A Collisional Family in the Classical Kuiper Belt

The dynamical evolution of Classical Kuiper Belt Objects (CKBOs) divides into two parts, according to the secular theory of test particle orbits. The first part is a forced oscillation driven by the planets, while the second part is a free oscillation whose amplitude is determined by the initial orbit of the test particle. We extract the free orbital inclinations and free orbital eccentricities from the osculating elements of 125 known CKBOs. The free inclinations of 32 CKBOs strongly cluster about 2 degrees at orbital semi-major axes between 44 and 45 AU. We propose that these objects comprise a collisional family, the first so identified in the Kuiper Belt. Members of this family are plausibly the fragments of an ancient parent body having a minimum diameter of \~800 km. This body was disrupted upon colliding with a comparably sized object, and generated ejecta having similar free inclinations. Our candidate family is dynamically akin to a sub-family of Koronis asteroids located at semi-major axes less than 2.91 AU; both families exhibit a wider range in free eccentricity than in free inclination, implying that the relative velocity between parent and projectile prior to impact lay mostly in the invariable plane of the solar system. We urge more discoveries of new CKBOs to test the reality of our candidate family and physical studies of candidate family members to probe the heretofore unseen interior of a massive, primitive planetesimal.Comment: final revised version, accepted to ApJ Letters, includes minor caveat regarding Koronis asteroid famil

Eccentricity Excitation and Apsidal Resonance Capture in the Planetary System Upsilon Andromedae

The orbits of the outer two known planets orbiting Upsilon Andromedae are remarkably eccentric. Planet C possesses an orbital eccentricity of e1 = 0.253. For the more distant planet D, e2 = 0.308. Previous dynamical analyses strongly suggest that the two orbits are nearly co-planar and are trapped in an apsidal resonance in which the difference between their longitudes of periastron undergoes a bounded oscillation about 0 degrees. Here we elucidate the origin of these large eccentricities and of the apsidal alignment. Resonant interactions between a remnant circumstellar disk of gas lying exterior to the orbits of both planets can smoothly grow e2. Secular interactions between planets D and C can siphon off the eccentricity of the former to grow that of the latter. Externally amplifying e2 during the phase of the apsidal oscillation when e2/e1 is smallest drives the oscillation amplitude towards zero. Thus, the substantial eccentricity of planet C and the locking of orbital apsides are both consequences of externally pumping the eccentricity of planet D over timescales exceeding apsidal precession periods of order 1e4 yr. We explain why the recently detected stellar companion to Upsilon Andromedae is largely dynamically decoupled from the planetary system.Comment: accepted to Ap

Spectral Energy Distributions of Passive T Tauri Disks: Inclination

We compute spectral energy distributions (SEDs) for passive T Tauri disks viewed at arbitrary inclinations. Semi-analytic models of disks in radiative and hydrostatic equilibrium are employed. Over viewing angles for which the flared disk does not occult the central star, the SED varies negligibly with inclination. For such aspects, the SED shortward of ~80 microns is particularly insensitive to orientation, since short wavelength disk emission is dominated by superheated surface layers which are optically thin. The SED of a nearly edge-on disk is that of a class I source. The outer disk occults inner disk regions, and emission shortward of ~30 microns is dramatically extinguished. Spectral features from dust grains may appear in absorption. However, millimeter wavelength fluxes decrease by at most a factor of 2 from face-on to edge-on orientations. We present illustrative applications of our SED models. The class I source 04108+2803B is considered a T Tauri star hidden from view by an inclined circumstellar disk. Fits to its observed SED yield model-dependent values for the disk mass of ~0.015 solar masses and a disk inclination of ~65 degrees relative to face-on. The class II source GM Aur represents a T Tauri star unobscured by its circumstellar disk. Fitted parameters include a disk mass of \~0.050 solar masses and an inclination of ~60 degrees.Comment: Accepted to ApJ, 20 pages, 7 figures, aaspp4.st

On the Plutinos and Twotinos of the Kuiper Belt

We illuminate dynamical properties of Kuiper Belt Objects (KBOs) in the 3:2 (``Plutino'') and 2:1 (``Twotino'') Neptunian resonances within the model of resonant capture and migration. We analyze a series of numerical integrations, each involving the 4 migratory giant planets and 400 test particles distributed throughout trans-Neptunian space, to measure efficiencies of capture as functions of migration speed. Snapshots of the spatial distribution of resonant KBOs reveal that Twotinos cluster +/- 75 degrees away from Neptune's longitude, while Plutinos cluster +/- 90 degrees away. Longitudinal clustering persists even for surveys that are not volume-limited in their ability to detect resonant KBOs. Remarkably, between -90 degrees and -60 degrees of Neptune's longitude, we find the sky density of Twotinos to nearly equal that of Plutinos, despite the greater average distance of Twotinos. We couple our findings to observations to crudely estimate that the intrinsic Twotino population is within a factor of 3 of the Plutino population. Most strikingly, the migration model predicts that more Twotinos may lie at longitudes behind that of Neptune than ahead of it. The magnitude of the asymmetry amplifies dramatically with faster rates of migration and can be as large as 300%. A differential measurement of the sky density of 2:1 resonant objects behind of and in front of Neptune's longitude would powerfully constrain the migration history of that planet.Comment: AJ, in press, to appear in December 2002 issue. For version with higher resolution figures, see http://astron.berkeley.edu/~echiang/ppp/ppp.htm

Excitation of Orbital Eccentricities by Repeated Resonance Crossings: Requirements

Divergent migration of planets within a viscous circumstellar disk can engender resonance crossings and dramatic excitation of orbital eccentricities. We provide quantitative criteria for the viability of this mechanism. For the orbits of two bodies to diverge, a ring of viscous material must be shepherded between them. As the ring diffuses in radius by virtue of its intrinsic viscosity, the two planets are wedged further apart. The ring mass must be smaller than the planetary masses so that the crossing of an individual resonance lasts longer than the resonant libration period. At the same time, the crossing cannot be of such long duration that the disk's direct influence on the bodies' eccentricities interferes with the resonant interaction between the two planets. This last criterion is robustly satisfied because resonant widths are typically tiny fractions of the orbital radius. We evaluate our criteria not only for giant planets within gaseous protoplanetary disks, but also for shepherd moons that bracket narrow planetary rings in the solar system. A shepherded ring of gas orbiting at a distance of 1 AU from a solar-type star and having a surface density of less than 500 g/cm^2, a dimensionless alpha viscosity of 0.1, and a height-to-radius aspect ratio of 0.05 can drive two Jovian-mass planets through the 2:1 and higher-order resonances so that their eccentricities amplify to values of several tenths. Because of the requirement that the disk mass in the vicinity of the planets be smaller than the planet masses, divergent resonance crossings may figure significantly into the orbital evolution of planets during the later stages of disk evolution, including the debris disk phase.Comment: ApJ, in press, to appear in February 2003 issu

Keck Pencil-Beam Survey for Faint Kuiper Belt Objects

We present the results of a pencil-beam survey of the Kuiper Belt using the Keck 10-m telescope. A single 0.01 square degree field is imaged 29 times for a total integration time of 4.8 hr. Combining exposures in software allows the detection of Kuiper Belt Objects (KBOs) having visual magnitude V < 27.9. Two new KBOs are discovered. One object having V = 25.5 lies at a probable heliocentric distance d = 33 AU. The second object at V = 27.2 is located at d = 44 AU. Both KBOs have diameters of about 50 km, assuming comet-like albedos of 4%. Data from all surveys are pooled to construct the luminosity function from red magnitude R = 20 to 27. The cumulative number of objects per square degree, N (< R), is fitted to a power law of the form log_(10) N = 0.52 (R - 23.5). Differences between power laws reported in the literature are due mainly to which survey data are incorporated, and not to the method of fitting. The luminosity function is consistent with a power-law size distribution for objects having diameters s = 50 to 500 km; dn ~ s^(-q) ds, where the differential size index q = 3.6 +/- 0.1. The distribution is such that the smallest objects possess most of the surface area, but the largest bodies contain the bulk of the mass. Though our inferred size index nearly matches that derived by Dohnanyi (1969), it is unknown whether catastrophic collisions are responsible for shaping the size distribution. Implications of the absence of detections of classical KBOs beyond 50 AU are discussed.Comment: Accepted to AJ. Final proof-edited version: references added, discussion of G98 revised in sections 4.3 and 5.

ISO LWS Spectra of T Tauri and Herbig AeBe stars

We present an analysis of ISO-LWS spectra of eight T Tauri and Herbig AeBe young stellar objects. Some of the objects are in the embedded phase of star-formation, whereas others have cleared their environs but are still surrounded by a circumstellar disk. Fine-structure lines of [OI] and [CII] are most likely excited by far-ultraviolet photons in the circumstellar environment rather than high-velocity outflows, based on comparisons of observed line strengths with predictions of photon-dominated and shock chemistry models. A subset of our stars and their ISO spectra are adequately explained by models constructed by Chiang & Goldreich (1997) and Chiang et al. (2001) of isolated, passively heated, flared circumstellar disks. For these sources, the bulk of the LWS flux at wavelengths longward of 55 µm arises from the disk interior which is heated diffusively by reprocessed radiation from the disk surface. At 45 µm, water ice emission bands appear in spectra of two of the coolest stars, and are thought to arise from icy grains irradiated by central starlight in optically thin disk surface layers

Hitting Time of Quantum Walks with Perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.Comment: 9 page