Newtonian and Relativistic Cosmologies

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed, which allows for such nonlinearity at small scales. We propose a relatively straightforward "dictionary"---which is exact at the linearized level---that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our "ordering scheme" to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We find that Einstein's equation fails to hold at "order 1" at small scales and at "order $\epsilon$" at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein's equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.Comment: 35 pages; minor change

A. Philip Randolph and Boston\u27s African-American Railroad Worker

On October 8, 1988, a group of retired Pullman car porters and dining car waiters gathered in Boston\u27s Back Bay Station for the unveiling of a larger-than-life statue of A. Philip Randolph. During the 1920s and 1930s, Randolph was a pioneering black labor leader who led the Brotherhood of Sleeping Car Porters. He came to be considered the father of the modern civil rights movement as a result of his efforts to desegregate World War II defense jobs and the military services. Randolph\u27s importance as a militant leader is highlighted by a quote inscribed on the base of the statue which reads, in part: Freedom is never granted; it is won. Justice is never given; it is exacted

The X-ray Iron Emission from Tycho's Supernova Remnant

We present the results of broadband fits to the X-ray spectrum of Tycho's supernova remnant obtained by the Solid-State Imaging Spectrometers on the ASCA Observatory. We use single-temperature, single-ionization-age, nonequilibrium ionization models to characterize the ejecta and the blast-shocked interstellar medium. Based on the Fe K emission at 6.5 keV, previous spectral studies have suggested that the Fe ejecta in this Type Ia remnant are stratified interior to the other ejecta. The ASCA data provide important constraints from the Fe L emission near 1 keV as well as the Fe K emission. We find that the simplest models, with emission from the ejecta and blast wave each at a single temperature and ionization age, severely underestimate the Fe K flux. We show that there is little Fe emission associated with the Si and S ejecta shell. The blast-shocked interstellar medium has abundances roughly 0.3 times the solar value, while the ejecta, with the exception of Fe, have relative abundances that are typical of Type Ia supernovae. The addition of another component of Fe emission, which we associate with ejecta, at a temperature at least two times higher and an ionization age $\sim$ 100 times lower than the Si ejecta, does provide a good fit to the spectrum. This model is consistent with X-ray imaging results. Although fluorescent emission from dust in the remnant may contribute to the Fe K flux, we conclude that it is unlikely to dominate.Comment: 23 pages, LaTex; 4 postscript figures, 2 postscript tables. To appear in ApJ, vol 49