Systems of Multiple Planets G. W. Marcy and D. A. Fischer University of California, Berkeley, Dept. of Astronomy, Berkeley, CA 94720 USA R. P. Butler Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road, NW, Washington DC 20015, USA S. S. Vogt UCO Lick Observatories, University of California, Santa Cruz, Santa Cruz, CA 95064 Abstract. To date, 10 stars are known which harbor two or three planets. These systems reveal sec- ular and mean motion resonances in some systems and consist of widely separated, eccentric orbits in others. Both of the triple planet systems, namely Upsilon And and 55 Cancri, exhibit evidence of resonances. The two planets orbiting GJ 876 exhibit both mean–motion and secular resonances and they perturb each other so strongly that the evolution of the orbits is revealed in the Doppler measurements. The common occurrence of resonances suggests that delicate dynamical processes often shape the architecture of planetary systems. Likely processes include planet migration in a viscous disk, eccentricity pumping by the planet–disk interaction, and resonance capture of two planets. We find a class of “hierarchical” double–planet systems characterized by two planets in widely separated orbits, defined to have orbital period ratios greater than 5 to 1. In such systems, resonant interactions are weak, leaving high–order interactions and Kozai resonances plausibly important. We compare the planets that are single with those in multiple systems. We find that neither the two mass distributions nor the two eccentricity distributions are significantly different. This similarity in single and multiple systems suggests that similar dynamical processes may operate in both. The origin of eccentricities may stem from a multi–planet past or from interactions between planets and disk. Multiple planets in resonances can pump their eccentricities pumping resulting in one planet being ejected from the system or sent into the star, leaving a (more massive) single planet in an eccentric orbit. The distribution of semimajor axes of all known extrasolar planets shows a rise toward larger orbits, portending a population of gas–giant planets that reside beyond 3 AU, arguably in less perturbed, more circular orbits. 1. Introduction It is remarkable to recall that only seven years ago, the totality of our knowledge about extrasolar planets resided in a modest plot of velocity versus time for the star 51 Pegasi (Mayor and Queloz 1995). We remain impressed that Michel and Didier abstained from a definitive interpretation of those velocities until the completion of a wide variety of studies of that star. For 1 1/2 years after first detecting the sinusoidal velocity variations, they carried out photometry and line shape mea- surements to search for stellar pulsations, and they examined the rotation of the star to rule out a stellar companion which would have tidally spun up the star. Thus, in their discovery paper they had fully anticipated and eliminated the two serious alternative explanations that others would lance against the planet interpretation. PlanetarySystems.tex; 28/12/2006; 12:00; p.99 90 Marcy, Fischer, Butler, Vogt 100 Mass = 2.22 M /sin i P = 2.89 yr JUP K = 44.7 ms−1 e = 0.13 100 ) −1 ) 50 −1 0 0 Velocity (m s −100 Velocity (m s −50 −1 RMS = 10.2 ms −200 1996 1998 2000 2002 1994 1996 1998 2000 2002 Time (Years) Time (yr) Figure 1. Evidence for multiple planets. Left: A fit to the measured velocities of 47 UMa that invokes only one planet. Coherent departures are obvious in 1997 and 2000, indicating the inadequacy of a single planet. Right: Measured velocities vs time for Upsilon Andromedae, also showing velocity variations on multiple time scales Our team followed a month later with next two planets, namely around 70 Vir and 47 UMa that created further disturbances (Butler and Marcy, 1996; Marcy and Butler, 1996). For the former, the orbital eccentricity of 0.4 demonstrated unambiguous Keplerian motion, eliminating stellar pulsation as an explanation. But that planet violated our expectations of circular orbits for planets. For 47 UMa the early Keplerian fit, while implying a nearly circular (e = 0.06) orbit, failed to follow the predictions of that orbit in subsequent velocity measurements (Fig. 1). Coherent departures from the predicted Keplerian curve are apparent both in 1997 and 2000 (Fig. 1). Even greater departures were seen in the predicted Keplerian orbit in the next planet discovered, namely around Upsilon And (Butler et al., 1999). Moreover the fitted velocities for the planet around 55 Cancri exhibited a trend in the residuals. Thus, among the first six planets discovered (including Tau Boo b), three exhibited evidence of multiple companions. To date, 10 stars are known for which the velocities are best interpreted by two or three planets, as listed in Table 1. Among them are five planetary systems apparently trapped in mean–motion and secular resonances. 2. Upsilon Andromedae Upsilon Andromedae was the first multiple-planet system discovered (Butler et al., 1999). Its velocities (from Lick Obs.) are shown in Fig. 1 obtained from 1993– 2002. A power spectrum (Fig. 2) shows a strong peak at 4.6 days, the orbital period of the inner planet. Fitting the velocities with a simple Keplerian orbit leaves residuals that reveal two additional periodicities, visible to the eye (Fig. 2). To find a solution, we collaborated with R.Noyes, T.Brown, and S.Korzennik who had obtained excellent velocity measurements with their AFOE spectrometer (Brown et al., 1998). PlanetarySystems.tex; 28/12/2006; 12:00; p.100 Multiple Planet Systems 91 Table I. Properties of the 10 known multiple–planet systems. Star MStar PKecc. M sin ia Comment (M)(d)(m/s)(MJUP)(AU) Ups And b 1.30 4.617 70.15 0.01 0.64 0.058 Ups And c 1.30 241.16 53.93 0.27 1.79 0.805 apsidal lock Ups And d 1.30 1276.15 60.62 0.25 3.53 2.543 apsidal lock 55 Cnc b 1.03 14.653 71.5 0.03 0.83 0.115 3:1 Resonance 55 Cnc c 1.03 44.3 11.2 0.40 0.18 0.241 3:1 Resonance 55 Cnc d 1.03 4400 50.2 0.34 3.69 5.2 GJ 876 b 0.32 61.020 210.0 0.10 1.89 0.207 2:1 Mean Motion & GJ 876 c 0.32 30.120 81.0 0.27 0.56 0.130 Secular Resonance 47 UMa b 1.03 1079.2 55.6 0.05 2.86 2.077 8:3 commensur.? 47 UMa c 1.03 2845.0 15.7 0.00 1.09 3.968 8:3 commensur.? HD 168443 b 1.01 58.1 470.0 0.53 7.64 0.295 HD 168443 c 1.01 1770.0 289.0 0.20 16.96 2.873 HD 37124 b 0.91 153.3 35.0 0.10 0.86 0.543 HD 37124 c 0.91 1942.0 19.0 0.60 1.00 2.952 HD 12661 b 1.07 263.6 74.4 0.35 2.30 0.823 Secular Resonance HD 12661 c 1.07 1444.5 27.6 0.20 1.57 2.557 Secular Resonance HD 38529 b 1.39 14.309 54.2 0.29 0.78 0.129 HD 38529 c 1.39 2174.3 170.5 0.36 12.7 3.68 HD 82943 b 1.05 444.6 46.0 0.41 1.63 1.159 2:1 Resonance HD 82943 c 1.05 221.6 34.0 0.54 0.88 0.728 2:1 Resonance HD 74156 b 1.05 51.6 112.0 0.65 1.61 0.278 HD 74156 c 1.05 >2650 125.0 0.35 >8.21 >3.82 Occam’s Razor suggests that the first multi–planet system would contain the minimum complexity: two detectable planets. This logic dissuaded us from invok- ing three planets until the residuals left no alternative. By 1999, with reluctance and many tests (Monte Carlo and comparisons with other F8V stars) we were forced to invoke three planets for Upsilon And (Butler et al., 1999) to explain the velocities within errors. The current fit to all three planets is shown in Fig. 2. The subsequent velocity measurements at Lick observatory have followed the pre- dicted triple-Keplerian orbit within the errors. No planet–planet interactions nor additional planets are revealed in our recent velocities. Interestingly, the line of apsides of the orbits of the outer two planets are nearly aligned, with current values of ω of 246◦ and 259◦, each with uncertainty of 4◦. Theoretical simulations indicates that libration of the apsides likely stems from a secular resonance. Treating the planets as smeared out mass distributions of “wire” along their orbits implies torques that cause oscillation of the orientation of the ma- PlanetarySystems.tex; 28/12/2006; 12:00; p.101 92 Marcy, Fischer, Butler, Vogt 60 150 4.6170 d ) 50 −1 100 40 50 30 0 Power 20 −50 10 −100 Velocity Residuals (m s 4.6−day Planet 0 −150 Removed. 10 100 1000 1992 1994 1996 1998 2000 2002 Period (days) Time (yr) Figure 2. Analysis for three planets orbiting Upsilon And. Left: The power spectrum of velocities shows several significant peaks, notably at 4.6 d, 2/3 yr, and several years. Right: Best two–planet fit to the velocities, after subtracting the effects of the inner (4.6 d) planet. Velocities have followed the prediction from a three–planets model for three years. jor axes (Chiang and Murray, 2002).