The Formation of Ice Giants in a Packed Oligarchy: Instability and Aftermath

As many as 5 ice giants--Neptune-mass planets composed of 90% ice and rock and 10% hydrogen--are thought to form at heliocentric distances of 10-25 AU on closely packed orbits spaced ~5 Hill radii apart. Such oligarchies are ultimately unstable. Once the parent disk of planetesimals is sufficiently depleted, oligarchs perturb one another onto crossing orbits. We explore both the onset and the outcome of the instability through numerical integrations, including dynamical friction cooling of planets by a planetesimal disk whose properties are held fixed. To trigger instability and the ejection of the first ice giant in systems having an original surface density in oligarchs of Sigma ~ 1 g/cm^2, the disk surface density s must fall below 0.1 g/cm^2. Ejections are predominantly by Jupiter and occur within 10 Myr. To eject more than 1 oligarch requires s < 0.03 g/cm^2. Systems starting with up to 4 oligarchs in addition to Jupiter and Saturn can readily yield solar-system-like outcomes in which 2 surviving ice giants lie inside 30 AU and have their orbits circularized by dynamical friction. Our numerical simulations support the idea that planetary systems begin in more crowded and compact configurations, like those of shear-dominated oligarchies. In contrast to previous studies, we identify s < 0.1 Sigma as the regime relevant for understanding the evolution of the outer solar system, and we encourage future studies to concentrate on this regime while relaxing our assumption of a fixed planetesimal disk.Comment: Accepted to ApJ Jan 27. Incorporates comments from the referee and community at large. 15 pages, 14 figures, including 7 colo

Formation of Narrow Dust Rings in Circumstellar Debris Disks

Narrow dust rings observed around some young stars (e.g., HR 4796A) need to be confined. We present a possible explanation for the formation and confinement of such rings in optically thin circumstellar disks, without invoking shepherding planets. If an enhancement of dust grains (e.g., due to a catastrophic collision) occurs somewhere in the disk, photoelectric emission from the grains can heat the gas to temperatures well above that of the dust. The gas orbits with super(sub)-Keplerian speeds inward (outward) of the associated pressure maximum. This tends to concentrate the grains into a narrow region. The rise in dust density leads to further heating and a stronger concentration of grains. A narrow dust ring forms as a result of this instability. We show that this mechanism not only operates around early-type stars that have high UV fluxes, but also around stars with spectral types as late as K. This implies that this process is generic and may have occurred during the lifetime of each circumstellar disk. We examine the stringent upper-limit on the H2 column density in the HR 4796A disk and find it to be compatible with the presence of a significant amount of hydrogen gas in the disk. We also compute the OI and CII infrared line fluxes expected from various debris disks and show that these will be easily detectable by the upcoming Herschel mission. Herschel will be instrumental in detecting and characterizing gas in these disks.Comment: Accepted for publication in ApJ; 14 pages, 7 figure

Neptune's Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations

Nbody simulations are used to examine the consequences of Neptune's outward migration into the Kuiper Belt, with the simulated endstates being compared rigorously and quantitatively to the observations. These simulations confirm the findings of Chiang et al. (2003), who showed that Neptune's migration into a previously stirred-up Kuiper Belt can account for the Kuiper Belt Objects (KBOs) known to librate at Neptune's 5:2 resonance. We also find that capture is possible at many other weak, high-order mean motion resonances, such as the 11:6, 13:7, 13:6, 9:4, 7:3, 12:5, 8:3, 3:1, 7:2, and the 4:1. The more distant of these resonances, such as the 9:4, 7:3, 5:2, and the 3:1, can also capture particles in stable, eccentric orbits beyond 50 AU, in the region of phase space conventionally known as the Scattered Disk. Indeed, 90% of the simulated particles that persist over the age of the Solar System in the so-called Scattered Disk zone never had a close encounter with Neptune, but instead were promoted into these eccentric orbits by Neptune's resonances during the migration epoch. This indicates that the observed Scattered Disk might not be so scattered. This model also produced only a handful of Centaurs, all of which originated at Neptune's mean motion resonances in the Kuiper Belt. We also report estimates of the abundances and masses of the Belt's various subpopulations (e.g., the resonant KBOs, the Main Belt, and the so-called Scattered Disk), and also provide upper limits on the abundance of Centaurs and Neptune's Trojans, as well as upper limits on the sizes and abundances of hypothetical KBOs that might inhabit the a>50 AU zone.Comment: 60 pages, 16 figures. Accepted for publication in the Astronomical Journa

On the Submillimeter Opacity of Protoplanetary Disks

Solid particles with the composition of interstellar dust and power-law size distribution dn/da propto a^{-p} for a 3 lambda and 3 < p < 4 will have submm opacity spectral index beta(lambda) = dln(kappa)/dln(nu) approx (p-3) beta_{ism}, where beta_{ism} approx 1.7 is the opacity spectral index of interstellar dust material in the Rayleigh limit. For the power-law index p approx 3.5 that characterizes interstellar dust, and that appears likely for particles growing by agglomeration in protoplanetary disks, grain growth to sizes a > 3 mm will result in beta(1 mm) < ~1. Grain growth can naturally account for beta approx 1 observed for protoplanetary disks, provided that a_{max} > ~ 3 lambda.Comment: Submitted to ApJ. 17 pages, 6 figure

The Size Distribution of Kuiper Belt Objects

We describe analytical and numerical collisional evolution calculations for the size distribution of icy bodies in the Kuiper Belt. For a wide range of bulk properties, initial masses, and orbital parameters, our results yield power-law cumulative size distributions, N_C propto r^{-q}, with q_L = 3.5 for large bodies with radii of 10-100 km, and q_s = 2.5-3 for small bodies with radii lesss than 0.1-1 km. The transition between the two power laws occurs at a break radius of 1-30 km. The break radius is more sensitive to the initial mass in the Kuiper Belt and the amount of stirring by Neptune than the bulk properties of individual Kuiper Belt objects (KBOs). Comparisons with observations indicate that most models can explain the observed sky surface density of KBOs for red magnitudes, R = 22-27. For R 28, the model surface density is sensitive to the amount of stirring by Neptune, suggesting that the size distribution of icy planets in the outer solar system provides independent constraints on the formation of Neptune.Comment: 24 pages of text, 12 figures; to appear in the Astronomical Journal, October 200

Prospects for Detection of Catastrophic Collisions in Debris Disks

We investigate the prospects for detecting dust from two body collisions during the late stages of planet formation at 1-150 AU. We develop an analytic model to describe the formation of a dusty cloud of debris and use numerical coagulation and n-body calculations to predict observable signals from these events. In a minimum mass solar nebula, collisions of 100-1000 km objects at distances of 3-5 AU or less from the parent star are observable at mid-infrared wavelengths as bright clumps or rings of dust. At 24 microns, the clumps are roughly 0.1-1 mag brighter than emission from dust in the background debris disk. In edge-on systems, dusty clumps produce eclipses with depths of 1.0 mag or less that last for roughly 100 orbital periods. Large-scale surveys for transits from exosolar planets, such as Kepler, can plausibly detect these eclipses and provide important constraints on the terrestrial environment for ages of less than or roughly 100-300 Myr.Comment: Astronomical Journal, in press; 23 pages of text, 11 figures, and 1 tabl

The Size Distribution of Trans-Neptunian Bodies

[Condensed] We search 0.02 deg^2 for trans-Neptunian objects (TNOs) with m<=29.2 (diameter ~15 km) using the ACS on HST. Three new objects are discovered, roughly 25 times fewer than expected from extrapolation of the differential sky density Sigma(m) of brighter objects. The ACS and other recent TNO surveys show departures from a power law size distribution. Division of the TNO sample into ``classical Kuiper belt'' (CKB) and ``Excited'' samples reveals that Sigma(m) differs for the two populations at 96% confidence. A double power law adequately fits all data. Implications include: The total mass of the CKB is ~0.010 M_Earth, only a few times Pluto's mass, and is predominately in the form of ~100 km bodies. The mass of Excited objects is perhaps a few times larger. The Excited class has a shallower bright-end size distribution; the largest objects, including Pluto, comprise tens of percent of the total mass whereas the largest CKBOs are only ~2% of its mass. The predicted mass of the largest Excited body is close to the Pluto mass; the largest CKBO is ~60 times less massive. The deficit of small TNOs occurs for sizes subject to disruption by present-day collisions, suggesting extensive depletion by collisions. Both accretion and erosion appearing to have proceeded to more advanced stages in the Excited class than the CKB. The absence of distant TNOs implies that any distant (60 AU) population must have less than the CKB mass in the form of objects 40 km or larger. The CKB population is sparser than theoretical estimates of the required precursor population for short period comets, but the Excited population could be a viable precursor population.Comment: Revised version accepted to the Astronomical Journal. Numerical results are very slightly revised. Implications for the origins of short-period comets are substantially revised, and tedious material on statistical tests has been collected into a new Appendi

Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth of icy planets in the outer regions of a planetesimal disk. In a quiescent minimum mass solar nebula, icy planets grow to sizes of 1000--3000 km on a timescale t = 15-20 Myr (a/30 AU)^3 where a is the distance from the central star. Planets form faster in more massive nebulae. Newly-formed planets stir up leftover planetesimals along their orbits and produce a collisional cascade where icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in beta Pic, HR 4796A, and other debris disks. We derive dust masses for small particles, 1 mm and smaller, and large particles, 1 mm and larger, as a function of the initial conditions in the planetesimal disk. The dust luminosities derived from these masses are similar to those observed in Vega, HR 4796A, and other debris disks. The calculations produce bright rings and dark gaps. Bright rings occur where 1000 km and larger planets have recently formed. Dark gaps are regions where planets have cleared out dust or shadows where planets have yet to form.Comment: to be published in the Astronomical Journal, January 2004; 7 pages of text; 17 figures at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-figures.pdf; 2 animations at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-movies.htm

Accretion in the Early Kuiper Belt II. Fragmentation

We describe new planetesimal accretion calculations in the Kuiper Belt that include fragmentation and velocity evolution. All models produce two power law cumulative size distributions, N_C propto r^{-q}, with q = 2.5 for radii less than 0.3-3 km and q = 3 for radii exceeding 1-3 km. The power law indices are nearly independent of the initial mass in the annulus, the initial eccentricity of the planetesimal swarm, and the initial size distribution of the planetesimal swarm. The transition between the two power laws moves to larger radii as the initial eccentricity increases. The maximum size of objects depends on their intrinsic tensile strength; Pluto formation requires a strength exceeding 300 erg per gram. Our models yield formation timescales for Pluto-sized objects of 30-40 Myr for a minimum mass solar nebula. The production of several `Plutos' and more than 10^5 50 km radius Kuiper Belt objects leaves most of the initial mass in 0.1-10 km radius objects that can be collisionally depleted over the age of the solar system. These results resolve the puzzle of large Kuiper Belt objects in a small mass Kuiper Belt.Comment: to appear in the Astronomical Journal (July 1999); 54 pages including 7 tables and 13 figure

Radial Distribution of Dust Grains Around HR 4796A

We present high-dynamic-range images of circumstellar dust around HR 4796A that were obtained with MIRLIN at the Keck II telescope at lambda = 7.9, 10.3, 12.5 and 24.5 um. We also present a new continuum measurement at 350 um obtained at the Caltech Submillimeter Observatory. Emission is resolved in Keck images at 12.5 and 24.5 um with PSF FWHM's of 0.37" and 0.55", respectively, and confirms the presence of an outer ring centered at 70 AU. Unresolved excess infrared emission is also detected at the stellar position and must originate well within 13 AU of the star. A model of dust emission fit to flux densities at 12.5, 20.8, and 24.5 um indicates dust grains are located 4(+3/-2) AU from the star with effective size, 28+/-6 um, and an associated temperature of 260+/-40 K. We simulate all extant data with a simple model of exozodiacal dust and an outer exo-Kuiper ring. A two-component outer ring is necessary to fit both Keck thermal infrared and HST scattered-light images. Bayesian parameter estimates yield a total cross-sectional area of 0.055 AU^2 for grains roughly 4 AU from the star and an outer-dust disk composed of a narrow large-grain ring embedded within a wider ring of smaller grains. The narrow ring is 14+/-1 AU wide with inner radius 66+/-1 AU and total cross-sectional area 245 AU^2. The outer ring is 80+/-15 AU wide with inner radius 45+/-5 AU and total cross-sectional area 90 AU^2. Dust grains in the narrow ring are about 10 times larger and have lower albedos than those in the wider ring. These properties are consistent with a picture in which radiation pressure dominates the dispersal of an exo-Kuiper belt.Comment: Accepted by Astrophysical Journal (Part1) on September 9, 2004. 13 pages, 10 figures, 2 table