arXiv:1010.4719v1 [astro-ph.EP] 22 Oct 2010 h eoiyfil.Terslto dpe sT32 ( T63L20 is th adopted represent resolution wer The arrows days field. the velocity 200 and the K) first (in the where 12 denote started, Colors at was taken simulation is the snapshot after The cir atmospheric locking. our tidal by assuming modelled ulations as 581g Gliese of surface the INTRODUCTION 1 † n as ⋆ well as , attributes and unique studies several a have driving such dwarf are M for stars. search M to nearby is route “exo-Ear promising — particularly -sized of characterization and o.Nt .Ato.Soc. Astron. R. Not. Mon. iue1. Figure ei Heng Kevin Earth: simulations of circulation version atmospheric scaled-up a as 581g Gliese umte 00Ot22. Oct 2010 Submitted 1 2 c wcyFlo,EHZuih nttt o srnm,Wolfg Astronomy, for Z¨urich, Institute ETH Fellow, Zwicky C/ikOsraoy nvriyo aiona 16High 1156 California, of University Observatory, UCO/Lick -al otuoikog(SSV) [email protected] E-mail: -al [email protected](KH) [email protected] E-mail: 00RAS 2010 h etfote netaoa lnthnigi h disco the is -hunting extrasolar in frontier next The oled rjcino h eprtr n eoiyfields velocity and temperature the of projection Mollweide 1 ⋆ n tvnS Vogt S. Steven and 000 – 21)Pitd2 coe 00(NL (MN 2010 October 25 Printed (2010) 1–5 , e words: Key decad next the in campaigns characterization w and which discovery exoplanets, q Earth-sized to habitable, solvers existen meteorological potentially the of on whether use the l of anticipates Independent specific study scale. our The global tidally-lock climate. is a exoplanet the on the occurs — whether on exoplanet globa depend the long-term, 581g M Gliese of the an surface examine of the and zone near Earth habitable of the version in scaled-up discovered atmosphe exoplanet the study sized to simulations three-dimensional use We ABSTRACT 192 × srbooy–paesadstlie:amshrs–metho – satellites: and planets – astrobiology 2 n-al-tas 7 H89,Z¨urich, Switzerland CH-8093, 27, ang-Pauli-Strasse 96 0Erhdays Earth 00 ieto of direction e uainsim- culation † discarded. e tet at rz A 56,U.S.A. 95064, CA. Cruz, Santa Street, × 20 h” A ths”. round ). very ext- near that wrsi yial oae nterange the sta in a exopla located massive zone typically orbiting ) least is an dwarfs (liquid the to habitable due classical As motion the stars. reflex Furthermore, nearby greatest the of have 72% they least th missions; at imaging stitute direct and interferometry generation n oobtlprosof periods orbital to ing nbigDplrrflxbrcnrcsgasa ml s1ms m 1 as small as signals leas barycentric s at reflex Keplerian of periodic Doppler factors strictly enabling realizing for decade, sensitivity increased a p in within few-Earth-mass a obtained of be cycles can of hundreds periods, surve short precision-Doppler such ground-based of capabilities the ayo h ers tr aebe rm agt o scruti for targets 200 de prime a al. over been for et have surveys Charbonneau stars precision-radial-velocity leading M 2007; by nearest al. the et Tarter of many 2007; commun on astronomical al. have the et (Scalo by attributes recognized st these widely similar-amplitude Although become of cently noise. presence Poisson the and in jitter even recovered be to ae riigti tr—oewt iiu asof mass minimum a with one — star ca exoplanet this more orbiting two dates announced apparent (2010) et (Selsis al. are et of zone Vogt (2009) Two Recently, habitable exoplane star. al. its et four straddle M3V Mayor that pc) least “super-” by (6.3 announced at nearby exoplanets a with orbiting the 581, 2009) al. Gliese et (Mayor is scrutinized being lyacpe Lme ta.21)ta,frselrmse b masses stellar for i that, It 2010) star. placi 0 parent al. AU, et its (Lammer of 0.15 accepted zone about habitable ally of the distance within squarely orbital it an and 581g) (Gliese uiae ihteohri epta akes uhtdll permanentl tidal face Such one darkness. perpetual keeps in it other that the such with origin, luminated its with of spin-synchronized Gyr or locked first tidally becomes zone able . A 6 T E M tl l v2.2) file style X n ftems niigadpoiaeeolntsystems exoplanet proximate and enticing most the of One ⊙ nErhms xpae riigayhr ntehabit- the in anywhere orbiting exoplanet Earth-mass an , ∼ l etepietreso exoplanet of targets prime the be ill atf h topei circulation atmospheric the uantify e. dadhwfs aitv cooling radiative fast how and ed 20 i iclto ntefis Earth- first the on circulation ric eo lee51 sconfirmed, is 581g Gliese of ce eprtr n idmaps wind and temperature l o5 as—wl-ace to well-matched — days 50 to etetGis 8ga a as 581g Gliese treat We . ctosfrhbtblt on habitability for ocations ∼ 0 . s numerical ds: 1 02A,correspond- AU, –0.2 gasand ignals aenow. cade l 2007). al. on M round s With ys. 3 gener- s ycon- ey . ocking 1 nthe in yre- ly lanet elow ellar il- y M 10 t ndi- net. − 9), ity ng ny rs, ly ⊕ ts 1 2 Heng & Vogt will greatly influence the climate across the exoplanet and figures prominently in any discussion of its potential habitability. Independent of whether the existence of Gliese 581g is even- tually confirmed, such discoveries legitimize the study of atmo- spheric circulation on exo-Earths using three-dimensional mete- orological solvers (Showman, Cho & Menou 2010), which is the focus of the present Letter. Our underlying philosophy is to ex- plore the atmospheric circulation on Gliese 581g as a scaled-up version of Earth — in the absence of observational constraints, we assume parameter values appropriate to the terrestrial atmo- sphere. Unlike previous studies (e.g., Joshi, Haberle & Reynolds 1997; Joshi 2003), we study only the essential dynamics of the , choosing not to model the radiative transfer and at- mospheric chemistry, an approach which is commensurate with the quality of data currently available for Gliese 581g. We examine two models: the first assumes that the exoplanet is tidally-locked, while the second relaxes this assumption and assumes that a planetary rotation is equal to one Earth . We are primarily interested in the long-term, quasi-stable, large-scale circulation patterns — the climate — as opposed to the short-term temporal variations (the weather). We describe our methods in §2, present our results in §3 and discuss their implications in §4.

2 METHODOLOGY We implement the spectral dynamical core of the Flexible Modeling System (FMS) developed by the Geophysical Fluid Dy- namics Laboratory at Princeton University (Anderson et al. 2004; Figure 2. Long-term, global temperature maps (in K) near the surface Heng, Menou & Phillipps 2010). Dynamical cores are codes that (P = 0.95 bar) of Gliese 581g. Top: with . Bottom: a plan- deal with the essential dynamics of atmospheric circulation, treat etary rotation is one Earth day. The substellar point is located at Θ = 180◦ radiative cooling in a simplified manner (via Newtonian relax- and Φ = 0◦. These maps are averaged over 1000 Earth days, where the ation) and omit atmospheric chemistry (Held & Suarez 1994). The first 200 days of the simulation are discarded. governing equations solved are the primitive equations of mete- orology, where the key assumption made is that of vertical hy- drostatic equilibrium (Vallis 2006; Goodman 2009). Following Held & Suarez (1994) and Heng, Menou & Phillipps (2010), the of κ ≡ R/cp. In the absence of observational constraints, we adopt first 200 Earth days of the simulations are discarded; they are −1 −1 terrestrial values for these quantities: cp = 1004.64 J kg K , then run for 1000 Earth days. The numerical resolution adopted is R = 287.04 J kg−1 K−1 and κ = 2/7. The surface pressure is T63L20 (192×96×20), which corresponds to a horizontal resolu- assumed to be P0 = 1 bar. For simplicity, we have not considered tion of about 300 km. By contrast, the vertical pressure scale height the possible presence of a tropopause. is H ≈ 60 km (T/200 K). For comparison, we note that the sim- We next scale the value of T0 in equation (1) to one appropri- ulations of Joshi, Haberle & Reynolds (1997) and Joshi (2003) use ate to Gliese 581g. Using the scaling, resolutions of T10L10 (32 × 16 × 10) and T21L22 (64 × 32 × 22), respectively. All of the simulations are started from an initial state 1/4 −1/2 T0 ∝L a , (2) of windless isothermality (vinit = 0, Tinit = 264 K) and executed with constant time steps of s (i.e., ∼ 5 time steps in ∆t = 900 10 where L is the stellar luminosity and a is the distance from the total). star, it follows that T0 = 278 K since has a luminosity The effects of stellar irradiation and geometry, known as the of 0.013 L⊙ and a = 0.14601 AU (Mayor et al. 2009; Vogt et al. thermal forcing, on the atmosphere are encapsulated in the forcing 2010). It is important to note that T0 is not the “equilibrium tem- function (Held & Suarez 1994). In the classic Held-Suarez Tforce perature” (i.e., blackbody equivalent) of the exoplanet (Selsis et al. benchmark, the thermal forcing function is designed to reproduce 2007), which is estimated to be Teq ≈ 230 K (assuming a Bond the observed large-scale climate patterns on Earth, of 0.3, typical for objects; Vogt et al. 2010). It κ 2 P 2 P is also important to note that typical estimates of Teq assume that Tforce = T0 − ∆TEP sin Φ − ∆Tz ln cos Φ ,  P0  P0  energy is not transported from the permanent day to the night side (1) (assuming tidal locking) of the exoplanet. On Earth, the tempera- where T0 = 315 K is the surface temperature at the equator, ture difference between the equator and the poles is not solely de- ∆TEP = 60 K is the temperature difference between the equator termined by solar irradiation (e.g., Vallis 2006), so the simple scal- and the poles, P represents the vertical pressure and Φ denotes the ing in equation (2) cannot be straightforwardly applied to ∆TEP. latitude. The third term in equation (1) is a stabilizing term where Therefore, we retain ∆TEP = 60 K in the case of a hypothetical ∆Tz = 10 K. Knowledge of the specific heat capacity at constant Gliese 581g with a rotational period of one Earth day. pressure cp and the ideal gas constant R allow for the specification In the case of a tidally-locked exoplanet, a simplified thermal

c 2010 RAS, MNRAS 000, 1–5 Gliese 581g as a scaled-up Earth 3

Figure 3. Same as Figure 2 but for the long-term, global, zonal wind maps. Figure 4. Same as Figure 3 but for the long-term, global, meridional wind Contour levels are in units of m s−1. maps. forcing is −2 in the same way: gp ≈ 1.46g⊕ ≈ 14.3 m s . Raising the value κ ′ P of the assumed mass to Mp = 4.3–5.0 M⊕ will not have a major Tforce = Teq , effect on our results, since the flow structure is mainly determined  P0  by the rotational rate (Ω ) and the details of the gas physics (c , R ′ ≡ ′ − ◦ (3) p p Tforce T0 +∆TEP cos (Θ 180 ) cos Φ and the radiative cooling time). P 2 The observed of Gliese 581g is 36.562 Earth − ∆Tz ln cos Φ, P0  days (Vogt et al. 2010). If the exoplanet is tidally-locked, then the angular rotational frequency is Ω = 1.9890 × 10−6 s−1. If it has where T ′ is now the surface temperature at the poles and Θ de- p 0 a rotational period of one Earth day, then Ω = 7.292 × 10−5 s−1 notes the longitude. The substellar point is located at Θ = 180◦ p (Held & Suarez 1994). and Φ = 0◦. Operationally, we find that Gliese 581g simulations Finally, since we are exploring the atmospheric circula- with ∆TEP = 60 K and assuming tidal locking do not come to tion in the spirit of a scaled-up Earth, we keep the hyper- quasi-equilibrium within the duration of the simulations, which is viscosity, Newtonian relaxation/cooling time and Rayleigh fric- contrary to expectations because radiative cooling occurs quickly tion/drag1 time to have the default values assumed in the Held- and the global temperature map should simply relax to the thermal Suarez benchmark unless otherwise specified. (See also Table1of forcing function. We therefore execute several simulations with dif- Heng, Menou & Phillipps 2010.) ferent values of ∆TEP to investigate this issue. We find that the global structure of the temperature and wind maps obtained are insensitive to the choice of ∆TEP within the range 10–60 K. For operational reasons, we therefore select ∆TEP = 10 K for the 3 RESULTS tidally-locked case. Using the scaled value of T0 previously de- Figure 1 shows the Mollweide projection2 of a snapshot from rived, we get T ′ = 268 K. 0 the simulation where Gliese 581g is assumed to be tidally-locked. Only the of Gliese 581g is currently known, Since the rotational period of about 37 days is much longer than but the dynamical stability analyses of Mayor et al. (2009) and the radiative cooling time (about 4 days), the structure of the flow Vogt et al. (2010) — assuming co-planar orbits — restrict 1/ sin i is sculpted by radiation rather than advection. The relatively fast to have upper limits of 1.6 and 1.4, respectively. For simplicity, we assume the minimum mass to be the actual mass, Mp = 3.1 M⊕. Since there are currently no observational constraints on the exo- 1 A simple linear prescription that mimicks boundary-layer friction be- planetary radius Rp, we assume — in the spirit of a scaled-up Earth tween the terrestrial atmosphere and surface. — that Gliese 581g has the same mass density as Earth, which 2 Pseudo-cylindrical projection of a globe which conserves area but not yields Rp ≈ 1.46R⊕ ≈ 9290 km. The surface gravity also scales angle or shape. Also called the “homalographic projection”.

c 2010 RAS, MNRAS 000, 1–5 4 Heng & Vogt

Figure 5. Same as Figure 1, but for a simulation where the radiative relax- ation and Rayleigh friction times are set to be 36.562 their original values. The snapshot is taken at 3000 Earth days, where the first 2000 days of the simulation are discarded. Colors denote temperature (in K) and the arrows represent the direction of the velocity field. cooling time implies that the global temperature map relaxes ap- proximately to the input thermal forcing function. While such visualizations are aesthetically pleasing, more in- sight is provided by looking at the temporally-averaged tempera- ture and wind maps as functions of longitude and latitude — the long-term, quasi-stable climate. This is shown in Figure 2, where we contrast both the tidally-locked and non-tidally-locked cases. For the tidally-locked case, the permanent day side of the exoplanet is just within the classical T = 0◦–100◦C habitable temperature Figure 6. Global, long-term zonal (top) and meridional (bottom) wind maps range. In the case where the rotational period is assumed to be for a simulation representative of Gliese 581g, where the radiative relax- equal to one Earth day, the flow is dominated by advection rather ation and Rayleigh friction times are set to be 36.562 times their original values. The maps are averaged over 1000 Earth days, where the first 2000 than radiation, with at the equator hovering around a days of the simulation were discarded. few degrees Celsius. The pair of global temperature maps in Figure 2 makes the point that conclusions on the exact locations for hab- itability on the surface of an exo-Earth depend upon whether the and discard the first 2000 days so as to attain quasi-equilibrium. assumption of tidal locking is made. Even on the cold night side, The Mollweide snapshot of the temperature and velocity fields, the temperatures are comparable to those experienced in Antarc- as well as the long-term wind maps, are shown in Figures 5 and tica where colonies of algae have been discovered and analyzed 6. Since advection occurs somewhat faster than radiative cool- (Edwards et al. 2004). All of these statements are made keeping in ing, zonal winds on the exoplanetary surface develop a stronger mind that temperature is a necessary but insufficient condition for east-west asymmetry and there are hints of energy transport from habitability (see §4). the permanent day to the night side. The chevron-shaped feature Figures 3 and 4 show the global zonal and meridional wind residing around the substellar point is reminiscent of that seen maps, respectively. In the case of a tidally-locked Gliese 581g, at ∼ 0.1 bar in 3D atmospheric circulation simulations of hot large-scale circulation cells transport fluid across hemispheric Jupiters (e.g., Heng, Menou & Phillipps 2010). Trailing the feature −1 scales at speeds ∼ 1 m s , comparable to typical wind speeds are large-scale vortices spanning about a third of the hemisphere in on Earth. These cells have a slight asymmetry from west to east size — their large sizes are a consequence of the Rossby deforma- due to the rotation of the exoplanet. If the exoplanet instead has a tion length scale being relatively larger due to the slower rotation rotational period of one Earth day, there is longitudinal homoge- of the exoplanet when tidally locked. nization of the winds with a counter-rotating jet at the equator and Finally, we show in Figure 7 the zonally- and temporally- super-rotating jets at mid-latitude. The meridional wind map is now averaged zonal wind speeds of the three models considered. The characterized by smaller structures. The slightly faster wind speeds models with tidal locking both have equatorial, super-rotating recovered from the simulation with a rotational period of one Earth winds, where a longer radiative cooling time leads to faster speeds day are artifacts of assuming a higher value of ∆TEP — neverthe- because of the increased effectiveness of advection. The model less, the global structure of the wind maps are robust predictions of which assumes a rotational period of one Earth day has a counter- the simulations. rotating wind at the equator; its faster speed is again an artifact of To further explore the interplay between radiative cooling and assuming a larger value of ∆TEP. advection, we execute another simulation where the radiative cool- ing (originally 4 Earth days) and Rayleigh friction (originally 1 Earth day) times are set to be 36.562 times their fiducial values 4 DISCUSSION — in essence, we are scaling by the ratio of the rotational periods of (a tidally-locked) Gliese 581g to Earth. Due to the longer cool- We have presented three-dimensional simulations of the at- ing time assumed, we now run the simulation for 3000 Earth days mospheric circulation on the exo-Earth Gliese 581g. Our starting

c 2010 RAS, MNRAS 000, 1–5 Gliese 581g as a scaled-up Earth 5

Although Gliese 581 itself is observed to exhibit weak Ca II H and K emission (Mayor et al. 2009), it is well known that M dwarfs in general are chromospherically active (Stauffer & Hartmann 1986; Scalo et al. 2007) and it is likely that stellar activity will mod- ify the exoplanetary atmosphere away from the terrestrial baseline (Selsis et al. 2007). One may also study the effects of atmospheric chemistry, cloud cover, oceans and a hydrological cycle on the atmospheric circulation of exo-Earths (Joshi, Haberle & Reynolds 1997; Joshi 2003), but in the absence of observational constraints on the atmosphere of Gliese 581g we have chosen to omit these additional details. As such observational constraints become avail- able, the models should evolve in sophistication to be commensu- rate with the astronomical data.

Figure 7. Zonally- and temporally-averaged zonal wind speeds near the sur- P = 0.95 face of Gliese 581g ( bar). Positive and negative values indicate ACKNOWLEDGMENTS super- and counter-rotation, respectively. K.H. acknowledges support from the Zwicky Prize Fellowship and the use of the Brutus computing cluster (adroitly managed by Olivier Bryde et al. ) at ETH Z¨urich. S.V. acknowledges support point is a dynamical model that is similar to the Held-Suarez bench- from NSF grant AST-0307493. K.H. is indebted to Kristen Menou mark for Earth, which is calibrated to reproduce terrestrial observa- for introducing him to this field of research and for many illumi- tions of large-scale climate patterns. Using this model as a baseline, nating discussions. This work benefited from the lively scientific we then present global temperature and wind maps which assume ◦ environment at the Institute for Astronomy of ETH Z¨urich. Gliese 581g to be tidally locked. In the context of the classical 0 – 100◦C range of temperatures for habitability, our main finding is that the specific locations for habitability on the surface of Gliese 581g — and exo-Earths in general — depend on whether the ex- REFERENCES oplanet is tidally-locked and how fast radiative cooling occurs on Anderson, J.L., et al. 2004, Journal of Climate, 17, 4641 a global scale. A shortcoming of our approach is that we have ne- Charbonneau, D., et al. 2009, Nature, 462, 891 glected the effects of radiative transfer, which may have little effect Dvorak, R., et al. 2010, Astrobiology, 10, 33 on the large-scale climate patterns but will almost certainly alter Edwards, H.G.M., Cockell, C.S., Newton, E.M., & Wynn- the absolute values of the temperatures — for example, including Williams, D.D. 2004, Journal of Raman Spectroscopy, 35, 463 the effects of CO2 may result in temperatures warmer than what we Goodman, J. 2009, ApJ, 693, 1645 find (i.e., the ). 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