1 Exoplanet secondary atmosphere loss and revival 2 3 Edwin S. Kite1 & Megan Barnett1 4 1. University of Chicago, Chicago, IL ([email protected]). 5 6 Abstract. 7 8 The next step on the path toward another Earth is to find atmospheres similar to those of 9 Earth and Venus – high-molecular-weight (secondary) atmospheres – on rocky exoplanets. 10 Many rocky exoplanets are born with thick (> 10 kbar) H2-dominated atmospheres but 11 subsequently lose their H2; this process has no known Solar System analog. We study the 12 consequences of early loss of a thick H2 atmosphere for subsequent occurrence of a high- 13 molecular-weight atmosphere using a simple model of atmosphere evolution (including 14 atmosphere loss to space, magma ocean crystallization, and volcanic outgassing). We also 15 calculate atmosphere survival for rocky worlds that start with no H2. Our results imply that 16 most rocky exoplanets interior to the Habitable Zone that were formed with thick H2- 17 dominated atmospheres lack high-molecular-weight atmospheres today. During early 18 magma ocean crystallization, high-molecular-weight species usually do not form long-lived 19 high-molecular-weight atmospheres; instead they are lost to space alongside H2. This early 20 volatile depletion makes it more difficult for later volcanic outgassing to revive the 21 atmosphere. The transition from primary to secondary atmospheres on exoplanets is 22 difficult, especially on planets orbiting M-stars. However, atmospheres should persist on 23 worlds that start with abundant volatiles (waterworlds). Our results imply that in order to 24 find high-molecular-weight atmospheres on warm exoplanets orbiting M-stars, we should 25 target worlds that formed H2-poor, that have anomalously large radii, or which orbit less 26 active stars. 27 28 Introduction. 29 30 The Solar System has three planets – Earth, Venus, and Mars – that have atmospheres 31 derived from H2-free solids (secondary atmospheres), and four giant planets whose 32 atmospheres are derived from H2-dominated protoplanetary nebula gas (primary 33 atmospheres) (Atreya et al. 1989, Marty et al. 2016). However, this clean separation in 34 process and outcome is apparently unrepresentative of the known exoplanets. 35 36 The two most common types of known exoplanet, the rocky super-Earth-sized planets 37 (planet radius Rpl < 1.6 R⊕, where “⊕” is the Earth symbol, planet density ρpl > 4 g/cc; 38 “super-Earths”) and the gas-shrouded sub-Neptunes (Rpl = 2 - 3 R⊕), are divided by a valley 39 in (planet radius)-(orbital period) space in which planets are less common (Fig. 1) 40 (Fulton et al. 2017). The radius valley can be understood if, and only if, a substantial 41 fraction of planets that are born with thick (>10 kbar) H2-dominated primary atmospheres 42 lose those atmospheres and shrink in radius to become rocky super-Earths (Van Eylen et al. 43 2018). This radius-shrinking process, which carves out the radius valley, may be the way 44 that most super-Earths form. There is no evidence that Earth and Venus underwent this 45 process, and primary atmospheres are not thought to have contributed to the origin of 1 46 major volatile elements in Earth (Dauphas & Morbidelli 2014). Both Venus and Earth have 47 secondary volatile envelopes (comprised of solid-derived volatiles, including H2O and CO2) 48 that are much less massive than the atmospheres of sub-Neptunes. Large surface reservoirs 49 of H2O, C species, and N species are essential to life on Earth and to Earth’s habitable 50 climate (Bergin et al. 2015, Catling & Kasting 2017). 51 52 It is not known whether or not being born with a thick primary atmosphere that is 53 subsequently lost – forming as a gas-shrouded sub-Neptune but ending up as a rocky 54 super-Earth – favors the planet ending up with a secondary atmosphere, like Venus and 55 Earth. Do primary atmospheres, in dying, shield high-molecular-weight species from loss 56 during the early era of atmosphere-stripping impacts and intense stellar activity, allowing 57 those constituents to later form a secondary atmosphere? Or does the light (H2-dominated) 58 and transient primary atmosphere drag away the higher-molecular weight species? Getting 59 physical insight into the transition from primary to secondary atmospheres is particularly 60 important for rocky exoplanets that are too hot for life. Hot rocky exoplanets are the 61 highest signal/noise rocky targets for upcoming missions such as James Webb Space 62 Telescope (JWST) (Kempton et al. 2018) and so will be the most useful for checking our 63 understanding of this atmospheric transition process. 64 65 Secondary atmospheres hold a central place in the exoplanet exploration strategy 66 (National Academy of Sciences 2018, Zahnle & Catling 2017). Nevertheless, to our 67 knowledge, this is the first study of the transition on exoplanets from primary to secondary 68 atmospheres (Urey 1951, Ozima & Zahnle 1993). 69 70 Gas survival during planetary volume reduction. 71 72 During the sub-Neptune to super-Earth conversion process, we suppose the planet 73 contains both nebular-derived H2 and also high-μ species (derived from the planet-forming 74 solid materials) that – if retained – could form a secondary atmosphere. Retention of 75 volatiles is controlled by atmospheric loss and atmosphere-interior exchange (Fig. 2). For 76 both sub-Neptunes and super-Earths, silicates (both magma and solid rock) apparently 77 make up most of the planet’s mass (e.g. Dai et al. 2019, Owen and Wu 2017). 78 79 Atmosphere loss is more difficult for high-molecular-weight volatiles than for H2 because 80 higher-molecular-weight volatiles such as H2O are more easily shielded within the silicate 81 interior and are also more resistant to escape. 82 83 This can be understood as follows. First, a basic control on atmosphere loss is the ratio, λ, of 84 gravitational binding energy to thermal energy: 85 86 λ = (μ / k Tua) (G Mpl / (R + z ) ) 4 87 ≈ 2.3 μ (10 K / Tua)( Mpl / 6 M⊕)/( (R + z ) / 2 R⊕) (1) 88 89 where μ is molecular mass, k is Boltzmann’s constant, Tua is upper-atmosphere 90 teMperature, G is the gravitational constant, Mpl is planet Mass, R is the radius of the silicate 91 planet, and z is atmosphere thickness. When λ ≲ 2, the upper atmosphere flows out to 2 92 space at a rate potentially limited only by the energy available from upper-atmosphere 93 absorption of light from the star (Watson et al. 1981). If the upper atmosphere absorbs 94 100 W/m2 of light from the star, the upper limit on loss rate is ~1000 bars/Myr. This 95 hydrodynamic outflow ejects the tenuous upper atmosphere at high speed, but the dense 96 lower part of the atmosphere remains close to hydrostatic equilibrium. When λ > 10, the 97 hydrodynamic outflow completely shuts down. For primary atmospheres, the mean 98 molecular weight μavg ≈ 2 Da (H2) while for secondary atmospheres, μavg is ≳10× higher 99 favoring secondary atmosphere retention. Moreover, for secondary atmospheres Tua is 100 lower, as many secondary-atmosphere constituents (e.g CO2) are much more effective 101 coolants than H2 (e.g. Kulikov et al. 2007, Johnstone et al. 2018). Atmospheric thickness z is 102 also sMaller for high-μavg atMospheres due to their sMaller scale height. For both secondary 103 atmospheres and primary atmospheres, proximity to the star drives λ to lower values by 104 increasing Tua and also increases the upper atmosphere outflow rate when the λ ≲ 2 105 condition is satisfied. Moreover, closer to the star impacts occur at higher velocities that 106 are more erosive (Kegerreis et al. 2020). Thus we expect massive worlds far from the star 107 to retain atmospheres and low-mass worlds closer to the star to lose them (Zahnle & 108 Catling 2017). This expectation, while physically valid, offers little guidance as to whether 109 or not super-Earths will have atmospheres. To go further, we need to consider the effect of 110 evolving atmospheric composition on loss rate (Eqn. 1) and also track the shielding of 111 volatiles within silicates (magma oceans and solid rock). 112 113 The atmospheres of young sub-Neptunes are directly underlain by magma oceans (e.g. 114 Vazan et al. 2018; Fig. S1). Equilibrium partitioning of a volatile i between the atmosphere 115 (where it is vulnerable to escape) and the magma ocean (where it is shielded from escape) 116 is set by 117 118 ci = ei + [ (ei / Amai) gmai (μavg/ μi ) ] si mmagma + other reservoirs (2) 119 120 where ci is the total inventory of the volatile, ei is the mass in the atmosphere, Amai (and 121 gmai) are the area of (and gravitational acceleration at) the magma-atmosphere interface, -1 122 μavg is the mean μ of the atmosphere, si is the solubility coefficient (mass fraction Pa ) of the 123 volatile in the magma, and mmagma is the mass of liquid in the magma ocean. The term in 124 square brackets in Eqn. (2) corresponds to the partial pressure of i at the magma- 125 atmosphere interface. Solubility in magma is higher for many secondary-atmosphere 126 constituents (e.g. CH4, H2S, H2O) than for H2. When the atmosphere contains both H2 and a 127 more-soluble, high-μ constituent, the H2 is less protected by shielding within the MagMa, so 128 the H2 takes the brunt of atmosphere loss processes that might otherwise remove the high- 129 μ species. Greater solubility in magma also protects high-μ species from impact shock 130 (Genda & Abe 2005). Other reservoirs include volatiles stored in the crystal phase. This is 131 an unimportant reservoir early on when the planet has a massive magma ocean, but 132 becomes important later (for mature rocky planets, such as the Earth, the rock is almost 133 entirely solid).