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 model independent lower limit on the number of Gamma Ray Burst hosts from repeater statistics

We present a general statistical analysis of Gamma Ray Bursts embedded in a host population. If no host generates more than one observed burst, then we show that there is a model independent lower bound on the number of hosts, $H$, of the form $H > c B^2$, where B is the number of observed bursts, and $c$ is a constant of order one which depends on the confidence level (CL) attached to the bound. An analysis by Tegmark et al. (1996) shows that the BATSE 3B catalog of 1122 bursts is consistent with no repeaters being present, and assuming that this is indeed the case, our result implies a host population with at least H=1.2x10^6 members. Without the explicit assumption of no repeaters, a Bayesian analysis based on the results of Tegmark et al. (1996) can be performed which gives the weaker bound of $H>1.7\times 10^5$ at the 90% CL. In the light of the non-detection of identifiable hosts in the small error-boxes associated with transient counterparts to GRBs, this result gives a model independent lower bound to the number of any rare or exotic hosts. If in fact GRBs are found to be associated with a particular sub-class of galaxies, then an analysis along the lines presented here can be used to place a lower bound on the fraction of galaxies in this sub-class. Another possibility is to treat galaxy clusters (rather than individual galaxies) as the host population, provided that the angular size of each cluster considered is less than the resolution of the detector. Finally, if repeaters are ever detected in a statistically significant manner, this analysis can be readily adapted to find upper and lower limits on $H$.Comment: 9 pages (LaTex, aaspp4.sty); revised version includes a detailed discussion of limits which can be set using present BATSE data; to be published in ApJ Letter

Wiggly Relativistic Strings

We derive the equations of motion for general strings, i.e. strings with arbitrary relation between tension $\tau$ and energy per unit length $\epsilon$. The renormalization of $\tau$ and $\epsilon$ that results from averaging out small scale wiggles on the string is obtained in the general case to lowest order in the amount of wiggliness. For Nambu-Goto strings we find deviations from the equation of state $\epsilon \tau = {\rm constant}$ in higher orders. Finally we argue that wiggliness may radically modify the gauge cosmic string scenario.Comment: 10 pages, LaTeX, UFIFT-HEP-92-1

Optical/Near-Infrared Observations of GRO J1744-28

We present results from a series of optical (g and r-band) and near-infrared (K'-band) observations of the region of the sky including the entire XTE and ROSAT error circles for the ``Bursting Pulsar'' GRO J1744-28. These data were taken with the Astrophysical Research Consortium's 3.5-m telescope at Apache Point Observatory and with the 2.2-m telescope at the European Southern Observatory. We see no new object, nor any significant brightening of any known object, in these error circles, with the exception of an object detected in our 8 February 1996 image. This object has already been proposed as a near-infrared counterpart to GRO J1744-28. While it is seen in only two of our ten 8 February frames, there is no evidence that this is an instrumental artifact, suggesting the possibility of near-infrared flares from GRO J1744-28, similar to those that have been reported from the Rapid Burster. The distance to the ``Bursting Pulsar'' must be more than 2 kpc, and we suggest that it is more than 7 kpc.Comment: 21 pages, 5 JPEG plates, 2 postscript figures. This paper will appear in the May 1, 1997 edition of the Astrophysical Journa

Constraints on Cosmic Strings due to Black Holes Formed from Collapsed Cosmic String Loops

The cosmological features of primordial black holes formed from collapsed cosmic string loops are studied. Observational restrictions on a population of primordial black holes are used to restrict $f$, the fraction of cosmic string loops which collapse to form black holes, and $\mu$, the cosmic string mass-per-unit-length. Using a realistic model of cosmic strings, we find the strongest restriction on the parameters $f$ and $\mu$ is due to the energy density in $100 MeV$ photons radiated by the black holes. We also find that inert black hole remnants cannot serve as the dark matter. If earlier, crude estimates of $f$ are reliable, our results severely restrict $\mu$, and therefore limit the viability of the cosmic string large-scale structure scenario.Comment: (Plain Tex, uses tables.tex -- wrapped lines corrected), 11 pages, FERMILAB-Pub-93/137-

Evolution of cosmic string configurations

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: $\xi$, related to the overall string density, $\bar\xi$, the persistence length along the string, and $\zeta$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$ initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.Comment: 61 pages, requires RevTex v3.0, SUSSEX-TH-93/3-4, IMPERIAL/TP/92-93/4