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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects 4 Formation of SMOs STARLIKE AND PLANETLIKE FORMATION Models for the origin of SMOs tend to fall into two categories that can be broadly characterized as starlike and planetlike formation.1 A third possibility, converting a normal, low-mass star into a SMO through mass loss to a binary companion, is considered unlikely (see presentation by F. Shu in this chapter). Starlike formation involves fragmentation and collapse of a piece of an interstellar molecular cloud to form an isolated brown dwarf, or multiple fragmentation episodes that produce a central star and one or more substellar companions. Planetlike formation requires the presence of a disk of gases and particulates in orbit about a parent star. The agglomeration or accretion of the solids leads perhaps to something grossly resembling Earth or Venus, by which time significant amounts of gas have begun to be gravitationally attracted to the growing planet. Continued growth of the solid core leads eventually to rapid buildup of the gaseous envelope and production of a planet comparable to or exceeding the mass of Jupiter. The difference between these two processes is potentially profound for at least one of the fundamental questions NASA seeks to address in its Origins program—the frequency with which planetary systems grossly similar to ours occur elsewhere in the cosmos. The starlike formation of a SMO is likely to exclude the production of a regular planetary system; in contrast, the planetlike process implies the presence of other solids nearer the central star, which can come together to form a suite of terrestrial planets (see presentation by D.C. Black in this chapter). There are, however, complications. Current numerical simulations of the formation of SMOs by fragmentation suggest a two-step process, the formation of a disk followed by rapid evolution of the disk to form massive companions (see presentation by P. Bodenheimer in this chapter). The disk itself is often disrupted during the formation or subsequent ejection of the companion. Conversely, the production of a giant planet in the course of planet formation can itself be disruptive both locally and globally. Simple gravitational scattering of planetesimals by the giant can truncate the growth of nearby planets. Global disruption is possible through the formation of a gap in the disk and subsequent inward migration of the giant planet—a process suggested strongly by the discovery of giant planets very close to their parent stars. Observational Evidence Observations to date do, in fact, hint at the contribution of two distinct processes in the production of SMOs. The mass function of SMO companions to stars, when corrected for various observational biases, drops with decreasing mass down to about 10 to 20 MJ and then 1 For a general review of formation processes, see, for example, Protostars and Planets III, E. Levy and J.I. Lunine (eds.), University of Arizona Press, Tucson, Ariz., 1993.
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects flattens or rises weakly—an indication that a second formation mechanism becomes available to produce objects perhaps 10 MJ and smaller. This second process is, by presumption, the planetlike process of solid and then gaseous accretion. Additional attempts to confirm this suggestion include plotting the masses of detected SMOs against their orbital eccentricity, since the planetlike process should tend to produce objects in circular orbits (a consequence of the averaging out of the differing orbital angular momenta of the accreting planetesimals). Indeed there seems to be a correlation such that the lower-mass candidates tend to have small or near-zero eccentricity. However, this correlation is not perfect and suffers both from the statistics of small numbers and the “sin i” ambiguity of radial-velocity detections. Various processes after formation can reduce or eliminate the initial eccentricity, particularly for low-mass objects in very close orbits about their parent star. Conversely, an SMO significantly more massive than Jupiter, formed in a disk, can have its eccentricity pumped up by gravitational interactions with the disk itself. Eccentricity, therefore, appears not to be a reliable indicator of formation mechanism. Formation of Close-In SMOs The formation of low-mass SMOs very close to their parent stars is perhaps the most active area of research on formation processes. Currently no consensus exists on a preferred mechanism. Formation in place is difficult because SMOs (whether formed by starlike direct fragmentation or the solid-gas, two-step planetlike process) are distended during collapse. As a result, tidal stresses will tend to tear them apart if they approach to within 0.05 AU of their parent stars—the present distance of 51 Pegasi B from its primary. However, accretion involving very refractory solids may keep envelope opacity and hence physical radius small, thus, perhaps, avoiding this problem. Most models invoke formation at distances farther from the parent star, followed by transport inward (see presentation by M.J. Duncan in this chapter). This transport may involve gravitational scattering involving one or two other giant planets, or interaction with the gaseous or particulate disk. Inward migration in a gaseous disk is a consequence of the gravitational interaction between planet and disk, such that a gap is formed in the disk and torques result in inward evolution of the planet and gap. How the migration is stopped remains a lively issue of discussion: the inner edge of the disk, stellar rotational torques, and mass transfer all may play a role. Likewise, inward migration of a giant planet in a purely particulate disk is possible through gravitational interactions, although significant movement requires a mass of particulates comparable to the mass of the planet itself. Relationship to Terrestrial Planets Formation models do not represent an academic exercise since, as noted above, all models have something to say about the likelihood of forming additional planets (including terrestrial ones) in systems containing SMOs. It must be emphasized that the discovery of SMOs comparable in mass to Jupiter does not imply the presence of other planets in that system. The existence of close-in giant planets does not preclude, on stability grounds, the presence of a planetary system like our solar system. However, the formation of such close-in objects or their migration inward would disrupt or delay the formation of other planets. Thus, the timing of the migration (early or late) in the history of the disk, and its effect on the disk, are critical to assessing the viability of smaller planets in those systems. The probability or frequency of giant
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects planet migrations is thus, potentially, a key factor in the frequency of occurrence of terrestrial planets in extrasolar planetary systems
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects FORMATION OF SUBSTELLAR-MASS COMPANIONS TO STARS David C. Black Lunar and Planetary Institute The formation of substellar-mass objects (SMOs) has long been an important problem, lying as it does at the intersection of stellar astrophysics and planetary science. It has only been recently, however, that tools have afforded astronomers the opportunity to explore this difficult region of observational phase space. I focus here on the question of the formation of companions to stars, more specifically on companions in systems with orbital periods P ≤ 104 days. This choice is motivated by the fact that this is the likely orbital realm of planetary systems, it is an area that is reasonably well studied with regard to both main sequence and premain sequence binaries, and there is now clear evidence that the mass function of secondary companions in such binary systems differs from that of field stars and secondaries in long-period systems (the latter being consistent with field stars). Throughout the discussion I use the notion that the distinction between planets and brown dwarfs is one of formation. The extent to which this distinction relates in an unambiguous manner to mass remains unclear, so mass cannot at this time be used as the sole indicator of the nature of a SMO. This only becomes critical in the transition region between what are clearly brown dwarfs (masses ~50 Jupiter masses) and what are clearly planets (masses ~10 Earth masses). The main messages that I would like to convey in my remarks are, in no special order: The formation of companion SMOs, particularly low-mass objects (i.e., masses ≤10 Jupiter masses), by classical, low-temperature fragmentation is unlikely. A possible trigger for formation of SMOs in disks exists through a combination of decreased opacity due to evaporation of dust grains, and dissociation of H2, both of which occur in the density/temperature regime that is found in the inner regions of circumstellar disks. These regions need not themselves be unstable in the Jeans' sense; they only need to seed instability in what is already a nonaxisymmetric, marginally stable system. Binary companions, including brown dwarfs, form very early in the game (≤105 years), and most of their orbital evolution appears to have taken place by that time. Planetary companions take substantially more time to form (≥106 years). There is no indication that orbital migration has played a significant role in establishing the orbital-period distribution of pre-main sequence binaries. Giant planets appear to form through a combination of dust accretion followed by rapid accretion of gas from their surroundings. A firm estimate of the upper limit to the mass of a planet is not currently available. The lower mass limit for brown dwarfs is unknown at present. The currently available mass distributions for SMOs is inadequate to quantitatively determine whether any particular segment of that population is over- or underabundant relative to its neighboring SMOs. It is possible at present to compare numbers with assumed power laws, but there is no independent evidence that such laws indeed describe the mass function. It is a start, but should not be overinterpreted at this time. Given the uncertainty in determining whether an object is a planet or another class of object based on intrinsic properties of the object, we should look to the nature of the system in which the companion exists. Brown dwarfs as binary companions to stars should be expected. However, the five examples that we have of companion systems believed to have formed via
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects accretion have multiple companions with nearly circular orbits. Companion multiplicity with low-eccentricity orbits is probably the most reliable “smoking gun” for identifying a planetary system and thereby whether a companion is a planet. The recent discoveries of SMOs open a new area of research that will challenge and enlighten our understanding of star and planetary-system formation alike. As we strive to interpret these exciting new results, we should take care not to overinterpret what we see. It should not be overlooked that, at this time in the history of these new observations, we have evidence only for binary companion systems. There is, as yet, no confirmed detection of a planetary system. FORMATION OF BROWN DWARFS BY MASS TRANSFER Frank Shu University of California, Berkeley Unlike the case for normal stars or giant planets, astronomers possess no commonly accepted theories or even a set of ideas concerning the formation of brown dwarfs, either singly by themselves or in binary systems with normal stars. A scenario that is frequently appealed to but that lacks a firm foundation in observations of the structure and dynamics of giant molecular clouds (GMCs) is Hoyle's idea of continued dynamical fragmentation until some smallest value limited by opacity effects is reached.2 The relatively long lifetimes of GMCs suggest that large-scale magnetic fields and the turbulence mediated by such fields play important roles in the support of GMCs against their self-gravity. In the presence of such fields, Mestel pointed out three decades ago that the problem of gravitational fragmentation has a character very different from Hoyle's original picture,3 and recent calculations suggest that the possibility may be less promising than even Mestel surmised. If the solution is to eliminate the source of the difficulty by the leakage of ambient magnetic fields through ambipolar diffusion, the result is to build up highly centrally concentrated “cores” that gravitationally collapse from the inside-out. The problem then quickly resolves itself to one of accretional infall by one or more compact objects from a surrounding envelope that generally has more than enough mass, even in highly clustered environments, to form a single brown dwarf. Brown dwarfs may still potentially occur by fragmentation out of the disk that normally surrounds a growing protostar, but tendencies exist in the rotating infall process to equalize the two centers of attraction (normal star and brown dwarf), unless mechanisms exist to shut off the inflow or to transfer mass from the less massive object to the more massive. We review the ideas developed for shutting off the inflow, by disk truncation, or by magnetocentrifugally driven outflows, and by mass transfer through Roche-lobe overflow. We conclude that the parameter space accessible to Roche-lobe overflow in young substellar objects 2 F. Hoyle, “On the Fragmentation of Gas Clouds into Galaxies and Stars,” Astrophysical Journal, 118: 513, 1953. 3 L. Mestel, “Problems in Star Formation,” Quarterly Journal of the Royal Astronomical Society, 6: 165 and 265, 1965.
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects is fairly small because of the relatively high internal densities of brown dwarfs during their long-lived phases. Therefore, the whittling down of normal low-mass stars to brown dwarfs by Roche-lobe overflow is probably not important except in a very small minority of special cases. Of the remaining possibilities for generating gaseous objects with masses intermediate between ordinary stars and planets, we argue that the mechanisms giving rise to brown dwarfs probably have more in common with star-formation processes than planet-formation processes. FORMATION OF BROWN DWARFS AND GIANT PLANETS Peter Bodenheimer University of California, Santa Cruz Recent observations have uncovered evidence for brown dwarfs in orbit around stars, in clusters, and in the general field. Also, evidence for planets around solar-type stars exists. These objects can be divided into three types: Those with nearly circular orbits more than 0.15 AU away from the star; Those with nearly circular orbits very close (0.05 AU) to the star; and Those with eccentric orbits. Three formation mechanisms for the substellar-mass objects have been discussed: Fragmentation of a collapsing rotating cloud into a system of major and minor fragments; Disk fragmentation by gravitational instability; and Accretion of small particles in a disk to form a solid core, followed by rapid capture of gas. The formation phase is likely in all cases to be followed by orbital evolution, accretion, encounters, and/or mergers. Work of Goldreich and Tremaine,4 Lin and Papaloizou,5 Ward,6 and Murray et al.7 strongly indicates that giant planets will migrate during and after formation, and a major problem is how to stop them at the orbital positions where they are observed. Basic constraints exist for each of these mechanisms. For the first mechanism, the minimum mass of a fragment is determined by the minimum Jeans mass in a (log temperature/log density) plot of the evolution of a collapsing cloud. The minimum occurs just after the central part of the cloud becomes optically thick. For the second mechanism, fragmentation in a disk is likely to occur only if the Toomre Q parameter is locally less than 1. If the minimum Q in a disk is about 1.3, the disk will develop saturated spiral arms and will 4 p. Goldreich and S. Tremaine, “Disk-Satellite Interactions,” Astrophysical Journal, 241: 425, 1980. 5 D.N.C. Lin and J.C.B. Papaloizou, “On the Tidal Interaction Between Protoplanets and the Protoplanetary Disk, III. Orbital Migration of Protoplanets,” Astrophysical Journal, 309: 846, 1986. 6 W.R. Ward, “Survival of Planetary Systems.” Astrophysical Journal, 482: L211, 1998. 7 N. Murray, B. Hansen, M. Holman, and S. Tremaine, “Migrating Planets,” Science, 279: 69, 1998.
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects evolve without fragmentation. For mechanism 3, there is a maximum mass for a protoplanet, as determined by the tidal truncation (gap-opening) criteria stated by Lin and Papaloizou in Protostars and Planets III.8 For standard disk models the upper limit is 1 to 2 Jupiter masses. An example of the first mechanism is given from the work of Burkert and Bodenheimer.9 An isothermal cloud collapse is calculated in three space dimensions on a set of nested Cartesian grids so that the inner regions, where fragmentation occurs, is reasonable well resolved. The initial density distribution is a 1/r-power law, and an initial m = 2 non-axisymmetric perturbation with a 10% amplitude is imposed. After a complicated series of fragmentations, the situation emerges where there is a predominant binary with a separation of 200 AU and masses on the order of 100 Jupiter masses, with a smaller object with a mass of about 10 Jupiter masses in orbit about one of the components. Thus, fragments over a wide range of masses can form in the same cloud. A number of issues remain to be resolved, including the survival of the companion, the fate of the fragments as influenced by the further accretion of gas and gravitational interactions between them, the effect of the numerical resolution of the calculations, and the effect of radiation transport, which was not included. Numerical calculations of the evolution of disks initially in equilibrium but subject to gravitational instability have been carried out by Greg Laughlin.10 A typical initial condition is a disk with a mass equal to that of the central star, a Gaussian surface-density profile, a polytropic equation of state, and a minimum Q value of about 1.3. A well-defined two-arm spiral mode emerges from a very small initial random perturbation, and the amplitude saturates at about the 10% level. Evolution results in accretion onto the star, transfer of angular momentum outward, and spreading of the outer part of the disk, but no fragmentation. If the minimum Q value in the disk is reduced to 1, fragmentation quickly occurs. Alan Boss has also carried out such calculations, in three space dimensions, with a minimum Q value of about 1; he also found fragmentation.11 The typical fragment mass in disk fragmentation is closer to 10 Jupiter masses than 1 Jupiter mass. A major issue to be resolved is whether cloud collapse to a disk will lead to conditions conducive to fragmentation or whether the spiral-arm type of evolution will dominate. A major problem with the formation of giant planets by the core-accretion/gas-capture process is that the build-up time of the core may be longer than the lifetime of a typical disk. A calculation is presented for the in situ formation of the companion of 47 Ursae Majoris. The solid material is assumed to accrete at a constant rate. For the nebular model adopted, the tidal truncation mass is about 2.3 Jupiter masses, the formation time is about 4 million years, the peak luminosity about 0.01 L◉, and the core mass 34 Earth masses. If the solid accretion rate is calculated in detail rather than assumed, then the disk would have to be very massive in order to get a formation time of less than 10 million years. Nevertheless it is suggested that objects of types 1 and 2 formed by this mechanism, while objects of type 3 formed by the fragmentation of collapsing clouds. 8 Protostars and Planets III, E. Levy and J.I. Lunine (eds.), University of Arizona Press, Tucson, Ariz., 1993. 9 A. Burkert and P. Bodenheimer, in preparation. 10 G. Laughlin and M. Rozyczka, “The Effect of Gravitational Instabilities on Protostellar Disks,” Astrophysical Journal, 456: 279, 1996. 11 A. Boss, “Formation of Giant Gaseous Protoplanets by Gravitational Instability, ” Science, 276: 1836, 1997.
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects LONG-TERM DYNAMICAL EVOLUTION OF MULTIPLE-COMPONENT SYSTEMS Martin J. Duncan Queen's University Numerical experiments conducted by several groups over the past decade have made it increasingly apparent that most orbits in our solar system (and probably those in other multicomponent planetary systems) exhibit the chaotic behaviour found in many nonlinear-Hamiltonian systems. However, it is a characteristic of many of these systems that the time scale for this underlying chaos to produce “macroscopic ” manifestations (e.g., orbit crossings, close encounters, ejections, etc.) can be millions to billions or more orbital periods. Numerical integrations of this duration have recently become feasible, and preliminary results suggest that dynamical effects (including instabilities) may have an important influence on the architecture of planetary systems. For example, it appears that there is very little room between the giant planets12 or between the terrestrials13.14 to squeeze in other planets that could survive the age of the solar system. Thus, the current planetary spacings may have resulted from a series of mergers and ejections resulting from dynamical instabilities occurring as our system evolved to its current state. Indeed, current hypotheses for the unexpected diversity of extrasolar planetary orbits typically rely on dynamical processes such as: Giant planet migration due to interaction with the gas15 or planetesimal disk;16 Gravitational scattering and/or merging among two,17 three,18 or more19 unstable giant planets; and The tidal influence of a stellar companion on an inclined single-planet system.20.21 Thus the populations and orbital characteristics of most planetary systems may have been established both by dynamical processes active during the late stages of planet formation and by a winnowing produced by billions of years of chaotic “natural selection.” 12 B. Gladman and M.J. Duncan, “On the Fate of Minor Bodies in the Outer Solar System.” Astronomical Journal, 100: 1680, 1990. 13 J. Laskar, “Large Scale Chaos in the Solar System,” Astronomy and Astrophysics, 287: L9, 1994. 14 J. Laskar, “Large Scale Chaos and the Spacings of the Inner Planets,” Astronomy and Astrophysics, 317: L75, 1997. 15 D.N.C. Lin, P. Bodenheimer, and D.C. Richardson, “Orbital Migration of the Planetary Companion of 51 Pegasi to its Present Location,” Nature, 380: 606, 1996. 16 N. Murray, B. Hansen, M. Holman, and S. Tremaine, “Migrating Planets,” Science, 279: 69, 1998. 17 F.A. Rasio and E.B. Ford, “Dynamical Instabilities and the Formation of Extrasolar Planetary Systems,” Science, 274: 954, 1996. 18 S.J. Weidenschilling and F. Marzari, “Gravitational Scattering as a Possible Origin for Giant Planets at Small Stellar Distances,” Nature, 384: 619, 1996. 19 D.N.C. Lin and S. Ida, “On the Origin of Massive Eccentric Planets,” Astrophysical Journal, 477: 781, 1997. 20 M. Holman, J. Touma, and S. Tremaine, “Chaotic Variations in the Eccentricity of the Planet Orbiting 16 Cyg B,” Nature, 386: 254, 1997. 21 T. Mazeh, Y. Krymolowski, and G. Rosenfeld, “The High Eccentricity of the Planet Orbiting 16 Cygni B,” Astrophysical Journal, 477, L103, 1997.
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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects In this talk I illustrate some of these features by drawing on some recent work I have done with Hal Levison and/or Jack Lissauer designed to study the stability of planetary systems. The simulations fall into two categories: Studies of the dependence on the masses of the satellites of the dynamical lifetime of the inner Uranian satellites,22 equal-mass three-planet systems, and the four giant planets.23 This set of simulations demonstrates interesting and as yet unexplained mass-scaling behaviour (especially for low-mass satellites). Studies using our new adaptive-timestep, symplectic code24 together with a crude recipe for gas drag and accretion designed to generate plausible giant-planet systems from a large number of planetary embryos.25 This set demonstrates the possible diversity, of giant-planet systems that are all ultimately stable for roughly 1 billion years. Of the approximately 30 systems generated, some are very similar to ours, some have somewhat more closely spaced planets, and some contain only two very widely spaced planets. Some systems have planets locked in mean-motion resonances, and the planets in some systems show large changes in eccentricity and inclination while remaining stable. In short, the systems show much of the behaviour that would have been thought highly unrealistic 2 to 3 years ago! 22 M.J. Duncan and J.J. Lissauer, “Orbital Stability of the Uranian Satellite System,” Icarus, 119: 1, 1997. 23 M.J. Duncan and J. J. Lissauer, “The Effects of Post-Main Sequence Solar Mass Loss on the Stability of our Planetary, System.” Icarus, in press, 1998. 24 M.J. Duncan, H.F. Levison, and M.H. Lee, “A Multiple Timestep Symplectic Algorithm for Integrating Close Encounters, ” Astronomical Journal, in press, 1998. 25 H.F. Levison, J.J. Lissauer, and M.J. Duncan, “Modeling the Diversity of Outer Planetary Systems.” Astronomical Journal, 116: 1998, 1998.
Representative terms from entire chapter: