{ 2 { of planetary systems and stability of planetary orbits in these systems (e.g., Marcy & Butler 1998, 2000; Queloz 2001). Obviously, the ultimate

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1 Orbital Stability of Terrestrial Planets inside the Habitable Zones of Extra-Solar Planetary Systems M. Noble, Z. E. Musielak, and M. Cuntz Department of Physics, Science Hall University of Texas at Arlington, Arlington, TX ABSTRACT We investigate orbital stability of terrestrial planets inside the habitable zones of three stellar systems, i.e., 51 Peg, 47 UMa and HD , with recently discovered giant planets. These systems have similar habitable zones, however, their giant planets have dierent masses and signicantly dierent orbital parameters. It is shown that stable orbits of terrestrial planets exist in the entire habitable zone of 51 Peg as well as in the inner part of the habitable zone of 47 UMa, but no stable orbits are found in the habitable zone of HD The obtained results allow to draw general conclusions on the existence of stable orbits in the habitable zones of newly found extra-solar planetary systems. Subject headings: astrobiology binaries: general planetary systems stars: late-type 1. Introduction The existence of planets orbiting almost 80 solar-type stars is now a well-established observational result. The main technique used to detect these extra-solar planets is the cyclic Doppler shift of stellar spectral lines. This technique is most sensitive to massive planets, so most detected objects are giant (Jupiter-like) planets (or brown dwarfs if M > 13M J ), although planets with sub-saturn masses (i.e., HD 83443c, HD 16141b, HD b, HD 46375b) as well as seven extra-solar planetary systems (i.e., And, HD , HD 83443, Gl 876, HD 82943, HD 74156, 47 UMa) have also been identi- ed (e.g., Marcy, Butler, & Vogt 2000; Mayor et al. 2001). Considerable theoretical eorts that accompanied these observations have greatly augmented our knowledge of formation

2 { 2 { of planetary systems and stability of planetary orbits in these systems (e.g., Marcy & Butler 1998, 2000; Queloz 2001). Obviously, the ultimate quest of these studies is to discover Earth-like planets located in the habitable zones (HZs) of their host stars. Even though the planet of lowest mass discovered to date (HD 83443c) exceeds the mass of the Earth by at least a factor of about 54, the presence of terrestrial planets around other stars is strongly implied by various observational ndings. These include: (1) the steep rise of the mass distribution of planets with decreasing mass (Marcy & Butler 2000), which implies that more small planets form than giant ones; (2) the detection of protoplanetary disks (with masses typically over ten times that of Jupiter) around more than half of all known young stars; and (3) evidence of rapid growth (within 0.1 Myr) of dust particles based on IR and mm-wave observations (Marcy et al. 2000b, and references therein). Long-term orbital stability of Earth-like planets in stellar HZs is necessary for the evolution of any form of life, including intelligent life. In previous studies of orbital stability in known planetary systems, notably And, the main emphasis has been given to the origin of dynamical instabilities that aect the orbits of planets in these systems (e.g., Butler et al. 1999; Lissauer 1999; Laughlin & Adams 1999; Rivera & Lissauer 2000; Stepinski, Malhotra, & Black 2000; Jiang & Ip 2001). Orbital stability of terrestrial planets inside stellar HZs has been investigated by Gehman, Adams, & Laughlin (1996), who considered several early discovered systems with giant planets, and more recently by Jones, Sleep, & Chambers (2001), who studied CrB, 47 UMa, Gl 876 and And. The main conclusion of the latter paper is that orbits of terrestrial planets in the HZs of the rst two stellar systems are likely to be stable over the length of time required for biological evolution, however, no long-term stability was found for either Gl 876 or And. Obviously, the extent of the HZ and the orbital position of the dominant giant planet in the considered star play an important role in the outcome of these calculations. Typically, stellar HZs are dened as regions near the host stars, where the physical conditions are favorable for liquid water to be available at the planet's surface for a period of time long enough so that biological evolution can occur (e.g., Franck et al. 2000b). A number of attempts have been made to determine the size of HZs around dierent types of main-sequence stars (e.g., Kasting, Whitmire, & Reynolds 1993; Forget & Pierrehumbert 1997; Kasting 1997; also Franck et al. 2000a,b). In this Letter, we investigate orbital stability of terrestrial planets inside the HZs of 51 Peg, 47 UMa, and HD Our choice of systems is motivated by the fact that they have similar HZs, owing to the stellar parameters of their host stars, and that their giant planets have dierent masses and signicantly dierent orbits. In case of 47 UMa, we will also consider the eects of the secondary giant planet recently discovered (Fischer et al. 2001). We will show which system can support Earth-like planets in its HZ, which will allow to draw general conclusions on the existence of stable orbits of terrestrial planets inside the

3 { 3 { HZs of newly detected extra-solar planetary systems. 2. Method and Model Parameters To perform our computations, we developed a numerical code that is based on a fourthorder Runge-Kutta integration scheme (e.g., Press et al. 1989). The code has been extensively tested against known analytical solutions, including two-body and restricted threebody problems, as well as against models of the Sun-Earth system. The simulation accuracy has been found to be within 0.017% for a time-step of 1:0 10?7 years. Our approach is more suitable to investigate a short-term (measured in hundred or thousand of years) orbital stability and diers from the method based on the second-order mixed-variable symplectic integrator (e.g., Jones et al. 2001), which is typically used to study long-term (measured in billion of years) stability of planetary orbits. The main advantage of our approach is that it can handle close encounters between planets, whereas the other method cannot. The obtained results (see x3) clearly show that characteristic dierences between the orbital behavior of the terrestrial planets in the considered systems become already visible in simulations after a relative short time ( 200 yrs). Even after this short simulation time, a clear distinction between stable and unstable planetary orbits can be made. The code requires specifying the basic physical parameters of the considered host stars (see Table 1) and their planetary systems (see Table 2). Since the Doppler technique allows only to deduce M p sini, where M p is the planetary mass and sini is the orbital inclination, one must know sini to determine masses of the giant planets in the considered systems. In case of the inner giant planet of 47 UMa, sini has been determined as 0.69 (Gonzalez 1998). Here we assume the same value for the outer giant planet. In case of 51 Peg, we use the results by Marcy et al. (1997) and subsequent work by the same authors. In case of HD , no reliable value for sini exits. Therefore, we assume the value of the stellar dust disk (Trilling, Brown, & Rivkin 2000) in agreement with the standard paradigm of planet formation. In our simulations, the mass of the terrestrial planet is always assumed to be equal to one Earth mass. Furthermore, the Earth-type planet and the giant planet(s) are assumed to be coplanar as motivated by the Solar System considering that the inclination between Jupiter's and Earth's orbit is only 1.3 o. Another parameter that is important for our computations is the stellar age of the host stars. This parameter is required to determine the extent and location of the stellar HZs as the stellar age aects the stellar luminosity. Typically, stellar ages can be obtained by analyzing the age-activity relations or isochrone tting (Henry et al. 1997). In case of 47 UMa, the age-activity relationship of Donahue (1993) implies 7 Gyr, in excellent

4 { 4 { agreement with the estimate of 6.9 Gyr by Edvardsson et al. (1993) from isochrone tting and subsequent work by Ng & Bertelli (1998). This latter technique has also been applied to determine the age of 51 Peg. Stellar HZs are dened as regions near the host stars, where the physical conditions allow the presence of liquid water. The position of HZs around stars thus depends on the stellar type and luminosity class, as well as on details of the planetary atmospheres. In recent years, the HZs around stars are believed to be more extended than originally thought partly because of the backwarming eects by CO 2. Kasting et al. (1993) have used a variety of criteria to dene the inner and outer boundaries of HZs for dierent types of stars, and followed them to the stellar subgiant phases. These results are also used for our study (Fig. 1). As inner boundary of the HZs, we assume the maximum distance from the star where a runaway greenhouse eect occurs leading to the evaporation of all surface water. As outer boundary, we assume the \early Mars limit" (most optimistic case), considering recent results that the HZs are believed to be more spatially extended than originally thought (Forget & Pierrehumbert 1997; Kasting 1997, 1998). We then interpolate between the Kasting et al.'s \hot start" and \cool start" solutions owing to the inherent diculty for life to develop on planets with originally complete global glaciation. Although this assumption makes the outer boundaries of the HZs ill dened, it does not signicantly impact the assessment of the dierent cases of orbital stability and habitability of systems in our study. 3. Orbital Stability of Terrestrial Planets The main aim of our study is to understand the basic dierences between the orbital behavior of terrestrial planets in the three dierent types of systems. Therefore, we facilitate a set of simulations for each system with dierent initial positions of the terrestrial planet inside the stellar HZ. These positions for the terrestrial planets are given by r j = r HZ;i + j (r HZ;o? r HZ;i ) with r HZ;i as inner radius of the HZ, r HZ;o as outer radius of the HZ and j = 0.1, 0.5, and 0.9 as distance parameter. The starting positions of giant planet(s) and the terrestrial planet are always chosen as = 0 (i.e., 3 o'clock position), unless noted otherwise. An interesting result is that the principle dierences between the orbital behavior of the terrestrial planets in the considered systems are already seen in our calculations after a relative short simulation time ( 200 yrs). Note that the accuracy of our method is very high for these short-period of times (see x2) but decreases for much longer periods of time. In case of 51 Peg, we nd that the terrestrial planet does not change noticeably its original orbit despite the gravitational impact of the Jupiter-size planet. For 1, we nd that the average orbital radius of the terrestrial planet is AU with a standard deviation of

5 { 5 { 1:075 10?6 (see Fig. 2). For 2 and 3, the average orbital radii are and AU with standard deviations of 1:071 10?6 and 1:489 10?6, respectively. These results show a high level of orbital stability for terrestrial planets independent of their position in the stellar HZ. In case of the planet position 2, we also tested the sensitivity of our results with respect to the time step of integration. We found that if the original time step is reduced by a factor of two, the orbital position of the terrestrial planet changes by about 3:28 10?6 % (i.e., 8 km), which shows that our results are not seriously aected by integration errors. Based on the above given results, one may conclude that the system 51 Peg, with its extended HZ that is seemingly unaected by the close-in giant planet located at 0.05 AU (see Fig. 2), would be the best candidate for supporting terrestrial planets in its HZ. However, this might not be the case at all. The reason is that the giant planet in this system probably did not form where it is observed now, but instead formed much further away from the star and then migrated inwards (e.g., Boss 1995). Consequently, it may have expelled thenexisting terrestrial planets by invoking orbital instability as demonstrated by our simulations of HD (see below). Now, with respect to 47 UMa two dierent cases can be identied. For a terrestrial planet in the inner part of the HZ (i.e., 1 ), the results are very similar to the case of 51 Peg (see Fig. 2). The average orbital radius of the terrestrial planet is AU with a standard deviation of 8:546 10?5, indicating that planets in this regime appear to have stable orbits. In the central and outer HZ, however, i.e., 2 and 3, orbital stability does not exist. In case of 2, the planet wanders from to AU during the time of orbital integration showing that habitability is very unlikely. In case of 3, the planet leaves the HZ only after 0.24 yrs. The fact that two dierent regimes of orbital stability for terrestrial planets exist within the HZ of 47 UMa has already been pointed out by Jones et al. (2001). However, in our work we also take into account the recently discovered secondary giant planet (Fischer et al. 2001). We nd that the stability of terrestrial planets in the inner part of the HZ of 47 UMa ( 1 ) is not seriously aected by this second Jupiter-size planet. The average orbital radius of terrestrial planets only diers by 5:1 10?2 % between both cases. In addition, the standard deviation of the terrestrial planetary orbits remains essentially the same indicating that the orbital stability and habitability remain unchanged. The results obtained for 47 UMa imply that stable orbits for terrestrial planets exist in the inner parts of its HZ. Since both giant planets are located beyond the outer edge the HZ (see Fig. 2 and Table 2), the arguments mentioned above for 51 Peg do not apply to this system. However, it should be noted that 47 UMa is not a zero main-sequence star as indicated by its age (see Table 1). Therefore, positional changes of the HZ with stellar age must be considered in future studies of long-term changes of the planetary biospheric

6 { 6 { conditions (see Franck et al. 2000b, for details). A system in which a terrestrial planet remains unconned to the HZ regardless of its original distance to the host star is HD (see Fig. 2). Here we nd that in case of 2 = 0:5, the terrestrial planet leaves the HZ of the central star after years for the rst time. Similar results are obtained for models with terrestrial planets at other starting distances. In order to highlight the eects of orbital instability in this system, we have varied the starting position of the terrestrial planet in the 2 models in 30 o increments (see Table 3). We nd that on average the terrestrial planet spends only 46.7 years in the HZ of this star, with a standard deviation of 20.9 years. The reason for this obvious orbital instability of the terrestrial planet is that the giant planet crosses the HZ due to its elliptical orbit forcing terrestrial planets out of the HZ. 4. Conclusions We have studied orbital stability of terrestrial planets inside the habitable zones of the following systems: 51 Peg, 47 UMa, and HD , with recently discovered giant planets. The systems have similar HZs, however, their giant planets have dierent masses and signicantly dierent orbital parameters. The obtained results clearly show that stable orbits of terrestrial planets exist in the entire HZ of 51 Peg as well as in the inner part of the HZ of 47 UMa, but no stable orbits are found in the outer region of the HZ of 47 UMa and in the entire HZ of HD In the case of 51 Peg, the giant planet is located far away from the HZ but near the host star (at approximately 0.05 AU) and, as a result, it does not aect the stability of terrestrial planets inside the HZ. However, this close-in giant planet may have expelled then-existing terrestrial planets while migrating inwards (see x3). The situation is dierent for 47 UMa as both of its giant planets are located outside of the HZ, with the more massive planet orbiting close to the edge of the HZ. The latter is responsible for unstable orbits in outer part of the HZ of this system but has much smaller eect on orbital stability in the inner part of the HZ. Finally, the giant planet of the system HD has elongated elliptical orbit that crosses the HZ and strongly inuences any terrestrial planet located in the HZ. Hence, all orbits of terrestrial planets in the HZ of this system are unstable. Based on these results, we may draw the following general conclusions regarding the existence of stable orbits of terrestrial planets in the HZs of newly detected extra-solar planetary systems. Stable orbits of terrestrial planets inside stellar HZs exist only if orbits of giant planets are located far away from either the inner or outer edge of these zones.

7 { 7 { Moreover, because of the process of planetary migration, the existence of Earth-type planets inside stellar HZs may be restricted to only those systems in which giant planets orbit their host stars far beyond the outer edge the HZs. This conclusion is obviously consistent with the planet distribution and the existence of life in our Solar System! This work has been supported by NATO under grant CRG (Z.E.M.). Z.E.M. also acknowledges support for this work by the Alexander von Humboldt Foundation. Boss, A. P. 1995, Science, 267, 360 REFERENCES Butler, R. P., Marcy, G. W., Fischer, D. A., Brown, T. M., Contos, A. R., Korzennik, S. G., Nisenson, P., & Noyes, R. W. 1999, ApJ, 526, 916 Donahue, R. A. 1993, Ph.D. thesis, New Mexico State Univ. Edvardsson, B., Andersen, J., Gustafsson, B., Lambert, D. L., Nissen, P. E., & Tomkin, J. 1993, A&A, 275, 101 Fischer, D. A., Marcy, G. W., Butler, R. P., Laughlin, G., & Vogt, S. S. 2001, ApJ, submitted Forget, F., & Pierrehumbert, R. T. 1997, Science, 278, 1273 Franck, S., Block, A., von Bloh, W., Bounama, C., Schellnhuber, H.-J., & Svirezhev, Y. 2000a, Tellus, 52B (1), 94 Franck, S., von Bloh, W., Bounama, C., Steen, M., Schonberner, D., & Schellnhuber, H.-J. 2000b, J. Geophys. Res., 105 (E1), 1651 Gehman, C. S., Adams, F. C., & Laughlin, G. 1996, PASP, 108, 1018 Gonzalez, G. 1998, A&A, 334, 221 Gonzalez, G., Wallerstein, G., & Saar, S. H. 1999, ApJ, 511, L111 Henry, G. W., Baliunas, S. L., Donahue, R. A., Fekel, F. C., & Soon, W. H. 2000, ApJ, 531, 415 Henry, G. W., Baliunas, S. L., Donahue, R. A., Soon, W. H., & Saar, S. H. 1997, ApJ, 474, 503

8 { 8 { Jiang, I.-G., & Ip, W.-H. 2001, A&A, 367, 943 Jones, B. W., Sleep, P. N., & Chambers, J. E. 2001, A&A, 366, 254 Kasting, J. F. 1997, Origins of Life, 27, 291 Kasting, J. F. 1998, BAAS, 30 (4), Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, Icarus, 101, 108 Laughlin, G., & Adams, F. C. 1999, ApJ, 526, 881 Lissauer, J. 1999, Nature, 398, 659 Marcy, G. W., & Butler, R. P. 1998, ARAA, 36, 57 Marcy, G. W., & Butler, R. P. 2000, PASP, 112, 137 Marcy, G. W., Butler, R. P., & Vogt, S. S. 2000a, ApJ, 536, L43 Marcy, G. W., Butler, R. P., Vogt, S. S., & Fischer, D. A. 2000b, BAAS, 32 (4), Marcy, G. W., Butler, R. P., Vogt, S. S., Fischer, D. A., & Liu, M. C. 1999, ApJ, 520, 239 Marcy, G. W., Butler, R. P., Williams, E., Bildsten, L., Graham, J. R., Ghez, A. M., & Jernigan, J. G. 1997, ApJ, 481, 926 Mayor, M., Naef, D., Pepe, F., Queloz, D., Santos, N. C., Udry, S., & Burnet, M. 2001, in Planetary Systems in the Universe: Observation, Formation and Evolution, ed. A. J. Penny et al. (San Francisco: ASP), in press Ng, Y. K., & Bertelli, G. 1998, A&A, 329, 943 Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. 1989, Numerical Recipes, The Art of Scientic Computing, Cambridge Univ. Press, New York Queloz, D. 2001, in Cool Stars, Stellar Systems, and the Sun XI, ed. R. J. Garca Lopez, R. Rebolo, & M. R. Zapatero Osorio, (San Francisco: ASP), Vol. 223, 59 Rivera, E., & Lissauer, J. 2000, ApJ, 530, 454 Stepinski, T. F., Malhotra, R., & Black, D. C. 2000, ApJ, 545, 1044 Trilling, D. E., Brown, R. H., & Rivkin, A. S. 2000, ApJ, 529, 499 This preprint was prepared with the AAS LA T EX macros v5.0.

9 { 9 { Table 1. Stellar Parameters 51 Peg a 47 UMa b HD c Sp. Type G2-3V G1V G0 T e (K) M (M ) R (R ) r HZ;i (AU) r HZ;o (AU) Age (Gyr) a From Henry et al. 2000, exept age. b From Henry et al and Gonzalez 1998, exept age. c From Gonzalez, Wallerstein, & Saar Table 2. Planetary Parameters 51 Peg a 47 UMa b HD c... planet 1 planet 2... d (AU) e M p sini (M J ) M p (M J ) a From Marcy et al. 1997, and subsequent work. b From Fischer et al. 2001, M p of both planets is calculated assuming sini = 0.69 (Gonzalez 1998). c From Marcy et al. 1999, M p is calculated assuming i = 40 o (Trilling et al. 2000).

10 { 10 { Table 3. Residence Time of Terrestrial Planets in the HZ of HD Starting Position t Res (y) 0 o o o o o o o 51.34

11 { 11 { Fig. 1. Orbital paths of the extra-solar giant planets for the three represented systems. For comparison, we also give the HZs for 47 UMa (1.05 to 1.83 AU) and 51 Peg (1.20 to 2.01 AU) (gray areas). The HZ for HD is similar to that of 51 Peg (see Table 1).

12 { 12 { A. 51 Peg Lower 10% boundary orbit. B. 47 UMa Target 10% boundary orbit. C. HD Upper 10% boundary orbit. Fig. 2. Evolution of the orbital paths of terrestrial-type planets around the central star of all three systems, which are: stable for the j = 0.1 case of 51 Peg and 47 UMa, and unstable for the = 0.1 case of HD