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

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.

Three-Dimensional Dynamics of Narrow Planetary Rings

Narrow planetary rings are eccentric and inclined. Particles within a given ring must therefore share the same pericenter and node. We solve for the three-dimensional geometries and mass distributions that enable the Uranian Alpha and Beta rings, and the Saturnian Maxwell and Colombo (Titan) rings, to maintain simultaneous apsidal and nodal lock. Ring self-gravity, interparticle collisions, and the quadrupole field of the host planet balance each other to achieve this equilibrium. We prove that such an equilibrium is linearly stable. Predictions for the Saturnian ringlets to be tested by the Cassini spacecraft include: (1) ringlet masses are of order 1e19 g, (2) surface mass densities should increase from ring midline to ring edges, and (3) rings are vertically warped such that the fractional variation of inclination across the ring is of order 10%. Analogous predictions are made for the Uranian rings. Simultaneous apsidal and nodal locking forces the narrowest portion of the ring--its ``pinch,'' where self-gravitational and collisional forces are strongest--to circulate relative to the node, and introduces previously unrecognized time-varying forces perpendicular to the planet's equator plane. We speculate that such periodic stressing might drive kilometer-scale bending waves at a frequency twice that of apsidal precession. Such flexing might be observed over a few weeks by Cassini.Comment: Final revised version, ApJ, in pres

Shifts of the nuclear resonance in the vortex lattice in YBa2_2Cu3_3O7_7

The NMR and NQR spectra of $^{63}$Cu in the CuO$_2$ plane of YBa$_2$Cu$_3$O$_7$ in the superconducting state are discussed in terms of the phenomenological theory of Ginzburg-Landau type extended to lower temperatures. We show that the observed spectra, Kumagai {\em et al.}, PRB {\bf 63}, 144502 (2001), can be explained by a standard theory of the Bernoulli potential with the charge transfer between CuO$_2$ planes and CuO chains assumed.Comment: 11 pages 7 figure

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

On the relation between entanglement and subsystem Hamiltonians

We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling range differs in both quantities and allow to investigate the effect.Comment: 7 pages, 2 figures version2: minor changes, typos correcte

Spatially Resolving the Inner Disk of TW Hya

We present Keck Interferometer observations of TW Hya that spatially resolve its emission at 2 micron wavelength. Analyzing these data together with existing K-band veiling and near-infrared photometric measurements, we conclude that the inner disk consists of optically thin, sub-micron-sized dust extending from ~4 AU to within 0.06 AU of the central star. The inner disk edge may be magnetospherically truncated. Even if we account for the presence of gas in the inner disk, these small dust grains have survival times against radiation blow-out that are orders of magnitude shorter than the age of the system, suggesting continual replenishment through collisions of larger bodies.Comment: 11 pages, including 2 figures. Accepted by ApJ

Why holes are not like electrons. II. The role of the electron-ion interaction

In recent work, we discussed the difference between electrons and holes in energy band in solids from a many-particle point of view, originating in the electron-electron interaction, and argued that it has fundamental consequences for superconductivity. Here we discuss the fact that there is also a fundamental difference between electrons and holes already at the single particle level, arising from the electron-ion interaction. The difference between electrons and holes due to this effect parallels the difference due to electron-electron interactions: {\it holes are more dressed than electrons}. We propose that superconductivity originates in 'undressing' of carriers from $both$ electron-electron and electron-ion interactions, and that both aspects of undressing have observable consequences.Comment: Continuation of Phys.Rev.B65, 184502 (2002) = cond-mat/0109385 (2001