Positional Coincidence between the High-latitude Steady Unidentified Gamma-ray Sources and Possibly Merging Clusters of Galaxies

We report an evidence for the first time that merging clusters of galaxies are a promising candidate for the origin of high galactic-latitude, steady unidentified EGRET gamma-ray sources. Instead of using past optical catalogs of eye-selected clusters, we made a matched-filter survey of galaxy clusters over 4\arcdeg \times 4\arcdeg areas around seven steady unidentified EGRET sources at |b|>45\arcdeg together with a 100 \sq \arcdeg area near the South Galactic Pole as a control field. In total, 154 Abell-like cluster candidates and 18 close pairs/groups of these clusters, expected to be possibly merging clusters, were identified within estimated redshift $z_{est}\leq 0.15$. Five among the seven EGRET sources have one or two cluster pairs/groups (CPGs) within 1\arcdeg from them. We assess the statistical significance of this result by several methods, and the confidence level of the real excess is maximally 99.8% and 97.8% in a conservative method. In contrast, we found no significant correlation with single clusters. In addition to the spatial correlation, we also found that the richness of CPGs associated with EGRET sources is considerably larger than those of CPGs in the control field. These results imply that a part of the steady unidentified EGRET sources at high-latitude are physically associated with close CPGs, not with single clusters. We also discuss possible interpretations of these results. We argue that, if these associations are real, they are difficult to explain by hadronic processes, but best explained by the inverse-Compton scattering by high energy electrons accelerated in shocks of cluster formation, as recently proposed.Comment: 9 pages, 2 PostScript figures, uses emulateapj5.sty, added new analysis and discussion, ApJ accepte

Efficient solar cells by space processing

Thin films of electron beam evaporated silicon were deposited on molybdenum, tantalum, tungsten and molybdenum disilicide under ultrahigh vacuum conditions. Mass spectra from a quadrapole residual gas analyzer were used to determine the partial pressure of 13 residual gases during each processing step. Surface contamination and interdiffusion were monitored by in situ Auger electron spectrometry. The presence of phosphorus in the silicon was responsible for attaining elevated temperatures with silicide formations. Heteroepitaxial silicon growth was sensitive to the presence of oxygen during deposition, the rate and length of deposition as well as the substrate orientation

Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

Quasar Clustering and the Lifetime of Quasars

Although the population of luminous quasars rises and falls over a period of 10^9 years, the typical lifetime of individual quasars is uncertain by several orders of magnitude. We show that quasar clustering measurements can substantially narrow the range of possible lifetimes with the assumption that luminous quasars reside in the most massive host halos. If quasars are long-lived, then they are rare phenomena that are highly biased with respect to the underlying dark matter, while if they are short-lived they reside in more typical halos that are less strongly clustered. For a given quasar lifetime, we calculate the minimum host halo mass by matching the observed space density of quasars, using the Press-Schechter approximation. We use the results of Mo & White to calculate the clustering of these halos, and hence of the quasars they contain, as a function of quasar lifetime. A lifetime of t_Q = 4 x 10^7 years, the e-folding timescale of an Eddington luminosity black hole with accretion efficiency eps=0.1, corresponds to a quasar correlation length r_0 ~ 10 Mpc/h in low-density cosmological models at z=2-3; this value is consistent with current clustering measurements, but these have large uncertainties. High-precision clustering measurements from the 2dF and Sloan quasar surveys will test our key assumption of a tight correlation between quasar luminosity and host halo mass, and if this assumption holds then they should determine t_Q to a factor of three or better. An accurate determination of the quasar lifetime will show whether supermassive black holes acquire most of their mass during high-luminosity accretion, and it will show whether the black holes in the nuclei of typical nearby galaxies were once the central engines of high-luminosity quasars.Comment: ApJ Accepted (Feb 2001). 30 pages, 8 embedded ps figures, AASTEX5. Added discussion of quasar luminosity evolution. Also available at http://www.ociw.edu/~martini/pubs

Interacting Boson Theory of the Magnetization Process of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain

The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are approximated by the $\delta$ function boson gas for which the Bethe ansatz solution is available. The finite temperature properties are calculated by solving the integral equation numerically. The comparison is made with Monte Carlo calculation and the limit of the applicability of the present approximation is discussed.Comment: 4 pages, 7 figure

Principal forms X^2 + nY^2 representing many integers

In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X^2+nY^2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.Comment: 10 pages, title has been changed, Sections 2 and 3 are new, to appear in Abh. Math. Sem. Univ. Hambur