Likelihood Analysis of Repeating in the BATSE Catalogue

I describe a new likelihood technique, based on counts-in-cells statistics, that I use to analyze repeating in the BATSE 1B and 2B catalogues. Using the 1B data, I find that repeating is preferred over non-repeating by 4.3:1 odds, with a well-defined peak at 5-6 repetitions per source. I find that the post-1B data are consistent with the repeating model inferred from the 1B data, after taking into account the lower fraction of bursts with well-determined positions. Combining the two data sets, I find that the odds favoring repeating over non-repeating are almost unaffected at 4:1, with a narrower peak at 5 repetitions per source. I conclude that the data sets are consistent both with each other and with repeating, and that for these data sets the odds favor repeating.Comment: 5 pages including 3 encapsulated figures, as a uuencoded, gzipped, Postscript file. To appear in Proc. of the 1995 La Jolla workshop ``High Velocity Neutron Stars and Gamma-Ray Bursts'' eds. Rothschild, R. et al., AIP, New Yor

A New Measure of the Clustering of QSO Heavy-Element Absorption-Line Systems

We examine the line-of-sight clustering of QSO heavy-element absorption-line systems, using a new measure of clustering, called the reduced second moment measure, that directly measures the mean over-density of absorbers. While closely related to other second-order measures such as the correlation function or the power spectrum, this measure has a number of distinct statistical properties which make possible a continuous exploration of clustering as a function of scale. From a sample of 352 C IV absorbers with median redshift 2.2, drawn from the spectra of 274 QSOs, we find that the absorbers are strongly clustered on scales from 1 to 20 Mpc. Furthermore, there appears to be a sharp break at 20 Mpc, with significant clustering on scales up to 100 Mpc in excess of that which would be expected from a smooth transition to homogeneity. There is no evidence of clustering on scales greater than 100 Mpc. These results suggest that strong C IV absorbers along a line of sight are indicators of clusters and possibly superclusters, a relationship that is supported by recent observations of ``Lyman break'' galaxies.Comment: 13 pages (LaTex, uses aaspp4.sty and psfig.sty), with 3 encapsulated PostScript figures. To appear in The Astrophysical Journal. Extended new discussion of the statistical properties of the reduced second moment measure, and a new figure highlighting the excess clustering on comoving scales greater than 20 Mp

Are The Four Gamma-Ray Bursts of 1996 October 27-29 Due to Repetition of a Single Source?

BATSE, Ulysses, and TGRS and KONUS on WIND detected four gamma-ray events within 1.8 days during 1996 October 27-29, consistent with coming from the same location on the sky. We assess the evidence that these events may be due to a series of bursts from a single source by calculating the probability that such a clustering in position and in time of occurrence might happen by chance. The calculation of this probability is afflicted by the usual problem of a posteriori statistics. We introduce a clustering statistic, which is formed from the "minimum circle radius" (i.e. the radius of the smallest circle that just encloses the positions of all the events) and the minimum time lapse (i.e. the time elapsed between the first and last event). We also introduce a second clustering statistic, which is formed from the "cluster likelihood function" and the minimum time lapse. We show that the use of these statistics largely eliminates the "a posteriori" nature of the problem. The two statistics yield significances of the clustering of $3.3\times 10^{-4}$ and $3.1\times 10^{-5}$, respectively, if we interpret the four events as four bursts, whereas the clustering is not significant if we interpret the four events as only three bursts. However, in the latter case one of the bursts is the longest ever observed by BATSE.Comment: 5 pages, 1 PostScript figure. Uses AIP conference proceedings LaTeX macros. To appear in the Proceedings of the Fourth Huntsville Gamma-Ray Burst Symposiu

Gravitational Lensing and the Hubble Deep Field

We calculate the expected number of multiply-imaged galaxies in the Hubble Deep Field (HDF), using photometric redshift information for galaxies with m_I < 27 that were detected in all four HDF passbands. A comparison of these expectations with the observed number of strongly lensed galaxies constrains the current value of Omega_m-Omega_Lambda, where Omega_m is the mean mass density of the universe and Omega_Lambda is the normalized cosmological constant. Based on current estimates of the HDF luminosity function and associated uncertainties in individual parameters, our 95% confidence lower limit on Omega_m-Omega_Lambda ranges between -0.44, if there are no strongly lensed galaxies in the HDF, and -0.73, if there are two strongly lensed galaxies in the HDF. If the only lensed galaxy in the HDF is the one presently viable candidate, then, in a flat universe (Omega_m+Omega_Lambda=1), Omega_Lambda < 0.79 (95% C.L.). These limits are compatible with estimates based on high-redshift supernovae and with previous limits based on gravitational lensing.Comment: 4 pages (aipproc.sty), 2 figures. To appear in "After the dark ages: when galaxies were young," proceedings of the 9th Annual October Astrophysics Conference, eds. S. S. Holt & E. P. Smit

Match Probability Statistics and Gamma Ray Burst Recurrences in the BATSE Catalog

We develop match probability statistics to test the recurrences of gamma ray bursts in the BATSE catalog 1B and 2B. We do not find a signal of repetitions at the match level of 1.e-3.Comment: 4 pages, LaTeX, two macros included (kluwer.sty, spacekap.sty) To appear in the proceedings of the Eslab29 symposium, ``gamma ray bursts: toward the source

Non-divergence of gravitational self-interactions for Goto-Nambu strings

The classical linearised gravitational self interaction of a Goto-Nambu string is examined in four spacetime dimensions. Using a conveniently gauge independent tensorial treatment, the divergent part of the self-force is shown to be exactly zero. This is due to cancelation by a contribution that was neglected in the previous treatments. This result has implications for many applications.Comment: 7 Pages. Final version to be published in Phys. Lett. B