Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties

This is the third in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the physical properties of a class of solutions to the Einstein equations for disks with constant angular velocity and constant relative density which was constructed in the first part. The metric for these spacetimes is given in terms of theta functions on a Riemann surface of genus 2. It is parameterized by two physical parameters, the central redshift and the relative density of the two counter-rotating streams in the disk. We discuss the dependence of the metric on these parameters using a combination of analytical and numerical methods. Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the static limit which gives a solution of the Morgan and Morgan class and the limit of a disk without counter-rotation. We study the mass and the angular momentum of the spacetime. At the disk we discuss the energy-momentum tensor, i.e. the angular velocities of the dust streams and the energy density of the disk. The solutions have ergospheres in strongly relativistic situations. The ultrarelativistic limit of the solution in which the central redshift diverges is discussed in detail: In the case of two counter-rotating dust components in the disk, the solutions describe a disk with diverging central density but finite mass. In the case of a disk made up of one component, the exterior of the disks can be interpreted as the extreme Kerr solution.Comment: 30 pages, 20 figures; to appear in Phys. Rev.

Quantum theory of large amplitude collective motion and the Born-Oppenheimer method

We study the quantum foundations of a theory of large amplitude collective motion for a Hamiltonian expressed in terms of canonical variables. In previous work the separation into slow and fast (collective and non-collective) variables was carried out without the explicit intervention of the Born Oppenheimer approach. The addition of the Born Oppenheimer assumption not only provides support for the results found previously in leading approximation, but also facilitates an extension of the theory to include an approximate description of the fast variables and their interaction with the slow ones. Among other corrections, one encounters the Berry vector and scalar potential. The formalism is illustrated with the aid of some simple examples, where the potentials in question are actually evaluated and where the accuracy of the Born Oppenheimer approximation is tested. Variational formulations of both Hamiltonian and Lagrangian type are described for the equations of motion for the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf styl

How Protostellar Outflows Help Massive Stars Form

We consider the effects of an outflow on radiation escaping from the infalling envelope around a massive protostar. Using numerical radiative transfer calculations, we show that outflows with properties comparable to those observed around massive stars lead to significant anisotropy in the stellar radiation field, which greatly reduces the radiation pressure experienced by gas in the infalling envelope. This means that radiation pressure is a much less significant barrier to massive star formation than has previously been thought.Comment: 4 pages, 2 figures, emulateapj, accepted for publication in ApJ Letter

Calculation of the properties of the rotational bands of 155,157^{155,157}Gd

We reexamine the long-standing problem of the microscopic derivation of a particle-core coupling model. We base our research on the Klein-Kerman approach, as amended by D\"onau and Frauendorf. We describe the formalism to calculate energy spectra and transition strengths in some detail. We apply our formalism to the rotational nuclei $^{155,157}$Gd, where recent experimental data requires an explanation. We find no clear evidence of a need for Coriolis attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st

Molecular Line Emission from Massive Protostellar Disks: Predictions for ALMA and the EVLA

We compute the molecular line emission of massive protostellar disks by solving the equation of radiative transfer through the cores and disks produced by the recent radiation-hydrodynamic simulations of Krumholz, Klein, & McKee. We find that in several representative lines the disks show brightness temperatures of hundreds of Kelvin over velocity channels ~10 km s^-1 wide, extending over regions hundreds of AU in size. We process the computed intensities to model the performance of next-generation radio and submillimeter telescopes. Our calculations show that observations using facilities such as the EVLA and ALMA should be able to detect massive protostellar disks and measure their rotation curves, at least in the nearest massive star-forming regions. They should also detect significant sub-structure and non-axisymmetry in the disks, and in some cases may be able to detect star-disk velocity offsets of a few km s^-1, both of which are the result of strong gravitational instability in massive disks. We use our simulations to explore the strengths and weaknesses of different observational techniques, and we also discuss how observations of massive protostellar disks may be used to distinguish between alternative models of massive star formation.Comment: 15 pages, 9 figures, emulateapj format, accepted for publication in ApJ. Resolution of figures severely degraded to fit within size limits. Download the full paper from http://www.astro.princeton.edu/~krumholz/recent.htm

Pixel classification for automated diabetic foot diagnosis

Worldwide, more than 180 million people suffer from diabetes mellitus. Approximately 50% of these patients will develop complications to their feet. Neuropathy, combined with poor blood supply and biomechanical changes results in a high risk for foot ulcers, which is a key problem in the diabetic foot; when these wounds become infected, this can ultimately result in lower extremity amputation, which has a serious effect on the quality of life of the patient, and causes a large economic burden on society.\ud \ud This was the motivation for a collaborate project (Vincent50) in which a photographic foot imaging device was developed. The system allows scanning of the foot soles on a daily basis which may lead to early recognition of foot problems. The goal of the present study is to determine whether pixel classification is a useful intermediate step towards automatically assessing the images of the foot soles for signs of diabetic foot disease. If successful, this approach will further relief health care professionals in assessing the foot and enable the placement of more devices in the future. \ud \ud The best agreement between automated recognition and expert diagnosis was achieved with a combination of RGB and derived features, proves that the RGB data is informative with respect to detection of ulcers. However, the automatic detection of pre-signs of ulcers and other anomalies needs more sophistication than pixel classification alone. Firstly, other physical features, such as hyperspectral data, infrared and/or textural features are expected to be more informative. Secondly, we expect to be able to boost the performance by using the context between neighboring pixels. Thirdly, an individualized and normalized classification process might help with the large variability in foot soles between individuals. \u

Exact Criterion for Determining Clustering vs. Reentrant Melting Behavior for Bounded Interaction Potentials

We examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials which do not diverge at the origin, are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity. By employing a mean field-density functional theory which is shown to become exact at high temperatures and/or densities, we establish a criterion which determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature.Comment: 5 pages, 3 figures, submitted to PRL on March 29, 2000 New version: 10 pages, 9 figures, forwarded to PRE on October 16, 200

Foundations of self-consistent particle-rotor models and of self-consistent cranking models

The Kerman-Klein formulation of the equations of motion for a nuclear shell model and its associated variational principle are reviewed briefly. It is then applied to the derivation of the self-consistent particle-rotor model and of the self-consistent cranking model, for both axially symmetric and triaxial nuclei. Two derivations of the particle-rotor model are given. One of these is of a form that lends itself to an expansion of the result in powers of the ratio of single-particle angular momentum to collective angular momentum, that is essentual to reach the cranking limit. The derivation also requires a distinct, angular-momentum violating, step. The structure of the result implies the possibility of tilted-axis cranking for the axial case and full three-dimensional cranking for the triaxial one. The final equations remain number conserving. In an appendix, the Kerman-Klein method is developed in more detail, and the outlines of several algorithms for obtaining solutions of the associated non-linear formalism are suggested.Comment: 29 page

Detection of OD towards the low-mass protostar IRAS16293-2422

Although water is an essential and widespread molecule in star-forming regions, its chemical formation pathways are still not very well constrained. Observing the level of deuterium fractionation of OH, a radical involved in the water chemical network, is a promising way to infer its chemical origin. We aim at understanding the formation mechanisms of water by investigating the origin of its deuterium fractionation. This can be achieved by observing the abundance of OD towards the low-mass protostar IRAS16293-2422, where the HDO distribution is already known. Using the GREAT receiver on board SOFIA, we observed the ground-state OD transition at 1391.5 GHz towards the low-mass protostar IRAS16293-2422. We also present the detection of the HDO 111-000 line using the APEX telescope. We compare the OD/HDO abundance ratio inferred from these observations with the predictions of chemical models. The OD line is detected in absorption towards the source continuum. This is the first detection of OD outside the solar system. The SOFIA observation, coupled to the observation of the HDO 111-000 line, provides an estimate of the abundance ratio OD/HDO ~ 17-90 in the gas where the absorption takes place. This value is fairly high compared with model predictions. This may be reconciled if reprocessing in the gas by means of the dissociative recombination of H2DO+ further fractionates OH with respect to water. The present observation demonstrates the capability of the SOFIA/GREAT instrument to detect the ground transition of OD towards star-forming regions in a frequency range that was not accessible before. Dissociative recombination of H2DO+ may play an important role in setting a high OD abundance. Measuring the branching ratios of this reaction in the laboratory will be of great value for chemical models.Comment: 6 pages, 6 figures, 3 tables, accepted for publication in A&A SOFIA/GREAT special issu

Exact relativistic treatment of stationary counter-rotating dust disks I: Boundary value problems and solutions

This is the first in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which describe counter-rotating disks of dust. These disks can serve as models for certain galaxies and accretion disks in astrophysics. We review the Newtonian theory for disks using Riemann-Hilbert methods which can be extended to some extent to the relativistic case where they lead to modular functions on Riemann surfaces. In the case of compact surfaces these are Korotkin's finite gap solutions which we will discuss in this paper. On the axis we establish for general genus relations between the metric functions and hence the multipoles which are enforced by the underlying hyperelliptic Riemann surface. Generalizing these results to the whole spacetime we are able in principle to study the classes of boundary value problems which can be solved on a given Riemann surface. We investigate the cases of genus 1 and 2 of the Riemann surface in detail and construct the explicit solution for a family of disks with constant angular velocity and constant relative energy density which was announced in a previous Physical Review Letter.Comment: 32 pages, 1 figure, to appear in Phys. Rev.