Habitable Planets in the Planetary System of HD 69830

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1 Habitable Planets in the Planetary System of HD Sarah Rügheimer Advisor: Nader Haghighipour ABSTRACT We present the results of a study of the dynamical evolution and habitability of HD planetary system. Being the first multiplanet extarsolar planetary system with three Neptune-sized objects, HD provides new grounds for testing the possibility of the existence of smaller objects, such as terrestrial planets, particularly in its habitable zone. We numerically integrated the orbits of the planets of this system for different values of their masses, and also studied the long-term stability of many Earth-like objects in its habitable zone. Results indicate that the planetary system of HD is dynamically stable and its habitable zone can harbor terrestrial planet for long times. The only exception is at AU inside this region where an island of stability appears. Subject headings: extrasolar planets: HD 69830: habitable planets 1. Introduction Among approximately 170 planetary systems discovered as of July 2006, 21 contain more than one planet 1. The planetary system of HD is one of such extrasolar multiplanet systems (Lovis et al. 2006). This system consists of a nearby K0V star at a distance of approximately 12.6pc from the Earth, and is host to 3 planets with minimum masses of 1, 11.8, 18.1 Earth-masses (Lovis et al. 2006). This is the first observed planetary system that, unlike other multiplanet systems in which the planets are gas-giant Jovian-type objects, contains only Neptune-mass bodies. There are many observational techniques that are used in searching for extrasolar planets. The precision radial velocity technique is by far the most celebrated one. This technique that has been successful in detecting more than 180 planets around other stars, measures the amplitude of variations in the radial velocity of a star as that star is affected by its orbiting 1 The extrasolar planets encyclopedia,

2 2 extrasolar planet. From Newton s law of gravitation, two orbiting bodies exert a mutually attractive gravitaional force on one another. As a planet orbits its host star, the planet s gravity causes the star to undergo small wobbling. For a star, whose mass is much greater than that of the planet, this effect, although very small, is detectable. Since stellar wobbling is the result of the gravitational pull of the planet, the radial velocity technique is far more sensitive to large close-orbiting objects. At present, with current technology, the sensitivity of this method is increasing, and still hasn t reached its limit. Current radial velocity techniques can measure velocity variations down to 1 m/s, allowing discovery of smaller and farther orbiting planets such as in the case of HD However the radial velocity technique is still not sensitive enough to measure the effects of terrestrial planets. Currently, theoretical investigations are the only ways to examine the possibility of the existance of a system with an Earth-like body. Another consideration with this technique is that fitting routines are not able to constrain the mass of planets precisely. Only the minimum mass can be found, and since the stability of a system changes for different planetary masses, a theoretical analysis accounting for this, is necessary when determining the long-term stability of a system HD HD is a main-sequence star with temperature and size similar to our Sun. This star is between 4 and 10 Gyr old, and its effective temperature is approximately 5385 K. The mass of HD is 0.86 ± 3M, and its luminosity is 0 ± 3L (Lovis et al. 2006). As mentioned in the introduction, HD is host to three planets. The innermost planet of this star is at 785AU, and the other two are located at 0.186AU and 30AU from this star. A summary of the orbital parameters for these 3 planets is given in Table Habitability Beyond having a stable energy source, the requirements for habitability are largely derived from conditions on Earth. Since life seems to be flourishing here, it is reasonable to impose certain conditions based on our experience when dealing with extrasolar planets. The Habitable Zone (HZ) of a star is defined as a spherical shell encompassing the star where liquid water would be able to be present on the surface of a habitable planet (Haghighipour 2006). This capability is dependent on many factors such as atmospheric circulation models

3 3 and also the amount of radiation the planet receives from the star [F (r)]. This radiation itself is a function of the star s luminosity (L), which depends on the star s radius (R), of the star and it s surface temperature (T ). Equation (1) presents the brightness at a distance r, F (r) = 1 4π L(R, T )r 2 = σt 4 R 2 r 2. (1) In this equation, σ is Boltzmann s constant and F (r) is the apparent brightness, which is the amount of radiation that is distributed over the unit area of a sphere with radius r. When calculating the HZ of a star, we compare that star with our Sun. We then determine the star s HZ as a place where an Earth-like planet would receive the same amount of energy as Earth receives from the Sun. That is, F (r) = ( T T ) 4 ( R R ) 2 ( r r ) 2 F (r ), (2) where T and R are the temperature and radius of the Sun, r is the distance of the Earth from the Sun, and F (r ) is the brightness of the Sun at the location of Earth. Setting F (r) for the star equal to F (r ), we obtain r 2 = ( T T ) 2 ( R R )r. (3) 1993), the corre- Given that the HZ of our Sun is between 0.95AU and 1.15AU (Kasting sponding HZ for HD will be from 0.736AU to 0.891AU. It should be mentioned that the orbital of an Earth-like planet is an impor- Table 1. Orbital Parameters of the three planets in the HD system Parameter HD b HD c HD d Orbital Period (days) ± ± ± 3 Semi-major Axis (AU) Eccentricity ± ± 6 7 ± 7 Longitude of periastron 340 ± ± ± 61 Minimum Mass (M ) Note. All orbital parameters and physical characteristics are from Lovis et al. (2006).

4 4 tant factor in its habitability. Since defines the closest and farthest 2 approaches a planet makes to a star, it is possible that large eccentricities keep the planet out of the habitable zone long enough so that it may effect the evolution of life. Unfortunately, most extrasolar planets appear to have large eccentricities and our solar system seems to be somewhat rare. 3 But this maybe due to a sampling bias. 2. Methodology and Results In this project we studied the general stability and the habitability of the planetary system HD We carried out numerical integrations of the equations of motion of the system, using the hybrid routine of the N-body integration package MERCURY (Chambers 1999). This routine requires a timestep of equal to or shorter than 1/20th of the smallest period in the system. The innermost planet of HD has a period of days. The time step for all integrations was chosen to be 3335 days General Stability of HD Using the orbital parameters listed in Table 1, we started by simulating the dynamics of the planetary system of HD Any orbital parameter not listed in that table, was taken to be zero. Results indicate that long-term stability of this system is very likely. Figures 1 and 2 show the plot of the semimajor axes and eccentricities of all three planets. As mentioned before, the radial velocity technique yields only the minimum mass of an extrasolar planet. Depending on the orientation of the orbit with respect to the plane of the sky, the mass of an object may be much larger. To test the stability of the system for different values of the masses of its planets, we scaled the three planets to have different effective masses by changing their inclinations. The largest planet in the system is HD d. This planet was taken to be the standard to which the other planets were scaled. We increased the mass of HD d to 0.1 M J, 1.0 M J, and 1.5 M J, (corresponding, repectively, to an inclination of 55.3,86.74, and 87.82, with respect to the plane of the sky) and scaled the other two planets by the same amount. The system was then numerically integrated for 10 Myr. Results indicate that the outer planet was most effected by the increase in mass, particularly with a mass of 1.0 M J (Fig. 3 and 4). 2 The closest and furthest approaches are given by a(1 e) and a(1 + e), respectively. 3 The average is approximately, and the Earth s is 2

5 Planet D Planet C 0.1 Planet B Fig. 1. Graph of the semimajor axes of the planets of HD for 10 Myr. The closest and furthes approaches, a(1 ± e), are also shown. HD b HD c HD d Fig. 2. Graph of the of the planets of HD for 10 Myr.

6 Scaled to 0.1 Mj Scaled to 1.0 Mj Scaled to 1.5 Mj Fig. 3. Graphs of the semimajor axes and a(1 ± e) for HD d scaled to 0.1 M J, 1.0 M J, and 1.5 M J. eccentricty Scaled to 0.1 Mj Scaled to 1.0 Mj Eccentricity Scaled to 1.5 Mj Fig. 4. Graphs of the for HD d scaled to 0.1 M J, 1.0 M J, and 1.5 M J.

7 7 We also investigated the possibility of an asteroid belt in the system. We numerically integrated a system of 500 test particles evenly distributed between 0.80 AU and 1.00 AU, the location of an asteroid belt as mentioned by Lovis et al. (2006). The particles were given random eccentricities between and 0.34, corresponding to the average eccentricities of particles in the Kuiper Belt. Simulations indicated that the system became unstable in a very short time Stability of an Earth-like Planet in HD Along with the general stability of the HD 69830, we also studied the habitability of this system. Since current detection techniques are incapable of detecting small terrestial planets, study of habitability is at present limited to theoretical modeling. To study the habitability, one has to first study the long term stability of a habitable planet in the HZ of the central star. We placed an Earth-like planet at 12 different locations within the HZ of HD and integrated its orbit for Myr. Except for one case in which the Earth-like planet was at a distance of 0.753AU, in general, the orbit of a habitable planet in the HZ of the system is stable. Figures 5 and 6 show the lifetimes and stability of these objects. At a distance of AU the Earth-like planet showed instability early on by making a large number of close encounters with the outer most planet (Fig. 7 and 8). All other simulations remained stable for 10 Myr. The of the Earth-like planet in these simulations showed variations between and Due to these variations, it is possible that some of the Earth-like planets at the inner edge of the HZ that appeared to be stable for 10 Myr, may eventually get too close to the orbit of HD d, and become unstable. At 0.788AU and beyond, these simulations are safely away from the orbit of HD d, and all are stable for Myr. Figures 9 and 10 show the results of one such simulation.

8 8 1e+08 1e+07 Survival Time (yrs) 1e+06 1e+05 1e+04 1e+03 1e+02 1e+01 1e Initial Semi-major Axis (AU) Fig. 5. The graph of the lifetime vs. the initial semimajor axis of an Earth-like planet in the HZ of HD Though some numerical integrations were carried out for 100 Myr, only the data up to 10 Myr are presented here. Eccentricity Semimajor (AU) 0.90 Fig. 6. The graph of vs. semimajor axis of all simulations for an Earth-like planet in the HZ of HD

9 Earth like Planet Planet D Planet C Planet B Fig. 7. Graphs of the semimajor axis for all planets with a Earth-like planet placed at 0.753AU 0.5 HD b HD c HD d Earthlike planet at AU Fig. 8. Graphs of the for all planets with a Earth-like planet placed at 0.753AU

10 Earth like Planet 0.8 Planet D Planet C Planet B Fig. 9. Graphs of the semimajor axis for all planets with a Earth-like planet placed at 0.805AU HD b HD c HD d Earthlike planet at AU Fig. 10. Graphs of the for all planets with a Earth-like planet placed at 0.805AU

11 11 3. Conclusion We have presented an analysis of the stability of the multiple planetary system of HD We also studied the habitability of this system by simulating the dynamics of an Earth-like planet in its HZ. Results indicate that the system is indeed long-term stable. An Earth-like planet within the HZ may not have long term stability for distances less that 0.788AU. This is most likely due to the interaction of the orbits of the outer planet with that of the latter object. All other Earth-like planets from 0.788AU to 0.891AU are stable for Myr. Due to the consistancy of the orbital parameters over these time periods, we believe that long-term stability is very likely. The orbital parameters of the Earth-like planet near the edge of the HZ would place that object briefly outside the HZ. However, since our estimate of the HZ of this system is very conservative, the actual HZ may extend to farther distances. In addition to the long-term stability of an Earth-like planet, we also presented evidence that HD system can be stable for planets of larger mass, given that the radial velocity technique provides only the minimum mass of each planet. We also studied the dynamics of an asteroid belt placed between 0.80 and 1.00 AU. Numerical integrations showed a high rate of collisions among these objects, implying that it is unlikely for the system to have an asteroid belt. We are thankful to Simon Poole and the Undergraduate Computer Laboratories at the University of Calgary for access to their computational facilities. This work has been supported by an NSF grant to the REU Program at the Institute for Astronomy at the University of Hawaii - Manoa. REFERENCES Chambers, J.E. 1999, MNRAS, 304, 793 Haghihgipour, N. 2006, ApJ, 644, 543 Kasting, J.F., Whitmire, D.P., & Reynolds, R.T. 1993, Icarus, 101, 108 Lovis et al. 2006, Nature, 441, 305 This preprint was prepared with the AAS L A TEX macros v5.0.