Dynamic habitability for Earth-like planets in 86 extrasolar planetary systems

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Planetary and Space Science 55 (2007) 651–660 www.elsevier.com/locate/pss

Dynamic habitability for Earth-like planets in 86 extrasolar planetary systems W. von Bloh, C. Bounama, S. Franck Potsdam Institute for Climate Impact Research (PIK), P.O. Box 601203, 14412 Potsdam, Germany Received 1 December 2005; accepted 21 June 2006 Available online 30 October 2006

Abstract In this paper we estimate the likelihood to find habitable Earth-like planets on stable orbits for 86 selected extrasolar planetary systems, where luminosity, effective temperature and stellar age are known. For determining the habitable zone (HZ) an integrated system approach is used taking into account a variety of climatological, biogeochemical, and geodynamical processes. Habitability is linked to the photosynthetic activity on the planetary surface. We find that habitability strongly depends on the age of the stellar system and the characteristics of a virtual Earth-like planet. In particular, the portion of land/ocean coverages plays an important role. We approximated the conditions for orbital stability using a method based on the Hill radius. Almost 60% of the investigated systems could harbour habitable Earth-like planets on stable orbits. In 18 extrasolar systems we find even better prerequisites for dynamic habitability than in our own solar system. In general our results are comparable to those with an HZ determination based only on climatic constraints. However, there are remarkable differences for land worlds and for systems older than about 7 Gyr. r 2006 Elsevier Ltd. All rights reserved. Keywords: Habitable zone; Orbital stability; Extrasolar planets; Geodynamics; Planetary climate

1. Introduction The search for extrasolar Earth-like planets is one of the main goals of present research. More than 170 extrasolar planets are known to orbit around main-sequence stars including several multiple-planet systems. Most of them are giant planets, with hydrogen and helium as the main constituents, and have atmospheres too turbulent to permit the emergence of life and have no underlying solid surfaces or oceans that could support a biosphere. Nevertheless, there is a possibility for habitable conditions at the surface of moons orbiting giant planets that are positioned within the habitable zone (HZ). Furthermore, Earth-like Trojan planets in 1:1 mean motion resonance on stable orbits with habitable conditions are possible (Dvorak et al., 2004). The distribution of masses of all known exoplanets lets scientists suppose that there must be a multitude of planets with lower masses (Marcy et al., 2003, 2005). A planet with Corresponding author. Tel.: +49 331 288 2603; fax: +49 331 288 2570.

E-mail address: [email protected] (W. von Bloh). 0032-0633/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2006.06.022

a mass of 14 Earth masses has been detected at a distance of 0.038 AU from the central star (McArthur et al., 2004). Whether this planet is a hot Neptune or a rocky ‘‘super Earth’’ it is clear that the planet is inhabitable. Also the recently discovered cool sub-Neptune-mass planet of 5.5 Earth masses orbiting a M-dwarf star at a distance 2:6 AU (Beaulieu et al., 2006) is not a candidate for a habitable world. The existence of Earth-type planets around stars other than the Sun is strongly implied by various observational findings including (1) the steep rise of the mass distribution of planets with decreasing mass, which implies that more small planets form than giant ones; (2) the detection of protoplanetary disks (with masses between 10 and 100 times that of Jupiter) around many solar-type stars younger than 3 Myr; and (3) the discovery of ‘‘debris disks’’ around middle-aged stars, the presumed analogs of the Kuiper Belt and zodiacal dust (Marcy et al., 2005; Santos et al., 2005, and references therein). Lineweaver and Grether (2003) conclude that 25–100% Sun-like stars harbour planets.

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Even if it seems today beyond the technical feasibility to detect Earth-mass planets we can apply computer models to investigate known exoplanetary systems to determine whether they could host Earth-like planets with surface conditions sufficient for the emergence and maintenance of life on a stable orbit. Such a configuration is described as dynamic habitable. Jones et al. (2001) have investigated the dynamic habitability of several exoplanetary systems. They used the boundaries of the HZ originating from Kasting et al. (1993). To test the intersection of stable orbits and the HZ, putative Earth-mass planets were launched into various orbits in the HZ and a symplectic integrator was used to calculate the celestial evolution of the extrasolar planetary system. Kasting et al. (1993) calculated the HZ boundaries for the luminosity and effective temperature of the present Sun as Rinner ¼ 0:84 AU and Router ¼ 1:37 AU. They defined the HZ of an Earth-like planet as the region where liquid water is present at the surface. According to this definition the inner boundary of the HZ is determined by the loss of water via photolysis and hydrogen escape. The outer boundary of the HZ is determined by the condensation of CO2 crystals out of the atmosphere that attenuate the incident sunlight by Rayleigh scattering. The critical CO2 partial pressure for the onset of this effect is about 5–6 bar. On the other hand, the effects of CO2 clouds have been challenged by Forget and Pierrehumbert (1997). CO2 clouds have the additional effect of reflecting the outgoing thermal radiation back to the surface. The precise inner and outer limits of the climatic HZ are still unknown because of the limitations of climate model used until now. For the present Sun it is probably smaller than the 0.7–2 AU region but it is still impossible to give a better constraint especially for the outer boundary of the HZ. In this paper, we adopt a somewhat different definition of the HZ already used by Franck et al. (1999, 2000a,b). Here habitability (i.e., presence of liquid water at all times) does not just depend on the parameters of the central star, but also on the properties of the planet itself. In particular, habitability is linked to the photosynthetic activity of the planet, which in turn depends on the planetary atmospheric CO2 concentration, and is thus strongly influenced by the planetary geodynamics. This leads to additional spatial and temporal limitations of habitability, as the stellar HZ (defined for a specific type of planet) becomes narrower with time due to the persistent decrease of the planetary atmospheric CO2 concentration. The stability of orbits of hypothetical Earth-like planets is calculated by a method of Jones et al. (2005). They evaluated the dynamic habitability using nRH derived from giant’s orbital eccentricity without carrying out timeconsuming orbital integrations, where RH is the Hill radius of the giant planet and n is a multiplier that depends on the giant’s orbital eccentricity. In the present paper we calculate the dynamic habitability of 86 extrasolar planetary systems in dependence of the relative continental area of a putative Earth-like planet.

2. Integrated system approach In our calculation of the HZ we are following an integrated system approach. On Earth, the carbonate–silicate cycle is the crucial element for a long-term homeostasis under increasing solar luminosity. In most studies (see, e.g., Caldeira and Kasting, 1992), the cycling of carbon is related to the present tectonic activities and to the present continental area as a snapshot of the Earth’s evolution. On the other hand, on geological time-scales the deeper parts of the Earth are considerable sinks and sources for carbon. In addition, the tectonic activity and the continental area change noticeably. Therefore, we favour the so-called geodynamical models that take into account both the growth of continental area and the decline in the spreading rate (Franck et al., 2000a). Our numerical model couples the stellar luminosity, L, the silicate-rock weathering rate, F wr , and the global energy balance to allow estimates of the partial pressure of atmospheric and soil carbon dioxide, Patm and Psoil , respectively, the mean global surface temperature, T surf , and the biological productivity, P, as a function of time (Fig. 1). The main feedback loop stabilising the planetary climate is given by the silicate rock weathering: an increase of the luminosity leads to a higher mean global temperature causing an increase in weathering. Then more CO2 is extracted from the atmosphere weakening the greenhouse

CENTRAL STAR LUMINOSITY

MEAN GLOBAL TEMPERATURE

ATMOSPHERIC CARBON DIOXIDE

BIOLOGICAL PRODUCTIVITY Text

SILICATE-ROCK WEATHERING

SPREADING RATE

CONTINENTAL AREA

HEAT FLOW

CONTINENTAL GROWTH MODEL

Fig. 1. Box model of the integrated system approach (Franck et al., 2000a). The arrows indicate the different forcings (dotted lines) and feedback mechanisms (solid lines). The main feedback loop stabilising the climate is marked with bold arrows.

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effect. Overall the temperature is lowered and homeostasis is achieved. The applied model is a simplified version of a box model of the global carbon cycle (Franck et al., 2002), which has been successfully used to describe the Earth’s evolution from the Archaean to the present state. Our evolution history and future is in coincidence with results of Schwartzman (1999) and Knauth and Lowe (2003). Furthermore, the re-evaluation of the origin and evolution of 44:2 Ga zircons by Nemchin et al. (2006) gives no convincing evidence of significantly heavy oxygen. This suggests no evidence in support for models of a cool early Earth in contrast to Peck et al. (2001) and Valley et al. (2002). The crucial point of the simplified model is the persistent balance between the CO2 sink in the atmosphere–ocean system and the metamorphic (plate-tectonic) sources. This is expressed with the help of dimensionless quantities (Berner et al., 1983; Kasting, 1984) f wr  f A ¼ f sr ,

(1)

where f wr  F wr =F wr;0 is the weathering rate normalised by the present value, f A  Ac =Ac;0 is the continental area normalised by the present value, and f sr  S=S 0 is the spreading rate normalised by the present value. Eq. (1) can be rearranged by introducing the geophysical forcing ratio, GFR (Volk, 1987): f wr ¼

f sr ¼: GFRðtÞ. fA

(2)

With the help of Eq. (2), we can calculate the normalised weathering rate from geodynamics based on the continental growth model and the spreading rate (Franck et al., 2000a). The spreading rate is determined with the help of the boundary layer theory of whole mantle convection (Turcotte and Schubert, 1982). On the other hand, the weathering rate, f wr , depends directly on the surface temperature and the atmospheric CO2 partial pressure (Walker et al., 1981): f wr ¼ f wr ðT surf ; Patm Þ.

(3)

The biological productivity P can in principle amplify the weathering rate by increasing the CO2 partial pressure in the soil. Then Patm in Eq. (3) has to be replaced by the partial pressure of CO2 in the soil, Psoil ¼ Psoil ðP; Patm Þ. Furthermore, recent studies show that the photosynthetic active biosphere has a direct impact on the Earth’s interior reservoirs via the energy and material cycle (Krumbein and Schellnhuber, 1992; Rosing, 2005; Rosing et al., 2006) neglected in our model. The connection between the stellar parameters and the planetary climate can be formulated by using a radiation balance equation (Williams, 1998) L ½1  aðT surf ; Patm Þ ¼ 4I R ðT surf ; Patm Þ. 4pR2

(4)

Here a denotes the planetary albedo, I R the outgoing infrared flux, and R the distance from the central star. With

653

the help of Eq. (4) it is possible to replace Patm by T surf in Eq. (3) and this results in: f wr ðT surf ; L; RÞ ¼ GFRðtÞ.

(5)

The evolution of the surface temperature can be derived by solving Eq. (5) for known luminosity, distance to the central star and GFR. Eq. (4) yields the corresponding evolution of the atmospheric CO2 partial pressure. In our model, biological productivity is considered to be solely a function of the surface temperature and the CO2 partial pressure in the atmosphere   ! P T surf  50  C 2 ¼ max 1 Pmax 50  C    Patm  Pmin  ;0 . ð6Þ P1=2 þ ðPatm  Pmin Þ Here Pmax denotes the maximum biological productivity, which is assumed to amount to twice the present value P0 (Volk, 1987). P1=2 þ Pmin is the value at which the pressuredependent factor is equal to 12, and Pmin is fixed at 105 bar, the presumed minimum value for C4-photosynthesis (Pearcy and Ehleringer, 1984; Larcher, 1995). The evolution of the biosphere and its adaption to even lower CO2 partial pressures are not taken into account in our model. For a given Patm , Eq. (6) yields maximum productivity at T surf ¼ 50  C and zero productivity for T surf p0  C and T surf X100  C. There exist hyperthermophilic life forms with a temperature tolerance well above 100  C. In general, these are chemoautotrophic organisms not included in this study. At this point we should emphasise that all calculations are done for a planet with Earth mass and size, and an Earth-like radioactive heating rate in its interior. The HZ in an extrasolar planetary system is defined as the spatial domain where the planetary surface temperature stays between 0 and 100  C and where the atmospheric CO2 partial pressure is higher than 105 bar to allow photosynthesis. This is equivalent to a non-vanishing biological productivity, P40, i.e., HZ:¼fR j PðPatm ðR; tÞ; T surf ðR; tÞÞ40g.

(7)

According to the definition in Eq. (7) the boundaries of the HZ are determined by the surface temperature extrema, T surf ¼ 0  C _ T surf ¼ 100  C, or by the minimum CO2 partial pressure, Patm ¼ 105 bar. Therefore, the specific parameterisation of the biological productivity (Eq. (6)) plays a minor role in the calculation of the HZ. In the approach by Kasting et al. (1993) the HZ is limited only by climatic constraints invoked by the luminosity of the central star, while our method relies on additional constraints. First, habitability is linked to the photosynthetic activity of the planet (Eq. (7)). In particular photosynthesis is most relevant for the direct detection of life on extrasolar terrestrial planets. The TPF and Darwin space missions of NASA and ESA are planning to detect O2 or its photolytic product O3 as a biosignature of life

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(Des Marais et al., 2002) built up by oxygenic photosynthesis. Second, habitability is strongly affected by the planetary geodynamics. In principle, this leads to additional spatial and temporal limitations of habitability. 3. Orbital stability Planetary habitability requires orbital stability of the Earth-type planet over a biologically significant length of times in the HZ. The analysis of orbital stability of (hypothetical) terrestrial planets in extrasolar planetary systems has to take into account the effects of the giant planet(s) in those systems. In many cases the giant planets restrict the orbital stability of the terrestrial planet to a small or very small orbital domain or prevent orbital stability completely. There exists a variety of papers discussing the orbital stability of (hypothetical) terrestrial planets in extrasolar planetary systems, which is strongly influenced by the masses, orbital positions and eccentricities of Jupiter-size planets in such systems (see, e.g., Noble et al., 2002; Menou and Tabachnik, 2003; Goz´dziewski, 2002; Asghari et al., 2004). Jones et al. (2001) analysed the stability of orbits of terrestrial planets in several known extrasolar planetary systems. They used a mixed-variable symplectic integrator by Chambers (1999) over a time scale of 109 years, while Pilat-Lohinger and Dvorak (2002) used a Lie-series method (e.g., Hanslmeier and Dvorak, 1984) for the calculation of the orbits of an Earth-like planet. In order to calculate the orbital stability we apply an approximation derived by Jones et al. (2005): if the Earthlike planet approaches three Hill radii of the giant planet severe orbital perturbations of the terrestrial planet occur. The Hill radius RH is defined as  m 1=3 RH ¼ a, (8) 3M where m is the mass of the giant planet, M the central star mass and a the semimajor axis. Then the inner and outer boundaries for unstable orbits around a giant planet are defined by Rint ¼ að1  eÞ  nint ðeÞRH ,

(9)

Rext ¼ að1 þ eÞ þ next ðeÞRH ,

(10)

where e is the eccentricity of the giant planet. The values of the functions nint ðeÞ and next ðeÞ are taken from Table 4 in Jones et al. (2005). They are in the range of ½2 . . . 3 for nint ðeÞ and ½3 . . . 16 for next ðeÞ. Even if the orbit is outside the boundaries given in Eqs. (9) and (10) the eccentricity of the Earth-like planet will generally increase until the orbit is possibly outside the HZ for a significant fraction of the orbital period. The critical limit for the eccentricity is between 0.5 and 0.7. Williams and Pollard (2002) conclude that even under such conditions an Earth-like planet might be habitable for a dense enough atmosphere. Jones et al.

(2005) found that the eccentricity is usually less than 0.3–0.4 outside the interval ½Rint ; Rext . In our study we use results of Espresate (2005) for the stellar parameters of 133 extrasolar planetary systems. Missing values for stellar ages were taken from Jones et al. (2005). For 86 of these 133 systems the stellar luminosities, effective temperatures and ages are given. These three values are printed in Table 1. It must be pointed out that the determination of the age of low mass stars is errorprone and has to be taken with care. Together with the corresponding orbital parameters and masses of the giant planets (data taken from Jean Schneider’s extrasolar planets encyclopaedia http://www.obspm.fr/encycl/encycl.html) the HZs and the orbital stability domains can be calculated using Eqs. (8), (9) and (10). 4. Results and discussion The HZ for a fixed central star luminosity of L  1L

and fixed effective temperature of T eff ¼ 5700 K is calculated as a function of the age of the planetary system. For the investigation of an Earth-like planet under the external forcing we adopt a model planet with a prescribed continental area. The fraction of continental area to the total planetary surface is varied between 0:1 and 0:9. According to Franck et al. (2000a, Table 1) a constant continental area yields the maximum life span of the biosphere. Therefore, we have chosen this scenario in order to get the most optimistic estimation of habitability of an extrasolar planetary system. The HZ is calculated by solving Eq. (5) for different distances to the central star R. According to Eq. (7) the inner and outer limits of the HZ are given by vanishing biological productivity (Eq. (6)). In Fig. 2 the colour shaded areas indicate the HZs for different constant continental areas of the Earth-like planet. While the inner limit of the HZ does not change significantly with age, the outer limit shows a non-trivial behaviour. Up to a critical age the outer limit is constant and is determined by the maximum CO2 atmospheric pressure (5 bar). Beyond this critical point the outer boundary moves inward due to geodynamic effects. At this point the source of carbon released into the atmosphere is too low to prevent the planet from freezing. An ultimate life span of the Earth-like planet is determined by the coincidence of the outer and inner boundary. For a planet older than this ultimate life span no habitability can be found. The critical age and the ultimate time span is a decreasing function of the relative continental area of the Earth-like planet. It is obvious that an almost completely ocean-covered planet (‘‘water world’’) has the highest likelihood of being habitable (Franck et al., 2003). For a central star with different luminosity and effective temperature the limits of the HZ have to be rescaled to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S eff ðT eff Þ 0 R ¼R , (11) L=L

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Table 1 Stellar parameters (luminosity, effective temperature T eff , age) and widths of dynamic HZ of an Earth-like planet for the solar system and for the 86 extrasolar planetary systems with different relative continental areas c ¼ 0:1; 0:3; 0:9 and using climate constraints only (Kasting et al., 1993) System

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Name

Sun HD73256 GJ436 55Cnc HD83443 HD46375 HD187123 tBoo HD330075 HD75289 HD209458 HD76700 51Peg HD68988 HD217107 HD162020 HD160691 HD130322 HD108147 HD38529 HD195019 HD6434 HD192263 rCrB HD168443 HD121504 HD16141 HD114762 HD80606 HD216770 70Vir HD52265 HD1237 HD37124 HD73526 HD82943 HD169830 HD8574 HD202206 HD89744 HD134987 HD40979 HD12661 iHor HD92788 HD28185 HD142415 HD154857 HD108874 HD4203 HD128311 HD210277 HD19994 HD188015 HD114783 HD147513 HD222582 HD183263 HD141937 HD41004A

Luminosity ðL Þ

1 0.69 0.025 0.61 0.88 1 1.4 2.3 0.47 2 1.6 1 1.2 1.8 0.94 0.25 1.8 0.5 1.9 6 1.1 1.1 0.34 1.9 1.9 1.5 2.5 1.8 0.75 0.79 3.1 2 0.66 0.74 2.2 1.6 4.6 2.2 1.1 6 1.2 2 1.2 1.5 1.2 1 1.1 4.9 1.3 1.2 0.28 0.93 3.8 1.4 0.4 0.98 1.1 2 1.2 0.65

T eff (K)

5700 5570 999 5250 5454 5770 5830 6498 5017 6000 6025 5423 5946 6338 5700 4830 5813 5330 6265 5370 5600 5835 4840 5860 5555 6075 5770 6110 5645 5229 5770 6060 5540 5556 5700 6028 6299 6080 5765 6166 5917 6095 5754 6125 5821 5705 6045 5628 5770 5946 5250 5570 6121 5745 5250 5883 5770 5936 5925 5010

Age (Gyr)

4.5 1 3a 5 3 10a 5a 2 6 5.5 5 10a 7.5a 6 8 6a 2 0.5 2 2.5a 3 4 1a 10 2.5 1 3a 5a 6.5a 3 8 4 1 4 9a 3 3 2a 5.5 2 2.5a 1.5 1.5 1.5 2 3 1 5 7a 6.5a 2 8.5 2.5 10 4.5a 0.5 5.5a 10 1.5 1.5

Width of dynamic HZ (AU)

Class

Climatic

c ¼ 0:1

c ¼ 0:3

c ¼ 0:9

0.56 0.47 0.19 0.46 0.54 0.55 0.64 0.75 0.42 0.75 0.67 0.58 0.59 0.68 0.54 0.31 0 0.41 0.71 0 0.58 0.58 0.36 0.76 0 0.66 0.87 0.69 0.33 0.41 0.97 0.74 0 0.44 0.64 0 0 0.39 0 0.59 0.033 0.27 0 0 0 0 0 0.61 0.023 0 0.084 0 0.31 0 0.32 0 0 0 0 0

0.78 0.67 0.26 0.64 0.76 0.14 0.89 1.1 0.58 1.1 0.94 0.16 0.54 0.95 0.38 0.43 0 0.58 1 0 0.82 0.82 0.51 0.17 0 0.94 1.2 0.97 0.6 0.69 0.55 1 0.17 0.37 0.27 0 0 0.84 0 1.3 0.36 0.69 0 0.29 0 0 0 1.3 0.023 0 0.042 0 0.89 0 0.27 0 0 0 0 0

0.46 0.66 0.26 0.29 0.75 0 0.39 1.1 0.15 0.33 0.41 0 0.092 0.21 0.074 0.12 0 0.58 1 0 0.81 0.8 0.51 0 0 0.93 1.2 0.42 0.079 0.69 0.087 0.9 0.17 0.36 0 0 0 0.84 0 1.3 0.36 0.69 0 0.29 0 0 0 0.37 0 0 0.037 0 0.89 0 0.26 0 0 0 0 0

0 0.11 0 0 0 0 0 0.012 0 0 0 0 0 0 0 0 0 0.17 0.014 0 0 0 0.084 0 0 0.093 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

I I I I I I I I I I I I I I I I IV I I III I I I I IV I I I II II I I II II II III IV II IV II II II II II IV III III II II III II III II III II III III III III III

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656 Table 1 (continued ) System

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87

Name

HD23079 HD186427 HD4208 HD45350 HD213240 HD10647 HD10697 47Uma HD190228 HD114729 HD111232 HD2039 HD136118 HD50554 HD196050 HD216437 HD216435 HD106252 14Her HD142022 HD72659 HD70642 HD33636 Eri HD117207 HD30177 HD190360

Luminosity ðL Þ

1.5 1 0.79 1.4 3.6 1.5 3.4 1.3 3.6 2.2 0.69 1.7 2.9 1.5 1.8 2.2 4.2 1.3 0.71 1 2.4 1.3 1.1 0.47 1.7 1.2 1.3

T eff (K)

6200 5760 5605 5616 5975 6143 5770 5780 5360 5915 5494 5675 6003 6050 5918 5887 5830 5890 5255 5500 6030 5670 5990 5180 5723 5320 5590

Age (Gyr)

3a 7a 4.5a 10 2.5 2 6.5a 7 3a 6 5 6a 3 4.5 1.5 6 5 5 4 12 7a 4 3 0.5 10 10a 6.5

Width of dynamic HZ (AU)

Class

Climatic

c ¼ 0:1

c ¼ 0:3

c ¼ 0:9

0.083 0 0.5 0 0 0.38 0 0.47 0 0 0.2 0 0 0 0.11 0.0026 0 0 0.38 0 0.83 0.65 0 0.25 0.72 0.47 0.64

0 0 0.46 0 0 0.28 0 0.36 0 0 0.13 0 0 0 0.012 0 0 0 0.31 0 0.88 0.91 0 0.19 0.18 0.18 0.75

0 0 0.45 0 0 0.27 0 0.12 0 0 0.11 0 0 0 0.00017 0 0 0 0.3 0 0.15 0.79 0 0.19 0 0 0.16

0 0 0 0 0 0.042 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.12 0 0 0

III IV II IV III II III II III III II III III IV II IV III IV II IV II I IV II I I II

Class I denotes unlimited dynamic habitability, class II partial limited dynamic habitability, class III possibility of habitable moons or Trojan planets only, and class IV no dynamic habitability. a Jones et al. (2005).

In Figs. 3 and 4 the intervals for orbital instability of an Earth-like planet are plotted for the 86 extrasolar planetary systems denoted in Table 1. For comparison they are rescaled to an equivalent solar distance R0 and the HZ from Fig. 2 is plotted additionally. The range of dynamic habitability can be easily derived by excluding the horizontal bars from the HZ for a certain relative continental area. We can distinguish four different classes:

Fig. 2. The habitable zone around a central star for a luminosity of L ¼ 1L and fixed effective temperature of the central star ðT eff ¼ 5700 KÞ as a function of the age of the Earth-like planet. The colour shaded areas indicate the extent of the HZ for different relative continental areas. The horizontal dashed lines indicate the HZ defined by climatic constraints only (Kasting et al., 1993).

where S eff ðT eff Þ describes the influence of the effective temperature T eff of the central star on the inner and outer boundary (Kasting et al., 1993).

(I) The HZ does not intersect with the intervals of orbital instability. An Earth-like planet can be dynamic habitable in the entire HZ. Twenty-nine extrasolar planetary systems belong to this class. (II) The HZ does partially intersect with the intervals of orbital instability. Twenty-five extrasolar planetary systems belong to this class. (III) The giant planet is located inside the HZ. A stable orbit of an Earth-like planet does not exist around the central star. However, a moon around the giant planet can be habitable at its surface (Williams and Pollard, 2002) or even a massive Trojan planet can be stable in 1:1 mean motion resonance. In particular Schwarz et al. (2005) have shown that in HD28185 (class III) an Earth-like planet can be dynamical habitable on such an orbit. Twenty extrasolar planetary systems belong to this class.

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Fig. 3. The intervals of unstable orbits in the vicinity of giant planets (denoted by numbers according to Table 1) of the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi solar system and of extrasolar planetary systems with a stellar age p5 Gyr. The intervals are rescaled to an equivalent solar distance R0 ¼ R Seff L =L. The colour shaded areas indicate the extent of the HZ for different relative continental areas. Open circles denote giant planets not limiting dynamic habitability (class I), grey shaded circles denote giant planets partially limiting dynamic habitability (class II), black shaded circles denote planets excluding dynamic habitability (class IV), while shaded squares denote giant planets with habitable moons or Trojan planets (class III).

(IV) The giant planet is outside the HZ and the interval of instable orbits fully covers the HZ. No habitable Earth-like planet is possible on a stable orbit. Twelve extrasolar planetary systems belong to this class. The likelihood that an Earth-like planet is both on a stable orbit and also within the HZ can be quantitatively estimated from the width of the HZ excluding the interval of orbital instability: DR ¼ maxðHZnfRint;i ; Rext;i gi¼1;np Þ  minðHZnfRint;i ; Rext;i gi¼1;np Þ,

ð12Þ

where np is the number of detected planets in the extrasolar planetary system and Rint;i and Rext;i are the inner and outer limits for unstable orbits, respectively. The widths DR of the dynamic HZs are shown in Fig. 5 ordered by the width of the HZ for the 55 extrasolar planetary systems with DR40 for different relative continental areas. For comparison the width of the dynamic HZ for the solar system is additionally plotted. Table 1 contains the widths of the dynamic HZ for a water world (relative continental area c ¼ 0:1), an Earth twin ðc ¼ 0:3Þ and a land planet ðc ¼ 0:9Þ. We find that 18 systems have a larger width of the HZ than the solar system. These systems are characterised by a more luminous star hosting a hot

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Fig. 4. Same plot as Fig. 3 for the intervals of unstable orbits in the vicinity of giant planets of extrasolar planetary systems with a stellar age 45 Gyr.

Jupiter not perturbing the orbit of an Earth-like planet. On the other hand, rather old systems like, e.g., 70 Vir, HD117207 and r CrB have much smaller HZs than the solar system. The HZ differs significantly from the HZ defined by climatic constraints only (Kasting et al., 1993). In between are systems with a giant planet outside the HZ partially destroying stability inside the HZ. Two examples are the systems 47 UMa and  Eri. 5. Conclusions We studied the principle possibility of orbitally stable Earth-like habitable planets in 86 extrasolar systems. In particular, we considered Earth-like planets with different ratios of land/ocean coverages and applied an integrated system approach. We found that in 54 out of 86 systems (63%) potential dynamic habitable Earth-like planets can exist (classes I þ II). In 20 systems the giant is located

within the HZ and could at least harbour a habitable moon or a Trojan planet (class III). Only in 12 systems (14%) there is no chance for the existence of dynamic habitable Earth-like planets (class IV). According to our results the solar system is a relatively ordinary planetary system as shown in Fig. 4. There are at least 18 extrasolar planetary systems with better prerequisites to harbour dynamic habitable Earth-like planets. This supports the so-called ‘‘Principle of Mediocrity’’. This principle proposes that our planetary system and life on Earth are about average and that life will develop by the same rules wherever the proper conditions and the needed time are given (Darling, 2001). Comparing our results based on the integrated system approach with those of the HZ determination following Kasting et al. (1993) there are, at least in some cases, remarkable differences. In particular, in our approach rather old extrasolar planetary systems are less probable for hosting dynamic habitable planets. On the other hand,

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We emphasise that the age of the extrasolar planetary system is very important in searching privileged targets for the remote spectroscopic detection of biological activity by future space borne missions like TPF and Darwin. However, for the target selection it might be useful to apply a broader definition of the HZ because precise values for the inner and outer boundaries are still controversial and the correct values of the stellar ages are difficult to determine. Nevertheless, our results can give an explanation for a possible absence of habitable conditions on Earth-like planets around old stars. Acknowledgements We would like to thank R. Dvorak and an anonymous reviewer for their constructive and helpful remarks. References

Fig. 5. Widths, DR, of the orbital range both warranting habitability and orbital stability for the solar system and extrasolar planetary systems (classes I and II) for different continental areas. The grey shaded area denotes the results for the HZ defined by climatic constraints only (Kasting et al., 1993). The numbers at the horizontal bars are the corresponding ages of the planetary systems.

the results of both approaches agree roughly if one considers water worlds with ages less than about 7 Gyr. Our results for land worlds, however, are less optimistic. It must be pointed out that two planets might follow different evolutions due to initial mass and composition. One planet at a given orbital distance might still be habitable at an age t while another planet with different initial characteristics might not. Even more important than different masses and compositions is the existence of plate tectonics. Based on the facts that some parameters in the Earth system model are poorly constraint and based on processes that are not well understood, we get at least qualitative trends distinct from previous studies. The most prominent features are the age dependent narrowing and the final disappearance of the HZ.

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