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 temperature 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 astrobiology, attributes and unique studies several a exoplanet have planets stars driving such dwarf are M for stars. search M to nearby is route “exo-Ear promising — particularly exoplanets Earth-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 planet-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 star 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 – atmospheres 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 water) 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-Earths” 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 atmosphere, 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 day. 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 tidal locking. 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 Gliese 581 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, albedo of 0.3, typical for Solar System 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