Are Gamma Ray Bursts due to Rotation Powered High

astro-ph/951111725Nov1995ApJ,inpressNSF-ITP/95-128AREGAMMA-RAYBURSTSDUETOROTATIONPOWEREDHIGHVELOCITYPULSARSINTHEHALO?DieterH.Hartmann1;3andRameshNarayan2;31Dept.ofPhysicsandAstronomy,ClemsonUniversity,Clemson,SC29634;[e-mail]2Harvard-SmithsonianCenterforAstrophysics,Cambridge,MA02138;[e-mail]3InstituteforTheoreticalPhysics,UniversityofCalifornia,SantaBarbara,CA93106AbstractTheBATSEexperimenthasnowobservedmorethan1100gamma-raybursts.Theobservedangulardistributionisisotropic,whilethebrightnessdistributionofburstsshowsareducednumberoffaintevents.Theseobservationsfavoracosmologicalburstorigin.Alterna-tively,veryextendedGalactichalo(EGH)modelshavebeenconsid-ered.Inthelatterscenario,thecurrentlyfavoredsourceofgamma-rayburstsinvolveshigh-velocitypulsarsejectedfromtheGalacticdisk.Tobecompatiblewiththeobservedisotropy,mostmodelsinvokeasamplingdistanceofD300kpc,aturn-ondelaytturnon3107yrs,andasourcelifetimetmax109yrs.Weconsidertheglobalenergyrequirementsofsuchmodelsandshowthatthelargestknownresource,rotationalkineticenergy,isinsucientbyordersofmagni-tudetoprovidetheobservedburstrate.Moreexoticenergysourcesordierentlytunedpulsarmodelsmaybeabletogetaroundtheglobalenergyconstraintbutatthecostofbecomingcontrived.Thus,whileextendedhalomodelsarenotruledout,ourargumentplacesasevereobstacleforsuchmodelsandweencourageproponentsofEGHmodelstoclearlyaddresstheissueofenergetics.1INTRODUCTIONThe\greatdebateonthedistancescaleofcosmicgamma-raybursts(GRB)(Fishman1995;Lamb1995;Paczynski1995)consideredtwoalternatives;cos-mologicalburstsandeventsthatoccurinanextendedGalactichalo.ThepreviousparadigmofnearbyGalacticneutronstarswithaPopulationIdis-tributionhasfallenoutoffavorbecauseofthecombinedobservationsof(i)anisotropicangulardistributionofGRBsand(ii)reducedsourcecountsatthefaintendoftheapparentuxdistribution(Meeganetal.1992;Briggsetal.1995).Theabsenceofevenahintofa\MilkyWaybandintheGRBdistributionmakesitveryhardtoretainthehypothesisthatlocalneutronstarsprovidetheunderlyingsourcepopulation.SomerecentreviewsoftheseandrelatedissuesareprovidedinBriggs(1995),Fishman&Meegan(1995),andHartmann(1995).TosavetheGalactichypothesisunderthetightconstraintofisotropyitisnecessarytoconsiderahighlyextendedstructurelargeenoughtominimizethedipoleduetothesolarosetfromtheGalacticcenter.Thecurrentmultipolelimits(Briggsetal.1995;Tegmark,etal.1995)requiregalacto-centricshellswithtypicalradii200kpc.Ontheotherhand,halosthataretoolargewillyieldanexcessofburststowardsM31,whichisnotobserved(e.g.,Hakkilaetal.1994,1995;Briggs,etal.1995).Becauseofthesetwinconstraints,mosthalomodelsinvokealimitingsamplingdistanceofabout300kpcfortheBATSEbursts.AnysourcepopulationthatcouplesdynamicallytotheGalacticpoten-tialislikelytohavearadialprolesimilartotheHubbleprolefrequentlyemployedindescriptionsoftheGalacticdarkmatterhalo.ThestudiesbyHakkilaetal.(1994,1995)ruleoutsuchasourcedensitydistributionforGRBssinceitwouldleadtoadetectableanisotropy.Similarly,scenariosthatinvolveoldsourcestrappedintheGalacticpotentialwouldalsoshowstronganisotropies,atleastintheinnerregionsoftheGalaxy.Anexampleofthelattersituationisapopulationofneutronstarsborninthehalo(Eichler&Silk1992;Hartmann1992),whichgeneratesahalodistributionthatcom-parespoorlywithBATSEdata(Briggsetal.1995).Highvelocityobjects(neutronstars)thatlefttheGalaxyalongtimeagoaredistributedroughlyuniformlybetweengalaxiesandwouldconstituteacosmologicalratherthanaGalacticmodel,althoughthedistancescalewouldbeintermediatebetweenthehaloscale(300kpc)andthecosmologicalscale(3,000Mpc)(Hartmann11995).Currently,theonlysurvivingGalactichalomodelisoneinwhichtheburstsareproducedbyhighvelocitysourcesborninthevicinityofthediskstreamingoutintothehalo(Li&Dermer1992;Bulik&Lamb1995;Podsi-adlowskietal.1995).Weconsiderthisscenariointhispaperandforde-nitenessassumethattherelevantsourcesarehighvelocitypulsars(HVPs).Therecentupwardrevisionofradiopulsarvelocities(Lyne&Lorimer1994)apparentlyprovidessomesupportandmotivationforsuchascenario.SomegeneralargumentscanbemadeabouttherequirementsofaHVPmodel.First,onedemandsofcoursethatessentiallynopulsarswithsmallvelocitiesproduceobservableGRBs,elsetheirstrongconcentrationtotheGalacticdiskwouldquicklyviolatetheisotropyconstraints.HVPmodelscomeintwoavors.In\free-streamingmodels,thepulsarsreceiveatfor-mationvelocitykicksinexcessoftheescapevelocityoftheGalaxyandstreamawayonmore-or-lessradialorbits.Insuchmodels,theminimumvelocitykickofthepulsarsis800kms1.Thisisalittlelargerthanthetypicalescapevelocityofvesc600kms1inordertocompensateforcaseswherepartofthekickiscancelledbyorbitalmotionintheGalacticdisk.Inthealternate\quasi-virializedhalomodels,somefractionofthestarsremainboundtotheGalaxy,andsothesourceshavesomewhatsmallervelocities.However,sincethetrappedstarsneedtollavolumeoutto300kpcinthehalotheirvelocitiescannotbemuchlessthanescape.Inourdiscussions,weassumeatypicalvelocityv103v3kms1.AllHVPmodelsrequireadelayedturn-onofobservableGRBactivityinthesources.Thedelaycouldbeduetoe