## Cosmological effects on the observed flux and fluence distributions of gamma-ray bursts: Are the most distant bursts in general the faintest ones?

^{1}
Charles University, Faculty of Mathematics and Physics,
Astronomical Institute, V Holešovičkách 2, 18000 Prague 8, Czech Republic

e-mail: meszaros@cesnet.cz, ripa@sirrah.troja.mff.cuni.cz

^{2}
Department of Physics, Royal Institute of Technology, AlbaNova
University Center, 10691
Stockholm,
Sweden

e-mail: felix@particle.kth.se

Received:
3
May
2010

Accepted:
19
January
2011

*Context.* Several claims have been put forward that an essential fraction
of long-duration BATSE gamma-ray bursts should lie at redshifts larger than 5. This
point-of-view follows from the natural assumption that fainter objects should, on average,
lie at larger redshifts. However, redshifts larger than 5 are rare for bursts observed by
Swift, seemingly contradicting the BATSE estimates.

*Aims.* The purpose of this article is to clarify this contradiction.

*Methods.* We derive the cosmological relationships between the observed
and emitted quantities, and we arrive at a prediction that can be tested on the ensembles
of bursts with determined redshifts. This analysis is independent on the assumed
cosmology, on the observational biases, as well as on any gamma-ray burst model. Four
different samples are studied: 8 BATSE bursts with redshifts, 13 bursts with derived
pseudo-redshifts, 134 Swift bursts with redshifts, and 6 *Fermi *bursts
with redshifts.

*Results.* The controversy can be explained by the fact that apparently
fainter bursts need not, in general, lie at large redshifts. Such a behaviour is possible,
when the luminosities (or emitted energies) in a sample of bursts increase more than the
dimming of the observed values with redshift. In such a case
d*P*(*z*)/d*z* > 0 can hold,
where *P*(*z*) is either the peak-flux or the fluence. All
four different samples of the long bursts suggest that this is really the case. This also
means that the hundreds of faint, long-duration BATSE bursts need not lie at high
redshifts, and that the observed redshift distribution of long Swift bursts might actually
represent the actual distribution.

Key words: gamma-ray burst: general / cosmology: miscellaneous

*© ESO, 2011*