Stratosphere Circulation on Tidally Locked Exoearths

MNRAS 473, 4672–4685 (2018) doi:10.1093/mnras/stx2732 Advance Access publication 2017 October 25

Stratosphere circulation on tidally locked ExoEarths

L. Carone,1‹ R. Keppens,2 L. Decin3 and Th. Henning1 1Max-Planck-Institute for Astronomy, Koenigsstuhl 17, D-69117 Heidelberg, Germany 2Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium 3Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium

Accepted 2017 October 12. Received 2017 October 12; in original form 2017 July 7 Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021

ABSTRACT Stratosphere circulation is important to interpret abundances of photochemically produced compounds like ozone which we aim to observe to assess habitability of exoplanets. We thus investigate a tidally locked ExoEarth scenario for TRAPPIST-1b, TRAPPIST-1d, Proxima Centauri b and GJ 667 C f with a simplified 3D atmosphere model and for different stratospheric wind breaking assumptions. These planets are representatives for different circulation regimes for orbital periods: Porb = 1–100 d. The circulation of exoplanets with Porb ≤ 25 d can be dominated by the standing tropical Rossby wave in the troposphere and also in the stratosphere: It leads to a strong equatorial eastward wind jet and to an ‘Anti-Brewer-Dobson’-circulation that confines airmasses to the stratospheric equatorial region. Thus, the distribution of photochemically produced species and aerosols may be limited to an ‘equatorial transport belt’. In contrast, planets with Porb > 25 d, like GJ 667 C f, exhibit efficient thermally driven circulation in the stratosphere which allows for a day side-wide distribution of airmasses. The influence of the standing tropical Rossby waves on tidally locked ExoEarths with Porb ≤ 25 d can, however, be circumvented with deep stratospheric wind breaking alone – allowing for equator-to-pole transport like on Earth. For planets with 3 ≤ Porb ≤ 6 d, the extratropical Rossby wave acts as an additional safeguard against the tropical Rossby wave in case of shallow wind breaking. Therefore, TRAPPIST-1d is less prone to have an equatorial transport belt in the stratosphere than Proxima Centauri b. Even our Earth model shows an equatorial wind jet, if stratosphere wind breaking is ineffi- cient. Key words: methods: numerical – planets and satellites: atmospheres.

greater than 20 km; see e.g. Barstow & Irwin 2016; Kreidberg & 1 INTRODUCTION Loeb 2016; Morley et al. 2017). To discuss habitability, we have Tidally locked planets in the habitable zone of cool red dwarf stars to reliably infer the properties of the underlying troposphere and like the TRAPPIST-1 planets, Proxima Centauri b, LHS 1140 b potentially habitable surface from upper atmosphere composition and GJ 667 C f (Anglada-Escudeetal.´ 2013, 2016; Gillon derived from infrared spectra. et al. 2016, 2017; Dittmann et al. 2017; Luger et al. 2017)are The abundances of molecular species and clouds that we can de- our next best hope to study conditions for habitability outside of tect on rocky planets by ‘far remote-sensing’ are modified by the the Solar system. Proxima Centauri b is the nearest exoplanet, general large-scale circulation. On Venus, surface reactions produce located only 1.295 pc away from the Sun. The TRAPPIST-1 planets COS and H2S that are transported upwards as part of the global are only 12 pc away and, in addition, all seven planets transit in front Hadley circulation cells. In the higher atmosphere, the sulphur - of their stars with relatively short orbital periods (Porb = 1.5–18.8 containing compounds are further processed via photochemistry d). Thus, the TRAPPIST-1 planets are particularly suited to search to SO2 and sulphuric acid to form clouds. The global superrotat- for bio-signatures in diverse environments by employing, e.g. in- ing flow results then in a continuous cloud blanket that enshrouds frared spectroscopy with JWST. However, infrared spectroscopy Venus completely (see e.g. Prinn & Fegley 1987,forareviewon mainly probes high atmospheric layers, which would correspond to Venus chemistry and climate). On Earth, the Brewer-Dobson- the stratosphere and mesosphere on Earth (p ≤ 0.1 bar or altitudes circulation in the stratosphere tends to transport the biomarker ozone from its main production regions in the tropical upper strato- sphere towards the polar lower stratosphere (e.g. Dobson 1931; E-mail: [email protected] Brewer 1949; Shaw & Shepherd 2008). Also, the abundances of

C 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society ExoEarth’s stratosphere circulation 4673 Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021

Figure 1. Different troposphere circulation states identified by Carone, Keppens & Decin (2015) for tidally locked terrestrial planets with respect to orbital period and planetary size, assuming Earth-like atmosphere and thermal forcing. Example planets show a cross-section of the planet’s temperature (colour) and wind flow (grey lines and black arrows) at the top of the troposphere p = 225 mbar and facing the substellar point. Red circles denote the radius and orbital period of the TRAPPIST-1 b,c,d,e,f,g,h planets in this ‘circulation state map’ from left to right. Blue circles denote the position of Proxima Centauri b, LHS 1440 b, GJ 667 C-c and -f, assuming Earth-like density for non-transiting planets. The black to white small circles denote the 3D climate simulations carried out by Carone et al. (2015).

CH4 – another biomarker – are affected by the stratospheric Brewer- For each circulation regime, we also investigate two different Dobson-circulation (Cordero & Kawa 2001). On Mars, 3D cir- stratosphere wind breaking assumptions. We chose the following culation is instrumental for the formation of a polar ozone layer representative examples for each circulation regime: a habitable (Montmessin & Lefevre` 2013). In summary, the 3D circulation is TRAPPIST-1b, TRAPPIST-1d, Proxima Centauri b and GJ 667 C crucial for the understanding of the abundances and distribution of f scenario. We will show that, on many tidally locked ExoEarths, aerosols, photochemically produced compounds and clouds in the planetary waves propagate vertically from the troposphere into the upper atmosphere of terrestrial, habitable exoplanets that we will stratosphere with different outcomes in stratosphere circulation: ei- characterize in the near future. ther circulation is confined to an ‘equatorial transport belt’ or circu- In this work, we will investigate stratosphere circulation on tidally lation favours a day side-wide distribution of airmass via thermally locked habitable planets with planetary obliquity zero in the hab- driven equator-to-pole-wards transport. itable zone of ultra-cool dwarf stars for a large range of relevant orbital periods (Porb = 1.5–39 d). We further assume to the first or- der Earth-like atmosphere composition and thermal forcing. Such 2MODEL planets develop highly interesting un-Earth-like circulation patterns We use the model introduced in Carone et al. (2014) for terres- that warrant in-depth investigations, as we already showed for the trial tidally locked planets with greenhouse gas atmospheres. We troposphere (Carone, Keppens & Decin 2014, 2015, 2016). extend the radiative-convective equilibrium temperatures derived We will investigate stratospheric circulation in different tropo- there with a stratosphere extension as described below. The ex- sphere circulation regimes that develop for specific orbital period tended radiative-convective equilibrium temperatures are used in ranges. One of the characteristics of these circulation regimes is that the Newtonian cooling framework as thermal forcing (see section troposphere winds are more or less forced into banded or zonally 2.3 in Carone et al. 2014) in the 3D global circulation model MIT- confined wind structures via two different Rossby waves. The trop- gcm (Adcroft et al. 2004) that solves the primitive hydro-static ical Rossby wave leads to a single equatorial superrotating jet, and equations (see section 2.1 in Carone et al. 2014). We furthermore the extratropical Rossby wave to two high-latitude wind jets. The use a Rayleigh surface friction prescription as described in section specific circulation regimes are (Fig. 1): 2.2 of Carone et al. (2014), where we vary in the following – when appropriate – the maximum surface friction time-scale τ s, fric be- (i) ultra-short orbital periods with a strong mixture of equatorial tween 0.1 and 10 d to establish different circulation states for one superrotation and high-latitude wind jets (Porb ≤ 3d) and the same planet (Carone et al. 2016). (ii) short orbital periods with dominance of either equatorial or high-latitude wind jets (P = 3–6 d) orb 2.1 Stratosphere temperature extension and vertical (iii) intermediate orbital periods with weak superrotation (P = orb resolution 6–25 d) and (iv) long orbital periods (Porb ≥ 25 d) with no standing Rossby We assume for the day-side troposphere the equations outlined in waves and therefore mainly radial wind flow instead of banded wind section 2.4.2 of Carone et al. (2014). These are combined with an structures. adaptation of the ‘modification of the Held and Suarez forcing to

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250 where the substellar point is located at φ = 0, ν = 0. We use for

165 240 165 the remainder of this work the parameters for the troposphere tem- 170 170 350 perature defined in Carone et al. (2014) for the Earth-case (see 230 10-2 175 175 Section 2.4 for more details). The equilibrium temperatures on the = −2 180 220 180 day side are shown in Fig. 2 for the surface gravity g 9.81 m s 300 185 185 and Earth-like atmosphere and surface temperatures. 210 190 190 We retain for the horizontal resolution the original C32 cubed 200 195 195 sphereresolutionasusedinCaroneetal.(2014). This set-up 250 10-1 200 yields a global resolution in longitude and latitude of 128 × 64 Pressure [bar] or 2.8◦ × 2.8◦. For the vertical resolution, we use in total 30 vertical levels between 1000 mbar surface pressure and 1 mbar: We 200 linearly resolve the vertical extent of the atmosphere with 18 times

210 230 22 2 2 270 310 290 50 40 3 3 Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021 370 30 0 50 mbar levels between 1000 and 100 mbar pressure, we logarithmi- 39 50 1 0 cally resolve the atmosphere between 100 and 10 mbar with eight -90 -60 -30 0 30 60 90 Latitude [degree] levels, and we further resolve linearly with four times 2.5 mbar levels the atmosphere between 10 and 1 mbar. This set-up ensures Figure 2. Radiative equilibrium temperatures on the day side with strato- sufficient vertical resolution for the development of the troposphere sphere modification. Contour intervals are 5 K for temperatures colder and and stratosphere wind system (see also Williamson et al. 1998). We 20 K for temperatures hotter than 250 K. Here, Earth radius and gravity use a dynamical time-step t = 300 s. g = 9.81 m s−2 are assumed. include stratospheric structure’ by Williamson, Olson & Boville 2.2 The role of wave breaking in the stratosphere (1998). More precisely, the new equilibrium temperature in the troposphere, Ttrop(ν, φ, p), is In previous works (e.g. section 2.2 in Carone et al. 2014), we have     used an upper atmosphere Rayleigh friction layer as a first order R/cp p approach to mimic gravity wave breaking. This upper atmosphere Ttrop(ν, φ, p) = max Tstr,min,TDS,s(ν, φ) , (1) ps friction layer was, however, mainly motivated to ensure numerical stability of the global circulation model by preventing non-physical where ν, φ, p and p are the planetary latitude, longitude, pressure s wave reflection at the upper boundary. The upper atmosphere fric- level and surface pressure, respectively. R is the specific gas constant tion layer is prescribed as an additional forcing term F =−k v and c the specific heat capacity of the atmosphere. T is the v R p str, min acting on the horizontal flow, where k is defined as minimum stratosphere temperature, where we use the value used R   = 2 by Williamson et al. (1998) for Earth, which is Tstr, min 200 K. p − p k = k low ifp ≥ p (5) TDS, s(ν, φ) is the day-side temperature as given in equation (23) of R max low plow Carone et al. (2014). kR = 0ifp

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Table 1. Planetary, atmosphere and stratosphere wind breaking parameters used in this work for simulating TRAPPIST-1b, -1d, Proxima Centauri b and GJ 667 C f.

Planets TRAPPIST-1b TRAPPIST-1d Proxima Centauri b GJ 667 C f

Planetary parameters a Planet radius RP [REarth] 1.086 0.772 1.4 1.4 Density ρP [ρEarth] 0.62 1 0.71 1 Planet mass MP [MEarth] 0.79 0.46 1.96 2.7 Surface gravity g [m s−2] 6.56 7.60 9.80 13.5 Orbital period [days] 1.51 4.05 11.186 39.03 Atmosphere parameters −2 a b Incident stellar irradiation I0 [Wm ] 1916 1555 900 790

Albedo 0.5 0.38 0.3 0.3 Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021 Surface pressure [bar] 1 1 1 1 Main constituent nitrogen Molecular mean mass μ [g/mol] 28 28 28 28 −1 Specific heat capacity cp [JgK ] 1.04 1.04 1.04 1.04 Average effective temperature Teff [K] 255 255 230 222 c Surface optical depth τ s 0.62 0.62 0.94 0.94 Stratosphere wind breaking parameters stratosphere friction time-scale deep (1/kmax) [days] 20 20 20 20 stratosphere friction time-scale shallow (1/kmax) [days] 10 1 20 20 a Notes. Would require a star with a radius of Rstar = 0.1RSun and an effective temperature Tstar, eff = 2095 K. bAssuming stellar luminosity from Delfosse et al. (2013), semi major axis a = 0.156 au and equation (11) from Carone et al. (2015). cUsing equation (23) from Carone et al. (2014).

The value for kmax in the deep wind breaking case is selected circulation structure: mid-latitude zonal wind jets in the troposphere such that it reproduces the Earth regime. It will be shown in the with wind speeds of 30 m s−1, and polar wind jets in the stratosphere. next subsection that the deep stratosphere wind breaking set-up with A deep stratosphere wind braking description with plow = 0.1 bar −1 −1 plow = 0.1 bar and kmax = 1/20 days is needed to reproduce qual- and kmax = 1/20 days furthermore reproduces the observed wind itatively the Earth stratosphere wind and circulation regime. These speeds (Fig. 3, upper panel). See e.g. Manabe & Hunt (1968)orthe values will be kept for all planets, when applying deep stratosphere review by Haynes (2005) for a comparison with the observed Earth wind breaking. zonal wind structure. The value for kmax in the shallow wind breaking case is mainly The polar zonal wind jets on Earth are strong indicators for the driven by the need to ensure numerical stability as plow = 0.005 bar presence of a Brewer-Dobson-circulation in the stratosphere. Both, is located very near the global circulation model top boundary, as the polar jet as well as the Brewer-Dobson-circulation, are driven in the original purely tropospheric set-up. Thus, kmax is increased by extratropical Rossby waves that originate in the troposphere, for the shallow wind breaking set-up and in the short orbital period propagate upwards and break in the stratosphere (see also fig. 8 in regime Porb ≤ 3 d, as also discussed in Carone et al. (2015). In- Showman & Kaspi 2013). terestingly, we found that for TRAPPIST-1d, a very strong kmax is Interestingly, when we test the shallow wind breaking scenario needed to ensure numerical stability. We attribute the need for an for the Earth model, that is set plow = 0.005 bar (see Section 2.2), unusually high stability near the upper boundary to the complex we not only find much faster polar jets but also a 40 m s−1 strong wave behaviour that can enfold in the stratosphere of this specific equatorial wind jet in the stratosphere (Fig. 4). See also fig. 2 in planet compared to all other planets, as will be shown in this study. Showman et al. (2013) which illustrates the tendency for equatorial See Table 1 for the specific values used for different scenarios. superrotation on rocky (exo)planets. The focus of this work is tidally locked exoplanets, but we note that future work may also aim to investigate under which circumstances superrotation may appear on 2.3 Earth benchmarking and eddy diagnostics Earth (see also a short discussion of superrotation in Earth climate We benchmark our model with an Earth-simulation to ensure that models in Section 4). we reproduce qualitatively Earth-like circulation not only in the In the following, we introduce two diagnostics to identify wave troposphere, but also in the stratosphere. The surface friction time- activity and circulation more directly. The momentum transport by scale is set here to the nominal value of 1 d, as defined by Held Rossby waves in our simulations can be identified by mapping the &Suarez(1994), the benchmark of which we adapted for tidally eddy momentum flux, which is defined as (see e.g. Holton (1992)     locked ExoEarths in Carone et al. (2014). We also tested slower U V  = UV − U · V . (6) and higher surface friction time-scales (τ fric = 0.1 and 10 d) to check if we can change the circulation state of Earth within the Here, U is the zonal wind and V is the meridional wind. Overbars framework of our model, but found no large effect in general cir- denote time-averaged flow, brackets denote zonally averaged flow culation. This is in contrast to tidally locked ExoEarths where the and primes indicate the eddy part of the flow. circulation state can change drastically for different surface fric- To identify circulation, we use the zonal average of the time- averaged meridional overturning streamfunction tion time-scales (Carone et al. 2016). We find that the selected surface friction and temperature prescription used by Williamson p = 2πRP  et al. (1998) generally reproduce the desired zonal wind and cos ν V dp , (7) g 0

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Figure 4. Zonally averaged zonal wind jets, averaged over 1000 d of sim- ulation time, for the Earth set-up with shallow stratosphere wind breaking. Contour level spacing is 10 m s−1.

state regime with respect to orbital period identified by Carone et al. (2015)(Fig.1). Earth-like thermal forcing may indeed be a valid assumption for TRAPPIST-1d (with some caveats), Proxima Centauri b and GJ 667 C f, based on incident stellar irradiation (Table 1). Wolf (2017) concludes that TRAPPIST-1e may have Earth-like surface temper- atures only with a higher content of greenhouse gases, whereas Turbet et al. (2017) state that TRAPPIST-1e should have liquid sur- face water for many atmosphere scenarios – including Earth-like Figure 3. Top: zonally averaged zonal wind jets, averaged over 1000 d of greenhouse. In any case, TRAPPIST-1b and -1c are receiving too simulation time, for the Earth benchmark set-up. Contour level spacing is much stellar irradiation for Earth-like thermal forcing. TRAPPIST- 5ms−1. Bottom: zonally and time-averaged eddy momentum flux in m2 s−2 1f, -1g and -1h receive, conversely, too little stellar irradiation to for the Earth set-up. Contour levels are arranged in steps of 100.1 between have Earth-like surface temperatures with an Earth-like atmosphere − − 102 and 100 m2 s 2 and −102 and −100 m2 s 2. White solid arrows denote composition. However, TRAPPIST-1f and -1g may still be hab- the direction of angular momentum transport. Dashed white lines denote the itable if they have a thick CO2-dominated atmosphere (>1and vertical propagation of extratropical Rossby waves. >5 bar, respectively) (Kopparapu et al. 2013; Turbet et al. 2017). Luger et al. (2017) speculate that TRAPPIST-1-h may be habit- where RP is the radius of the planet and g its surface gravity. is pos- able if it migrated from the inner region of the planetary system to itive for clockwise circulation and negative for counter-clockwise its current location quickly enough to build an atmosphere that is circulation. significantly enriched in hydrogen via outgassing. Fig. 3, lower panel, shows the expected momentum transport For the habitable TRAPPIST-1b scenario, we acknowledge that due to Rossby waves in the troposphere and stratosphere, which this simulation is for now a hypothetical scenario that would re- explains the location of the zonal wind jets in Fig. 3, upper panel quire a colder host star than TRAPPIST-1. More specifically, we (see also Holton (1992)). Fig. 5 shows qualitatively the equator- find that a TRAPPIST-1b-equivalent habitable planet would re- to-pole-wards airmass transport in the stratosphere (Brewer 1949; quire a star with an effective temperature Tstar, eff = 2095 K, that Vallis 2006), as well as the three circulation cells per hemisphere in is 340 K cooler than TRAPPIST-1, to reside at the very inner edge the troposphere (see e.g. Vallis 2006; Showman et al. 2013). In the of the habitable zone. That is, we fix the albedo to the highest following, a combination of zonal wind, eddy momentum transport possible value of 0.5 (Yang, Cowan & Abbot 2013;Yangetal.2014; and circulation maps will be used to identify if and under which Boutle et al. 2017), assume a stellar radius of Rstar = 0.1RSun,ap- conditions thermally driven and wave-driven circulation can operate propriate for ultra-cool M dwarfs and brown dwarfs (e.g. Deleuil 2 in the stratosphere of tidally locked ExoEarths. = 4 Rstar et al. 2008; Gillon et al. 2017), and calculate I0 σTstar,eff a , where σ is the Stefan Boltzmann constant and a the planet’s semi major axis. We furthermore require I = I (1 − α) = 2.4 Planetary parameters net 0 958 W m−2 (see Table 1). The same exercise yields for TRAPPIST- We investigate in this work the basic principles of stratosphere cir- 1c, which resides in the same circulation state regime, a hypothetical culation for different possible circulation states on rocky, tidally host star with Tstar, eff = 2452 K, only 100 K cooler than TRAPPIST- locked habitable ExoEarths. Here, we no longer have to rely 1. Due to the large number of cool dwarf stars and surveys like on hypothetical rocky exoplanets orbiting ultra-cool red dwarfs CARMENES that search for planetary systems around such stars like in Carone et al. (2015). Instead, we can directly apply our (Quirrenbach et al. 2010), it is very much possible that potentially model to TRAPPIST-1b, TRAPPIST-1d, Proxima Centauri b and rocky planets with three days orbital periods or less will be found. GJ 667 C f. When assuming Earth-like atmosphere composition and For TRAPPIST-1d, we assume an Earth-like atmosphere com- thermal forcing, these planets cover the entire possible circulation position and an Earth-like greenhouse effect, which is realized in

MNRAS 473, 4672–4685 (2018) ExoEarth’s stratosphere circulation 4677 our simplified model by setting surface optical depth τ s = 0.68. et al. (2017) for the emerging picture of a radius and compositional We further assume a net irradiation of Inet = I0(1 − α) = 958 W gap between 1.5 and 2 Earth radii in the exoplanetary population. −2 m ,whereI0 is incident irradiation. These assumptions yield for Furthermore, the following assumptions were made to derive TRAPPIST-1d an albedo α = 0.38. The habitability of TRAPPIST- surface gravities: The surface gravity for all investigated planets 1d is, however, contested as it may undergo a runaway greenhouse can in principle be calculated via effect, if the planet is covered by oceans (Gillon et al. 2017; Kop- g = GM /R2, (8) parapu et al. 2017; Turbet et al. 2017;Wolf2017). Apparently, the P P

‘parasol mechanism’ by clouds at the substellar point, proposed by if the planetary mass (MP) and radius (RP) are both known. For the Yang et al. (2014) to avoid the runaway greenhouse effect at the TRAPPIST-1 planets, both properties are known, but their masses inner edge of the habitable zone, is not effective for this planet. An come with relatively large uncertainties compared to their radii. If understanding of the basic atmosphere dynamics explains why the the mass and radius ranges allow it, we assumed Earth-like density, −3 parasol mechanism was based on a circulation scenario for a tidally that is, ρP = ρEarth = 5.51 g cm . This is indeed the case for locked planet with an orbital period of 60 d. As noted in Yang et al. TRAPPIST -1d (Gillon et al. 2017;Wangetal.2017). Recent Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021 (2013, 2014) and Carone et al. (2016), the mechanism requires the updates on the masses of the TRAPPIST-1 planets by Wang et al. strong unperturbed direct upwelling branch of the direct circulation (2017) imply that the density of TRAPPIST-1b is smaller than the cell at the substellar point. This is obviously the case for slowly Earth. We take the updated mean mass estimate for this planet 1 rotating planets with orbital periods larger than 25 d, where direct (MP = 0.79MEarth). circulation dominates (see e.g. Fig. 1). For a habitable TRAPPIST- For Proxima Centauri b and GJ 667 C f, there are no ra- 1d scenario with an orbital period of 4.05 d, the strength of the dius constraints as these planets are not transiting. Furthermore, direct circulation cell is diminished by at least one order of magni- ‘only’ their minimum masses have been measured. For Proxima tude compared to the slowly rotating ExoEarths with Porb > 25 d Centauri b, we select for now the radius and mass estimated from (see fig. 18 in Carone et al. 2016). The relatively weak upwelling the evolution models of Zuluaga & Bustamante (2016), which leads apparently does not produce the necessary cloud coverage to effec- to a Mars-like bulk composition (0.71 ρEarth). For GJ 667 C f, we use tively shield the planet from stellar irradiation in the 3D models of the measured minimum mass msin (i) as the real mass and assume Wolf (2017) and Kopparapu et al. (2017), with the caveat that these Earth-like density. models only captured one out of two possible circulation states. Eventually, we derive surface gravity by inserting into equation Abe et al. (2011) and Zsom et al. (2013)have identified, however, (8) the planetary mass expressed as another possibility (2011) to avoid a runaway greenhouse at the 4 inner edge of the habitable zone: a reduced water content or a ‘desert = 3 MP ρP πRP. (9) planet’ scenario. Calculations by Bolmont et al. (2017) also show 3 that the planet may have lost(2013) some of its water content in the Table 1 lists the planetary, atmospheric and stratosphere wind break- past, but that it can still retain some water, thus remaining habitable. ing parameters used in this work. In light of the uncertainties in circulation state and water content, we therefore still assume that TRAPPIST-1d may be habitable. In addition, the same statement holds for TRAPPIST-1d than for 3 SIMULATIONS TRAPPIST-1b: Even if this particular planet may not be habitable, In the following, we investigate stratosphere wind systems and cir- a similar planet around a cooler M dwarf star may be. culation for representative planets in each Rossby wave or circu- For Proxima Centauri b, the incoming irradiation is lower than lation regime for different orbital periods as identified in Carone −2 on Earth (I0 = 900 W m ). For this case, we assume an Earth-like et al. (2015) (see also Fig. 1). These planets are TRAPPIST-1b, -1d, albedo α = 0.3, but use a more efficient greenhouse effect with Proxima Centauri b and GJ 667 C f. For every circulation state, we τ s = 0.94. We thus assume the greenhouse efficiency found by investigate the deep and shallow stratosphere wind breaking sce- Edson et al. (2011) for tidally locked ExoEarths in a dry planet nario. For TRAPPIST-1b and -1d, we use different surface friction set-up, where it was confirmed in Carone et al. (2016) that this time-scales to enforce two different circulation states for one and set-up generally yields similar results in terms of large-scale cir- the same planet: one dominated by the tropical and one dominated culation dynamics compared to the less efficient more Earth-like by the extratropical Rossby wave. Thus, for every planet four to two greenhouse effect with τ s = 0.62. Our prescription for Proxima different scenarios are investigated. Centauri b is different from the set-up investigated by Boutle et al. (2017), who chose a weaker greenhouse effect but with a global sea surface. Despite the weaker greenhouse, simulations by Boutle 3.1 Ultra-short orbital periods or the TRAPPIST-1b scenario et al. (2017) still resulted in surface temperatures above the freezing First, we study TRAPPIST-1b as a habitable ExoEarth scenario. point of water for a large fraction of the eternal day side in their 1:1 This planet has an orbital period of 1.51 d (Table 1). As outlined spin-orbit resonance case. in Carone et al. (2015) (see also Fig. 1), the circulation on such a For GJ 667 C f, we also use an increased greenhouse gas effect planet is strongly determined by Rossby waves (tropical and ex- = by assuming τ s 0.94 and an Earth-like albedo. This set-up results tratropical). These lead to three possible ‘banded’ wind structures, in effective and surface temperatures that are about eight degrees that is zonal wind jet regimes: The planet develops (1) two high- colder than on Proxima Centauri b, placing this planet at the outer latitude eastward wind jets, (2) a strong eastward equatorial wind edge of its star’s habitable zone. We select this non-transiting planet because it is one of the very few tidally locked planets (a) with an orbital period larger than 25 d, (b) that is in the habitable zone of 1 We note for future updates on the masses of the TRAPPIST-1 planets that its star and (c) has a mass small enough to ensure that the planet is changes in the assumed planetary mass and thus in the estimated surface indeed rocky and not a mini-Neptune. For the same reason, planets gravity by 50 per cent or less are not going to fundamentally change the with radii larger than 1.5 Earth radius were excluded. See e.g. Fulton circulation patterns discussed in this work.

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extratropical and tropical Rossby wave circulations, respectively. The third mixed case was not separately investigated. For each scenario, we further investigate two stratosphere wind breaking scenarios: the deep and shallow wind braking scenario as outlined in Section 2.2 (see also Table 1). Fig. 6 shows the zonal wind structure for the four investigated scenarios: Scenario (a): Extratropical Rossby wave circulation and shallow wind breaking Scenario (b): Extratropical Rossby wave circulation and deep wind breaking Scenario (c): Tropical Rossby wave circulation and shallow wind Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021 breaking Scenario (d): Tropical Rossby wave circulation and deep wind breaking. Figure 5. Meridional stream function in kg s−1 for the Earth set-up. Contour levels are arranged in steps of 100.1 between 1011 and 108 kg s−1 and −1011 Scenario (a) (Fig. 6, top left): This simulation shows that while and −108 kg s−1, respectively. Dashed white arrows denote the direction of the extratropical Rossby wave dominates over the tropical Rossby circulation in the stratosphere. wave in the troposphere (p > 0.1 bar), the situation reverses in the stratosphere (p < 0.1 bar). Consequently, we find an equatorial, jet or (3) an equal mixture of both. In the first case, extratropical superrotating stratospheric jet. Circulation shows the development Rossby waves dominate. In the second case, tropical Rossby waves of an ‘Anti-Brewer-Dobson-circulation’ (Fig. 7, top left). The cir- dominate. In the third case, both waves are equally strong. culation is exactly reverse in direction compared to the Earth case Generally, an extratropical Rossby wave circulation state is found (Fig. 5): instead of transporting airmasses from the equator towards to be much more clement than a tropical Rossby wave circulation the poles, stratosphere circulation rather confines them at the equa- state. In the tropical Rossby wave circulation state, strong equatorial tor. Thus, chemical species produced in the stratosphere would in wind jets in the troposphere severely disrupt heat transport from the such a scenario tend to accumulate at the equator. day to the night side. One may even speak of an ‘evil twin–good Scenario (b): The zonal wind map in this simulation shows no twin circulation scenario’. equatorial stratospheric jet (Fig. 6, top right). Close inspection of the Using Carone et al. (2016), we set the surface friction time-scale eddy momentum flux, however, shows that the tropical Rossby wave to τ s, fric = 10 d and τ s, fric = 0.1 d to reliably ‘toggle’ between becomes here also dominant over the extratropical Rossby wave in

Figure 6. The four faces of a habitable TRAPPIST-1b scenario: zonally averaged zonal wind jets for identical thermal forcing but different circulation states and stratosphere wind breaking. Contour level spacing is 10 m s−1.

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Figure 7. The four faces of a habitable TRAPPIST-1b scenario: meridional stream function in kg s−1 for identical thermal forcing but different circulation states and stratosphere wind breaking. Thin (thick) contour levels are arranged in steps of 100.1 (101) between 1011 and 108 kg s−1 and −1011 and −108 kg s−1, respectively. Dashed white arrows denote the direction of circulation in the stratosphere. the stratosphere. The action of the tropical wave is made apparent every investigated scenario. Planets with orbital periods less than by the tendency to drive momentum equator-wards for p < 0.1 bar, three days will always suffer from an Anti-Brewer-Dobson circula- whereas for p > 0.1 bar (troposphere), the extratropical Rossby wave tion that constrains airmasses at the equator. The specific circulation drives momentum pole-wards (Fig. 8). The absence of the strato- state and stratosphere wind breaking scenario ‘only’ determine to sphere jet is thus entirely due to the effective friction mechanism of which degree stratosphere equator-to-pole-wards circulation is dis- the deep wind breaking scenario. While the stratospheric equatorial rupted. wind jet is almost entirely suppressed, the same cannot be said for the associated Anti-Brewer-Dobson-circulation (Fig. 7, top right). The tropical Rossby wave thus hampers the distribution of airmasses away from the equator even in this case, but not as severely as for 3.2 Short orbital periods or the TRAPPIST-1d scenario shallow stratosphere wind breaking. Interestingly, a weak Brewer- Dobson-like circulation with an equator-to-pole-wards circulation If Trappist-1d is habitable (see Section 2.4), its relatively short or- is discernible above the Anti-Brewer-Dobson-circulation. This pic- bital period of 4.05 d will place the planet into the circulation region ture is confirmed by weak pole-wards eddy momentum transport domain that is still strongly dominated by Rossby waves (Fig. 1). visible at the top of the investigated atmosphere (Fig. 8) and an asso- TRAPPIST-1d – if tidally locked – can have two different circu- ciated weak polar jet (Fig. 6, top right). Some pole-wards transport lation states for the same Earth-like thermal forcing. We ‘switch’ is thus possible, if stratospheric winds are efficiently suppressed. again between those circulation states by changing the effective Scenario (c) and Scenario (d): Both cases are depicted in the surface friction time-scale. We also investigate deep and shallow bottom panels of Figs 6 and 7. These two simulations show that stratosphere wind braking scenarios (Fig. 9). the troposphere equatorial wind jet can extend far upwards into the Fig. 9 shows the zonal wind structure for the four investigated stratosphere. Consequently, the ‘Anti-Brewer-Dobson-circulation’ scenarios: is very prominent and leaves no room for the Earth-like Brewer- Dobson-circulation. Therefore, again, species that are photochemi- Scenario (a): Extratropical Rossby wave circulation and shallow cally produced over the substellar point (such as potentially ozone) wind breaking should accumulate over the equator and cannot be transported to- Scenario (b): Extratropical Rossby wave circulation and deep wards the polar regions. The main difference between shallow and wind breaking deep stratosphere wind breaking scenario is that the jet extends Scenario (c): Tropical Rossby wave circulation and shallow wind farther upwards in the latter case. breaking In conclusion, the ‘evil circulation scenario’ with a dominant Scenario (d): Tropical Rossby wave circulation and deep wind tropical Rossby wave eventually wins out in the stratosphere for breaking.

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The eddy momentum transport is in so far Earth-like as pole- wards momentum transport – associated with the extratropical Rossby wave – propagates vertically upwards. See Fig. 3, bot- tom panel, in the Earth case for a comparison. The eddy mo- mentum transport is, however, also un-Earth-like because also a standing tropical Rossby wave propagates vertically upwards and increases in strength. While the tropical Rossby wave never gains completely the upper hand in the stratosphere, as was the case for TRAPPIST-1b, it still manages to diminish the pole-wards mo- mentum transport. The tropical Rossby wave, thus, probably also diminishes the equator-to-pole-wards circulation enabled by the ex- tratropical Rossby wave (Fig. 11, top left).

Scenario (b): A weak stratospheric high-latitude wind jet system Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021 is present in the stratosphere. No clear pole-wards eddy momentum transport can be identified in the stratosphere (Fig. 10, right). But Figure 8. TRAPPIST-1b: eddy momentum flux in m2 s−2 for extratropi- neither is equator-wards momentum transport discernible. There- cal Rossby circulation and deep stratosphere wind breaking. Thin (thick) fore, both, tropical and extratropical Rossby waves, are efficiently contour levels are arranged in steps of 100.1 (101) between 102 and suppressed by deep stratosphere wind breaking, which is unlike 100 m2 s−2 and −102 and −100 m2 s−2. White arrows denote the direction the Earth scenario (Fig. 3, bottom panel). Since the Earth is rotat- of momentum transport. ing four times faster than TRAPPIST-1d and since the strength of Rossby waves diminishes with slower rotation (see e.g. Showman While the troposphere wind systems of TRAPPIST-1d resem- & Polvani 2011; Holton 1992; Carone et al. 2015), it is no surprise ble those of TRAPPIST-1b, the stratospheric wind jet systems are that Rossby waves on TRAPPIST-1d are more easily suppressed fundamentally different. than in the Earth case (Section 2.2). Scenario (a): The extratropical Rossby wave dominates in the Conversely, the strength of thermally driven circulation increases troposphere as evidenced by the two high-latitude zonal wind jets with slower rotation (see e.g. Carone et al. 2015; Held & Hou 1980). for p > 0.1 bar (Fig. 9, top left). In the stratosphere, we find a Therefore, thermally driven circulation can assume the role on second set of high-latitude wind jets on the top of the tropospheric TRAPPIST-1d that the wave-driven Brewer-Dobson-circulation has ones. These stratosphere wind jets superficially resemble Earth-like on Earth: to transport airmasses – and thus aerosols and photochem- polar wind jets (Fig. 3, top panel) that induce a Brewer-Dobson ically produced species – from the equator towards higher latitudes. circulation. Inspection of the eddy momentum transport, however, Indeed, stratospheric equator-to-pole-wards circulation is very dom- reveals that the underlying physics is not entirely Earth-like (Fig. 10, inant (Fig. 11, bottom left). The circulation is even stronger than left). in Scenario (a), where, in principle, the combination of thermally

Figure 9. The four faces of a habitable TRAPPIST-1d scenario: zonally averaged zonal wind jets for identical thermal forcing but different circulation states and stratosphere wind breaking scenarios. Left-hand panels show the deep stratosphere wind braking scenario. Contour level spacing is 10 m s−1.

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Figure 10. Eddy momentum transport in TRAPPIST-1d’s extratropical Rossby wave circulation scenario. Eddy momentum flux is in m2 s−2. Thin (thick) contour levels are arranged in steps of 100.2 (101) between 102 and 100 m2 s−2 and −102 and −100 m2 s−2. White arrows denote the direction of momentum transport. Dashed arrows denote the vertical propagation of waves.

Figure 11. The four faces of a habitable TRAPPIST-1d scenario: meridional stream function in kg s−1 for identical thermal forcing but different circulation states and stratosphere wind breaking. Thin (thick) contour levels are arranged in steps of 100.1 (101) between 1011 and 108 kg s−1 and −1011 and −108 kg s−1, respectively. Dashed white arrows denote the direction of circulation in the stratosphere. and wave-driven circulations should lead to a stronger circulation pole-wards circulation, as was the case for TRAPPIST-1b (see compared to only thermally driven circulation. We attribute this previous subsection). Another difference to the circulation scenario contradiction to the background presence of the tropical Rossby (c) of TRAPPIST-1b is that the equatorial wind jet in the troposphere wave in Scenario (a) that counteracts any pole-wards circulation. does not transcend into the stratosphere (Fig. 9, bottom panels). In- Scenario (c): This simulation shows more clearly the counteract- stead, a second stratospheric equatorial wind jet develops on the ing stratosphere circulation tendency by the tropical Rossby wave top which may still disturb pole-wards transport (Fig. 9, bottom for the TRAPPIST-1d case. In the zonal wind picture, the tropical left). Rossby wave dominates in the troposphere and drives an equato- Scenario (d): For deep stratospheric wind breaking, the forma- rial wind jet there (Fig. 9, bottom left). In the circulation picture, tion of a second stratospheric equatorial wind jet on the top of an Anti-Brewer-Dobson-circulation is clearly discernible (Fig. 11, the tropospheric one is clearly inhibited (Fig. 9, bottom right). bottom left), but does not completely supersede the thermally driven The Anti-Brewer-Dobson circulation is even less capable to disrupt

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Figure 12. The two faces of a habitable Proxima Centauri b scenario. Top panels: zonally averaged zonal wind jets. Contour level spacing is 10 m s−1. Bottom panels: meridional stream function in kg s−1 for identical thermal forcing but different stratosphere wind breaking. Thin (thick) contour levels are arranged in steps of 100.1 (101) between 1011 and 108 kg s−1 and −1011 and −108 kg s−1, respectively. Dashed white arrows denote the direction of circulation in the stratosphere. the thermally driven equator-to-pole-wards stratosphere circulation Scenario (a): Weak tropical Rossby wave circulation with shal- (Fig. 11, bottom right). low wind breaking Generally, we can conclude that the slower orbital period of Scenario (b): Weak tropical Rossby wave circulation and deep TRAPPIST-1d compared to TRAPPIST-1b makes the global trans- stratosphere wind breaking scenario. port of aerosols and photochemically produced compounds more likely. In the extratropical Rossby wave circulation state, the trop- ical Rossby wave is efficiently prevented from creating havoc in the stratosphere, with and without deep stratosphere wind break- Scenario (a): Although Proxima Centauri b has a relatively weak ing. Thermally driven circulation establishes efficient equator-to- tropical Rossby wave compared to TRAPPIST-1b and 1d, it is still pole-wards transport. Since the tropical Rossby wave is weaker, an strong enough to induce a strong equatorial wind jet in the strato- equatorial stratospheric wind jet and an Anti-Brewer-Dobson cir- sphere with an Anti-Brewer-Dobson-circulation (Fig. 12, left-hand culation that could hamper day side-wide transport are also weaker, panels). even in the worst case scenario, when the troposphere is in the Scenario (b): Here, the tropical Rossby wave is efficiently damped tropical Rossby wave circulation state and when stratosphere wind in the stratosphere: No equatorial jet and no Anti-Brewer-Dobson breaking is inefficient. circulation can be found in the stratosphere (Fig. 12, right-hand panels). Proxima Centauri b appears thus to be more prone to the adverse 3.3 Weak superrotation or the Proxima Centauri b scenario effects of the tropical Rossby wave than the habitable TRAPPIST-1d If TRAPPIST-1e to 1-h, LHS 1140 b, GJ 667 C c and Proxima case (see previous subsection) – even though the disruptive trop- Centauri b are habitable tidally locked ExoEarths, they will lie in ical Rossby wave is weaker. This counter-intuitive result can be the weak superrotation regime (Fig. 1). They will thus be very explained when we consider that the extratropical Rossby wave is similar in circulation state, assuming a habitable atmosphere. We missing for Proxima Centauti b: Only deep, efficient stratosphere choose Proxima Centauri b as the prototype case for this circulation wind breaking can ‘save’ the planet from the adverse effects of the state region. tropical Rossby wave. In this case, the strong thermally driven cir- Because standing extratropical Rossby waves cannot form for or- culation can take over the role that the wave-driven Brewer-Dobson- bital periods greater than six days (assuming Earth size), only one circulation has on Earth: to transport aerosols and photochemically circulation state scenario is possible on Proxima Centauri b. Thus, produced species from the equator to the poles. we do not assume extreme values of surface friction to switch be- If the tropical Rossby wave is not efficiently damped in the strato- tween different circulation states as in the previous sections. Instead, sphere, the formation of an equatorial ‘transport belt’ instead of a we adopt for this planet the nominal surface friction time-scale of day side-wide transport regime is a distinct possibility, like for τ s, fric = 1 d. Two scenarios are considered in the following: TRAPPIST-1b.

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Figure 13. The habitable GJ 667 C e scenario. Left: zonally averaged zonal winds. Contour level spacing is 5 m s−1. Right: meridional stream function in kg s−1. Thin (thick) contour levels are arranged in steps of 100.1 (101) between 1011 and 108 kg s−1 and −1011 and −108 kg s−1, respectively. Dashed white arrows denote the direction of circulation in the stratosphere. Both properties are shown for shallow wind breaking.

3.4 Direct circulation dominance or the GJ 667 C f scenario 4 SUMMARY AND DISCUSSION We take GJ 667 C f as the prototype for a circulation state Stratosphere circulation on rocky exoplanets is determined by plan- entirely dominated by strong direct circulation (Fig. 1). Since etary waves that form in the underlying troposphere and propagate only very weak zonal wind tendencies can be found, we dis- upwards. Thus, the state of stratosphere circulation may reflect the play only one case: direct circulation with weak stratosphere wind state of troposphere circulation, even if the latter cannot be di- breaking. rectly observed. For tidally locked ExoEarths, in contrast to Earth, Fig. 13 (left) shows indeed that a tidally locked habitable the standing tropical Rossby wave is of supreme importance and ExoEarth with a 39 d orbital period has no strong eastward wind can even suppress day side-wide stratosphere circulation: Tropical tendencies, neither in the troposphere nor in the stratosphere. Con- Rossby waves induce a strong equatorial superrotating jet in the sequently, direct circulation is very efficient in the troposphere and stratosphere, with wind speeds of about 100 m s−1, and an Anti- stratosphere and can transport material in the stratosphere over the Brewer-Dobson-circulation that confines airmasses at the equator. whole day side. Indeed, the wind flow on such planets is not banded Both effects disrupt equator-to-pole-wards airmass transport, which but mainly radial (see Fig. 1) and flows on top of the troposphere is ensured on Earth by the normal Brewer-Dobson-circulation, from the substellar point towards polar regions and the day side- driven by extratropical Rossby waves. night side terminators. All ExoEarths with orbital periods shorter than 25 d are in danger We speculate that, for tidally locked planets with orbital periods from these disruptions. That is, stratosphere circulation on Prox- greater than 25 d, the amount of ozone produced on the day side may ima Centauri b, LHS 1440 b, and TRAPPIST-1b and -1g may be be distributed over the whole day side and may even be depleted confined to an equatorial ‘transport belt’. by vigorous transport away from the production region towards the More specifically, we found that tidally locked ExoEarths with night side by direct circulation. This picture is confirmed by Proe- very short orbital periods (Porb ≤ 3 d), like TRAPPIST-1b, are drou & Hocke (2016), who modelled a tidally locked Earth with very unlikely to have a equator-to-pole-wards stratosphere circula- an orbital period of 365 d: Their Fig. 4 shows indeed a relatively tion: Tropical Rossby waves always dominate in the stratosphere, uniform ozone distribution over the whole day side in the strato- regardless if the troposphere circulation is dominated by the trop- sphere. Even higher up, in the mesosphere, transport time-scales are ical Rossby wave or by its antagonist, the extratropical Rossby faster than chemical reaction time-scales, leading to the depletion wave. Thus, the stratosphere circulation would be severely ham- of ozone at the day side and the accumulation of ozone at the night pered by the associated Anti-Brewer-Dobson-circulation. Aerosols side. and photochemically produced substances could not be efficiently On such a planet, mesospheric ozone that is streaming towards redistributed over the day side towards higher latitude. Instead, they the night side could be detected via transmission spectroscopy may accumulate over the equator. While TRAPPIST-1b itself is not that probes the limbs of the planetary atmosphere (Barstow & habitable, the results are directly transferable to exoplanets around Irwin 2016). Stratospheric ozone that stays on and is dis- stars or brown dwarfs that are even colder than TRAPPIST-1 (see tributed over the whole day side could rather be detected by Section 2.4). day-side thermal emissions, as proposed by Kreidberg & Loeb The larger the orbital period, the less problematic the tropical (2016). Rossby wave becomes – if it can be counterbalanced by an ex- However, future work is warranted to better connect circulation, tratropical Rossby wave or if it is damped by stratosphere wind photochemistry and observations and to investigate if the results breaking. Therefore, TRAPPIST-1d with an orbital period of 4.05 d found by Proedrou & Hocke (2016) still hold for planets like GJ exhibits efficient equator-to-pole-wards transport in the troposphere 667 C f with shorter orbital periods and thus less vigorous direct and the stratosphere – as long as the planet’s troposphere is dom- circulation. Furthermore, future work needs to take into account inated by the extratropical Rossby wave. This is the only circula- that the host stars of such planets are much redder than the Sun and tion state modelled by Wolf (2017) and Kopparapu et al. (2017). are frequently flaring. If the troposphere of TRAPPIST-1d is dominated by the tropical

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Rossby wave instead, the tropical Rossby wave also dominates in Turbet et al. (2017) and Boutle et al. (2017), (b) observations of the stratosphere – but can be dampened there by deep stratosphere biosignatures (Barstow & Irwin 2016; Kreidberg & Loeb 2016)and wind breaking. Then, again thermally driven circulation can ensure (c) evaluations of surface habitability (Segura et al. 2010; O’Malley- efficient equator-to-pole-wards transport in the stratosphere. James & Kaltenegger 2017). It is a first step to understand how 3D The standing extratropical Rossby wave can only form for short transport may affect photochemistry of tidally locked exoplanets orbital periods (Porb ≤ 6 d for 1 Earth radii planets), but the stand- around ultra-cool dwarf stars for a wide range of relevant circula- ing tropical Rossby wave forms for intermediate orbital periods tion scenarios – from very short (Porb = 1.51 d) to large (Porb = 39 6 ≤ Porb ≤ 25 d. Proxima Centauri b, for example, lies in this or- d) orbital periods. Next, the production and transport of photochem- bital period regime (Fig. 1). Without the extratropical Rossby wave ically produced species need to be investigated in more detail with as ‘safe guard’, planets like Proxima Centauri b, also LHS 1440b a photochemical model coupled to our 3D circulation model to gain and TRAPPIST-1g, can have their equator-to-pole-wards strato- better insights about the prospects of detecting, e.g. ozone around sphere circulation being disrupted by equatorial wind jets in the very red dwarf stars like TRAPPIST-1. stratosphere and Anti-Brewer-Dobson-circulation. The only avail- Clearly, understanding the connection between photochemistry Downloaded from https://academic.oup.com/mnras/article/473/4/4672/4564445 by guest on 24 September 2021 able option to ‘save’ day side-wide stratosphere circulation on Prox- and stratosphere circulation on alien ExoEarths is one of the nec- ima Centauri b and similar planets is deep stratosphere wind break- essary steps to take before we can even start to infer habitability ing. Future models of Proxima Centauri b thus potentially need to from observations. What is more, understanding the stratosphere take into account two scenarios when considering photochemistry circulation on alien ExoEarths may even help to assess the limits of and aerosol distribution in the stratosphere: an equatorial transport habitability on the one planet of which we definitely know that it is belt and day side-wide transport by thermally driven circulation. currently habitable: Earth. Tidally locked ExoEarths with comparatively large orbital pe- riods (Porb ≥ 25 d) like GJ 667 C e are completely safe from the tropical Rossby wave that cannot form efficient standing waves ACKNOWLEDGEMENTS in this rotation regime. Thermally driven circulation is then ef- We acknowledge support from the KU Leuven projects ficiently transporting airmasses in the stratosphere from the sub- IDO/10/2013 and GOA/2015-014 (2014–2018 KU Leuven). The stellar point radially away towards the night side. This circulation computational resources and services used in this work were can potentially lead to a day side-wide distribution of ozone in the provided by the VSC (Flemish Supercomputer Center), funded stratosphere, as indicated by Proedrou & Hocke (2016)butfora by the Hercules Foundation and the Flemish Government – = very slowly rotating (Porb 365 d) tidally locked ExoEarth. Future department EWI. LD acknowledges support from the ERC con- work is needed to evaluate how the ozone content and distribution solidator grant 646758 AEROSOL and the FWO Research Project change for more faster rotating tidally locked planets in the habit- grant G086217N. LC thanks Patrick Barth for useful discussions. able zone of red dwarfs, e.g. with orbital periods between 30 and We would also like to thank the anonymous referee for her/his in- 40 d. Furthermore, the inherent time variability of ozone formation sightful comments that greatly helped to improve this manuscript. in planets around red dwarfs needs to be addressed in a 3D frame- work, extending work by Stelzer et al. (2013) and Grenfell et al. (2014). It will be also interesting to reevaluate in a 3D context the REFERENCES statement of Segura et al. (2010) that even a flaring star may not Abe Y., Abe-Ouchi A., Sleep N. H., Zahnle K. 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MNRAS 473, 4672–4685 (2018)