DYNAMICAL STABILITY OF IMAGED PLANETARY SYSTEMS IN FORMATION: APPLICATION TO HL TAU

A recent ALMA image revealed several concentric gaps in the protoplanetary disk surrounding the young star HL Tau. We consider the hypothesis that these gaps are carved by planets, and present a general framework for understanding the dynamical stability of such systems over typical disk lifetimes, providing estimates for the maximum planetary masses. We collect these easily evaluated constraints into a workflow that can help guide the design and interpretation of new observational campaigns and numerical simulations of gap opening in such systems. We argue that the locations of resonances should be significantly shifted in massive disks like HL Tau, and that theoretical uncertainties in the exact offset, together with observational errors, imply a large uncertainty in the dynamical state and stability in such disks. This presents an important barrier to using systems like HL Tau as a proxy for the initial conditions following planet formation. An important observational avenue to breaking this degeneracy is to search for eccentric gaps, which could implicate resonantly interacting planets. Unfortunately, massive disks like HL Tau should induce swift pericenter precession that would smear out any such eccentric features of planetary origin. This motivates pushing toward more typical, less massive disks. For a nominal non-resonant model of the HL Tau system with five planets, we find a maximum mass for the outer three bodies of approximately 2 Neptune masses. In a resonant configuration, these planets can reach at least the mass of Saturn. The inner two planets' masses are unconstrained by dynamical stability arguments.

[1]  Planetary migration and extrasolar planets in the 2/1 mean-motion resonance , 2004, astro-ph/0404166.

[2]  Dimitri Veras,et al.  Simulations of two-planet systems through all phases of stellar evolution: implications for the instability boundary and white dwarf pollution , 2013, 1302.3615.

[3]  Jonathan P. Williams,et al.  Protoplanetary Disks and Their Evolution , 2011, 1103.0556.

[4]  K. Menou,et al.  PLANETESIMAL AND PROTOPLANET DYNAMICS IN A TURBULENT PROTOPLANETARY DISK: IDEAL UNSTRATIFIED DISKS , 2009, Proceedings of the International Astronomical Union.

[5]  W. Ward.  Protoplanet Migration by Nebula Tides , 1997 .

[6]  Richard Greenberg,et al.  Stability Limits in Extrasolar Planetary Systems , 2006, astro-ph/0607210.

[7]  C. Murray,et al.  Solar System Dynamics: Expansion of the Disturbing Function , 1999 .

[8]  L. Fouchet,et al.  Planet gaps in the dust layer of 3D protoplanetary disks - I. Hydrodynamical simulations of T Tauri disks , 2010, 1005.4557.

[9]  On the orbital evolution and growth of protoplanets embedded in a gaseous disc , 1999, astro-ph/9911431.

[10]  C. Hayashi.  Structure of the Solar Nebula, Growth and Decay of Magnetic Fields and Effects of Magnetic and Turbulent Viscosities on the Nebula , 1981 .

[11]  Francesco Marzari,et al.  Eccentric Extrasolar Planets: The Jumping Jupiter Model , 2002 .

[12]  K. Menou,et al.  Diffusive Migration of Low-Mass Protoplanets in Turbulent Disks , 2006, astro-ph/0603235.

[13]  Konstantin Batygin,et al.  DISSIPATIVE DIVERGENCE OF RESONANT ORBITS , 2012, 1204.2791.

[14]  R. Rafikov.  PLANET FORMATION IN SMALL SEPARATION BINARIES: NOT SO SECULARLY EXCITED BY THE COMPANION , 2012, 1212.1465.

[15]  Jeffrey S. Oishi,et al.  Turbulent Torques on Protoplanets in a Dead Zone , 2007, astro-ph/0702549.

[16]  Laurent Loinard,et al.  VLBA Determination of the Distance to Nearby Star-forming Regions. II. Hubble 4 and HDE 283572 in Taurus , 2007, 0708.4403.

[17]  Yanqin Wu,et al.  THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT , 2010, 1012.3706.

[18]  P. Message.  On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case , 1966 .

[19]  N. W. Evans,et al.  Stability of power‐law discs — I. The Fredholm integral equation , 1998 .

[20]  P. Artymowicz.  DYNAMICS OF BINARY AND PLANETARY SYSTEM INTERACTION WITH DISKS: ECCENTRICITY CHANGES , 1992 .

[21]  F. Marzari,et al.  Dynamical behaviour of multiplanet systems close to their stability limit , 2014, 1405.1667.

[22]  E. Ford,et al.  Dynamical Outcomes of Planet-Planet Scattering , 2007, astro-ph/0703166.

[23]  Richard Greenberg,et al.  LONG-LIVED CHAOTIC ORBITAL EVOLUTION OF EXOPLANETS IN MEAN MOTION RESONANCES WITH MUTUAL INCLINATIONS , 2015, 1501.03231.

[24]  Peter Goldreich,et al.  Disk-Satellite Interactions , 1980 .

[25]  E. Chiang,et al.  GRAVITO-TURBULENT DISKS IN THREE DIMENSIONS: TURBULENT VELOCITIES VERSUS DEPTH , 2014, 1405.3291.

[26]  Ruobing Dong,et al.  Observational Signatures of Planets in Protoplanetary Disks I: Gaps Opened by Single and Multiple Young Planets in Disks , 2014, 1411.6063.

[27]  H. Rein,et al.  REBOUND: An open-source multi-purpose N-body code for collisional dynamics , 2011, 1110.4876.

[28]  Hanno Rein,et al.  ias15: a fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits , 2014, 1409.4779.

[29]  K. Flaherty,et al.  SIGNATURES OF MRI-DRIVEN TURBULENCE IN PROTOPLANETARY DISKS: PREDICTIONS FOR ALMA OBSERVATIONS , 2015, 1501.02808.

[30]  Peter Bodenheimer,et al.  On the Interaction between Protoplanets and Protostellar Disks , 2000 .

[31]  Y. Lithwick,et al.  RESONANT REPULSION OF KEPLER PLANET PAIRS , 2012, 1204.2555.

[32]  C. Terquem,et al.  Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance , 2014, 1406.2189.

[33]  Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions , 2002, astro-ph/0210577.

[34]  P. Artymowicz.  Disk-Satellite Interaction via Density Waves and the Eccentricity Evolution of Bodies Embedded in Disks , 1993 .

[35]  Konstantin Batygin,et al.  CHAOTIC DISINTEGRATION OF THE INNER SOLAR SYSTEM , 2014, 1411.5066.

[36]  CONDITION FOR CAPTURE INTO FIRST-ORDER MEAN MOTION RESONANCES AND APPLICATION TO CONSTRAINTS ON THE ORIGIN OF RESONANT SYSTEMS , 2013, 1307.7776.

[37]  James Binney,et al.  Galactic Dynamics: Second Edition , 2008 .

[38]  D. Wilner,et al.  EMPIRICAL CONSTRAINTS ON TURBULENCE IN PROTOPLANETARY ACCRETION DISKS , 2010, 1011.3826.

[39]  P. Goldreich,et al.  OVERSTABLE LIBRATIONS CAN ACCOUNT FOR THE PAUCITY OF MEAN MOTION RESONANCES AMONG EXOPLANET PAIRS , 2013, 1308.4688.

[40]  Y. Lithwick,et al.  SECULAR CHAOS AND THE PRODUCTION OF HOT JUPITERS , 2010, 1012.3475.

[41]  Willy Benz,et al.  Models of giant planet formation with migration and disc evolution , 2004 .

[42]  On the migration-induced resonances in a system of two planets with masses in the Earth mass range , 2005, astro-ph/0507611.

[43]  S. J. Peale,et al.  Orbital resonances, unusual configurations and exotic rotation states among planetary satellites , 1987 .

[44]  John E. Chambers,et al.  The Stability of Multi-Planet Systems , 1996 .

[45]  L. Mundy,et al.  RESOLVING THE CIRCUMSTELLAR DISK OF HL TAURI AT MILLIMETER WAVELENGTHS , 2011, 1107.5275.

[46]  G. Lodato,et al.  Stability of self-gravitating discs under irradiation , 2011, 1108.1194.

[47]  F. Marzari,et al.  Frequency map analysis of the 3/1 resonance between planets b and c in the 55 Cancri system , 2005 .

[48]  Eccentricity Evolution for Planets in Gaseous Disks , 2002, astro-ph/0202462.

[49]  Elizabeth A. Lada,et al.  Disk Frequencies and Lifetimes in Young Clusters , 2001, astro-ph/0104347.

[50]  P. Armitage,et al.  TURBULENT LINEWIDTHS IN PROTOPLANETARY DISKS: PREDICTIONS FROM NUMERICAL SIMULATIONS , 2011, 1107.3561.

[51]  Brett Gladman,et al.  Dynamics of Systems of Two Close Planets , 1993 .

[52]  On the dynamics of planetesimals embedded in turbulent protoplanetary discs , 2010, 1007.1144.

[53]  R. Greenberg.  Tidal evolution of the Galilean satellites: A linearized theory , 1981 .

[54]  Katherine M. Deck,et al.  FIRST-ORDER RESONANCE OVERLAP AND THE STABILITY OF CLOSE TWO-PLANET SYSTEMS , 2013, 1307.8119.

[55]  J. Papaloizou,et al.  On the evolution of mean motion resonances through stochastic forcing: fast and slow libration modes and the origin of HD 128311 , 2008, 0811.1813.

[56]  A. Cumming,et al.  SHEDDING LIGHT ON THE ECCENTRICITY VALLEY: GAP HEATING AND ECCENTRICITY EXCITATION OF GIANT PLANETS IN PROTOPLANETARY DISKS , 2013, 1310.8627.

[57]  S. Beckwith,et al.  A Survey for Circumstellar Disks around Young Stellar Objects , 1990 .

[58]  John C B Papaloizou,et al.  Planet formation and migration , 2006 .

[59]  R. Nelson,et al.  On the dynamics of planetesimals embedded in turbulent protoplanetary discs with dead zones , 2010, 1104.3987.

[60]  European Southern Observatory,et al.  FIRST RESULTS FROM HIGH ANGULAR RESOLUTION ALMA OBSERVATIO NS TOWARD THE HL TAU REGION , 2015, 1503.02649.

[61]  A. Morbidelli,et al.  On the width and shape of gaps in protoplanetary disks , 2006 .

[62]  Gilles Bertrand,et al.  On the dynamics , 2007, Image Vis. Comput..

[63]  Christian Marchal,et al.  Hill stability and distance curves for the general three-body problem , 1982 .

[64]  Andrea Milani,et al.  On topological stability in the general three-body problem , 1983 .

[65]  F. Marzari,et al.  A numerical study of the 2:1 planetary resonance , 2006 .

[66]  Jack J. Lissauer,et al.  Formation of the Giant Planets by Concurrent Accretion of Solids and Gas , 1995 .

[67]  On the orbital evolution of low mass protoplanets in turbulent, magnetised disks , 2005, astro-ph/0508486.

[68]  D. Lynden-Bell,et al.  Global stability of self-similar Newtonian gaseous disks against axisymmetric perturbations , 1991 .

[69]  Dynamics and Origin of the 2:1 Orbital Resonances of the GJ 876 Planets , 2001, astro-ph/0108104.

[70]  G. Rieke,et al.  A DEEP SPITZER SURVEY OF CIRCUMSTELLAR DISKS IN THE YOUNG DOUBLE CLUSTER, h AND χ PERSEI , 2014, 1408.1724.