Gamma-ray bursts and density evolution of neutron star binar

The evolution of the comoving cosmic merger-rate density of neutron star binaries n_c(z) is calculated using a distribution of their merging times provided by population-synthesis computations of binary stars. We adopt an exponential law for the star forma

A&Amanuscriptno.

(willbeinsertedbyhandlater)

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991 ebF 9 1v4902089/hp-ortsa:viXra1.Introduction

Therecentdiscoveriesofopticalcounterpartsoftheγ-rayburstsGRB970228(Grootetal.1997)andGRB970508(Bond1997)andthemeasuredemission-lineredshiftofz=0.853(Metzgeretal.1997)forthelatterprovideev-idencefortheircosmologicalorigin.Apossiblesourceforγ-raybursts(GRBs)maybethemergingoftwoneutronstarsinaclosebinary(Blinnikovetal.1984).

Forcosmologieswithnovacuumenergy,thebright-nessdistributionofburstintensitiesexpectedforauni-formsourcepopulationisconsistentwiththeBATSEdis-tributionifthelimitingredshiftisaboutunity(e.g.Der-mer1992;Mao&Paczy´nski1992).However,cosmologicaltime-dilatione ectsintheBATSEsampleindicatethatthedimmestsourcesshouldbelocatedatz≈2(Nor-risetal.1995).Ifthisistheactuallimitingredshift,asourcepopulationwithacomovingratedensityoftheformnc(z)∝(1+z)βiscompatiblewiththeBATSEdis-tributionfor1.5～<β～

<2(Horacketal.1995).Therefore,itisworthwhiletoexaminewhetherthecomovingmergerratedensityofneutron-starbinariesevolvesinasimilarfashion.

Bymeansofpopulationsynthesiscomputationsforbi-narystarsthemergerrateofneutron-starbinaries[here-after(ns,ns)]canbecomputed(seePortegiesZwart&Yungelson1998andreferencestherein).Usingthisap-proachLipunovetal.(1995)computedtheevolutionof(ns,ns)mergersasafunctionofredshiftandlogN logSdistributionsofGRBsforacosmicpopulationwhichcon-tainsgalaxieswithaconstantstar-formationrateandalsogalaxieswithinitialburstsofstarformationindi erentproportions.Totani(1997)computedtheevolutionoftheGRBsratedensityfrom(ns,ns)mergersinamodelbasedontheobservationallydeterminedhistoryofcosmicstarformationandinamodelderivedfromdetailedgalaxyevolution.Totaniassumedadistributionofmergingtimes

f(tc)∝t 1

for(ns,ns)systems1.Wegoastepfurtherbyadoptingc

forallgalaxiesexponentiallydecreasingstarformationrates(SFR)withdi erenttimescalesdepend-ingongalaxymorphology(e.g.Sandage1986).WeapplythedistributionoftcfrommodelBofPortegiesZwart&Yungelson(1998,henceforthPZY98)whichprovidesthe