arXiv:1102.3926v2 [astro-ph.EP] 22 Feb 2011 n uioiyo 0 of a and n l51,wt iiu asso .6ad8.3 and 5.06 of 581c minimum Gl with system, 581d, this Gl in and “super-” so-called two fpriua neett h td fpaeaysineand science is planetary 581g of Gl study that the Note to 581g. interest Gl particular and of 581f super-Earth additional Gl two namely of al. existence planets, authors et the The Vogt of discovery. favor 2010, in controversial argue still in Finally, has a 581d AU. reported Gl 0.22 (2010) of as position re-identified the Meanwhile super-Earth been 2009). another al. discovered, et In was respectively. (Mayor AU, 581e 0.25 Gl and 0.073 2009, of axes semi-major with sa itneo .6p;i a aso bu 0 about of a has it pc; 581 6.26 Gl of V). distance (M3 detec- 581 a the Gl at around reported is planet (2005) Neptune-size al. (e.g., a et of speculative Bonfils tion highly 2006). al. been et has plan- Butler systems super-Earth recently extrasolar and until in Earth-type this that ets of around noteworthy existence planets is possible six and It the to discovered. efforts, up been search possibly tar- have but planetary important four, ongoing an far and is so previous 581 of Gliese dwarf get M-type nearby The Introduction 1. edopitrqet to requests offprint Send srnm Astrophysics & Astronomy uut2,2021 23, August ae n dye l 20)anucdtedtcinof detection the announced (2007) al. et Udry on, Later sG 8g a enetmtdt ebten31ad4.3 and clima 3.1 stellar between be the to of estimated midst been the has in 581g, located Gl 581 as Gliese of system 2 1 Aims. ¡date¿ Accepted / ¡date¿ Received a led enue oguetepicplpsiiiyo l of possibility principal the gauge long-te to its Methods. explores used that been concept already used has previously a on based ixd.Tehbtbezn sdtrie ytelmt fph coverag of ocean limits / the land of by ratios determined Results. different is with Models zone surface. habitable The dioxide. 0 ocrigsprErhpaes hc pert emr abu more words. be Key to appear which planets, super-Earth high. concerning relatively is ar coverage continental posit Conclusions. ocean systemat planetary Goldilock 581g’s reflect relative perfect Gl not the if almost however on an does depend model critically our that of estimate framework an the 581g, Gl of . 1 U hc eitsb utafwpret(eedn nthe on (depending percent few a just by deviates which AU, 015 eateto hsc,Uiest fTxsa rigo,Bo Arlington, at Texas of University Physics, of Department osa nttt o lmt matRsac,PO o 01 60 Box P.O. Research, Impact e-mail: Climate for Institute Potsdam n21,dtie bevtoshv enpbihdta see that published been have observations detailed 2010, In h aiu iesa o aial odtosi tandf attained is conditions habitable for span time maximum The hra vlto oe o ue-atsi sdt calcul to used is super- for model evolution thermal A [email protected] aiaiiyo h odlcspae lee581g: Gliese planet Goldilocks the of Habitability tr:idvda:G 8 tr:paeaysses—astro — systems planetary : — 581 Gl individual: stars: u eut r ute tptwr dniyn h possib the identifying toward step further a are results Our . 013 .vnBloh von W. : ± 0 .vnBloh von W. aucitn.final no. manuscript . 002 eut rmgoyai models geodynamic from Results L ⊙ sebelow). (see 1 .Cuntz M. , Rsac Note) (Research M . 31 ⊕ ABSTRACT M and 2 .Franck S. , ⊙ a edn osdrbeavnaet h osblt fl of possibility the to advantage considerable a lending ea, M mpsiiiyo htsnhtcboaspouto,whic production, biomass photosynthetic of possibility rm f eadn h ue-atsG 8cadG 581d. Gl and 581c Gl super-Earths the regarding ife ⊕ r pursued. are e itneo l51 setmtdt e0 be to estimated The is 0.2. 581g that exceeds Gl eccentricities of assumption orbital distance the planetary by the constrained of none partially is limit mass a lmtlgclhbtbezn.Isms setmtdto estimated is 4.3 and mass 3.1 Its between stel- zone. the be of habitable midst the climatological in lar positioned is it because r aorbefrlqi ae oeita h lntssur- planet’s the at exist to conditions re- liquid physical the as for lies where favourable defined star are are it central HZs the whether stellar around Typically, by gions i.e., (2010). argued already al. , as et (HZ), Vogt of zone habitable possibility stellar the within principal the 2009). undergoing fers al. al. systems et et as Franck Bloh well (von 2003; evolution as al. branch 2003), et giant al. (Cuntz red et Cnc Bloh 55 of von simulations and 2003; and to systems, UMa as 581c other 47 well various Gl as i.e., in 2007), planets to al. super-Earth applied et hypothetical Bloh previously been appropriate. (von model 581d already if Gl laws our has scaling 581g approach using Gl indeed This Earth, is for the this for consider that developed and hypothesis a case, In the with Earth. adopt the of masses we that Earth following, to ten akin the composition about mineral to and one chemical from planets rocky zero. to identical almost is eccentricity its and ooia aial oe h aso h lnt known planet, the of mass The zone. habitable tological nti td,w netgt h aiaiiyo l581g Gl of habitability the investigate we study, this In . dn hnpeiul surmised. previously than ndant o sraie.Teeitneo aiaiiyi on to found is habitability of existence The realized. is ion 95,Alntn X709 USA 76019, TX Arlington, 19059, x tsnhtcbooia rdciiyo h planetary the on productivity biological otosynthetic h anqeto swehrG 8g feitn,of- existing, if 581g, Gl whether is question main The are super-Earths (2006), al. et Valencia to According cucranisihrn normdl hrfr,in Therefore, model. our in inherent uncertainties ic 3 41 osa,Germany Potsdam, 14412 03, 2 dpe tla uioiy rmteata position actual the from luminosity) stellar adopted oidct nte ue-at lnti the in planet super-Earth another indicate to m 1 n .Bounama C. and , t h ore n ik famshrccarbon atmospheric of sinks and sources the ate lt flf eodteSlrSse,especially System, Solar the beyond life of ility rwtrwrd tapsto faot0 about of position a at worlds water or biology M ⊕ oigta h uaieupper putative the that noting , 1 . 14601 ±

c 0 . S 2021 ESO 01 AU, 00014 . 14 ife ± h 2 W. von Bloh et al.: Goldilocks planet (RN)

face for a period of time sufficient for biological evolution to CENTRAL STAR occur. Kasting et al. (1993) calculated the HZ boundaries LUMINOSITY for the luminosity and effective of the present as Rin = 0.82 AU and Rout = 1.62 AU. They defined the HZ of an Earth-like planet as the region where liquid MEAN GLOBAL water is present at the surface. TEMPERATURE According to this definition, the inner boundary of the

HZ is determined by the loss of water via photolysis and hy- ATMOSPHERIC BIOLOGICAL drogen escape. The outer boundary of the HZ is determined PRODUCTIVITY Text SILICATE-ROCK by the condensation of CO2 crystals out of the WEATHERING that attenuate the incident sunlight by Mie scattering. The critical CO2 partial pressure for the onset of this effect is about 5 to 6 bar. However, the cooling effect of CO2 clouds SPREADING CONTINENTAL has been challenged by Forget & Pierrehumbert (1997). RATE AREA CO2 clouds have the additional effect of reflecting the out- going thermal radiation back to the surface. The precise in- ner and outer limits of the climatic habitable zone are still CONTINENTAL HEAT FLOW unknown due to the limitations of the existing climate mod- GROWTH MODEL els. Recently, Heller et al. (2011) extended the concept of the HZ by including constraints arising from tidal processes Fig. 1. Earth system box model. The arrows indicate the due to the planet’s spin orientation and rate. Effects caused different forcing and feedback mechanisms. The bold ar- by tilt erosion, tidal heating, and tidal equilibrium rotation rows indicate negative feedback operating towards climate seem to be especially important for potentially habitable stabilization. planets (as Gl 581d and Gl 581g) around low-mass stars. For limitations of the of M-type stars see, e.g., Tarter et al. (2007), Guinan & Engle (2009), and with Sin(Te) and Sout(Te) described as second order poly- Segura et al. (2011). nomials. The luminosity and age of the central star play im- To assess the habitability of a , an portant roles in the manifestation of habitability. The lu- Earth-system model is applied to calculate the evolution of minosity of Gl 581 can be obtained by (1) photometry the temperature and atmospheric CO2 concentration. On (Bonfils et al. 2005; Udry et al. 2007), and (2) the applica- Earth, the carbonate–silicate cycle is the crucial element for tion of the mass–radius relationship (Ribas 2006) together a long-term homeostasis under increasing . with the spectroscopically determined stellar effective tem- On geological time-scales, the deeper parts of the Earth are perature of Te = 3480 K (Bean et al. 2006). Both methods considerable sinks and sources of carbon. yield L = 0.013 ± 0.002 L⊙. Selsis et al. (2007) estimated Our numerical model previously applied to Gl 581c and the stellar age as at least 7 Gyr based on the non-detection Gl 581d (von Bloh et al. 2007) couples the stellar luminos- of Gl 581’s X-ray flux considering the sensitivity limit of ity L, the silicate–rock weathering rate Fwr and the global ROSAT (Schmitt et al. 1995; Voges et al. 2000). energy balance to obtain estimates of the partial pressure of In the following, we adopt a definition of the HZ pre- atmospheric carbon dioxide PCO2 , the mean global surface viously used by Franck et al. (2000a,b). Here habitability temperature Tsurf, and the biological productivity Π as a at all times does not just depend on the parameters of the function of time t (Fig. 1). The main point is the persistent central star, but also on the properties of the planet. In balance between the CO2 sink in the atmosphere–ocean particular, habitability is linked to the photosynthetic ac- system and the metamorphic (plate tectonic) sources. This tivity of the planet, which in turn depends on the planetary is expressed through the dimensionless quantities atmospheric CO2 concentration together with the presence of liquid water, and is thus strongly influenced by the plan- fwr(t) · fA(t)= fsr(t), (2) etary dynamics. We call this definition the photosynthesis- sustaining habitable zone, pHZ. In principle, this leads to where fwr(t) ≡ Fwr(t)/Fwr,0 is the weathering rate, fA(t) ≡ and temporal additional spatial limitations of habitability Ac(t)/Ac,0 is the continental area, and fsr(t) ≡ S(t)/S0 because the pHZ (defined for a specific type of planet) be- is the areal spreading rate, which are all normalized by comes narrower with time owing to the persistent decrease their present values of Earth. Eq. (2) can be rearranged by of the planetary atmospheric CO2 concentration. introducing the geophysical forcing ratio GFR (Volk 1987) as

2. Habitability of super-Earth planets fsr fwr(Tsurf , PCO2 )= =: GFR(t). (3) 2.1. Photosynthesis-sustaining habitable zone (pHZ) fA The climatic habitable zone at a given time for a star with Here we assume that the weathering rate only depends on luminosity L and effective temperature Te different from the the global surface temperature and the atmospheric CO2 Sun can be calculated following Underwood et al. (2003) concentration. For the investigation of a super-Earth under based on previous work by Kasting et al. (1993) as external forcing, we adopt a model planet with a prescribed

1 1 continental area. The fraction of continental area with re- 2 2 L L spect to the total planetary surface fA is varied between Rin = , Rout = (1) L⊙ · Sin(Te) L⊙ · Sout(Te) 0.1 and 0.9. W. von Bloh et al.: Goldilocks planet Gliese 581g (RN) 3

Table 1. Size and gravity parameters of the Gl 581g models

Parameter Value Unit Description ... 1M⊕ 3.1M⊕ 4.3M⊕ ...... 2 g 9.81 16.5 19.2 m s− gravitational acceleration Rp 6378 8657 9456 m planetary radius Rc 3471 4711 5146 m inner radius of the mantle Rm 6271 8511 9298 m outer radius of the mantle

The connection between the stellar parameters and the in accord with our previous work focused on Gl 581c and planetary climate can be obtained by using a radiation bal- Gl 581d; see von Bloh et al. (2007), for details. A key ele- ance equation (Williams 1998) ment is the computation of the areal spreading rate S; note that S is a function of the average mantle temperature T , L m the surface temperature Tsurf , the heat flow from the mantle 2 [1 − a(Tsurf , PCO2 )]=4IR(Tsurf , PCO2 ), (4) 4πR qm, and the area of ocean basins A0 (Turcotte & Schubert where a denotes the planetary , IR the outgoing in- 2002). It is given as frared flux, and R the distance from the central star. The 2 qmπκA0 climate model does not include clouds, which are particu- S = 2 2 , (6) larly important for determining the inner boundary of the 4k (Tm − Tsurf ) HZ (Selsis et al. 2007). The Eqs. (3) and (4) constitute a where κ is the thermal diffusivity and k the thermal con- set of two coupled equations with two unknowns, Tsurf and ductivity. To calculate the spreading rate, the thermal evo- PCO2 , if the parameterization of the weathering rate, the lution of the mantle has be to computed: luminosity, the distance to the central star and the geo- 4 3 3 dTm 2 4 3 3 physical forcing ratio are specified. Therefore, a numerical πρc(Rm − Rc ) = −4πRmqm + πE(t)(Rm − Rc), (7) solution can be attained in a straightforward manner. 3 dt 3 The photosynthesis-sustaining HZ around Gl 581 is de- where ρ is the density, c is the specific heat at constant fined as the spatial domain of all distances R from the cen- pressure, E is the energy production rate by decay of ra- tral star where the biological productivity is greater than diogenic heat sources in the mantle per unit volume, and zero, i.e., Rm and Rc are the outer and inner radii of the mantle, re- spectively. To calculate the thermal evolution for a planet pHZ := {R | Π(PCO (R,t),Tsurf (R,t)) > 0}. (5) 2 with several Earth masses, i.e., 3.1 and 4.3 M⊕ as pursued In our model, biological productivity is considered to be for Gl 581g in our present study, the planetary parameters solely a function of the surface temperature and the CO2 have to be adjusted. Thus we assume partial pressure in the atmosphere. Our parameterization 0.27 ◦ ◦ Rp M yields zero productivity for Tsurf ≤ 0 C or Tsurf ≥ 100 C = , (8) −5 R⊕ M⊕  or PCO2 ≤ 10 bar (Franck et al. 2000a). The inner and outer boundaries of the pHZ do not depend on the detailed where Rp is the planetary radius, see Valencia et al. (2006). parameterization of the biological productivity within the The total radius, mantle thickness, core size, and average temperature and pressure tolerance window. density are all functions of mass, with the subscript ⊕ de- noting Earth values. The exponent of 0.27 has been ob- 2.2. Comments on the thermal evolution model tained for super-Earths. The values of Rp, Rm, Rc, as well as the other planetary properties are scaled accordingly. It Parameterized convection models are the simplest models means that Rp, Rm and Rc increase by a factor of 1.36 for for investigating the thermal evolution of terrestrial planets M =3.1M⊕ and 1.48 for M =4.3M⊕. and satellites. They have been successfully applied to the Table 1 gives a summary of the size parameters for the evolution of , , Earth, , and the models of the planets with 3.1 and 4.3 M⊕; see the study by (Stevenson et al. 1983; Sleep 2000). Franck & Bounama von Bloh et al. (2007) for additional information. The val- (1995) studied the thermal and volatile history of Earth and ues for an Earth-size planet are included for comparison. Venus in the framework of comparative planetology. The in- The onset of plate tectonics on massive terrestrial planets ternal structure of massive terrestrial planets with one to is a topic of controversy. While O’Neill & Lenardic (2007) ten Earth masses has been investigated by Valencia et al. stated that there might be in an episodic or stagnant lid (2006) to obtain scaling laws for total radius, mantle thick- regime, Valencia & O’Connell (2009) proposed that a more ness, core size, and average density as a function of mass. massive planet is likely to convect in a plate tectonic regime Similar scaling laws were found for different compositions. similar to Earth. Thus, the more massive the planet is, We will use these scaling laws for the mass-dependent prop- the higher the Rayleigh number that controls convection, erties of super-Earths and also the mass-independent ma- the thinner the top boundary layer (lithosphere), and the terial properties given by Franck & Bounama (1995). higher the convective velocities. In the framework of our The thermal history and future of a super-Earth has model, a plate-tectonic-driven carbon cycle is considered to be determined to calculate the spreading rate for solving necessary for carbon-based life. This approach follows the key Eq. (2). A parameterized model of whole mantle convec- previous work by von Bloh et al. (2007), who gave a de- tion including the volatile exchange between the mantle and tailed discussion of the equations and parameters used in surface reservoirs (Franck & Bounama 1995; Franck 1998) their study for the super-Earths with 5 and 8 M⊕, identified is applied. The key equations used in our present study are as Gl 581c and Gl 581d, respectively. 4 W. von Bloh et al.: Goldilocks planet Gliese 581g (RN)

Fig. 3. Life span for Gl 581g with M = 3.1M⊕ (+) and M = 4.3M⊕ (×) as a function of the relative continental area. For comparison the dashed curve denotes the life span of an Earth-mass planet. The horizontal line indicates the lower limit for the age estimate of 7 Gyr.

This maximum life span can be realized for a super- Earth at a distance from the central star of about 0.14 ± 0.015 AU. This uncertainty is reflective of the uncertainty in the luminosity estimate of Gl 581, noting however that our models are also subject to various systematic uncertain- ties (see Sect. 2). A full assessment of those uncertainties, which are expected to be larger than the impact of the un- certainty in the stellar luminosity, can best be obtained by a comparison with future alternative models. It is noteworthy that the orbital position of Gl 581g at 0.146 AU, if existing, Fig. 2. The pHZ of Gl 581 for a super-Earth of (a) M = is largely consistent with this ideal position. Thus, we can 3.1M⊕ and (b) M = 4.3M⊕ as a function of planetary conclude that Gl 581g has an almost perfect Goldilock po- age. The relative continental area is varied from 0.1 to 0.9. sition in the star–planet system of Gl 581, and it is the best The stellar luminosity is assumed to be 0.013L⊙. Following candidate for extra-terrestrial habitability so far. Because Selsis et al. (2007) and references therein, the stellar age is of the Goldilock position, located well within the HZ, clouds at least 7 Gyr, indicated by a dashed line. For comparison, play no major role for our results. Any shift (within limits) we show the positions of Venus, Earth, and Mars scaled to of the inner or outer boundary of the HZ will not affect the the luminosity of Gl 581. Note that the position of Gl 581g maximum life span obtained by our model. The optimum almost exactly coincides with the luminosity-scaled position position is not only the geometric mean of the pHZ, but of Earth. it is also the position where the maximum life span of the biosphere is realized. But the pHZ also strongly depends on the planetary age. Figure 3 depicts the life span for a super-Earth with 3.1 and 3. Results and discussion 4.3 M⊕ at 0.146 AU as a function of the relative continental area r. For a relative continental area larger than 0.6, the The photosynthesis-sustaining habitable zone is calculated realized life span is shorter than 7 Gyr, which is the esti- for super-Earth planets with 3.1 and 4.3 M⊙ and the re- mated lower limit for the stellar age of Gl 581 star–planet sults are depicted in Fig. 2. The maximum life span of a system. In this case, no habitable conditions on Gl 581g biosphere is given at the point in time when the pHZ van- would exist in the framework of the adopted geodynamic ishes. This maximum life span strongly depends on the rel- model. If we place an Earth twin (r ≃ 0.29) at the orbital ative continental area r and increases with decreasing r. position of Gl 581g, habitable conditions would cease just Therefore, “water worlds” are favored in the facilitation of at an age of 7 Gyr. In conclusion, we have to await future habitability as previously obtained in models of fictitious missions to identify the pertinent geodynamical features of super-Earth planets for 47 UMa and 55 Cnc (Franck et al. Gl 581g (in case it does exist) and to search for biosigna- 2003; von Bloh et al. 2003). In this context, water worlds tures in its atmosphere to gain insight into whether or not are planets of non-vanishing continental area mostly cov- Gl 581g harbors life. ered by oceans. The climate of a planet fully covered by oceans is not stabilized by the carbonate–silicate cycle. The References maximum life span for a water world with r = 0.1 and a planetary mass of M = 3.1M⊕ is 15.4 Gyr, whereas it is Bean, J. L., Benedict, G. F., & Endl, M. 2006, ApJ, 653, L65 Bonfils, X., Forveille, T., Delfosse, X., et al. 2005, A&A, 443, L15 16.3 Gyr for M = 4.3M⊕. Both times are considerably Butler, R. P., Wright, J. T., Marcy, G. W., et al. 2006, ApJ, 646, 505 longer than the estimated age limit of Gl 581, which is Cuntz, M., von Bloh, W., Bounama, C., & Franck, S. 2003, Icarus, 7 Gyr (Selsis et al. 2007). 162, 215 W. von Bloh et al.: Goldilocks planet Gliese 581g (RN) 5

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