Analytic constraints on gamma-ray burst luminosity functions

Details Analytic constraints on gamma-ray burst luminosity functions Analytic constraints on gamma-ray burst luminosity functions

Aug 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aipc..384..412h&link_type=abstract

Gamma-ray bursts: 3rd Huntsville symposium. AIP Conference Proceedings, Volume 384, pp. 412-416 (1996).

Mathematics

Logic

Gamma-Ray Sources, Gamma-Ray Bursts, Observational Cosmology

Scientific paper

The brightness distribution of detected gamma-ray bursts enables constraints to be placed on their luminosities; specifically, analyses by previous authors have demonstrated that the range of luminosity from which approximately 90% of the observed bursts are drawn is very likely less than an order of magnitude. It has also been demonstrated that when power-law functional forms with infinite ranges of luminosity (a.) from 0 to Lmax or (b.) from Lmin to ∞ are employed, it is necessary (but perhaps not sufficient) to restrict the power-law index β<1.8 and β>2.5, respectively, in order to obtain consistency with the observed brightness distribution. Similarly, these previous works have demonstrated that when 1.8<β<2.5, the range of the burst luminosity function must be restricted and cannot be arbitrarily large. We present here analytic derivations of these results valid for any spatial density function and for both Euclidean and cosmological scenarios. This analysis shows that the limiting values of β are simply the maximum and minimum absolute value logarithmic slopes of the brightness distribution. We also demonstrate that this result is consistent with those requiring a narrow range in luminosity for a majority of the detected bursts.

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