et al., 2014, Masuda, 2014, Jontof-Hutter et al., 2016] and radial velocity (RV) measurements [e.g. Batalha et al., 2011, Weiss et al., 2013, Howard et al., 2013, Dressing et al., 2015]. Nevertheless, the RV and TTV methods have only yielded masses for a fraction of these systems to date. Unlike the low-mass planets in our Solar System, several of these small-radius planets that were expected to be rocky (e.g. the Kepler-11 system, Lissauer et al. [2013]), were later found by way of their mass and inferred bulk density to have large H/He envelopes. Although radius might act as a first order proxy for a planet’s

124 composition and H/He fraction [Lopez and Fortney, 2014, Rogers, 2015], there is no one-to-one mapping between planet radius and mass for sub-gas giant planets [Wolfgang et al., 2016]. Considerable compositional degeneracies exist in theoretical mass-radius relations for low-mass exoplanets [Fortney et al., 2007, Seager et al., 2007]. Furthermore, observations of the spectra of transiting exoplanets require knowledge of the planet’s surface gravity, and therefore its mass, to correctly interpret key properties such as the thermal structure, atmospheric composition, and presence of aerosols. Mass measurements are therefore a necessary first step toward understanding the population of sub-jovian exoplanets. Determining masses through RVs (effective for massive planets around bright, quiet stars) and TTV analyses (effective for closely spaced planets in multi-planet systems) is a technical challenge, which in the case of low-mass planets is often insurmountable with current instruments. The current state-of-the art in RV observations is ∼0.8 m s−1 while an Earth-mass planet in the habitable zones of a −1 Sun-like star and a 0.1 M M-dwarf, respectively, will produce a 0.09 m s and a 0.9 m s−1 signal [Fischer et al., 2016]. Although a number of RV instruments able to measure masses down to an Earth-mass and below are currently in development [see Fischer et al., 2016], most will only begin operation ∼1-3 years after the launch of the James Webb Space Telescope (JWST). Yet a key priority of the JWST mission is to characterize the atmospheres of low-mass exoplanets. In the interest of bypassing resource-intensive RVs to determine exoplanet masses, a technique for determining the mass of a transiting exoplanet from atmospheric observations alone – via its transmission spectrum – was proposed by de Wit and Seager [2013]. This method, termed MassSpec, relies on accurate determinations of atmospheric temperature, T , mean molecular weight (MMW), µ, and scale height, 2 kT kT Rp H = µg , because the mass of the planet is Mp = µGH . For transiting planets, Rp (planet radius) is known, T is estimated based on the planet’s equilibrium temperature, and H is constrained from the strength of absorption features in the transmission spectrum. For hot Jupiters, the MMW is approximately known a priori because these planets are assumed to have H/He-dominated atmospheres with µ ≈ 2.3 amu. In this case, MassSpec can be used to verify or determine exoplanet masses. Low-mass planets, however, could be rocky, icy, or they could have large H/He envelopes. The implied atmospheric composition that accompanies each type of

125 planet spans a wide range. This poses a challenge for retrieving masses because µ is essentially unconstrained. Here, we investigate the extent of these degeneracies and determine the feasibility of extracting masses specifically from JWST observations of the transmission spectra of small-radius planets without any a priori knowledge of planet mass.

6.1 Theoretical Setup to Investigate Degeneracies

In order to investigate degeneracies in transmission spectra for planets of unknown mass, we use the Exo-Transmit radiative transfer package [Kempton et al., 2016] to compute a grid of spectra where we vary both the planet’s surface gravity and atmospheric composition while keeping the planet’s size fixed. We then inter- compare the spectra to determine which ones are observationally distinguishable from one another. In all cases, we fix the temperature-pressure profile to an isothermal T =400 K and the planet’s radius at Rp = 1.5 R⊕. This planet size was specifically chosen to reflect the point of greatest compositional uncertainty, which corresponds to the maximum size after which planets tend to decrease in density with increasing radius, indicating a H/He-envelope [Weiss and Marcy, 2014, Rogers,

2015]. In other words, a 1.5 R⊕ planet could be rocky, icy, or could have a large H/He envelope with approximately equal probability.

For simplicity, we consider atmospheres that are a mix of only H2 and H2O– two of the major constituent materials for low-mass exoplanets. This approach is motivated because any absorptive gas will produce the same qualitative behaviors as what we describe in the following sections. Additionally, barring very high C/O planets, self-consistent models that include photochemistry, thermochemistry and kinetic-transport always show large H2O components, regardless of H2 content [Hu and Seager, 2014]. Therefore, additional molecules are not expected to change our results. In our model grid, we vary surface gravity from 5 - 25 m/s2, in steps of 1.4 2 −3 1 m/s , and the ratio of H2O to H2 (by volume) from 10 - 10 in log steps of

0.4 dex, creating a total of 150 models. This range of parameters covers H2-rich mini-Neptunes, H2O-rich water worlds, and rocky planets with H2-H2O atmospheres. We also generate a limited number of spectra for cloudy atmospheres where a fully optically thick gray cloud has been inserted at a specified atmospheric pressure.

126 Because we only investigate H2-H2O atmospheres, the sole opacity sources in the cloud-free models are the vibration-rotation bands of water vapor in the near- and mid-IR, collision-induced absorption (CIA), and Rayleigh scattering off of H2 and

H2O gas (see Freedman et al. [2008, 2014] and Lupu et al. [2014] for a more detailed description of the opacity data). Exo-Transmit includes H2-H2 CIA opacities but not H2-H2O or H2O-H2O. The non-inclusion of H2O CIA should not affect our results because these opacities tend to be only weakly wavelength dependent. For our cloudy models, the cloud opacity is treated as an infinite opacity source at the location of the cloud deck. We use PandExo to model JWST observations. Unless otherwise specified, each observation simulation is computed for 100 transits. Each transit is composed of

1 hour in-transit, the approximate transit duration for a 400 K, 1.5 R⊕ planet orbiting a GJ-1214-like star, and 1-hour out-of-transit (200 hours for 100 transits). For reference, this is approximately double the number of observing hours spent on the longest campaigns for single exoplanet targets to date with HST [Kreidberg et al., 2014b,a, Stevenson et al., 2014]. However, it may be realistic to expect long observing campaigns for the most promising potentially habitable small-radius exoplanets with JWST. The simulated observations from de Wit and Seager [2013] are also composed of 200 hours of observing time, but they only consider in-transit data, which are assumed to be spread across three NIRSpec grisms (66.67 hrs in each). Our observing time is larger by a factor of 3 because we do not assume the time is split between three modes. This only further emphasizes the difficulties in constraining masses via transmission spectroscopy.

6.2 A Comparison of Forward Models

To determine the absolute degree of difference between pairs of model transmission spectra, we directly inter-compare the mean-subtracted spectra at native instrument resolving power without any added noise to find the maximum deviation at a single wavelength. For this comparison of the spectral models, we produce our full model grid (as described in Section 6.1) for both a Sun-like and a GJ 1214b-like (0.2 R ) host star. We find that in each of the observing modes, for the larger Sun-like host star, over 70% of the planet-pair scenarios have maximum spectral differences of less than 50 ppm. For reference, this is the noise floor that has been suggested for

127 ihisln ria eidadsaltastdpho prxmtl 0 ppm. 200 approximately of depth transit small and period orbital long its with pairs between difference maximum the cases, of 70% over in that say, to is That with J11-iesa,w n .%(0 oa ar)o ae ob eeeaewith degenerate be to cases of pairs) total (505 4.5% find we star, with 1214-like JWST GJ a with characterization atmospheric for attainable ∼ be to shown for been target of challenging temperatures a with is Super-Earths star Sun-like because a expected orbiting is percentage super-Earth of high amount K any This 400 for distinction. a challenging the be reveal would to it time that observing enough small is models of on detectors near-IR with achieved level noise mid-IR the m/s 9.3 of gravity m/s surface 20.7 a of have gravity #1’s surface are model a All have star. #2’s Sun-like model a and star host each of power 6.1. Figure Model #1: Gravity = 9.3 m/s 2

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2 -0.3 2 n all and , JWST JWST 0.1

2 0.6

1.0 maximum differences of 50 ppm or less in the NIRISS band, 5.5% (615 total pairs) in the NIRSpec G395H band and 13% (1471 total pairs) in the MIRI LRS band. As expected, these numbers are dependent on the bin size. For example, if a NIRISS observation is binned down from its native resolving power (R = 700) to R = 100, the number of degenerate planet pairs at the 50 ppm level increases from 4.5% to 9% (1086 total pairs). In Figure 6.1 we illustrate the degenerate parameter space by isolating two representative gravities (9.3 and 20.7 m/s2) and showing the maximum spectral differences as a function of composition, with scaling for both the GJ 1214-type and Sun-like host star. We choose these two gravities to illustrate cases where degeneracies would exist, yet the implied planet types are very different. The planet denoted as model #1 has a density of 3.5 g/cm3 as opposed to 7.7 g/cm3 for model #2. By comparing against theoretical mass-radius relationships for low- mass planets [Fortney et al., 2007, Seager et al., 2007], the former is a low-density planet with a considerable volatile component – either an ice-rich water-world or a hydrogen-rich mini-Neptune – whereas the latter is a rocky planet consistent with an Earth-like bulk composition. The least degenerate region of Figure 6.1 lies in the lower right-hand corner where the high surface gravity planet combined with a high MMW atmosphere will produce much smaller spectral features than a low surface gravity, low MMW atmosphere. The most degenerate regions occur along a diagonal that cuts across the top portion of each panel of Figure 6.1. This is the region where both model #1 and model #2 produce comparably sized spectral features, which takes place where the low surface gravity planet has a higher MMW atmosphere and vice versa. This qualitative behavior extends to other surface gravity pairings. We point out that the relative strength of spectral features in transmission grows proportionately with temperature, as will the maximum spectral differences between models. Planets with T > 400 K will therefore be more easily distinguishable from one another, and less so for T < 400 K. The metric employed in Figure 6.1 for distinguishing between atmospheric scenarios assumes that model discrepancies at a single wavelength are sufficient for ascertaining the best-fit model parameters. More realistically, instrumental noise along with finite observing time will limit the degree to which an atmosphere can be characterized. To quantify these effects, in Figure 6.2, we isolate a single

129 g=9.3 m/s 2,log H 20/H 2=1.0 g=20.7 m/s 2, log H 20/H 2=−0.3

100

0 (ppm)

-100 Case 1: NIRISS SOSS Relative Transit Depth RelativeTransit 1 1.5 2 2.5 80

40

0 (ppm) -40 Case 2: NIRSpec G395H

Relative Transit Depth Depth RelativeTransit -80 3 3.5 4 4.5 5

100

0 (ppm)

-100 Case 3: MIRI LRS Relative Transit Depth RelativeTransit 6 8 10 12 Wavelength (micron)

Figure 6.2. JWST simulations for NIRISS SOSS (top), NIRSpec G395H (middle), MIRI LRS (bottom) with no noise floor. Each simulation is done for 100 transits in each observing mode. One transit observation consists of 1 hour in-transit and 1 hour out-of-transit. All simulations are for a GJ 1214-type host star with J = 8, for the same planet parameters as in Figure 6.1. The only difference between the simulations is the gravity and metallicity (H2O/H2), indicated in the color legend. All spectra are binned to R = 100. The red error bars represent the proposed ±20 ppm noise floor for NIRISS/NIRSpec and ±50 ppm noise floor for MIRI [Greene et al., 2016]. degenerate planet pair from Figure 6.1 and show each resulting simulated observation in the three different JWST modes using PandExo. The two planets shown in 2 2 Figure 6.2 have g = 9.3 m/s with log[H2O/H2] = 1.0 and g = 20.7 m/s with log[H2O/H2] = −0.3. The former case represents a water world with a water- dominated atmosphere, whereas the latter would be a rocky planet with an outgassed hydrogen-dominated atmosphere. On average over each observational band pass, the difference between the two observations is ∼10 ppm. For NIRISS SOSS (the least degenerate observation),

130 only considering pure shot and read noise, the errors after 100 transits are ∼5 ppm. The reduced-χ2 for one NIRISS observation using the opposing model as a 2 2 template is χred = 1.3 — right at the 3-σ interval for 230 DOF (χred < 1.27) it would just be on the cusp of non-degeneracy. In reality though, 5 ppm error bars are highly unlikely given the current state of the art using Hubble [e.g. Line and Parmentier, 2016], as well as current knowledge of instrument systematics [Greene et al., 2016]. If we were to include a 20 ppm noise floor, the reduced-χ2 shrinks 2 2 to χred = 1.06. Within the 1-σ interval for 230 DOF (χred < 1.09), these cases could only be distinguished with a priori knowledge of the planet’s mass. Given

2 2 g=20.7 m/s ,log H 20/H 2=−0.3 g=7.8 m/s , log H 20/H 2=0.1 40 transits No cloud 100 No cloud

0

Depth (ppm) Depth -100 Relative Transit RelativeTransit

100 100 transits 10 milibar cloud 50 No cloud

0 Depth (ppm) Depth

Relative Transit RelativeTransit -50

-100 1 1.5 2 2.5 Wavelength (micron)

Figure 6.3. Simulated data for a GJ 1214-type system for the same stellar and planetary parameters as the previous two figures. The two simulations differ in their assumed gravity, metallicity (H2O/H2), indicated in the color legend, and cloud assumptions. In the top panel neither model has clouds. In the bottom panel, the low gravity, high metallicity model has a 10 millibar cloud that reduces the strength of its absorption features. Observations were simulated for NIRISS SOSS with no noise floor and binned to R=100. Top panel observations were simulated with 40 transits (80 hrs). Bottom were simulated with 100 transits (200 hrs). Some error bars are too small to see. The red error bars represent the proposed ±20 ppm noise floor for NIRISS [Greene et al., 2016]. the considerable number of non-degenerate planet pairs, especially for the M-dwarf

131 host star, it may seem that MassSpec could be a productive method for measuring exoplanet masses in some situations where RVs are unattainable. However, the aforementioned cases were all modeled without the presence of aerosols (clouds and haze). As we know from ground and space-based observations, aerosols are practically ubiquitous in the transmission spectra of exoplanets [e.g. Kreidberg et al., 2014a, Sing et al., 2016]. Aerosols add an additional layer of degeneracy to the retrieval of physical parameters from transmission spectra and can therefore further complicate the extraction of mass information from atmospheric observations. This occurs because both the presence of clouds and an increase in metallicity can have the same dampening effect on molecular absorption features. In Figure 6.3, we demonstrate this effect by adding a gray opacity source to one of two planet cases whose cloud-free spectra were initially non-degenerate. We show that when 2 a 10 mbar cloud is added to a target with g = 7.8 m/s and log[H2O/H2] = 0.1 it becomes degenerate with a target that has a no clouds, g = 20.7 m/s2, and

log[H2O/H2] = −0.3. Figure 6.3 is a single illustration of a general effect, in which we expect the presence of aerosols to dramatically increase the number of planet pairs that are degenerate with one another.

6.3 Implications on Future Observations of Small Plan- ets

To investigate degeneracies between gravity and composition in small planets, we have inter-compared 150 forward model transmission spectra for a planet with a

H2-H2O atmosphere, radius of R = 1.5 R⊕, and isothermal temperature of 400 K. The surface gravity and atmospheric composition were allowed to vary with the goal of determining whether the planet’s mass (via its surface gravity) is recoverable from transmission spectrum observations. We found that a considerable fraction of the planet pairs were identical to one another at or below the 50 ppm level — more so for a larger Sun-like host star. With the addition of clouds, these degeneracies were exacerbated. The 50 ppm level is important because it is the approximate minimum noise level, or noise floor, that has been suggested for mid-IR JWST instruments [Greene et al., 2016]. Barring any unforeseen circumstances, the near-IR instruments will likely have a lower noise floor of 20-30 ppm.

132 By modeling the JWST noise sources we determined that even 100 transits (equivalent here to 200 hrs) in key observing modes is not sufficient to discern between many planet pairs, even assuming no systematic noise floor. A shorter time span of observations, smaller planetary radius, larger stellar radius, or lower planetary temperature will further enhance the difficulties with extracting a planet’s mass from its transmission spectrum. These conclusions paint a far more pessimistic picture of mass extraction via transmission spectroscopy than de Wit and Seager [2013]. Yet our results are fully consistent with retrieval studies [Benneke and Seager, 2012, Benneke and Seager, 2013, Barstow et al., 2015, Greene et al., 2016], which attempt to constrain the atmospheres of super-Earths and mini-Neptunes with simulated JWST data, even when the masses are known. For example, Greene et al. [2016] find that

only a log[H2O] > −7 lower limit can be placed on the water mixing ratio of a

cloud-free, 100% H2O, 500 K, 2.1 R⊕ planet orbiting an K=8 M0.0V star with a high SNR 1-11 µm observation. Similarly, Benneke and Seager [2012] cannot reliably determine whether the observed absorber is the main constituent of the atmosphere or just a minor species when the mixing ratio is less than 0.1%, and there is no observation of the molecular Rayleigh scattering (< 1µm). We speculate that de Wit and Seager [2013]’s optimistic results may be in part because of narrow bounds on priors, assumptions of higher JWST duty cycles, their modeling of only in-transit observations, and/or their lack of systematic noise.

Our choice to model a 1.5 R⊕ planet was motivated by the observation that planets of this size have bulk densities that are equally likely to indicate a rocky planet as one that is volatile [Lopez and Fortney, 2014, Rogers, 2015]. These two planet types have very different implied formation histories, with the latter more likely to have formed beyond the snow line and migrated inward. Yet we have shown a case where a water world is indistinguishable from a high surface gravity rocky planet with JWST observations (Figure 6.2), and many more similar degenerate planet pairs exist in our full grid. Therefore, independently determining the mass of small-radius planets is required in order to correctly interpret the composition of a planet’s atmosphere and its formation history. We caution that JWST observations undertaken for atmospheric characteriza- tion of small-radius planets whose masses are unknown may not yield fruitful results. Further down the road, spectroscopic characterization efforts for directly-imaged

133 near Earth-size planets are also likely to present substantial model degeneracies, absent mass measurements. In the JWST era and beyond, successful interpretation of exoplanet spectra for small-radius planets will therefore rely necessarily on the success of future precision RV instruments such as CARMENES, KPF, EXPRES, HPF, MAROON-X, NEID, Spirou, and Veloce.

134 Chapter 7 | Conclusions and Future Work

7.1 Conclusions

We will soon have the technological capabilities needed to measure the atmospheric composition of Earth-sized temperate planets orbiting nearby stars. Interpreting these atmospheric signals poses an interesting challenge. Unlike, jovian-like at- mospheres, which are composed of primordial material that was accreted upon formation, terrestrial planet atmospheres are likely comprised of secondary at- mospheres, which have gone through a high degree of evolution from volcanic outgassing and escape and their bulk compositions will be highly unconstrained. Several forces are at play in this scenario: stellar evolution, geological processes, atmospheric escape, etc. Each of these individual processes contribute to the planetary system as a whole. In order to illustrate the intricacies of modeling a terrestrial planet system, I leveraged early Mars as a case study. Mars is perhaps the most well-studied planet in our Solar System, besides Earth of course. The combination of geographical data, remote sensing data, and martian meteorite analyses have given us powerful insights into what the martian environment is currently like, and has left several open questions about what Mars was like in its past. One study suggested that early Mars could be warmed with a 3 bar 95% CO2, 5% H2 atmosphere [Ramirez et al., 2014]. My first goal was to create a self-consistent model that matched this profile. This is highly similar to the problem that exoplanet scientists will face. That is, giving a composition, temperature, and pressure, we will have to create models to determine likely theoretical scenarios for what we are observing. For early Mars, I leveraged

135 a combination of climate, photochemical and energy balance models. Doing so, I showed that several assumptions are needed to construct a self-consistent model, but that a martian atmosphere with 5% H2 was feasible with the right amount of direct outgassing. Furthermore, I showed that under these atmospheric conditions, early Mars probably underwent dramatic climate cycles. But the exact nature of these cycles is also dictated by the modeling assumptions. In reality, the currently available martian data is in stark contrast to the data we will one day attain to characterize the atmospheres of exoplanets. Namely, unlike models of the early martian atmosphere, which were motivated by observations of the planet’s surface, models of exoplanet atmospheres will be motivated by observations of the planet’s atmosphere. Currently though, the only attainable observations of exoplanet atmospheres from the Hubble Space Telescope and the Spitzer Space Telescope are those of hot Jupiters (Jupiter-sized planets with T>1500 K) and warm Neptunes (Neptune-sized planets with T∼600-1000 K). Therefore, our next major goal here was to determine optimal strategies for accurately characterizing both hot Jupiters & warm Neptunes and temperate rocky low-mass (1-10 M⊕) planets which could be observed with the James Webb Space Telescope (JWST). Since JWST has not yet launched, as a first step I developed an open source tool for creating observation simulations of all eleven observatory-supported time-series spectroscopy modes. Next, I used information content theory to develop optimal strategies for characterizing exoplanets. I tested this methodology by using a Bayesian retrieval scheme on the atmospheres of key hot Jupiters and warm Neptunes and found good agreement between the two. Finally, I applied this method to a canonical temperate rocky low-mass planet, TRAPPIST-1f. By doing so I, showed that if TRAPPIST-1f is a typical rocky planet system we can expect to constrain the compositions of their atmospheres by ∼0.5-1 dex depending on the extend of cloud coverage. Lastly, degeneracies exist between mass and composition. Therefore, RV methods will be needed in the future to constrain the masses of temperate rocky planets, if we want to retrieve accurate atmospheric composition information. Taking it full circle to the modeling exercise of early Mars, my initial task was to create a self-consistent model of an early martian atmosphere with 5% H2 and 95%

CO2. Doing so was feasible, but required numerous assumptions that were made possible from in situ observations. If we draw the analogy to an exoplanet study

136 with the error bars obtained with the TRAPPIST-1f study, the modeling becomes:

create a self-consistent model of an atmosphere with log H2 volume mixing ratio

(vmr)= −.3±1 and log CO2 vmr= .−2±1. From an observational standpoint, these constraints would be considered “state-of-the-art”. From a modeling standpoint,

the difference between 5% and 0.05% H2 would drastically change the theoretically problem at hand. Given the challenging nature of this, creating self-consistent models of terrestrial planets in the JWST era will be incredibly challenging and if done, will require several theoretical assumptions. Nevertheless, I end by concluding that this is not entirely pessimistic as it still does not preclude the pure detection of atmospheric features in temperate rocky worlds, which opens the door to future studies with more advanced modeling. This is very similar to the current state-of-the-art observations of warm Neptunes and hot Jupiters with the Hubble Space Telescope. And given the larger wavelength range and higher resolution modes on board JWST, the field of exoplanet characterization in the upcoming decade will undoubtedly be revolutionized.

7.2 Future Work

7.2.1 Connecting Forward Models to Retrievals

The James Webb Space Telescope Guaranteed Time Observers have already selected their targets for Cycle 1. TRAPPIST-1e is slated to be observed with five transits of NIRSpec Prism, TRAPPIST-1f and g are slated to be observed with five transits of NIRISS SOSS, and LHS 1140b is slated to be observed with five transits of NIRISS SOSS and five transits of NIRSpec G395H. Given the work done in this thesis, this number of transits is not enough to yield tight constraints on composition and temperature. By the end of Cycle 2 (2020), however we may be able to constrain atmospheric compositions of terrestrial planets by ∼ 0.5 − 1.0 dex (log volume mixing ratio). In my concluding remarks, I made the analogy between the forward modeling problem of early Mars and forward modeling temperate terrestrial exoplanets and stated that self-consistent models of temperate terrestrial exoplanets will only be possible by making several assumptions and forward models are unlikely to yield meaningful results. In the future, I plan to show, quantitatively, to what degree this is true. One way of testing this would be to wrap a forward

137 model within a retrieval scheme. Currently, forward models have only been paired with retrievals for planets that are in chemical equilibrium. As discussed in Chapter 1, chemical equilibrium models have several dozen fewer input parameters. Furthermore, there are several aspects of the 1D photochemical model that would prohibit it from yielding fruitful results:

• Long-lived species, short-lived species, and the chemical network are fixed and would need to be determined a priori

• Boundary conditions are set at the surface and at the top of the atmosphere, yet retrieved data from transit transmission spectra will likely not be able to constrain composition near the surface

• An initial guess is required for each run, which cannot deviate largely from the correct answer.

• Some boundary conditions are in data blocks within the code and changing them requires recompilation.

Changing the first three aspects of this code are not trivial and require a high degree of model development. Before embarking on a long model development journey I plan to first determine to what degree our photochemical forward models could be useful in understanding the atmospheres of temperate rocky exoplanets. The simplest way to test this is to create a self-consistent forward model of a known system (i.e. TRAPPIST-1f), which includes first modeling the photochemistry, then producing a transit transmission spectrum, then adding the instrumental noise in order to create a full synthetic observation. From the synthetic observation, I would first retrieve the atmospheric composition and temperature and from first principles, I would then try and reconstruct the forward model with any associated error bars. Because the number of retrievable parameters are significantly less than the quantity of model input parameters, I expect to find that several parameters within the photochemical model are degenerate with each other. However, under- standing exactly what these forward model parameters are will guide us towards understanding what claims can and cannot be reliably made about an exoplanet given what can be retrieved from transit transmission spectra. It will also prioritize the model development goals described above. And ultimately, when we have JWST

138 data on the ground, I will be well positioned to interpret the transit transmission spectroscopy results.

7.2.2 Preparation for Direct Imaging

Transit transmission spectra will be instrumental in improving our understanding of exoplanetary atmospheres but there are several advantages to observing planets via direct imaging. In transmission spectra, aerosols and clouds can inhibit altitudes near the surface to be probed. Also in transmission, depending on the viewing geometry of the system, refraction effects can also place limits on the how deep the atmosphere can be probed. Direct imaging has been slow to yield atmospheric characterization data because of the technological challenges. In order to directly image planets the light from the parent star must be suppressed with a coronograph, starshade, or an interferometer. Currently, only young giant planets at large distances have been observed. The missions following JWST (e.g. WFIRST, LUVOIR) will all contain some degree of direct imaging, which will require an entirely new set of tools and models. Namely, instead of modeling the light that is filtered through the annulus of the atmosphere, direct imaging requires models of the light that is directly emitted from the planet. Currently, the most well-known model for the type of exoplanets WFIRST expects to observe was developed by Cahoy et al. [2010]. Recently however, it was shown that the forward scattering in this model is not implemented correctly and would yield incorrect results if it were used to retrieval the atmospheric composition of directly imaged planets. Additionally, the model is not versatile enough for the range of planets that will be observed with WFIRST and eventually, LUVOIR. Therefore, I plan to start from first principles and rewrite the Cahoy et al. [2010] model in a modern language that can be used in a retrieval scheme just as the modern-day transit transmission spectral models are used today. This will ensure that I am well positioned to be a part of the missions past JWST’s lifetime.

139 Appendix A| Photochemical Reaction Rates

For photolysis reactions (Reaction #’s 177-215), the values provided in the “Reaction Rate Constant” column are in fact the photolysis rates at the top of the atmosphere for the case described in Chapter 3. For reaction rate constants, T is temperature and ρ is density.

140 Rxn # Reaction Reaction Rate Constant Reference 1 −10 1 H2O + O D −−→ OH + OH 2.2 · 10 Sander et al. [2006] 1 −10 2 H2 + O D −−→ OH + H 1.0 · 10 Sander et al. [2006] −15 −1460/T 6.52 3 H2 + O −−→ OH + H 1.34 · 10 × e × (T/298) Robie et al. [1990] −12 −2000/T 4 H2 + OH −−→ H2O + H 5.5 · 10 × e Sander et al. [2006] −10 −470/T 5 H + O3 −−→ OH + O2 1.4 · 10 × e Sander et al. [2006] −32 1.6 6 H + O2 −−→ HO2 k0 = 5.7 · 10 × (T/298) Sander et al. [2006] −11 k∞ = 7.5 · 10 −12 7 H + HO2 −−→ H2 + O2 6.9 · 10 Sander et al. [2006] −12 8 H + HO2 −−→ H2O + O 1.62 · 10 Sander et al. [2006] −11 9 H + HO2 −−→ OH + OH 7.29 · 10 Sander et al. [2006] −11 120/T 10 OH + O −−→ H + O2 2.2 · 10 × e Sander et al. [2006] −11 250/T 11 OH + HO2 −−→ H2O + O2 4.8 · 10 × e Sander et al. [2006] −12 −940/T 12 OH + O3 −−→ HO2 + O2 1.6 · 10 × e Sander et al. [2006] −11 200/T 13 HO2 + O −−→ OH + O2 3.0 · 10 × e Sander et al. [2006] −14 −490/T 14 HO2 + O3 −−→ OH + O2 + O2 1.1 · 10 × e Sander et al. [2006] −13 590/T 15 HO2 + HO2 −−→ H2O2 + O2 k0 = 2.3 · 10 × e Sander et al. [2006] −12 −160/T 16 H2O2 + OH −−→ HO2 + H2O 2.9 · 10 × e Sander et al. [2006] −34 480/T 17 O + O −−→ O2 9.46 · 10 × e × ρ Campbell and Gray [1973] −34 −11 2.40 18 O + O2 −−→ O3 6 · 10 × 3 · 10 × (T/298) Sander et al. [2006] −12 −2060/T 19 O + O3 −−→ O2 + O2 8.0 · 10 × e Sander et al. [2006] −12 −240/T 20 OH + OH −−→ H2O + O 4.2 · 10 × e Sander et al. [2006] 21 O1D + M −−→ O + M 1.8 · 10−11 × e110/T Sander et al. [2006] 1 −11 70/T 22 O D + O2 −−→ O + O2 3.2 · 10 × e Sander et al. [2006] −13 23 CO + OH −−→ CO2 + H 1.5 · 10 × (1 + 0.6 × ρ) Sander et al. [2006] −33 −1515/T 24 CO + O −−→ CO2 1.7 · 10 × e × ρ Tsang and Hampson [1986] 25 H + CO −−→ HCO 5.29 · 10−34 × e−100/T × ρ Baulch et al. [1994] −10 26 H + HCO −−→ H2 + CO 1.5 · 10 Baulch et al. [1992] −11 27 HCO + HCO −−→ H2CO + CO 3.0 · 10 Tsang and Hampson [1986] −10 28 OH + HCO −−→ H2O + CO 1.7 · 10 Baulch et al. [1992] −11 29 O + HCO −−→ H + CO2 5.0 · 10 Tsang and Hampson [1986] 30 O + HCO −−→ OH + CO 1.0 · 10−10 Hampson Jr and Garvin [1977] −12 −1090/T 1.62 31 H2CO + H −−→ H2 + HCO 2.14 · 10 × e × (T/298) Baulch et al. [1994] + −33 −0.6 32 H + H M −−→ H2 + M 8.85 · 10 × (T/298) × ρ Baulch et al. [1994] −12 −0.4 33 HCO + O2 −−→ HO2 + CO 5.6 · 10 × (T/298) Kasting [1990] −12 125/T 34 H2CO + OH −−→ H2O + HCO 5.5 · 10 × e Sander et al. [2006] + −31 −2 35 H + OH M −−→ H2O + M 6.7 · 10 × (T/300) × ρ McEwan and Phillips [1975] −31 −11 0.08 36 OH + OH −−→ H2O2 6.9 · 10 × 1.5 · 10 × (T/298) Sander et al. [2006] −11 −1600/T 37 H2CO + O −−→ HCO + OH 3.4 · 10 × e Sander et al. [2006] −12 −2000/T 38 H2O2 + O −−→ OH + HO2 1.4 · 10 × e Sander et al. [2006] −12 −1775/T 39 CH4 + OH −−→ CH3 + H2O 2.45 · 10 × e Sander et al. [2006] 1 −10 40 CH4 + O D −−→ CH3 + OH 1.28 · 10 Sander et al. [2006] 1 −11 41 CH4 + O D −−→ H2CO + H2 2.25 · 10 Sander et al. [2006] 1 −12 −5050/T 42 CH2 + CH4 −−→ CH3 + CH3 7.14 · 10 × e Böhland et al. [1985] 1 −11 43 CH2 + O2 −−→ HCO + OH 3 · 10 Ashfold et al. [1981] 1 3 −12 44 CH2 + M −−→ CH2 + M 8.8 · 10 Ashfold et al. [1981] 3 −15 45 CH2 + H2 −−→ CH3 + H 5 · 10 Tsang and Hampson [1986] 3 −12 −5050/T 46 CH2 + CH4 −−→ CH3 + CH3 7.14 · 10 × e Böhland et al. [1985] 3 −12 47 CH2 + O2 −−→ HCO + OH 1.5 · 10 Tian et al. [2014] −31 −3.6 48 CH3 + O2 −−→ H2CO + OH k0 = 4.0 · 10 × (T/300) Sander et al. [2006] −12 −1.1 k∞ = 1.2 · 10 × (T/300) −11 49 CH3 + OH −−→ H2CO + H2 9.3 · 10 Humpfer et al. [1995] −10 50 CH3 + O −−→ H2CO + H 1.1 · 10 Sander et al. [2006]

141 Rxn # Reaction Reaction Rate Constant Reference −12 −220/T 51 CH3 + O3 −−→ H2CO + HO2 5.4 · 10 × e Sander et al. [2006] + −24 −1390/T −7.0 52 CH3 + CH3 M −−→ C2H6 + M k0 = 4.0 · 10 × e × (T/300) Wagner and Wardlaw [1988] −10 −329/T k∞ = 1.79 · 10 × e + −28 −1.8 53 CH3 + H M −−→ CH4 + M k0 = 6.0 · 10 × (T/298) Baulch et al. [1994] −10 −0.40 k∞ = 2.0 · 10 × (T/298) Tsang and Hampson [1986] −10 54 CH3 + HCO −−→ CH4 + CO 2.01 · 10 Tsang and Hampson [1986] −11 −176/T 0.6 55 CH3 + HNO −−→ CH4 + NO 1.85 cot 10 × e × (T/298) Choi and Lin [2005] −16 899/T 6.10 56 CH3 + H2CO −−→ CH4 + HCO 1.60 cot 10 × e × (T/298) Baulch et al. [1994] 57 H + NO+M −−→ HNO + M 2.1 · 10−32 × (T/298)1.00 × ρ Hampson Jr and Garvin [1977] −12 −1400/T 58 NO + O3 −−→ NO2 + O2 2.0 · 10 × e Sander et al. [2006] + −31 −11 1.5 59 NO + O M −−→ NO2 + M 9 · 10 × 3 · 10 × (T/298) Sander et al. [2006] −12 250/T 60 NO + HO2 −−→ NO2 + OH 3.5 · 10 × e Sander et al. [2006] + −31 2.6 61 NO + OH M −−→ HNO2 + M k0 = 7.0 · 10 × (T/298) Sander et al. [2006] −11 0.1 k∞ = 3.6 · 10 × (T/298) −12 180/T 62 NO2 + O −−→ NO + O2 5.6 · 10 × e Sander et al. [2006] + −30 3.0 63 NO2 + OH M −−→ HNO3 + M k0 = 2.0 · 10 × (T/298) Sander et al. [2006] −11 k∞ = 2.5 · 10 −10 −340/T 64 NO2 + H −−→ NO + OH 4 · 10 × e Sander et al. [2006] −15 −785/T 65 HNO3 + OH −−→ H2O + NO2 + O 7.2 · 10 × e + Sander et al. [2006] (1.9 · 10−33 × e725/T × ρ)/ (1 + 4.6 · 10−16 × e−715/T × ρ) 66 HCO + NO −−→ HNO + CO 1.2 · 10−11 Tsang and Hampson [1986] −32 1.00 67 H + HNO −−→ H2 + NO 5.7 · 10 × (T/298) × ρ Tsang and Herron [1991] 68 O + HNO −−→ OH + NO 5 · 10−12 Albers et al. [1969] −11 69 OH + HNO −−→ H2O + NO 5 · 10 Sun et al. [2001] −11 −390/T 70 HNO2 + OH −−→ H2O + NO2 1.8 · 10 × e Sander et al. [2006] −12 −4330/T 1.5 71 CH4 + O −−→ CH3 + OH 8.75 · 10 × e × (T/298) Tsang and Hampson [1986] 1 −15 72 CH2 + H2 −−→ CH3 + H 5 · 10 Tsang and Hampson [1986] 1 −12 73 CH2 + CO2 −−→ H2CO + CO 1 · 10 Zahnle [1986] 3 −11 74 CH2 + O −−→ HCO + H 1 · 10 Huebner and Giguere [1980] 3 −14 75 CH2 + CO2 −−→ H2CO + CO 3.9 · 10 Laufer [1981] −12 −1070/T 76 C2H6 + OH −−→ C2H5 + H2O 8.54 · 10 × e Sander et al. [2006] −12 −2920/T 1.5 77 C2H6 + O −−→ C2H5 + OH 8.62 · 10 × e × (T/300) Baulch et al. [1994] −10 78 C2H6 + O1D −−→ C2H5 + OH 6.29 · 10 Matsumi et al. [1993] −11 79 C2H5 + H −−→ CH3 + CH3 7.95 · 10 Gladstone et al. [1996] −10 80 C2H5 + O −−→ CH3 + HCO + H 1.1 · 10 Pavlov et al. [2001] −28 3.0 81 C2H5 + O2 −−→ CH3 + HCO + OH k0 = 1.5 · 10 × (T/300) Sander et al. [2006] −12 k∞ = 8 · 10 −11 82 C2H5 + HCO −−→ C2H6 + CO 5 · 10 Pavlov et al. [2001] −14 83 C2H5 + HNO −−→ C2H6 + NO 3 · 10 Pavlov et al. [2001] −10 84 C2H5 + OH −−→ CH3 + HCO + H2 1.1 · 10 Pavlov et al. [2001] −13 −2370/T 85 SO + O2 −−→ O + SO2 2.4 · 10 × e Sander et al. [2006] −11 86 SO + HO2 −−→ SO2 + OH 2.8 · 10 Kasting [1990] + −31 87 SO + O M −−→ SO2 + M 6.0 · 10 × ρ Sander et al. [2006] −11 88 SO + OH −−→ SO2 + H 8.6 · 10 Sander et al. [2006] + −31 3.3 89 SO2 + OH M −−→ HSO3 + M k0 = 3 · 10 × (T/298) Sander et al. [2006] −12 k∞ = 1.5 · 10 + −22 −3.6 90 SO2 + O M −−→ SO3 + M k0 = 1.3 · 10 × (T/298) Sander et al. [2006] −11 k∞ = 1.5 · 10 −15 91 SO3 + H2O −−→ H2SO4 1.2 · 10 Sander et al. [2006] −12 −330/T 92 HSO3 + O2 −−→ HO2 + SO3 1.3 · 10 × e Sander et al. [2006] −11 93 HSO3 + OH −−→ H2O + SO3 1.0 · 10 Kasting [1990] −11 94 HSO3 + H −−→ H2 + SO3 1.0 · 10 Kasting [1990]

142 Rxn # Reaction Reaction Rate Constant Reference −11 95 HSO3 + O −−→ OH + SO3 1.0 · 10 Kasting [1990] 1 3 −12 96 SO2 + M −−→ SO2 + M 1.0 · 10 Turco et al. [1982] 1 −11 97 SO2 + M −−→ SO2 + M 1.0 · 10 Turco et al. [1982] 1 −16 98 SO2 + O2 −−→ SO3 + O 1.0 · 10 Turco et al. [1982] 1 −12 99 SO2 + SO2 −−→ SO3 + SO 4.0 · 10 Turco et al. [1982] 3 −13 100 SO2 + M −−→ SO2 + M 1.5 · 10 Turco et al. [1982] 3 −14 101 SO2 + SO2 −−→ SO3 + SO 7.0 · 10 Turco et al. [1982] −11 102 SO + NO2 −−→ SO2 + NO 1.4 · 10 Sander et al. [2006] −12 −1170/T 103 SO + O3 −−→ SO2 + O2 4.5 · 10 × e Atkinson and et al. [2004] −16 104 SO2 + HO2 −−→ SO3 + OH 8.63 · 10 Lloyd [1974] −15 105 SO3 + SO −−→ SO2 + SO2 2.010˙ Chung et al. [1975] −11 106 SO + HO2 −−→ HSO + O2 2.8 · 10 Kasting [1990] −12 −0.4 107 SO + HCO −−→ HSO + CO 5.6 · 10 × (T/298) Assumed same as k(HCO + O2) −32 1.6 + 108 H + SO −−→ HSO k0 = 5.7 · 10 × (T/298) Assumed same as k(H O2) −11 k∞ = 7.5 · 10 −12 250/T 109 HSO + NO −−→ HNO + SO 3.5 · 10 × e Assumed same as k(NO + HO2) −11 250/T 110 HSO + OH −−→ H2O + SO 4.8 · 10 × e Assumed same as k(HO2 + OH) −12 111 HSO + H −−→ H2 + SO 6.48 · 10 Assumed same as k(HO2 + H) −11 −200/T 112 HSO + O −−→ OH + SO 3.0 · 10 × e Assumed same as k(HO2 + O) 1 −11 113 CH2 + O2 −−→ H2CO + O 3 · 10 Tian et al. [2014] 3 +00 114 CH2 + O2 −−→ H2CO + O 00 · 10 Tian et al. [2014] 3 −11 115 CH2 + O −−→ CO + H + H 8.3 · 10 Homann and Wellmann [1983] 3 −30 457/T 116 CH2 + H −−→ CH3 k0 = 3.1 · 10 × e Gladstone et al. [1996] −10 k∞ = 1.5 · 10 −31 −3.0 117 CH3 + O2 −−→ CH3O2 4.49 · 10 × (T/298) DeMore et al. [1997] −12 −4450/T 118 CH3 + H2CO −−→ CH4 + HCO 6.8 · 10 × e Baulch et al. [1994] −12 119 CH3 + OH −−→ CO + H2 + H2 6.7 · 10 Fenimore [1969] −11 120 CH3O2 + H −−→ CH4 + O2 1.4 · 10 Bogdanchikov et al. [2004] −11 121 CH3O2 + H −−→ H2O + H2CO 1 · 10 Zahnle et al. [2006] −11 122 CH3O2 + O −−→ H2CO + HO2 1 · 10 Vaghjiani and Ravishankara [1990] −10 123 CH3CO + H −−→ CH4 + CO 1 · 10 Zahnle [1986] −11 124 CH3CO + O −−→ H2CO + HCO 5 · 10 Zahnle [1986] −11 125 CH3CO + CH3 −−→ C2H6 + CO 5.4 · 10 Adachi et al. [1981] −10 126 C2H5 + OH −−→ CH3 + HCO + H2 1 · 10 Pavlov et al. [2001] −10 127 C2H5 + O −−→ CH3 + HCO + H 1 · 10 Pavlov et al. [2001] −23 −1040/T 128 C2H5 + H −−→ C2H6 k0 = 5.5 · 10 × e Gladstone et al. [1996] −10 k∞ = 1.5 · 10 −11 −1600/T 129 O + H2CO −−→ OH + HCO 3.4 · 10 × e Tsang and Hampson [1986] −11 130 CH21 + H2 −−→ CH23 + H2 1.62 · 10 Romani et al. [1993] −17 131 HCO + H2CO −−→ CH3O + CO 3.8 · 10 Krasnoperov et al. [2004] −11 −5940/T 132 CH3O + CO −−→ CH3 + CO2 2.6 · 10 × e Wen et al. [1989] −12 −75/T 133 H2S + OH −−→ H2O + HS 6.0 · 10 × e Sander et al. [2006] −11 −860/T 134 H2S + H −−→ H2 + HS 1.3 · 10 × e Sander et al. [2006] −12 −1800/T 135 H2S + O −−→ OH + HS 9.2 · 10 × e Sander et al. [2006] 136 HS + O −−→ H + SO 1.6 · 10−10 Sander et al. [2006] −19 137 HS + O2 −−→ OH + SO 4.0 · 10 Sander et al. [2006] −11 138 HS + HO2 −−→ H2S + O2 3.0 · 10 Stachnik and Molina [1987] −11 139 HS + HS −−→ H2S + S 1.2 · 10 Schofield [1973] −11 140 HS + HCO −−→ H2S + CO 5.0 · 10 Kasting [1990] −11 141 HS + H −−→ H2 + S 1.0 · 10 Schofield [1973] −11 −800/T 142 HS + H2CO −−→ H2S + HCO 1.7 · 10 × e Sander et al. [2006] −12 −280/T 143 HS + O3 −−→ HSO + O2 9.0 · 10 × e Sander et al. [2006]

143 Rxn # Reaction Reaction Rate Constant Reference −11 240/T 144 HS + NO2 −−→ HSO + NO 2.9 · 10 × e Sander et al. [2006] −12 145 S + O2 −−→ SO + O 2.3 · 10 Sander et al. [2006] 146 S + OH −−→ SO + H 6.6·−11 Sander et al. [2006] 147 S + HCO −−→ HS + CO 5.0 · 10−11 Kasting [1990] −11 148 S + HO2 −−→ HS + O2 1.5 · 10 Kasting [1990] −11 149 S + HO2 −−→ SO + OH 1.5 · 10 Kasting [1990] −34 480/T 150 S + O3 −−→ SO + O2 9.46 · 10 × e × ρ Assumed same as k(O + O) −11 151 S + CO2 −−→ SO + CO 1.2 · 10 Sander et al. [2006] −11 152 HSO + H −−→ HS + OH 7.29 · 10 Assumed same as k(HO2 + H) −12 153 HSO + HS −−→ H2S + SO 1 · 10 Kasting [1990] 154 HSO + S −−→ HS + SO 1 · 10−11 Kasting [1990] −12 −710/T 155 NH3 + OH −−→ NH2 + H2O 1.7 · 10 × e Sander et al. [2006] −10 156 NH3 + O1D −−→ NH2 + OH 2.5 · 10 Sander et al. [2006] −30 −20 157 NH2 + H + M −−→ NH3 + M (6 · 10 × ρ)/(1 + 3 · 10 × ρ) Gordon et al. [1971] −12 450/T 158 NH2 + NO −−→ N2 + H2O 3.8 · 10 × e Sander et al. [2006] −10 159 NH2 + NH2 −−→ N2H4 + 1 · 10 Gordon et al. [1971] −12 160 NH2 + O −−→ NH + OH 5 · 10 Albers et al. [1969] −12 161 NH2 + O −−→ HNO + H 5 · 10 Albers et al. [1969] −11 162 NH + NO −−→ N2 + O + H 4.9 · 10 Sander et al. [2006] 163 NH + O −−→ N + OH 1 · 10−11 Kasting [1982] −12 −1200/T 164 N2H4 + H −−→ N2H3 + H2 9.9 · 10 × e Stief and Payne [1976] −12 165 N2H3 + H −−→ NH2 + NH2 2.7 · 10 Gehring et al. [1971] −11 166 N2H3 + N2H3 −−→ N2H4 + N2 + H2 6 · 10 Kuhn and Atreya [1979] −30 −20 + 167 NH + H + M −−→ NH2 + M (6 · 10 × ρ)/(1 + 3 · 10 × ρ) Assumed same as k(NH2 H) −11 168 NH2* + M −−→ NH2 + M 3 · 10 Kasting [1982] −11 169 NH2* + H2 −−→ NH3 + H 3 · 10 Kasting [1982] −11 170 NH2 + HCO −−→ NH3 + CO 1 · 10 Pavlov et al. [2001] −11 171 NH + HCO −−→ NH2 + CO 1 · 10 Pavlov et al. [2001] −32 172 N + N −−→ N2 1.25 · 10 Knipovich et al. [1988] −11 −360/T 173 N + O2 −−→ NO + O 1.5 · 10 × e Sander et al. [2006] −16 174 N + O3 −−→ NO + O2 2.01 · 10 DeMore et al. [1997] 175 N + OH −−→ NO + H 4.7 · 10−11 Baulch et al. [1994] −11 176 N + NO −−→ N2 + O 3.4 · 10 Sander et al. [2006] +03 177 SO23 + hν −−→ SO2 + hν 1.13 · 10 Turco et al. [1982] +03 178 SO21 + hν −−→ SO23 + hν 1.50 · 10 Turco et al. [1982] +04 179 SO21 + hν −−→ SO2 + hν 2.20 · 10 Turco et al. [1982] −13 180 O2 + hν −−→ O + O1D 6.02 · 10 −08 181 O2 + hν −−→ O + O 3.78 · 10 −07 182 H2O + hν −−→ H + OH 5.89 · 10 −03 183 O3 + hν −−→ O2 + O1D 2.71 · 10 −03 184 O3 + hν −−→ O2 + O 1.91 · 10 −05 185 H2O2 + hν −−→ OH + OH 5.64 · 10 −10 186 CO2+ hν −−→ CO + O 5.84 · 10 −05 187 H2CO + hν −−→ H2 + CO 2.57 · 10 −05 188 H2CO + hν −−→ HCO + H 3.32 · 10 189 HCO+ hν −−→ H + CO 3.32 · 10−05 190 NO+ hν −−→ N + O 1.85 · 10−06 191 NH+ hν −−→ N + H 6.12 · 10−05 −05 192 NH2 + hν −−→ NH + H 6.12 · 10 −03 193 NH2 + hν −−→ NH2X 3.08 · 10 +05 194 NH2X + hν −−→ NH2 + hν 1.20 · 10 −04 195 N2H4 + hν −−→ N2H3 + H 1.12 · 10 196 HSO + hν −−→ HS + O 1.62 · 10−04

144 Rxn # Reaction Reaction Rate Constant Reference −04 197 H2S + hν −−→ HS + H 3.96 · 10 −05 198 NH3 + hν −−→ NH2 + H 6.12 · 10 −07 199 C2H6 + hν −−→ CH3 + CH3 1.55 · 10 −07 200 CH4 + hν −−→ CH23 + H + H 8.50 · 10 −06 201 CH4 + hν −−→ CH3 + H 1.73 · 10 +03 202 CO2 + hν −−→ CO + O1D 2.73 · 10 −05 203 SO2 + hν −−→ SO21 9.87 · 10 −07 204 SO2 + hν −−→ SO23 3.47 · 10 −15 205 SO3 + hν −−→ SO2 + O 2.0 · 10 −04 206 HO2 + hν −−→ OH + O 3.96 · 10 −06 207 CH4 + hν −−→ CH21 + H2 1.05 · 10 +00 208 C2H6 + hν −−→ CH23 + C2H3 + H2 0.00 · 10 −07 209 C2H6 + hν −−→ CH4 + C2H1 4.8 · 10 −03 210 HNO2 + hν −−→ NO + OH 1.70 · 10 −05 211 HNO3 + hν −−→ NO2 + OH 8.63 · 10 −03 212 NO2 + hν −−→ NO + O 2.31 · 10 213 HNO + hν −−→ NO + H 1.70 · 10−03 −04 214 CH3 + hν −−→ CH21 + H 2.01 · 10 −05 215 SO2 + hν −−→ SO + O 9.96 · 10

145 Appendix B| Energy Balance Model Parametriza- tion

Our Energy Balance Model (EBM, Chapter 3.3), was originally created by Williams and Kasting [Williams and Kasting, 1997]. We updated this EBM with new radiative transfer parameterizations from our 1-D climate model (Chapter 3.1). The original radiative transfer parameterizations, from Williams and Kasting [1997], were replaced for this study with new parameterizations based on the 1-D model of Kopparapu et al. [2013]. We follow the procedure of Williams and Kasting [1997], Haqq-Misra et al. [2016] with the exception that we fit for hydrogen mixing ratio

because our early Mars 1D climate model is dependent on both CO2 and H2, as

opposed to just CO2. Therefore, we parameterize over total surface pressure, Ps,

instead of the partial pressure of CO2. Over 40,000 calculations with the 1-D model were used to investigate the dependence of radiative fluxes on different parameters. The outgoing long wave

flux, FOLR, was calculated as a 4th-order polynomial in surface pressure, surface

temperature, and volume mixing ratio of H2. The top-of-atmosphere albedo, α, (which is related to the absorbed solar flux) was split into two 3rd-order polynomials. This degree of polynomials were the orders that gave the best fit while not overfitting the data. If the parameters covered a large range (temperature and pressure), we used a logarithmic scale without a normalization. We convert back to linear scale to recover the final OLR or albedo. The first set of equations is for surface temperatures less than 250 K and the second is for surface temperatures between 250 K and 350 K. Both fits are calculated

as a function of zenith angle, surface pressure, surface temperature, H2 volume

146 mixing ratio and surface albedo because those are the dependent variables that drive the outgoing long wave radiation and the surface albedo. Both the OLR and albedo parameterizations assume early Mars’ solar constant and Mars’ radius.

They also assume an H2O-H2-CO2 atmosphere. In the equations below Tk is surface temperature, fH2 is H2 volume mixing ratio, Ps is surface pressure, µk is zenith angle, and as is surface albedo.

1 F = 10A1+A2+A3+A4 (B.1) OLR 1000

Where:

4 A1 =4.69e + 01 × log10 Tk − 3 8.52e + 00 × log10 Tk × (1.0 − fH2)− 3 3.65e + 00 × log10 Tk × log10 Ps− 3 4.70e + 02 × log10 Tk − 2 2 2.16e + 00 × log10 Tk × (1.0 − fH2) − (B.2) 2 8.94e − 01 × log10 Tk × (1.0 − fH2) × log10 Ps+ 2 6.18e + 01 × log10 Tk × (1.0 − fH2)+ 2 2 2.80e + 00 × log10 Tk × log10 Ps + 2 4.08e + 01 × log10 Tk × log10 Ps

147 2 A2 = + 1.76e + 03 × log10 Tk − 3 4.06e + 00 × log10 Tk × (1.0 − fH2) + 2 4.79e − 01 × log10 Tk × (1.0 − fH2) × log10 Ps+ 2 2.01e + 01 × log10 Tk × (1.0 − fH2) + 2 2.61e − 02 × log Tk × (1.0 − fH2) × log P + 10 10 s (B.3) 3.54e + 00 × log10 Tk × (1.0 − fH2) × log10 Ps−

1.57e + 02 × log10 Tk × (1.0 − fH2)− 3 3.18e − 01 × log10 Tk × log10 Ps − 2 1.50e + 01 × log10 Tk × log10 Ps −

1.34e + 02 × log10 Tk × log10 Ps

A3 = − 2.95e + 03 × log10 Tk− 4 7.75e − 01 × (1.0 − fH2) + 3 5.86e − 01 × (1.0 − fH2) × log10 Ps+ 3 1.28e + 01 × (1.0 − fH2) − 2 2 2.43e − 02 × (1.0 − fH2) × log P − 10 s (B.4) 2 2.52e + 00 × (1.0 − fH2) × log10 Ps− 2 4.02e + 01 × (1.0 − fH2) − 3 1.85e − 02 × (1.0 − fH2) × log10 Ps − 2 5.12e − 02 × (1.0 − fH2) × log10 Ps −

2.13e + 00 × (1.0 − fH2) × log10 Ps

148 A4 = + 1.41e + 02 × (1.0 − fH2)+ 4 1.95e − 02 × log10 Ps + 8.69e − 01 × log P 3+ 10 s (B.5) 2 1.99e + 01 × log10 Ps +

1.36e + 02 × log10 Ps+ 1.85e + 03

αk(Tk ≤ 250) = B1 + B2 + B3 + B4 + B5 + B6 (B.6)

Where:

3 B1 = − 3.41e − 01 × µk− 2 7.90e − 01 × µk × as− 2 2.72e − 01 × µk × log10 Tk+ 2 1.03e − 02 × µk × (1.0 − fH2)+ 2 8.50e − 03 × µk × log10 Ps+ (B.7) 2 1.93e + 00 × µk+ 2 4.14e − 02 × µk × as−

3.07e − 02 × µk × as × log10 Tk+

1.14e − 02 × µk × as × (1.0 − fH2)

149 B2 = − 5.54e − 02 × µk × as × log10 Ps+

1.17e + 00 × µk × as+ 2 2.88e + 00 × µk × log10 Tk −

3.19e − 02 × µk × log10 Tk × (1.0 − fH2)−

3.92e − 01 × µk × log Tk × log Ps− 10 10 (B.8) 1.35e + 01 × µk × log10 Tk− 2 3.58e − 03 × µk × (1.0 − fH2) +

1.15e − 04 × µk × (1.0 − fH2) × log10 Ps+

6.58e − 02 × µk × (1.0 − fH2)+ 2 1.54e − 02 × µk × log10 Ps

B3 = + 9.58e − 01 × µk × log10 Ps+

1.46e + 01 × µk+ 3 3.59e − 02 × as+ 2 6.11e − 02 × as × log10 Tk+ 2 1.07e − 03 × a × (1.0 − fH2)+ s (B.9) 2 5.41e − 02 × as × log10 Ps− 2 1.02e − 01 × as− 2 3.19e + 00 × as × log10 Tk +

8.11e − 02 × as × log10 Tk × (1.0 − fH2)−

8.41e − 03 × as × log10 Tk × log10 Ps

150 B4 = + 1.42e + 01 × as × log10 Tk− 2 1.52e − 02 × as × (1.0 − fH2) −

2.00e − 03 × as × (1.0 − fH2) × log10 Ps−

1.73e − 01 × as × (1.0 − fH2)− 2 5.15e − 02 × as × log P − 10 s (B.10) 2.33e − 01 × as × log10 Ps−

1.56e + 01 × as− 3 2.01e + 01 × log10 Tk + 2 7.67e − 01 × log10 Tk × (1.0 − fH2)+ 2 1.17e + 00 × log10 Tk × log10 Ps

2 B5 = + 1.38e + 02 × log10 Tk − 2 8.58e − 02 × log10 Tk × (1.0 − fH2) −

6.28e − 02 × log10 Tk × (1.0 − fH2) × log10 Ps−

3.52e + 00 × log10 Tk × (1.0 − fH2)− 2 5.73e − 02 × log Tk × log P − 10 10 s (B.11) 5.29e + 00 × log10 Tk × log10 Ps−

3.16e + 02 × log10 Tk+ 3 1.87e − 02 × (1.0 − fH2) − 2 4.99e − 03 × (1.0 − fH2) × log10 Ps+ 2 1.58e − 01 × (1.0 − fH2)

151 2 B6 = + 2.03e − 03 × (1.0 − fH2) × log10 Ps +

1.59e − 01 × (1.0 − fH2) × log10 Ps+

4.08e + 00 × (1.0 − fH2)+ 3 4.92e − 03 × log10 Ps + (B.12) 2 1.76e − 01 × log10 Ps +

6.08e + 00 × log10 Ps+ 2.41e + 02

αk(250 ≤ Tk ≤ 350) = C1 + C2 + C3 + C4 + C5 + C6 (B.13)

Where:

3 C1 = − 3.70e − 01 × µk− 2 3.45e − 01 × µk × as+ 2 7.75e − 01 × µk × log10 Tk− 2 4.37e − 03 × µk × (1.0 − fH2)+ 2 8.30e − 03 × µk × log10 Ps− (B.14) 2 8.08e − 01 × µk+ 2 6.19e − 02 × µk × as−

1.86e + 00 × µk × as × log10 Tk+

2.97e − 02 × µk × as × (1.0 − fH2)

152 C2 = − 6.47e − 02 × µk × as × log10 Ps+

5.09e + 00 × µk × as− 2 2.22e + 00 × µk × log10 Tk +

8.04e − 02 × µk × log10 Tk × (1.0 − fH2)+

1.62e − 01 × µk × log Tk × log Ps+ 10 10 (B.15) 1.08e + 01 × µk × log10 Tk− 2 5.47e − 03 × µk × (1.0 − fH2) −

6.47e − 03 × µk × (1.0 − fH2) × log10 Ps−

2.01e − 01 × µk × (1.0 − fH2)+ 2 1.68e − 02 × µk × log10 Ps

C3 = − 3.73e − 01 × µk × log10 Ps−

1.42e + 01 × µk+ 3 8.02e − 02 × as− 2 5.72e − 02 × as × log10 Tk+ 2 2.26e − 03 × a × (1.0 − fH2)+ s (B.16) 2 2.71e − 02 × as × log10 Ps+ 2 5.70e − 02 × as− 2 6.10e + 00 × as × log10 Tk +

4.07e − 01 × as × log10 Tk × (1.0 − fH2)+

6.95e − 01 × as × log10 Tk × log10 Ps

153 C4 = + 2.87e + 01 × as × log10 Tk− 2 4.65e − 02 × as × (1.0 − fH2) −

1.55e − 02 × as × (1.0 − fH2) × log10 Ps−

9.29e − 01 × as × (1.0 − fH2)− 2 3.30e − 02 × as × log P − 10 s (B.17) 1.85e + 00 × as × log10 Ps−

3.34e + 01 × as+ 3 4.19e + 01 × log10 Tk − 2 2.41e + 00 × log10 Tk × (1.0 − fH2)− 2 3.65e − 01 × log10 Tk × log10 Ps

2 C5 = − 3.05e + 02 × log10 Tk + 2 2.36e − 02 × log10 Tk × (1.0 − fH2) −

6.45e − 02 × log10 Tk × (1.0 − fH2) × log10 Ps+

1.16e + 01 × log10 Tk × (1.0 − fH2)+ 2 1.46e − 01 × log Tk × log P + 10 10 s (B.18) 1.81e + 00 × log10 Tk × log10 Ps+

7.41e + 02 × log10 Tk+ 3 4.92e − 02 × (1.0 − fH2) + 2 5.17e − 03 × (1.0 − fH2) × log10 Ps− 2 1.43e − 01 × (1.0 − fH2)

154 2 C6 = − 3.42e − 03 × (1.0 − fH2) × log10 Ps +

1.48e − 01 × (1.0 − fH2) × log10 Ps−

1.41e + 01 × (1.0 − fH2)+ 3 3.78e − 03 × log10 Ps − (B.19) 2 3.24e − 01 × log10 Ps −

2.11e + 00 × log10 Ps− 5.98e + 02

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182 Vita Natasha E. Batalha

Education 2017 Dual PhD Pennsylvani State University Astronomy & Astrophysics and Astrobiology Advisors: James F. Kasting & Steinn Sigurdsson 2013 B.A. Cornell University, Physics and Astronomy University of New South Wales, Physics and Astronomy Awards and Fellowships 2017 Ford Foundation Fellow Honorable Mention 2016 Alfred P. Sloan Foundation’s Minority Graduate Scholarship 2016 Kavli Student Fellow 2015 NAI Early Career Collaboration Award 2015 Stephen B. Brumbach Graduate Fellowship in Astrophysics 2014 National Science Foundation Graudate Research Fellowship 2013 STEM Scholar Graduate Feelow 2012 Douglas and Dorothy K. Wood Scholarship 2011 NASA/NY Space Grant Consortium Publications 2017 Batalha, N.E., et al., PandExo: A Community Tool for Exoplanet Science with the JWST and HST PASP, 129, 976 Batalha, N.E., Kempton, E., & Mbarek, R., Challenges in Constraining Exoplanet Masses via Transmission Spectroscopy, 2017, ApJL, 836, L5 Batalha, N.E., & Line, M.R., Information Content Analysis for Selection of Optimal JWST Observing Modes for Transiting Exoplanet Atmospheres. AJ, 153, 4 2016 Batalha, N.E., et al., Climate Cycling on Early Mars Caused by the Carbonate- Silicate Cycle EPSL, 455, 7-13 Haqq-Misra, J., Kopparapu, R., Batalha, N.E., et al. Limit Cycles Can Reduce the Width of the Habitable Zone, ApJ 2015 Batalha, N.E., et al., Testing the Early Mars H2-CO2 Greenhouse Hypothesis with a 1-D Photochemical Model. Icarus, 258, 337-349 Cowan, N.B, Greene, T., Angerhausen., D., Batalha, N.E. et al. Characteriz- ing Transiting Planet Atmospheres Through 2025 PASP, 127, 949 2014 Batalha, N.E., et al. Transiting Exoplanet Simulations with the James Webb Space Telescope. JWST White Paper, https://arxiv.org/abs/1507.02655 2011 Agueros, M., Covey, K., 3 others, Batalha, N.E. et al., The Factory and the Beehive. I. Rotation Periods of Low-Mass Stars in Praesepe. Apj, 740, 110