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

Collisional Cascades in Planetesimal Disks I. Stellar Flybys

We use a new multiannulus planetesimal accretion code to investigate the evolution of a planetesimal disk following a moderately close encounter with a passing star. The calculations include fragmentation, gas and Poynting-Robertson drag, and velocity evolution from dynamical friction and viscous stirring. We assume that the stellar encounter increases planetesimal velocities to the shattering velocity, initiating a collisional cascade in the disk. During the early stages of our calculations, erosive collisions damp particle velocities and produce substantial amounts of dust. For a wide range of initial conditions and input parameters, the time evolution of the dust luminosity follows a simple relation, L_d/L_{\star} = L_0 / [alpha + (t/t_d)^{beta}]. The maximum dust luminosity L_0 and the damping time t_d depend on the disk mass, with L_0 proportional to M_d and t_d proportional to M_d^{-1}. For disks with dust masses of 1% to 100% of the `minimum mass solar nebula' (1--100 earth masses at 30--150 AU), our calculations yield t_d approx 1--10 Myr, alpha approx 1--2, beta = 1, and dust luminosities similar to the range observed in known `debris disk' systems, L_0 approx 10^{-3} to 10^{-5}. Less massive disks produce smaller dust luminosities and damp on longer timescales. Because encounters with field stars are rare, these results imply that moderately close stellar flybys cannot explain collisional cascades in debris disk systems with stellar ages of 100 Myr or longer.Comment: 33 pages of text, 12 figures, and an animation. The paper will appear in the March 2002 issue of the Astronmomical Journal. The animation and a copy of the paper with full resolution figures are at S. Kenyon's planet formation website: http://cfa-www.harvard.edu/~kenyon/p

Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence

Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive body precursors. This paper presents the main elements of this process of turbulent concentration. In the terrestrial planet region, both the characteristic size and size distribution of chondrules are explained. "Fluffier" particles would be concentrated in nebula regions which were at a lower gas density and/or more intensely turbulent. The spatial distribution of concentrated particle density obeys multifractal scaling}, suggesting a close tie to the turbulent cascade process. This scaling behavior allows predictions of the probability distributions for concentration in the protoplanetary nebula to be made. Large concentration factors (>10^5) are readily obtained, implying that numerous zones of particle density significantly exceeding the gas density could exist. If most of the available solids were actually in chondrule sized particles, the ensuing particle mass density would become so large that the feedback effects on gas turbulence due to mass loading could no longer be neglected. This paper describes the process, presenting its basic elements and some implications, without including the effects of mass loading.Comment: 34 pages, 7 figures; in press for Astrophys. J; expected Jan 01 2001 issu

Accretion in the Early Kuiper Belt I. Coagulation and Velocity Evolution

We describe planetesimal accretion calculations in the Kuiper Belt. Our evolution code simulates planetesimal growth in a single annulus and includes velocity evolution but not fragmentation. Test results match analytic solutions and duplicate previous simulations at 1 AU. In the Kuiper Belt, simulations without velocity evolution produce a single runaway body with a radius of 1000 km on a time scale inversely proportional to the initial mass in the annulus. Runaway growth occurs in 100 Myr for 10 earth masses and an initial eccentricity of 0.001 in a 6 AU annulus centered at 35 AU. This mass is close to the amount of dusty material expected in a minimum mass solar nebula extrapolated into the Kuiper Belt. Simulations with velocity evolution produce runaway growth on a wide range of time scales. Dynamical friction and viscous stirring increase particle velocities in models with large (8 km radius) initial bodies. This velocity increase delays runaway growth by a factor of two compared to models without velocity evolution. In contrast, collisional damping dominates over dynamical friction and viscous stirring in models with small (80--800 m radius) initial bodies. Collisional damping decreases the time scale to runaway growth by factors of 4--10 relative to constant velocity calculations. Simulations with minimum mass solar nebulae, 10 earth masses, reach runaway growth on time scales of 20-40 Myr with 80 m initial bodies, 50-100 Myr with 800 m bodies, and 75-250 Myr for 8 km initial bodies. These growth times vary linearly with the mass of the annulus but are less sensitive to the initial eccentricity than constant velocity models.Comment: 45 pages of text (including 5 tables), 31 pages of figur

Exotic smooth structures and symplectic forms on closed manifolds

We give a short proof of the (known) result that there are no Kaehler structures on exotic tori. This yields a negative solution to a problem posed by Benson and Gordon. W discuss the symplectic version of the problem and analyze results which yield an evidence for the conjecture that there are no symplectic structures on exotic tori.Comment: AMSLaTeX, 16 pages, a new version. A survey of the symplectic version of the problem is adde

Evidence for Companion-Induced Secular Changes in the Turbulent Disk of a Be Star in the LMC MACHO Database

The light curve of a blue variable in the MACHO LMC database (FTS ID 78.5979.72) appeared nearly unvarying for ~4 years (quasi-flat segment) but then rapidly changed to become periodic with noisy minima for the remaining 4 years (periodic segment); there are no antecedent indications of a gradual approach to this change. Lomb Periodogram analyses indicate the presence of two distinct periods of ~61 days and 8 days in both the quasi-flat and the periodic segments. Minima of the periodic segment cover at least 50% of the orbital period and contain spikes of light with the 8-day period; maxima do not show this short period. The system typically shows maxima to be redder than minima. The most recent OGLE-III light curve shows only a 30-day periodicity. The variable's V and R magnitudes and color are those of a Be star, and recent sets of near infrared spectra four days apart, secured during the time of the OGLE-III data, show H-alpha emission near and at a maximum, confirming its Be star characteristics. The model that best fits the photometric behavior consists of a thin ring-like circumstellar disk of low mass with four obscuring sectors orbiting the central B star in unison at the 61-day period. The central star peers through the three equi- spaced separations between the four sectors producing the 8-day period. The remainder of the disk contains hydrogen in emission making maxima appear redder. A companion star of lower mass in an inclined and highly eccentric orbit produces an impulsive perturbation near its periastron to change the disk's orientation, changing eclipses from partial to complete within ~ 10 days.Comment: 42 pages, 14 figures, and 2 tables Submitted to AJ v3: Title changed, figures added, model modifie

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Thermodynamics, Disequilibrium, Evolution: Far-From-Equilibrium Geological and Chemical Considerations for Origin-Of-Life Research

The authors wish to thank the Earth-Life Science Institute of the Tokyo Institute of Technology for supporting and hosting the TDE Focus Group meeting on which this publication is based. The Thermodynamics, Disequilibrium, Evolution (TDE) Focus Group is supported by the NASA Astrobiology Institute (NAI). Parts of this work were carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration; LMB and MJR are supported by NAI (Icy Worlds). ES thanks the ORIGINS COST Action (TD1308) for the STSM Reference Number: COST-STSM-TD1308-26973. ES is supported by Agreement ASI/INAF 2015 - 002 - R.O. JHEC acknowledges the financial support of the Spanish MINCINN project FIS2013-48444-C2-2-P

Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic

Detection of a transit of the super-Earth 55 Cnc e with Warm Spitzer

We report on the detection of a transit of the super-Earth 55 Cnc e with warm Spitzer in IRAC's 4.5-micron band. Our MCMC analysis includes an extensive modeling of the systematic effects affecting warm Spitzer photometry, and yields a transit depth of 410 +- 63 ppm, which translates to a planetary radius of 2.08 +- 0.16 R_Earth as measured in IRAC 4.5-micron channel. A planetary mass of 7.81 +- 0.58 M_Earth is derived from an extensive set of radial-velocity data, yielding a mean planetary density of 4.8 +- 1.3 g cm-3. Thanks to the brightness of its host star (V = 6, K = 4), 55 Cnc e is a unique target for the thorough characterization of a super-Earth orbiting around a solar-type star.Comment: Accepted for publication in A&A on 31 July 2011. 9 pages, 7 figures and 3 tables. Minor changes. The revised version includes a baseline models comparison and a new figure presenting the spatially- and time-dependent terms of the model function used in Eq.