Secular Instability and Planetesimal Formation in the Dust Layer

Late in the gaseous phase of a protostellar disk, centimeter-sized bodies probably settle into a thin ``dust layer'' at the midplane. A velocity difference between the dust layer and the gas gives rise to turbulence, which prevents further settling and direct gravitational instability of the layer. The associated drag on the surface of the layer causes orbital decay in a few thousand years---as opposed to a few hundred years for an isolated meter-sized body. Within this widely-accepted theoretical framework, we show that the turbulent drag causes radial instabilities even if the selfgravity of the layer is negligible. We formulate axisymmetric, height-integrated dynamical equations for the layer that incorporate turbulent diffusion of mass and momentum in radius and height, vertical settling, selfgravity, and resistance to compression due to gas entrained within the dust layer. In steady-state, the equations describe the inward radial drift of a uniform dust layer. In perturbation, overdense rings form on an orbital timescale with widths comparable to the dust-layer thickness. Selfgravity is almost irrelevant to the linear growth rate but will eventually fragment and collapse the rings into planetesimals larger than a kilometer. We estimate that the drag instability is most efficient at 1 AU when most of the ``dust'' mass lies in the size range 0.1-10 meters.Comment: 25 pp., 2 figures. Uses aastex version 5.0

The growth of deactivated layers on CsI(Na) scintillating crystals

An effective and sensitive measurement of the depth of a deactivated or dead layer can be obtained from the relative attenuation of the 22.162 KeV and 87.9 KeV X-rays emitted by Cd 109. The alpha-particles emitted by Am 241 are also useful in measuring dead layers less than 25 microns. The properties and temporal development of dead layers are discussed in detail. The rate of growth of a deal layer is closely related to the ambient humidity, and the damage to the crystal is irreversible by any known process. The dead layer can be minimized by polishing all crystal surfaces and by keeping the crystal in a vacuum or a dry atmosphere. Since a dead layer seriously inhibits the response of a crystal to X-rays of energies below approximately 20 keV, CsI(Na) detectors should not be used at these energies unless precautions are taken to ensure that no dead layer forms

Scintillation Caustics in Planetary Occultation Light Curves

We revisit the GSC5249-01240 light curve obtained during its occultation by Saturn's North polar region. In addition to refractive scintillations, the power spectrum of intensity fluctuations shows an enhancement of power between refractive and diffractive regimes. We identify this excess power as due to high amplitude spikes in the light curve and suggest that these spikes are due to caustics associated with ray crossing situations. The flux variation in individual spikes follows the expected caustic behavior, including diffraction fringes which we have observed for the first time in a planetary occultation light curve. The presence of caustics in scintillation light curves require an inner scale cut off to the power spectrum of underlying density fluctuations associated with turbulence. Another possibility is the presence of gravity waves in the atmosphere. While occultation light curves previously showed the existence of refractive scintillations, a combination of small projected stellar size and a low relative velocity during the event have allowed us to identify caustics in this occultation. This has led us to re-examine previous data sets, in which we have also found likely examples of caustics.Comment: 4 pages, 3 figures; ApJL submitte

A geometric approach to high resolution TVD schemes

A geometric approach, similar to Van Leer's MUSCL schemes, is used to construct a second-order accurate generalization of Godunov's method for solving scalar conservation laws. By making suitable approximations, a scheme is obtained which is easy to implement and total variation diminishing. The entropy condition is also investigated from the standpoint of the spreading of rarefaction waves. Quantitative information is obtained for Godunov's method on the rate of spreading which explain the kinks in rarefaction waves often observed at the sonic point

Correlations and fluctuations of a confined electron gas

The grand potential $\Omega$ and the response $R = - \partial \Omega /\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\mu$ or external parameter $x$. We compute their autocorrelation as a function of $\mu$, $x$ and temperature. The result is related to the short-time dynamics of the corresponding classical system, implying in general the absence of a universal regime. Chaotic, diffusive and integrable motions are investigated, and illustrated numerically. The autocorrelation of the persistent current of a disordered mesoscopic ring is also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.

Interstellar Scintillations of Polarization of Compact Sources

We demostrate that the measurement of fluctuations of polarization due to the galactic interstellar scintillations may be used to study the structure of the radiation field at compact radio sources. We develop a mathematical formalism and demonstrate it on a simple analytical model in which the scale of the polarization variation through the source is comparable to the source size. The predicted amplitude of modulation of the polarized radiation flux is ~20% x (pi_s) x (m_sc), where (pi_s) is the characteristic degree of polarization of radiation at the source and (m_sc) is the typical modulation index due to scattering, i.e., (m_sc)~1 for diffractive scintillations and (m_sc)<1 for refractive scintillations.Comment: 5 pages, 2 figures, emilateapj.sty. Submitted to ApJ