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James M. Gelb

Publications and source records attributed to James M. Gelb.

10 recordsLinked to original sources
arXiv2000

Relativistic electrons on a rotating spherical magnetic dipole: surface orbitals

The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy, canonical azimuthal angular momentum, and magnetic field strength. Magnetic flux enclosed by orbits is quantized very close to the poles, suggesting a quantum Hall-like state. Application of this system to neutron star surfaces is outlined. The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy, canonical azimuthal angular momentum, and magnetic field strength. Magnetic flux enclosed by orbits is quantized very close to the poles, suggesting a quantum Hall-like state. Application of this system to neutron star surfaces is outlined.

astro-ph↗
arXiv2000

Relativistic electrons in a rotating spherical magnetic dipole: localized three-dimensional states

Paralleling a previous paper, we examine single- and many-body states of relativistic electrons in an intense, rotating magnetic dipole field. Single-body orbitals are derived semiclassically and then applied to the many-body case via the Thomas-Fermi approximation. The many-body case is reminiscent of the quantum Hall state. Electrons in a realistic neutron star crust are considered with both fixed density profiles and constant Fermi energy. In the first case, applicable to young neutron star crusts, the varying magnetic field and relativistic Coriolis correction lead to a varying Fermi energy and macroscopic currents. In the second, relevant to older crusts, the electron density is redistributed by the magnetic field.

astro-ph↗
arXiv2000

A Mass Matrix for Atmospheric, Solar, and LSND Neutrino Oscillations

We construct a mass matrix for the four neutrino flavors, three active and one sterile, needed to fit oscillations in all three neutrino experiments: atmospheric, solar, and LSND, simultaneously. It organizes the neutrinos into two doublets whose central values are about 1 eV apart, and whose splittings are of the order of 10^(-3) eV. Atmospheric neutrino oscillations are described as maximal mixing within the upper doublet, and solar as the same within the lower doublet. Then LSND is a weak transition from one doublet to the other. We comment on the Majorana versus Dirac nature of the active neutrinos and show that our mass matrix can be derived from an S_2 x S_2 permutation symmetry plus an equal splitting rule.

hep-ph↗
arXiv1999

Comment on the broadening of the $^7$Be neutrino line in vacuum oscillation solutions of the solar neutrino

We consider the effect of thermal broadening of the $^7$Be neutrino on vacuum oscillation solutions of the solar neutrino problem and analyze the conditions under which the electron-neutrino survival probability must be averaged over neutrino energy. For "just-so" solutions with $Δm^2$ of order $5 \times 10^{-11}~{\rm eV}^2$ averaging is not necessary, but for much larger values, it is. We analyze the effective broadening due to the extended production region in the Sun and find similar results. We also comment on the possibility of seasonal variations of the $^7$Be neutrino signal.

hep-ph↗
arXiv1999

Another Look at Just-So Solar Neutrino Oscillations

We take another look at ``Just-So'' solar neutrino oscillations, characterizing them by the energy $E_{π/2}$ at which the distance-varying angle is $π/2$, instead of the usual $Δm^2$. The rising spectrum recently observed by SuperKamiokande is consistent with $E_{π/2}\sim$ 6-9 MeV and marginally with 48 MeV. The pp neutrinos must then be reduced to one-half the standard solar model prediction, and $^7$Be neutrinos must make up a significant part of the SAGE and GALLEX gallium signal. For $E_{π/2}$ close to 9 and 48 MeV, the $^7$Be neutrinos will also show a large seasonal variation, emphasizing the importance of direct measurements of the $^7$Be neutrinos.

hep-ph↗
arXiv1996

Searching for the MSW Enhancement

We point out that the length scale associated with the MSW effect is the radius of the Earth. Therefore to verify matter enhancement of neutrino oscillations, it will be necessary to study neutrinos passing through the Earth. For the parameters of MSW solutions to the solar neutrino problem, the only detectable effects occur in a narrow band of energies from 5 to 10 MeV. We propose that serious consideration be given to mounting an experiment at a location within 9.5 degrees of the equator.

hep-ph↗
arXiv1994

Cold Dark Matter I: The Formation of Dark Halos

We use numerical simulations of critically-closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to $256^3$ particles using the particle-mesh (PM) method and with up to $144^3$ particles using the adaptive particle-particle --particle-mesh (P$^3$M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all $Ω=1$ CDM models for linear amplitude $σ_8\gsim 0.5$ because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low mass halos. The distribution of halos characterized by their circular velocities for the P$^3$M simulations is in reasonable agreement with the observations for $150\kms\lsim V_{\rm circ} \lsim 350\kms$.}}

astro-ph↗
arXiv1994

Cold Dark Matter II: Spatial and Velocity Statistics

We examine high-resolution gravitational N-body simulations of the $Ω=1$ cold dark matter (CDM) model in order to determine whether there is any normalization of the initial density fluctuation spectrum that yields acceptable results for galaxy clustering and velocities. Dense dark matter halos in the evolved mass distribution are identified with luminous galaxies; the most massive halos are also considered as sites for galaxy groups, with a range of possibilities explored for the group mass to light ratios. We verify the earlier conclusions of White et al. (1987) for the low amplitude (high bias) CDM model --- the galaxy correlation function is marginally acceptable but that there are too many galaxies. We also show that the peak biasing method does not accurately reproduce the results obtained using dense halos identified in the simulations themselves. The COBE anisotropy implies a higher normalization, resulting in problems with excessive pairwise galaxy velocity dispersion unless a strong velocity bias is present. Although we confirm the strong velocity bias of halos reported by Couchman \& Carlberg (1992), we show that the galaxy motions are still too large on small scales. We find no amplitude for which the CDM model can reconcile simultaneously the galaxy correlation function, the low pairwise velocity dispersion, and the richness distribution of groups and clusters. With the normalization implied by COBE, the CDM spectrum has too much power on small scales if $Ω=1$.

astro-ph↗
arXiv1993

Evolution of One-Point Distributions from Gaussian Initial Fluctuations

We study the quasilinear evolution of the one-point probability density functions (PDFs) of the smoothed density and velocity fields in a cosmological gravitating system beginning with Gaussian initial fluctuations. Our analytic results are based on the Zel'dovich approximation and laminar flow. A numerical analysis extends the results into the multistreaming regime using the smoothed fields of a CDM N-body simulation. We find that the PDF of velocity, both Lagrangian and Eulerian, remains Gaussian under the laminar Zel'dovich approximation, and it is almost indistinguishable from Gaussian in the simulations. The PDF of mass density deviates from a normal distribution early in the quasilinear regime and it develops a shape remarkably similar to a lognormal distribution with one parameter, the \rms density fluctuation $σ$. Applying these results to currently available data we find that the PDFs of the velocity and density fields, as recovered by the \pot\ procedure from observed velocities assuming $Ω=1$, or as deduced from a redshift survey of \iras\ galaxies assuming that galaxies trace mass, are consistent with Gaussian initial fluctuations.

astro-ph↗