Habitability in the Upsilon Andromedae System Adrienne Dove University of Missouri Columbia Institute for Astronomy University of Hawaii Mentor: Nader Haghighipour ABSTRACT We investigate the habitability of the Upsilon Andromedae planetary system as it evolves from a hypothetical four-planet system into what is observed today. We initially considered a fourth planet at a distance of 4.76 AU from the central star. We simulated the dynamics of this system until the fourth planet was ejected due to gravitational interactions with the other planets. Results demonstrated that an Earth-like planet could not remain stable in the HZ of this system. We also show, through extensive testing of the parameter space, that it is important to include the inner planet of this system in simulations of its dynamical evolution. INTRODUCTION Over the past decade, Doppler spectroscopy has revealed the presence of more than 155 extrasolar planets. Radial velocity variations of these systems indicate that at least 14 of them have more than one planet. 1 The orbital parameters of these systems have proven to be quite different from the fairly flat, circular solar system. Thus far, all extrasolar planets orbiting at radii greater than 0.2AU have been found to have relatively high eccentricities, above 0.1 (Butler et al. 1999). Planet-planet scattering and discplanet interactions have been cited as mechanisms that could cause perturbations to excite the eccentricities of these planets. Upsilon Andromedae (Ups And) is an F8 V star with a stellar companion at about 750AU. In 1997, Keplerian fits to Doppler velocity measurements of this star indicated the presence of a planet with a period of ~ 4.6-day (Butler et al. 1997). While this planet dominated the signal, residual velocity variations could not be explained by stellar characteristics. As a result of fitting the residual stellar wobble, two additional planets were detected in this system with periods of about 241 and 1267 days. The detection of these planets made the Ups And system the first extrasolar planetary system around a main sequence star (Butler et al. 1999). Continued observations of this star have further refined the orbital parameters of its planets (Table 1), and have made Ups And one of the most tightly constrained extrasolar planetary systems. This is particularly the case for the inner planet of this system. The two outer planets of the system show the same high eccentricities as are now commonly observed in extrasolar planets. Most models of Upsilon Andromedae show a periodic oscillation of its middle planet s eccentricity between its high observed value and a near-zero value (Ford et al. 2005, henceforth Ford05). Several studies have also indicated that the orbits of the two outer planets are in apsidal alignment 1. exoplanets.org California and Carnegie Planet Search
2 Planet Period (days) ecc omega (deg) Vel Amp, K (m/s) Msini (M J ) a (AU) b 4.6171 0.012 73 70.2 0.69 0.059 c 241.5 0.28 250 53.9 1.89 0.829 d 1284 0.27 260 61.1 3.75 2.53 Table 1. Orbital Parameters of the planets orbiting Upsilon Andromedae Figure 1. Planets c and d are in apsidal alignment. (Ford et al., 2005) (Chiang et al. 2001, Malhotra 2002). Such configurations could produce the variations in the planets eccentricities. Apsidal alignment is most likely produced by a sudden perturbation of the system, which excites the eccentricities of the planets in such a way that they evolve into an apsidally resonant configuration (Figure 1). Possible sources of a sudden perturbation may be planet-planet scattering, which may cause the ejection of one planet from the system due to gravitational interactions with others. Planet-disc interaction, in which torques from a residual circumstellar disc excites the eccentricity of a planet (Chiang et al. 2001), has also been reported as a means of pumping eccentricities. In the case of Ups And, planet-planet scattering has been considered by many to be the origin of the high eccentricities of its two outer planets (Butler et al. 1999, Ford et al. 2003, Marzari & Weidenschilling, 2002). A recent study
3 of this kind is due to Ford05. In that paper, the authors have demonstrated that, if a fourth planet once existed in the system, but was subsequently ejected, it could cause the observed eccentricities for the two planets in the Ups And planetary system. Figure 1 shows one such arrangement. In light of this recent work, the goal of this study is to assess the habitability of the Ups And planetary system as it evolves, due to planet-planet scattering, from a fourplanet system into the configuration observed today. To evaluate habitability, we consider the stability of an Earth-like planet placed inside the habitable zone of the primary star of Ups And. Current observational techniques do not have the resolution to detect low, approximately Earth-mass planets. Astronomers use numerical simulations to test the stability of exoplanetary systems, and to determine whether a planet could remain stable in the HZ of such a system. A habitable zone (HZ) is defined as the region in which water on the surface of a planet can remain in its liquid phase. This depends partially on the composition of the planetary atmosphere, but more importantly, on stellar luminosity. Stellar radiation provides energy to heat the planet, so that the amount of energy incident on the planet depends on its distance from the star. The luminosity of a star is defined by its radius and temperature, L = 4!R 2 "T 4. At large distance, this luminosity decreases as L 4!d 2, where d is distance from the star. The radius of the habitable zone for a star similar to the sun is proportional to the luminosity of the star relative to the sun. In order to calculate the location of the habitable zone around Ups And, we determined the distance at which an Earth-like planet would receive the same luminosity as the Earth receives from the Sun at 1AU. Taking the HZ of the sun to be at 0.8 1.3 AU, the statement above implies, L 4!d = L 2 p 4!d, (1) 2 " where d p is the distance of the planet from the star, and d is the distance of the Earth from the Sun. The resulting HZ around Ups And is between 1.4 2.5 AU. NUMERICAL ANALYSIS Previous studies of the Ups And system have found that configurations in which an Earth-sized planet is placed inside the HZ are highly unstable (Jones and Sleep 2002; Lissauer and Rivera 2001, Rivera and Haghighipour 2004). These studies have not considered the evolution of the system in which a fourth planet was initially present. Additionally, some simulations, including that of Ford05 do not include the inner planet in their integrations. This planet is relatively small and close to the star, and of sufficient distance from the outer planets that its perturbative effect is often considered negligible. However, for accuracy, and because the inner planet has an effect on the stability of systems in apsidal resonance (Chiang et al. 2001), it was included in all of our calculations. This paper will assess the stability of an Earth-like planet placed inside the calculated HZ of the Ups And primary star, where the planetary system is initially comprised of four planets and subsequently undergoes the chaotic evolution associated with planet-planet scattering.
4 N-body simulations of the extrasolar planetary system of Upsilon Andromedae were performed using the hybrid/burlirsch-stoer integrator in the MERCURY 6.2 integration package (Chambers, 1999). Since previous studies did not include the innermost planet, we first ran simulations with all four planets included and with the initial parameters from the model in Ford05. In running these simulations, the goal was to determine the initial conditions for a system which, after the ejection of the fourth planet, would resemble the observed Ups And planetary system. This required an extensive search of the system s parameter space, as there is little restriction on the parameters of the hypothetical fourth planet. We chose to test parameters in a small range around those given in Ford05 for planet e. The orbital parameters of planet b were the most difficult to constrain to today s parameters. Table 2 lists the models tested. Parameters are listed for planets b and e the mass of planet b used was 0.677MJ. Planets c and d were kept consistent from Ford05, with semi-major axes at 0.83 and 3.49, and eccentricities of 0.000 and 0.003, respectively. Integrating various four-planet models produced five models that ejected the fourth planet and then evolved to reproduce current orbital parameters in Upsilon Andromedae to within error. Figure 2 shows the best-fit system, integrated over 10Myr. Both of the outer planets show appropriate high eccentricity, and the eccentricity of planet c periodically returns the planet to a near-circular orbit. This model has the parameters from Ford05 for planet e, and takes planet b to have a semi-major axis of 0.055AU and an eccentricity of 0.003. When including the inner planet in simulations, a smaller timestep equivalent to 1/20 th of the period of the inner planet (0.23 days) was used. To examine the habitability of the system, using the model that most closely reproduced the current orbital parameters of Ups And at the end of a10myr integration, we placed Earth-like planets, with increments of 0.01AU, on circular orbits in the HZ of the system. We simulated the dynamics of the entire six-body system for at least 5Myr, or until the Earth-like planet was lost from system. Figure 3 shows the survival time of Earth-like planets in the HZ of Upsilon Andromedae. A total of 110 models were run to test the viability of these systems. In 89 simulations, the Earth-like planet was either ejected or collided with the star. The longest time for any Earth-like planet to remain in the system was approximately 7.23x10 5 years. Nine of the models underwent too many close encounters within the system. A close encounter is defined here as two planets coming within three Hill radii of each other. In these cases, the hybrid integration takes over to handle the system. Too many close encounters indicate that the orbits are unstable they too frequently come within three Hill radii. These are the gaps observed in Figure 3. In the remaining twelve simulations, the Earth-like planet remained stable, but the planetary system at the end of the integration no longer resembled the observed Ups And system. In every system in which the Earth-like planet survived, only planets d and e were lost from the system. The ejection of these planets leaves the remaining planets in a more stable configuration, so that the Earth-like planet remains. In five of these systems, the Earth-like planets is contained in the HZ throughout the integration, although since the configuration no longer resembles that of the Ups And system, it cannot be seen as a successful simulation for this study.
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Figure 2. Semi-major axis and eccentricity of the best-fit four-planet simulation. 6
7 Figure 3. Survival time of Earth-like planets. CONCLUSIONS We have studied the stability of an Earth-like planet in the habitable zone of the Upsilon Andromedae planetary system, assuming that the system underwent chaotic evolution after a fourth planet was scattered from the system. Prior to integrating the orbits of Earth-like planets in the system, it was found that the inclusion of the innermost planet in simulations was necessary to accurately model the stability of the system. This is an important aspect to consider when constructing models of the Ups And system, and may produce inaccurate results if not included. The results of our integrations demonstrate that the Ups And system could not harbor an Earth-like planet throughout its chaotic evolution during planet-planet interactions. In the integrations in which the terrestrial planet did survive for the lifetime of the integration, the planetary configurations no longer resembled that of the Ups And system. Previous studies have been done to test the habitability of the Ups And system (Jones & Sleep 2002, Jones et al. 2005, Rivera & Haghighipour 2004). However, none of these studies analyzed the affect of planet-planet scattering. Neither did they study the effect of the inclusion of an initial fourth planet in the system. Similar to those studies, the four-planet system was found to be inhabitable.
8 Additional studies have tested the viability of test particles at various radii within the Ups And system, including its HZ. Due to the fact that Earth-like planets are considerably smaller than Jupiter-mass planets, to the lowest order of approximation, massless test particles simulations can provide useful information about the habitability of the system. However, when trying to test the viability of a planet within a planetary system, is it important to be as accurate as possible. Thus, this study used the mass of Earth, as it may have a slight affect on the surrounding planets. Also, the inclusion of the inner planet ensures that all sources that may have an effect on gravitational interactions are accounted for. It has been shown that the habitable zone surrounding a star will migrate over the lifetime of the star (Kasting et al. 1993). This evolution was not considered in this study. As the star evolves, its luminosity will change, and the radius of the HZ will change accordingly, (Equation 1). It is important to mention that the planets considered here all have minimum masses. That is, the system was taken to be coplanar. Similar studies may be done for the same system with planets on higher inclinations, which may also have been instigated by planet-planet scattering. REFERENCES Butler, R.P. et al. 1999, ApJ, 526, 916 Chambers, J. E. 1999, MNRAS, 304, 793 Chiang, E. I., Tabachnik, S., & Tremaine, S. 2001, ApJ, 122, 1607 Ford, E. B., Lystad, V., & Rasio, F. A. 2005, Nature, 434, 873 Jones, B. W., Sleep, N. P. 2002, ASP Conference proceedings (astro-ph/0211022) Jones, B. W., Underwood, D. R., & Sleep, N.P. 2005, ApJ, 622, 1091 Lissauer, J. J., & Rivera, E. J. 2001, ApJ, 554, 1141 Malhotra, R. 2002, ApJ, 575, L33 Marzari, E. F., & Weidenschilling, S. J. 2002, Icarus, 156, 570 Rivera, E. J., & Haghighipour, N. 2004, ApJ submitted (astro-ph/0406429)