Local Lagrangian Approximations for the Evolution of the Density Distribution Function in Large-Scale Structure

We examine local Lagrangian approximations for the gravitational evolution of the density distribution function. In these approximations, the final density at a Lagrangian point q at a time t is taken to be a function only of t and of the initial density at the same Lagrangian point. A general expression is given for the evolved density distribution function for such approximations, and we show that the vertex generating function for a local Lagrangian mapping applied to an initially Gaussian density field bears a simple relation to the mapping itself. Using this result, we design a local Lagrangian mapping which reproduces nearly exactly the hierarchical amplitudes given by perturbation theory for gravitational evolution. When extended to smoothed density fields and applied to Gaussian initial conditions, this mapping produces a final density distribution function in excellent agreement with full numerical simulations of gravitational clustering. We also examine the application of these local Lagrangian approximations to non-Gaussian initial conditions.Comment: LaTeX, 22 pages, and 11 postscript figure

Cogenerating and Pre-annihilating Dark Matter by a New Gauge Interaction in a Unified Model

Grand unified theories based on large groups (with rank greater or equal to 6 are a natural context for dark matter models. They contain Standard-Model-singlet fermions that could be dark matter candidates, and can contain new non-abelian interactions whose sphalerons convert baryons, leptons, and dark matter into each other, "cogenerating" a dark matter asymmetry comparable to the baryon asymmetry. In this paper it is shown that the same non-abelian interactions can "pre-annihilate" the symmetric component of heavy dark matter particles, which then decay late into light stable dark matter particles that inherit their asymmetry. It is shown that such decays can come from d=5 operators that are Planck or GUT suppressed. We derive constraints on such models and present a simple realization based on the group SU(7).Comment: 14 pages, a fully unified model presented in much greater detai

Radiation can never again dominate Matter in a Vacuum Dominated Universe

We demonstrate that in a vacuum-energy-dominated expansion phase, surprisingly neither the decay of matter nor matter-antimatter annihilation into relativistic particles can ever cause radiation to once again dominate over matter in the future history of the universe.Comment: updated version, as it will appear in Phys. Rev D. Title change, and some other minor alteration

The rotation of the Sun: Observations at Stanford

Daily observations of the photospheric rotation rate using the Doppler effect made at the Stanford Solar Observatory since May 1976 are analyzed. Results show that these observations show no daily or long period variations in the rotation rate that exceed the observational error of about one percent. The average rotation rate is the same as that of the sunspot and the large-scale magnetic field structures

Annual and solar-magnetic-cycle variations in the interplanetary magnetic field, 1926-1971

The analysis of forty-five years of inferred interplanetary magnetic field polarity shows an annual variation and a variation of about twenty years, associated here with the solar magnetic cycle. On the average the phase of the annual variation of the interplanetary field changes about 2 and 2/3 years after sunspot maximum, i.e. for about ten consecutive years the predominant polarity of the interplanetary field is away from the sun during the six-month interval in which the earth is at southern heliographic latitudes. Then a change of phase occurs so that for about the next ten years the predominant polarity is toward the sun, while the earth is at southern heliographic latitudes. The annual variation changes its predominant polarity within a few days of the times when the heliographic latitude of the earth is zero

A physical mechanism for the prediction of the sunspot number during solar cycle 21

On physical grounds it is suggested that the sun's polar field strength near a solar minimum is closely related to the following cycle's solar activity. Four methods of estimating the sun's polar magnetic field strength near solar minimum are employed to provide an estimate of cycle 21's yearly mean sunspot number at solar maximum of 140 plus or minus 20. This estimate is considered to be a first order attempt to predict the cycle's activity using one parameter of physical importance

The equatorial rotation velocity of the photosphere is measured to be the same as sunspots

The equatorial rotation rate of the photosphere was measured at effect data. It was found that scattered light has a large influence and must be taken into account properly. When this was done it was found that the rotation rate from Doppler shifts agreed very well with the rate found for sunspots. Short-term fluctuations in rotation rate (i.e. from day to day) were less than plus or minus 15 m/s and were thus within observational errors