Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites

We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15R_J for Jupiter and rCS ∼ 22R_S for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (R_H), which we choose to be ∼R_H/5 (located at ∼150 R_J near the inner irregular satellites for Jupiter, and ∼200R_S near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼10⁶ years, Iapetus in 10⁶-10⁷ years, Ganymede in 10³-10⁴ years, and Titan in 10⁴-10⁵ years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100R_J. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH₃ present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H₂O as well as other issues that may help to test our model.     

Merging of low-mass systems and the origin of the fundamental plane

We present the preliminary results of a study of how small stellar systems merge to form larger ones. As we display the families of galaxies in the μ_e - R_e plane (effective surface brightness versus effective radius) we realize that different morphological types occupy different loci, evidencing the different physical mechanisms operating in each family. As proposed by Capaccioli et al. (1992) this diagram is the logical equivalent of the HR diagram for stars. Here we take some initial steps in understanding of how we can establish the evolutionary tracks, solely due to dynamical processes, in the μ_e - R_e plane, ultimately making a dwarf elliptical to turn into a normal elliptical galaxy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Formation and cooling of the giant HXIS arches of November 6–7, 1980

Giant arches, first detected by the HXIS instrument aboard SMM, are still a poorly understood component of the flare scenario. Their origin remains uncertain and their behavior, quite different in separate events, has not yet been satisfactorily explained. The purpose of the present paper is to analyze the giant arches imaged on November 6–7, 1980, which, in contrast to that observed on May 21, 1980, were not stationary and had shorter cooling times. In particular, we use a procedure, already applied to the May 21 case, to compute the three-dimensional topology of the magnetic field which forms by reconnection over the active region containing the November arches. This technique allows us to verify that the observed structures are aligned with the computed field lines, lending support to the hypothesis that they originate through a reconnection process which occurs at progressively larger altitudes. Moreover, a calculation of the magnetic energy liberated by reconnection shows that enough energy may be thereby released to account for the observed thermal energy enhancement of the HXIS arches. Finally, the lifetime of the features is shown to be consistent with that predicted by cooling via radiation and field-aligned conduction to the underlying chromosphere.     

An introduction to Maslov's asymptotic method

Summary. Familiar concepts such as asymptotic ray theory and geometrical spreading are now recognized as an asymptotic form of a more general asymptotic solution to the non-separable wave equation. In seismology, the name Maslov asymptotic theory has been attached to this solution. In its simplest form, it may be thought of as a justification of disc-ray theory and it can be reduced to the WKBJ seismogram. It is a uniformly valid asymptotic solution, though. The method involves properties of the wavefronts and ray paths of the wave equation which have been established for over a century. The integral operators which build on these properties have been investigated only comparatively recently. These operators are introduced very simply by appealing to the asymptotic Fourier transform of Ziolkowski & Deschamps. This leads quite naturally to the result that phase functions in different domains of the spatial Fourier transform are related by a Legendre transformation. The amplitude transformation can also be inferred by this method. Liouville's theorem (the incompressibility of a phase space of position and slowness) ensures that it is always possible to obtain a uniformly asymptotic solution. This theorem can be derived by methods familiar to seismologists and which do not rely on the traditional formalism of classical mechanics. It can also be derived from the sympletic property of the equations of geometrical spreading and canonical transformations in general. The symplectic property plays a central role in the theory of high-frequency beams in inhomogeneous media.     

Magnetohydrodynamic flow of a non-Newtonian fluid past a porous plate

This article studies the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The Laplace transform technique has been employed to solve the basic differential equations. The solutions of the velocity profile and skin-friction are obtained and the effects of the visco-elastic parameter, the magnetic field and the time parameter on the fluid flow have been studied in several tables.     

AN EVALUATION OF SAS/GRAPH SOFTWARE FOR COMPUTER CARTOGRAPHY1

The SAS® computer software system, widely used and respected for its capabilities in statistical analysis and data base management, now includes a new set of graphic and cartographic procedures called SAS GRAPH?. We have used these cartographic procedures in research on mapping ethno-cultural census data from metropolitan areas in Ontario and in undergraduate and graduate courses in computer cartography. On the basis of that experience, we describe and evaluate SAS/GRAPH'S cartographic capabilities and illustrate with maps drawn by various devices.     

Electron microscopy study of the iron meteorite Santa Catharina

Abstract— Characterization of the microstructural features of the metal of the Santa Catharina meteorite was performed using a variety of electron optical techniques. Sample USNM#6293 is chemically homogeneous on the micron scale and has a Ni content of 28.2 wt.%. Its microstructure is similar to that of the Twin City ataxite and contains clear taenite II, i.e., fcc taenite with domains of tetrataenite, < 10 nm in size. Sample USNM#3043 is a more typical Santa Catharina specimen with dark and light regions as observed with the light optical microscope. The dark regions are inhomogeneous and contain 45–50 wt.% Ni and 7–12 wt.% O. The light regions are homogeneous and contain 35 wt.% Ni and no detectable oxygen. The microstructure is that of cloudy zone, i.e., islands of tetrataenite, ～20 nm in size, in a honeycomb matrix. The honeycomb phase contains Ni rich oxide in the dark regions and contains metal, fcc taenite, in the light regions. The original metal structure of USNM#3043 is cloudy zone which formed during cooling into the low temperature miscibility gap of the Fe-Ni phase diagram. The dark regions were developed from the metal by selective corrosion of the honeycomb structure, transforming it into Ni containing oxides, possibly non-stoichiometric Fe₂NiO₄ while retaining the tetrataenite islands. Using the results of this study, many of the existing discrepancies concerning the microstructure of Santa Catharina can be explained.