The brightest events in a time series of cosmological transients obey an observation time dependence which is often overlooked. This dependence can be exploited to probe the global properties of electromagnetic and gravitational wave transients (Howe
ll et al. 2007a, Coward & Burman 2005). We describe a new relation based on a peak flux--observation time distribution and show that it is invariant to the luminosity distribution of the sources (Howell et al. 2007b). Applying this relation, in combination with a new data analysis filter, to emph{Swift} gamma-ray burst data, we demonstrate that it can constrain their rate density.
Using pulsewidth data for 872 isolated radio pulsars we test the hypothesis that pulsars evolve through a progressive narrowing of the emission cone combined with progressive alignment of the spin and magnetic axes. The new data provide strong eviden
ce for the alignment over a time-scale of about 1 Myr with a log standard deviation of around 0.8 across the observed population. This time-scale is shorter than the time-scale of about 10 Myr found by previous authors, but the log standard deviation is larger. The results are inconsistent with models based on magnetic field decay alone or monotonic counter-alignment to orthogonal rotation. The best fits are obtained for a braking index parameter n_gamma approximately equal to 2.3, consistent the mean of the six measured values, but based on a much larger sample of young pulsars. The least-squares fitted models are used to predict the mean inclination angle between the spin and magnetic axes as a function of log characteristic age. Comparing these predictions to existing estimates it is found that the model in which pulsars are born with a random angle of inclination gives the best fit to the data. Plots of the mean beaming fraction as a function of characteristic age are presented using the best-fitting model parameters.
We compare the detection rates and redshift distributions of low-luminosity (LL) GRBs localized by Swift with those expected to be observed by the new generation satellite detectors on GLAST (now Fermi) and, in future, EXIST. Although the GLAST burst
telescope will be less sensitive than Swifts in the 15--150 keV band, its large field-of-view implies that it will double Swifts detection rate of LL bursts. We show that Swift, GLAST and EXIST should detect about 1, 2 & 30 LL GRBs, respectively, over a 5-year operational period. The burst telescope on EXIST should detect LL GRBs at a rate of more than an order of magnitude greater than that of Swifts BAT. We show that the detection horizon for LL GRBs will be extended from $z simeq 0.4$ for Swift to $z simeq 1.1$ in the EXIST era. Also, the contribution of LL bursts to the observed GRB redshift distribution will contribute to an identifiable feature in the distribution at $z simeq 1$.
In the redshift range z = 0-1, the gamma ray burst (GRB) redshift distribution should increase rapidly because of increasing differential volume sizes and strong evolution in the star formation rate. This feature is not observed in the Swift redshift
distribution and to account for this discrepancy, a dominant bias, independent of the Swift sensitivity, is required. Furthermore, despite rapid localization, about 40-50% of Swift and pre-Swift GRBs do not have a measured redshift. We employ a heuristic technique to extract this redshift bias using 66 GRBs localized by Swift with redshifts determined from absorption or emission spectroscopy. For the Swift and HETE+BeppoSAX redshift distributions, the best model fit to the bias in z < 1 implies that if GRB rate evolution follows the SFR, the bias cancels this rate increase. We find that the same bias is affecting both Swift and HETE+BeppoSAX measurements similarly in z < 1. Using a bias model constrained at a 98% KS probability, we find that 72% of GRBs in z < 2 will not have measurable redshifts and about 55% in z > 2. To achieve this high KS probability requires increasing the GRB rate density in small z compared to the high-z rate. This provides further evidence for a low-luminosity population of GRBs that are observed in only a small volume because of their faintness.
It has been shown that the observed temporal distribution of transient events in the cosmos can be used to constrain their rate density. Here we show that the peak flux--observation time relation takes the form of a power law that is invariant to the
luminosity distribution of the sources, and that the method can be greatly improved by invoking time reversal invariance and the temporal cosmological principle. We demonstrate how the method can be used to constrain distributions of transient events, by applying it to Swift gamma-ray burst data and show that the peak flux--observation time relation is in good agreement with recent estimates of source parameters. We additionally show that the intrinsic time dependence allows the method to be used as a predictive tool. Within the next year of Swift observation, we find a 50% chance of obtaining a peak flux greater than that of GRB 060017 -- the highest Swift peak flux to date -- and the same probability of detecting a burst with peak flux > 100 photons s^{-1} cm^{-2} within 6 years.
