“HABITABLE EXTRASOLAR PLANETARY SYSTEMS, THE CASE OF 55 CNC” Desiree Cotto-Figueroa University of Puerto Rico at Humacao Institute for Astronomy, University of Hawaii Mentor : Nader Haghighipour ABSTRACT The results of a study of the orbital evolution and habitability of the ρ Cnc system are presented. Initial integration of the system using the reported orbital parameters (McArthur et. al 2004) indicates that the system is unstable. In search of the stable planetary orbits, an extensive search of the parameter-space of the system was carried out and a stable region was identified. Within this region, dynamical stability of an Earth- like planet in the habitable zone of the system was studied and two regions of harboring habitable planets were recognized. INTRODUCTION: The notion of planetary worlds orbiting stars other than our Sun is not new. History has revealed that human ponderings over the possibility of other solar systems beyond our own dates as far back as early Greek times, when the Greek philosopher Epicurus wrote: “There exist countless worlds like ours also as well as others.” It wasn’t until 1991 when radio signals from the pulsar PSR B1257+12 in the constellation Virgo led Alexander Wolszczan, an astronomer from Pennstate University to discover the first planets ever known outside our solar system. Later, in the following year, using radial velocity measurements, Michel Mayor and Didier Queloz from the University of Geneva announced the discovery of the first extrasolar planet around a main sequence star (51 Pegasi) (Mayor & Queloz ,1995). Two years later, at the Lick Observatory, Geoffrey Marcy and Paul Butler confirmed the existence of that planet using the Hamilton Spectrograph (Marcy et al. 1997). Since then more than 160 planets have been detected. Considering the vastness of the universe, containing in all probability millions of planets, it is difficult to imagine that our solar system is unique and our planet is the only one that harbors life. In fact, discovery of multiple planets around a star is not unexpected. Among the currently known extrasolar planetary systems, there are over 14 systems with more than one planet. The planetary system of ρ Cancri (55Cnc) is one of such systems. This project has to do with exploring the possibility of habitable worlds in the ρ Cancri system. The single most crucial factor in the evolution of life is the availability of liquid water. In our solar system, the habitable zone (HZ) lies approximately between 0.8 to 1.3 AU where water can sustain its liquid form. In a extrasolar multiple planet system, one Table 1. Element ρ Cnc e ρ Cnc b ρ Cnc c ρ Cnc d Orbital Period 2.808 ± 0.002 14.67±0.01 43.93±0.25 4517.4±77.8 (days) Eccentricity 0.174±0.127 0.0197±0.012 0.44±0.08 0.327±0.28 ω (°) 261.65±41.14 131.49±33.27 244.39±10.65 234.73±6.74 a (AU) 0.038±0.001 0.115±0.003 0.240±0.008 5.257±0.208 M (MJUP) 0.056±0.017 0.982±0.19 0.272±0.07 4.9±1.1 Velocity 6.665±0.81 67.365±0.82 12.946±0.86 49.786±1.53 Amplitude (ms-1) major question, would then be; Can the system support a habitable planet? The HZ of a main-sequence star is defined as where liquid water can exist on the surface of a planet. This implies a moderate planetary surface temperature suitable for the development and subsistence of life. The size and location of the HZ depend on the physical properties of the star in question. ρ Cancri (55 Cnc) is a visual binary system in the constellation of Cancer. It consists of a middle-aged, Sun-like (G8V) primary of high metallicity (Rho A) and a red dwarf companion mass (Rho B). A mean distance of approximately 1,150 AU separates these two stars. Four planets, Ab, Ac, Ad, and Ae, have been discovered in orbits around the primary star. Table 1 shows the orbital parameters of these objects. This is the largest number of planets currently known to exist around a star other than our Sun. Ab was announced as the fourth extrasolar planet discovered (Butler et al. 1997) and apparently also was listed as the second "Hot Jupiter" found after 51 Pegasi b. In 2002, the second planet Ad, a high-mass classical jovian, was discovered (Marcy et al. 2002). When signals of the first two planets were removed from the radial velocity measurements of ρ Cancri, a sharp peak remained indicating the possibility of a lower mass planet with a period of 44 days. Despite the similarity between the planet’s period and the period of the rotation of the star (35-42 days), the third planet Ac, was tentatively added to the list of extrasolar planets. Since ρ Cancri is a quiet star, showing no signs of photospheric irregularities, the planet interpretation is more likely viable. Analysis of the dynamics of this planet indicates that it orbits bring it very close to Ab, resulting in a near 3:1 resonance. The most recent planet discovered in the ρ Cnc system, Ae, is a "Neptune-class" extrasolar planet (McArthur et al. 2004). The discovery of this planet confirmed the existence of Ac as well. Ac shows an amplitude of the signal of 12 m s-1 when the effects produced by stellar activity normally do not exceed 3 ms-1. Having the largest number of planets and an outer planet that orbits at 5.3 AU which is comparable to Jupiter’s distance from our Sun, ρ Cancri becomes one of the most interesting systems for investigating the following question: Could a planet harbors life in this system? METHOD The goal of this project is to identify regions within the habitable zone of ρ Cancri where a life-harboring planet can have a long-term stable orbit. The habitable zone of the system is identified as the appropriate position for an Earth-like planet where it would receive the same amount of radiation as our Earth receives from our Sun. The amount of radiation emitted by a star depends on its luminosity, and varies with the radius and surface temperature of the star (Stefan-Boltzman law E=σT4). That is, L=4πr2b(r)= 4πR2σT4 Where L is the luminosity of the star, R is its radius, T is the star’s surface temperature, and b(r) represents the star’s brightness at a distance r. From this equation, the amount of radiation receive by a planet at a distance r relative to the radiation received by Earth from the sun is given by This equation indicates a habitable zone with an inner edge at 0.598 AU and an outer edge at 0.972 AU. Previous studies, however, reported different boundaries for this region (Table 2). In this paper, in order to be consistent with previous studies, we choose the habitable zone to have a range of 0.4 to 1.3 AU. Table 2 Reference Habitable Zone Menou & Tabachnick (2003) 1.00 ± 0.10 AU Rivera &Haghighipour (2003) 0.7 – 1.3 AU Bloh,Cuntz,Franck &Bounama (2003) 0.66 ± 0.02 – 1.14 ± 0.04 AU Whitmire et. al (1998) 0.95 – 1.15 AU The orbit of an Earth-like planet along with the orbits of the four planets of the system were integrated numerically using Mercury N-body integrator (Chambers 1999). The time step of integrations were set to 0.14 days, equivalent to 1/20 of the inner planet’s orbital period (2.808 days). We simulated the dynamics of ρ Cnc system with the orbital parameters reported by McArthur et al. (2004), and assumed coplanarity of the system. Using these orbital elements, our simulations indicated that the system was unstable. There was an ejection of Planet Ae from the system at 23,877 years. Figure 1 shows the semi-major axes of these planets. Searching the orbital parameters space of the system, we were able to identify a region of the parameter space where the system is stable. Figure 2 shows the semi-major axis of the planets of the system for one of such cases. As shown here the system is stable for 10 million years. Figure 1 Figure 2 Using the orbital parameters of the system of Figure 2 as our initial parameters, we simulated the dynamics of an Earth-like planet in the Habitable Zone of the system. The results are shown in Figure 3. An Earth-like planet with an initial semi-major axis of 0.4 AU was ejected at 4,579 years. Simulations testing the following three regions: 0.5 - 0.85 AU, 1 AU, and 1.13 - 1.3 AU, were unsuccessful: the Earth-like planet escaped the Habitable Zone in parts of it’s orbit. At 0.98 AU planet E was ejected at 4.4 Myr and at 1.03 AU planet E collided with the star at 6.8 Myr. Our studies have shown that in order for an Earth-like planet to survive in the ρ Cnc planetary system and remain habitable, it must reside within the ranges of : 0.9 - 0.95 AU or 1.05 - 1.1 AU. Figure 4 shows the semi-major axes of the four planets of the system and that of a hypothetical Earth-like planet for a stable and also an unstable configuration. 1.E+08 1.E+07 1.E+06 1.E+05 1.E+04 Time (yrs) 1.E+03 1.E+02 1.E+01 1.E+00 0.40 0.60 0.70 0.90 1.00 1.08 1.10 1.20 0.50 0.80 0.85 0.93 0.95 0.98 1.03 1.05 1.13 1.15 1.30 Initial Semi-major Axis (AU) Figure 3 (a) (b) Figure 4 Fig.