GAS GIANT PLANETS AS DYNAMICAL BARRIERS to INWARD-MIGRATING SUPER-EARTHS André Izidoro1,2,3, Sean N
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The Astrophysical Journal Letters, 800:L22 (5pp), 2015 February 20 doi:10.1088/2041-8205/800/2/L22 © 2015. The American Astronomical Society. All rights reserved. GAS GIANT PLANETS AS DYNAMICAL BARRIERS TO INWARD-MIGRATING SUPER-EARTHS André Izidoro1,2,3, Sean N. Raymond3,4, Alessandro Morbidelli1, Franck Hersant3,4, and Arnaud Pierens3,4 1 University of Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Laboratoire Lagrange, BP4229, F-06304 NICE Cedex 4, France; [email protected] 2 Capes Foundation, Ministry of Education of Brazil, Brasília/DF 70040-020, Brazil 3 Univ. Bordeaux, Laboratoire d’Astrophysique de Bordeaux, UMR 5804, F-33270 Floirac, France 4 CNRS, Laboratoire d’Astrophysique de Bordeaux, UMR 5804, F-33270 Floirac, France Received 2014 November 14; accepted 2015 January 24; published 2015 February 17 ABSTRACT Planets of 1–4 times Earth’s size on orbits shorter than 100 days exist around 30–50% of all Sun-like stars. In fact, the Solar System is particularly outstanding in its lack of “hot super-Earths” (or “mini-Neptunes”). These planets—or their building blocks—may have formed on wider orbits and migrated inward due to interactions with the gaseous protoplanetary disk. Here, we use a suite of dynamical simulations to show that gas giant planets act as barriers to the inward migration of super-Earths initially placed on more distant orbits. Jupiter’s early formation may have prevented Uranus and Neptune (and perhaps Saturn’s core) from becoming hot super-Earths. Our model predicts that the populations of hot super-Earth systems and Jupiter-like planets should be anti-correlated: gas giants (especially if they form early) should be rare in systems with many hot super-Earths. Testing this prediction will constitute a crucial assessment of the validity of the migration hypothesis for the origin of close-in super- Earths. Key words: planets and satellites: formation – planet–disk interactions 1. INTRODUCTION Papaloizou 2007; Ida & Lin 2010; McNeil & Nelson 2010; Cossou et al. 2014; Raymond & Cossou 2014). Unlike the According to the standard core accretion model (Pollack et al. 1996), gas giant planets form in a few million years in inward migration model, the in situ formation scenario requires either congenital high disk mass or the effective drift of solid gas-dominated disks. A solid core of a few to dozens of Earth ( ) masses grows then accretes a thick gaseous envelope. It is precursors approximately cenitmeter-to-meter size objects to the inner regions of the disk creating enhanced surface densities believed that giant planet cores form preferentially in a region ( of the protoplanetary disk where the radial drift speed of dust, of solids Boley & Ford 2013; Chatterjee & Tan 2014; ) pebbles, and small planetesimals is slowed, creating a localized Hansen 2014 . ( Super-Earths are so abundant that any model for their origin enhancement in the density of solid material Johansen fi et al. 2009). One favorable location for this to happen is at must be very ef cient. The key question then becomes the the snowline (Kokubo & Ida 1998; Morbidelli et al. 2008; following: Why are there no hot super-Earths in our Solar Pierens et al. 2013; Bitsch et al. 2014a, 2014b) where water System? condenses as ice (Lecar et al. 2006). Planet formation models Here we propose that an interplay between growing gas tend to produce not one but multiple planet cores beyond the giants and migrating super-Earths can solve this mystery. If ( ) snowline (Kokubo & Ida 1998; Lambrechts et al. 2014). super-Earths or their constituent embryos form in the outer However, observational evidence suggests that not all emer- disk and migrate toward the central star, then some of these ( ging planetary cores are able to accrete enough gas to become objects must on occasion become giant planetary cores see ) gas giant planets. Indeed, Uranus and Neptune may be thought Cossou et al. 2014 . If the innermost super-Earth in a young of as “failed” giant planet cores, and Neptune-sized exoplanets planetary system grows into a gas giant, then the later have been found to be far more abundant than Jupiter-sized dynamical evolution of the system is drastically changed. The ones (Howard et al. 2010; Mayor et al. 2011). giant planet blocks the super-Earths’ inward migration. In this Super-Earths are extremely abundant (Mayor et al. 2011; context, Jupiter may have prevented Uranus and Neptune—and Howard et al. 2012; here, “super-Earths” are defined as all perhaps Saturn’s core—from migrating inward and becoming planets between 1 and 20 Earth masses or 1 and 4 Earth radii). super-Earths. This model—which we test below with numerical An extraordinary number of planetary systems with multiple simulations—predicts an anti-correlation between the popula- super-Earths have been found (Howard et al. 2010, 2012; tions of giant exoplanets and super-Earths that will be tested in Mayor et al. 2011; Fressin et al. 2013; Marcy et al. 2014). future data sets. No such anti-correlation is expected from the These planets’ orbits are typically found in tightly packed in situ model of super-Earth formation (Schlaufman 2014). configurations and located much closer to their stars than This therefore represents a testable way to differentiate between expected, well inside the primordial snowline (Lissauer models. et al. 2011a). The origin of these systems is an open question We first test the concept of gas giants as barriers to inward- (Raymond et al. 2008, 2014). There are two competing migrating super-Earths or planetary embryos in Section 2.We models: super-Earths either formed in situ (Raymond then analyze the expected observational consequences and et al. 2008; Hansen & Murray 2012, 2013; Chiang & make specific testable predictions in Section 3. We also discuss Laughlin 2013) or migrated toward the central star from the the uncertainties and how much can be inferred from upcoming outer regions of their proto-planetary disks (Terquem & observations. 1 The Astrophysical Journal Letters, 800:L22 (5pp), 2015 February 20 Izidoro et al. 2. THE MODEL: GAS GIANTS AS defined as TYPE I MIGRATION BARRIERS 1 We ran a suite of N-body simulations to test whether giant æ M ö3 ç SE ÷ planets act as dynamical barriers for inward migrating super- Rhm, = ç ÷ ()aa12+ (,1) èç 12 M ø÷ Earths. Our simulations represented the middle stages of planet formation in gas-dominated circumstellar disks. The simula- where M and M are the individual masses of the super- tions included a population of super-Earths initially located SE Earths and the central star, respectively. a1 and a2 are the beyond the orbit of one or two fully formed gas giants. Our semimajor axes of any two adjacent super-Earths. Initially, the – code incorporated the relevant planet disk interactions, cali- eccentricities of the super-Earths and the giant planets brated to match complex hydrodynamical simulations. eccentricities and inclinations are set to zero. Orbital A Jupiter-mass planet opens a gap in the protoplanetary disk inclinations of the super-Earths were initially chosen and type II migrates inward (Lin & Papaloizou 1986; Crida & randomly from 0◦.001 to 0◦.01. The argument of pericenter Morbidelli 2007). Type-II migration of gas giants is signifi- and longitutude of ascending node of the super-Earths are cantly slower than the type-I migration of super-Earths (for randomly selected between 0° and 360°. super-Earths of ∼3 Earth masses or larger for traditional disk Collisions were treated as inelastic mergers that conserved parameters). Of course, if there is enough time, then a giant linear momentum. Objects were removed from the system if planet would migrate close to the star and any super-Earth they strayed beyond 100 AU from the central star. In beyond its orbit would as well. However, most giant planets do simulations with both Jupiter and Saturn, to ensure the not appear to have this fate. The vast majority of giant dynamical stability between the two giant planets, the exoplanets around FGK stars are found at a few AU from their eccentricities of the latter planets are artificially damped if host stars (Udry & Santos 2007; Mayor et al. 2011). Only they increase to beyond those values observed in hydrodyna- about 0.5–1% of Sun-like stars host hot-Jupiters (Cumming mical simulations (0.03–0.05). et al. 2008; Howard et al. 2010, 2012; Wright et al. 2012). However, radial velocity and microlensing surveys hint that the 2.1.1. Disk of Gas ( abundance of long-period gas giants is at least 15% Gould Both the speed and direction of type-I migration are sensitive ) et al. 2010; Mayor et al. 2011 . This dissemblance may be a to the properties of the gaseous disk. Numerical studies have consequence of the inside-out photo-evaporation of the disk, shown that planetary embryos can migrate outward in radiative which creates an inner very low-density cavity in the disks (e.g., Kley & Crida 2008; Paardekooper & Papaloizou protoplanetary disk that stops inward migration (Alexander & 2008; Paardekooper et al. 2010, 2011). However, outward Pascucci 2012). In the case of the solar system, the proximity migration is only possible for a limited range of planetary and mass ratio of Jupiter and Saturn may have prevented the masses (e.g., Bitsch et al. 2014a). Migration is directed inwards inward migration of the giant planets (Morbidelli & Crida in the regions of the disk where viscous heating is a sufficiently 2007) or even forced their outward migration (Walsh weak heat source. Because the surface density of a disk decays et al. 2011). In our simulations, we assume for simplicity that with time, the region of outward migration shifts inward and the giant planet does not migrate, as a proxy of all cases in eventually disappears.