In the format provided by the authors and unedited. SUPPLEMENTARY INFORMATION DOI: 10.1038/NGEO2887 Elevated atmospheric escape of atomic hydrogen from Mars induced by high-altitude water M. S. Chaffin, J. Deighan, N. M. Schneider and A. I. F. Stewart 200 Altitude [km] Calculated self-consistently from lower boundary condition 150 O 100 Adopted from Krasnopolsky [2010] Binary diffusion coefficients from Hunten [1973] H 2 H Saturation threshold from Washburn [1924] Adopted from Matta et al. [2013] 50 0 10 10 Total number density [cm -3 ] 10 18 130 200 280 Temperature [K] Eddy diffusion profile from Krasnopolsky [1993] Column total 6.97 pr-um 6.94 pr-um SPICAM-derived water profile 10 6 10 9 0 100 10 0 10 5 + Water vapor CO Diffusion coefficients 2 concentration [ppm] concentration [cm -3 ] Supplementary Figure 1: Overview of major model inputs. See text for additional discussion. Total number density, temperature profile (from Krasnopolsky [S1]), and diffusion coefficients (from Krasnopolsky [S2] and Hunten [S3]) are all standard. In fourth panel, blue curves show the model water vapor profile for standard photochemistry (dark blue) and the high-altitude water case (light blue), as well as the total precipitable column and the saturation vapor pressure for the assumed temperature. Points and uncertainties show water vapor concentrations derived by Maltagliati et al. [S4] on MEX Orbit 6857, which observed Southern mid-latitudes in summer (Ls 250). A self-consistent ionosphere is not included in this work; instead, we adopt a reference CO + 2 profile from Matta, Withers, and Mendillo [S5]. NATURE GEOSCIENCE www.nature.com/naturegeoscience 1 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
Supplementary Table 1: Reaction network used in the present work. All photolysis rates are self-consistently computed as described in Methods. 2 Column Rate [cm 2 s 1 ] Reaction Rate Coefficient Standard Case High Water Case CO 2 + hν CO + O 1.04 10 12 4.35 10 11 CO + O( 1 D) 1.39 10 11 1.02 10 11 O 2 + hν O + O 1.61 10 11 1.46 10 12 O + O( 1 D) 1.47 10 10 1.05 10 11 O 3 + hν O 2 + O 7.39 10 11 2.33 10 14 O 2 + O( 1 D) 4.29 10 12 3.59 10 14 O + O + O 0.00 0.00 H 2 + hν H + H 9.78 10 4 1.98 10 4 OH + hν O + H 3.51 10 5 1.95 10 6 O( 1 D) + H 2.13 10 1 2.94 HO 2 + hν OH + O 2.13 10 10 1.64 10 9 H 2 O + hν H + OH 3.26 10 10 9.71 10 9 H 2 + O( 1 D) 3.14 10 7 2.45 10 7 H + H + O 0.00 0.00 H 2 O 2 + hν OH + OH 5.84 10 10 9.09 10 8 HO 2 + H 3.04 10 9 5.14 10 7 H 2 O + O( 1 D) 0.00 0.00 O + O + M O 2 + M 1.8 3.0 10 33 (300/T ) 3.25 1.20 10 11 2.21 10 10 O + O 2 + N 2 O 3 + N 2 5 10 35 exp(724/t ) 5.23 10 10 5.77 10 12 O + O 2 + CO 2 O 3 + CO 2 2.5 6.0 10 34 (300/T ) 2.4 5.06 10 12 5.87 10 14 O + O 3 O 2 + O 2 8.0 10 12 exp( 2060/T ) 3.53 10 7 6.34 10 10 O + CO + M CO 2 + M 2.2 10 33 exp( 1780/T ) 3.64 10 7 1.86 10 6 O( 1 D) + O 2 O + O 2 3.2 10 11 exp(70/t ) 2.13 10 9 5.98 10 12 O( 1 D) + O 3 O 2 + O 2 1.2 10 10 8.28 10 4 2.76 10 9 O + O + O 2 1.2 10 10 8.28 10 4 2.76 10 9 O( 1 D) + H 2 H + OH 1.2 10 10 6.38 10 7 3.70 10 8 Continued on next page
3 Supplementary Table 1 continued from previous page Column Rate [cm 2 s 1 ] Reaction Rate Coefficient Standard Case High Water Case O( 1 D) + CO 2 O + CO 2 7.5 10 11 exp(115/t ) 4.44 10 12 3.54 10 14 O( 1 D) + H 2 O OH + OH 1.63 10 10 exp(60/t ) 6.26 10 8 4.43 10 10 H 2 + O OH + H 6.34 10 12 exp( 4000/T ) 1.28 10 6 2.58 10 5 OH + H 2 H 2 O + H 9.01 10 13 exp( 1526/T ) 2.85 10 8 4.65 10 8 H + H + CO 2 H 2 + CO 2 1.6 10 32 (298/T ) 2.27 5.44 10 5 5.19 10 6 H + OH + CO 2 H 2 O + CO 2 1.9 6.8 10 31 (300/T ) 2 7.00 10 5 1.33 10 6 H + HO 2 OH + OH 7.2 10 11 1.02 10 10 1.75 10 10 H 2 O + O( 1 D) 1.6 10 12 2.26 10 8 3.88 10 8 H 2 + O 2 3.4 10 12 4.88 10 8 8.37 10 8 H + H 2 O 2 HO 2 + H 2 2.8 10 12 exp( 1890/T ) 1.45 10 5 3.09 10 2 H 2 O + OH 1.7 10 11 exp( 1800/T ) 1.41 10 6 3.55 10 3 H + O 2 + M HO 2 k 0 = 2.0 4.4 10 32 (T/300) 1.3 1.24 10 12 1.48 10 12 k = 7.5 10 11 (T/300) 0.2 H + O 3 OH + O 2 1.4 10 10 exp( 470/T ) 8.02 10 10 3.82 10 11 O + OH O 2 + H 1.8 10 11 exp(180/t ) 1.45 10 11 1.34 10 12 O + HO 2 OH + O 2 3.0 11 exp(200/t ) 1.08 10 12 1.53 10 12 O + H 2 O 2 OH + HO 2 1.4 10 12 exp( 2000/T ) 7.33 10 6 1.39 10 6 OH + OH H 2 O + O 1.8 10 12 3.07 10 6 3.91 10 8 OH + OH + M H 2 O 2 k 0 = 1.3 6.9 10 31 (T/300) 1.0 3.99 10 4 1.32 10 7 k = 2.6 10 11 OH + O 3 HO 2 + O 2 1.7 10 12 exp( 940/T ) 9.18 10 6 1.65 10 11 OH + HO 2 H 2 O + O 2 4.8 10 11 exp(250/t ) 1.14 10 10 5.07 10 10 OH + H 2 O 2 H 2 O + HO 2 1.8 10 12 1.49 10 9 1.95 10 9 HO 2 + O 3 OH + O 2 + O 2 1.0 10 14 exp( 490/T ) 2.39 10 8 4.51 10 10 HO 2 + HO 2 H 2 O 2 + O 2 3.0 10 13 exp(460/t ) 6.19 10 10 2.85 10 9 HO 2 + HO 2 + M H 2 O 2 + O 2 + M 2 2.1 10 33 exp(920/t ) 9.98 10 8 5.05 10 7 CO + OH + M CO 2 + H k 0 = 1.5 10 13 (T/300) 0.6 1.17 10 12 5.34 10 11 k = 2.1 10 9 (T/300) 6.1 Continued on next page
Supplementary Table 1 continued from previous page Column Rate [cm 2 s 1 ] Reaction Rate Coefficient Standard Case High Water Case HOCO k 0 = 5.9 10 33 (T/300) 1.4 7.17 10 9 2.98 10 9 k = 1.1 10 12 (T/300) 1.3 HOCO + O 2 HO 2 + CO 2 2.0 10 12 7.17 10 9 2.98 10 9 CO + 2 + H 2 CO 2 + H + H 8.7 10 10 1.36 10 8 3.07 10 7 Sander et al. [S6] defines expressions to compute rates involving k 0 and k coefficients: k f ([M],T ) = k 0 [M] 1 +k 0 [M]/k 0.6 1/{1+(log 10 [k 0[M]/k ])2 } For all reactions except CO + OH CO 2 + H, the standard expression for termolecular reactions applies, but a special formula for this reaction is necessary because the reaction takes place on a potential energy surface that contains the radical HOCO (see Sander et al. [S6]): 4 k ca f ([M],T ) = k 0 1 +k 0 [M]/k 0.6 1/{1+(log 10 [k 0[M]/k ])2 }
Supplementary Table 2: Model boundary conditions. For those species not listed, a zero-flux condition is assumed at the top and bottom boundary of the model. Boundary Species Condition lower CO 2 n = 2.1 10 17 cm 3 Ar n = 4.2 10 15 cm 3 n = 4.0 10 15 cm 3 N 2 upper O φ = 1.2 10 8 cm 2 s 1 H 2 v = 3.4 10 1 cm s 1 H v = 3.1 10 3 cm s 1 5 6 Supplementary Figure reporting absolute number densities O( 1 D) H H 2 ArN 2 H H 2 ArN 2 a b H 2 O H 2 O CO 2 CO 2 + OH O 3 CO 2 + CO 2 HO 2 OH H 2 O 2 HOCO HO 2 O 3 O CO O 2 O( 1 D) HOCO H 2 O 2 O CO O 2 Supplementary Figure 2: Equilibrium photochemical model output. Number density of all model species are shown at all model altitudes. (a) The model reproduces the well-known photochemistry of the Mars atmosphere for a standard water profile. Long lived species such as H 2 have constant mixing ratios in the well-mixed lower atmosphere and follow their own scale height above the homopause. (b) With the introduction of upper atmospheric water, the equilibrium photochemistry is greatly perturbed. Compared to the standard model, the abundance of molecular oxygen is greatly increased, the O 2 /CO ratio is much larger, and the abundance of hydrogen resulting from water breakdown is decreased in the lower atmosphere. 5
7 8 9 10 11 12 Supplementary note on response to assumed water profiles Explicit numerical details of the first year of the atmospheric response to the assumed input conditions are displayed in Figure 3 is given in Supplementary Table 1. A figure illustrating the H escape response of the atmosphere to steady-state water perturbations over ten million year timescales is given in Supplementary Figure 3. Altitude [km] H Escape Flux [cm -2 s -1 ] Supplementary Figure 3: Sensitivity of atmospheric response to altitude and magnitude of water parcel injected over the first 10 million years of simulated time. (left) Water vapor profiles instantaneously introduced into the standard water photochemistry, colored by altitude of injection. (right) Response of atmospheric escape to water introduction. Within each altitude group, magnitude of response is intuitive: more water injection results in a larger impact on escape rates. After the first year, in which a prompt enhancement in H production at altitude increases escape rates, the subsequent enhancement is due to effects of the water bulge on the bulk H 2 concentration of the atmosphere. On very long timescales, the enhanced escape of H from the system results in an O 2 buildup, which throttles H 2 production, reducing the atmospheric mixing ratio until stoichiometric balance is reached or the end of the simulated timespan is reached. On million-year timescales, the zero-flux boundary condition at the bottom of the atmosphere is likely invalid, and could act as a sink for atmospheric oxygen, increasing the timescale of any decrease in the H escape flux. 6
Supplementary Table 1: Response of the model atmosphere to different assumed water profiles. For each profile, a Gaussian parcel with a one sigma width of 12.5 km was added at the specified altitude and peak mixing ratio. These profiles modified the initial assumed inventory of 6.94 precipitable microns, adding the indicated amount of water to the atmosphere. After one year, these water profiles affect the atmosphere, increasing the escaping H flux at the top of the atmosphere, with the greatest effect caused by parcels added at 60 and 80 km. Parcels added at lower altitudes take longer to affect escape, as indicated by the time the system takes to reach one-half the final escape flux. Altitude Peak Concentration Total water Ratio of increased Time to half final [km] [ppm] added [pr-µm] to prior flux value [ 10 4 s] 20 20 0.583 1.003 428 40 1.17 1.006 428 60 1.75 1.009 428 80 2.33 1.012 428 40 20 0.085 1.137 142 40 0.170 1.241 142 60 0.255 1.332 138 80 0.341 1.415 138 60 20 0.811 10 2 2.101 75.3 40 1.62 10 2 3.022 72.9 60 2.43 10 2 3.865 70.5 80 3.25 10 2 4.657 68.2 80 20 0.503 10 3 2.547 36.1 40 1.01 10 3 4.306 36.1 60 1.51 10 3 5.491 34.9 80 2.01 10 3 6.919 34.9 100 20 2.64 10 5 1.468 10.8 40 5.27 10 5 1.934 10.8 60 7.91 10 5 2.400 10.8 80 10.6 10 5 2.864 10.8 120 20 1.87 10 6 1.054 2.85 40 3.74 10 6 1.108 2.85 60 5.61 10 6 1.161 2.85 80 7.49 10 6 1.215 2.85 13 14 15 16 17 Supplementary Note on Stoichiometric Balance Adding water to an equilibrated atmosphere and running to equilibrium (where all photochemical reactions are in balance) represents a departure from an atmospheric steady state (a situation in which the atmospheric model inputs, such as temperature, or in our case the assumed water column, are constant in time or oscillatory about some well-defined mean). 7
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 We know that Mars has experienced departures from a steady state in the past, resulting from changes in insolation, obliquity, and overall atmospheric loss. The present work demonstrates that such changes must have affected the relative escape of H and O, so that the question of whether escape is stoichiometrically balanced amounts to the question of how the Mars atmosphere has departed from a steady state over its history. To illuminate the point further, it is instructive to consider the time evolution of each equilibrium endmember case shown in Figure 1 after swapping the water profiles (Supplementary Figure 4). Introduction of high-altitude water into the standard atmosphere produces a photochemical imbalance which lasts some ten million years. Upon addition of the water, H escape increases immediately, with O escape fixed by ionospheric properties largely unaffected by increased upper atmospheric water [S7]. O builds up in the atmosphere over the next ten million years until the reaction H + O 2 + M HO 2 + M shifts the H/HO 2 balance so far in favor of HO 2 that H 2 production by H + HO 2 H 2 + O 2 is suppressed and stoichiometric escape is restored. However, this restoration of photochemical equilibrium does not represent a return to an atmospheric steady state, because the water column is still perturbed. Thus, the net addition of high-altitude water to the atmosphere has led to excess escape of H relative to O, and the atmosphere is in a more oxidized state as a result. If we then remove the excess water and run to photochemical equilibrium, we are returning the atmosphere to an equilibrium steady state. Upon removal of the water, H loss is suppressed immediately, but O continues escaping at the same constant rate, draining the atmosphere of O 2 until H 2 production is restored and instantaneous stoichiometric balance in the escaping species is restored. After equilibrium is restored, the simultaneous return to steady state ensures that the integrated loss of H and O across the entire perturbation is in a 2:1 ratio. In this paper, we suggest that the Mars atmosphere could be experiencing departures from a photochemical steady state that are driving the system toward a more oxidized state through excess hydrogen escape. This proposition is not unreasonable: we know the Mars atmosphere has not been in a steady state throughout its history because the geology of the planet records evidence of a much warmer and wetter atmosphere in the distant past. Present-day departures from the climatological steady state exist in form of dust storms every several Mars years, indicating that the system is highly variable in ways we do not fully understand. It is possible for the Mars atmosphere to be near or in photochemical equilibrium without having been in a steady state: in fact this is the most likely outcome given what we know about the climate and orbital history of Mars. Assessments of stoichiometric balance in the future should acknowledge this distinction and make some attempt to address it. 8
Supplementary Figure 4: H escape rate as a function of time after adding/removing a high altitude water parcel to the column in the low/high equilibrium case. H escape rates depart from instantaneous equilibrium in both cases, but if water is added, run to equilibrium, and then removed and run to equilibrium again, the total amount of H lost is twice that of the O loss on the same timescale. H and O stoichiometric balance is therefore a consequence of an atmospheric steady state rather than photochemical equilibrium. 52 Supplementary References 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 [S1] [S2] [S3] [S4] [S5] [S6] Vladimir A. Krasnopolsky. Solar activity variations of thermospheric temperatures on Mars and a problem of CO in the lower atmosphere. In: Icarus 207.2 (2010), pp. 638 647. issn: 0019-1035. doi: 10.1016/j.icarus.2009.12.036. url: http: //dx.doi.org/10.1016/j.icarus.2009.12.036. V. A. Krasnopolsky. Photochemistry of the Martian atmosphere (mean conditions). In: Icarus 101 (Feb. 1993), pp. 313 332. doi: 10.1006/icar.1993.1027. D. M. Hunten. The Escape of Light Gases from Planetary Atmospheres. In: J. Atmos. Sci. 30 (Nov. 1973), pp. 1481 1494. doi: 10.1175/1520-0469(1973)030<1481: TEOLGF>2.0.CO;2. L. Maltagliati et al. Annual survey of water vapor vertical distribution and wateraerosol coupling in the martian atmosphere observed by SPICAM/MEx solar occultations. In: Icarus 223.2 (2013), pp. 942 962. issn: 0019-1035. doi: 10.1016/j. icarus.2012.12.012. url: http://dx.doi.org/10.1016/j.icarus.2012.12.012. Majd Matta, Paul Withers, and Michael Mendillo. The composition of Mars topside ionosphere: Effects of hydrogen. In: Journal of Geophysical Research: Space Physics 118.5 (2013), pp. 2681 2693. issn: 2169-9380. doi: 10.1002/jgra.50104. url: http: //dx.doi.org/10.1002/jgra.50104. S. P. Sander et al. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation Number 17. Tech. rep. JPL, 2011. 9
72 73 74 75 [S7] Michael B. McElroy, Ten Ying Kong, and Yuk Ling Yung. Photochemistry and evolution of Mars atmosphere: A Viking perspective. In: Journal of Geophysical Research 82.28 (1977), 43794388. issn: 0148-0227. doi:10.1029/js082i028p04379. url:http: //dx.doi.org/10.1029/js082i028p04379. 10