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ApJ,inpress PreprinttypesetusingLATEXstyleemulateapjv.04/03/99 HIGH-REDSHIFT GAMMA-RAY BURSTS FROM POPULATION III PROGENITORS Volker Bromm 1 and Abraham Loeb2 ApJ, in press ABSTRACT Detection of gamma-ray bursts (GRBs) from redshifts z > 7 would open a new window into the earliest epoch of cosmic star formation. We construct separate∼star formation histories at high redshifts for normal(PopI and II) stars, andfor predominantly massive (PopIII) stars. Basedon these separate 6 histories, we predict the GRB redshift distribution to be observed by the Swift mission. Regardless 0 of whether Pop III progenitors are able to trigger GRBs, we find that a fraction 10% of all bursts ∼ 0 detected by Swift will originate at z > 5. This baseline contribution is due to Pop I/II star formation 2 which must have extended out to hig∼h redshifts in rare massive galaxies that were enriched by heavy n elements earlier than the typical galaxies. In addition, we consider the possible contribution of Pop III a progenitors to the observable GRB rate. Pop III stars are viable progenitors for long-duration GRBs J which are triggered by the collapsar mechanism, as long as they can lose their outer envelope through 0 mass transfer to a companion star in a close binary. We find that the likelihood of Pop III binaries to 1 satisfy the conditions required by the collapsar mechanism could be enhanced significantly relative to Pop I/II binaries. If Pop III binaries are common, Swift will be the first observatory to probe Pop III 2 star formation at redshifts z >7. v ∼ 3 Subject headings: binaries: general — cosmology: theory — gamma rays: bursts — stars: formation 0 3 1. INTRODUCTION Gou et al. 2004; Inoue, Omukai, & Ciardi 2005; Ioka 9 & M´esza´ros 2005) at redshifts z > 7, beyond the cur- 0 The first stars in the universe, so-called Population III rent horizon of galaxy and quasar s∼urveys. GRBs are the 5 (hereafter Pop III), formed out of metal-free gas at the brightest electromagnetic explosions in the universe (for 0 end of the cosmic dark ages or redshifts z > 10 (for re- recent reviews, see, van Paradijs, Kouveliotou, & Wijers / views, see, e.g., Barkana & Loeb 2001; Brom∼m & Larson h 2000;M´esza´ros2002;Piran2004)andtheiremissionisde- 2004; Ciardi & Ferrara 2005; Glover 2005). These stars p tectable out to z >10. The detectability of their gamma- - are predicted to have been predominantly very massive o with M∗ >100M⊙ (Bromm, Coppi, & Larson1999,2002; rayemission(Lam∼b&Reichart2000)allowssimultaneous r monitoring of a major portion of the sky, while the de- Abel, Br∼yan, & Norman 2002; Nakamura & Umemura t s 2001), and to have left a mark on the thermal and chem- tectability of their afterglow (Ciardi & Loeb 2000) allows a todeterminetheirhighredshiftfromtheappearanceofthe ical evolution of the intergalactic medium (IGM). First, : v their predictedhighsurfacetemperatures (e.g.,Bond,Ar- intergalactic Lyα absorption trough in the infrared (Loeb Xi nett, & Carr 1984) implies that they may have been effi- 2003;Barkana&Loeb2004). Thepopularcollapsarmodel forthecentralengineoflong-durationGRBs(MacFadyen, cient sources of ionizing photons (e.g., Tumlinson & Shull r Woosley, & Heger 2001 and references therein), involves a 2000; Bromm, Kudritzki, & Loeb 2001b; Schaerer 2002). the collapse of a massive star to a black hole (BH). This A contribution from Pop III stars to the reionization of modelnaturallyexplains the observedassociationoflong- the IGM may be required to account for the large optical duration GRBs with star-forming regions (e.g., Fruchter depth to Thomson scattering inferred by the Wilkinson et al. 1999; Djorgovski et al. 2001; Bloom, Kulkarni, & Microwave Anisotropy Probe (WMAP; Kogutet al. 2003) Djorgovski2002a)and the Type Ib/c supernova signature duringitsfirstyearofoperation(e.g.,Cen2003;Wyithe& on the spectra of rapidly decaying afterglow lightcurves Loeb2003a,2003b). Second,sincethestellarevolutionary timescaleformassivePopIIIstarsisshort 106yr,there- (e.g.,Bloomet al. 2002b;Hjorthetal. 2003;Mathesonet ∼ al. 2003; Stanek et al. 2003). sulting initialenrichmentoftheIGMwithheavyelements Becauseoftheirhighcharacteristicmasses,PopIIIstars could have occurred rather promptly (e.g., Mori, Ferrara, could potentially lead to high redshift GRBs. The re- &Madau2002;Bromm,Yoshida,&Hernquist2003;Wada cently launched Swift satellite3 (Gehrels et al. 2004) is & Venkatesan2003;Yoshida, Bromm,& Hernquist 2004). ideally suited to utilize this novel window into the high- Gamma-Ray Bursts (GRBs) offer unique prospects for redshift universe. In the following sections we address the probing the cosmic star formation (Totani 1997; Wijers underlying question: which fraction of high-redshift bursts et al. 1998; Blain & Natarajan 2000; Porciani & Madau could originate from Pop IIIprogenitors? Theactualfrac- 2001; Bromm & Loeb 2002; Hernquist & Springel 2003; tion and distribution of high-z GRBs to be measured by Mesinger, Perna, & Haiman 2005; Natarajan et al. 2005) Swift,mightreflecttheabsenceorpresenceofthepotential as well as the IGM (Loeb 2003; Barkana & Loeb 2004; Pop III contribution. 1DepartmentofAstronomy,UniversityofTexas,Austin,TX78712; [email protected] 2DepartmentofAstronomy,HarvardUniversity,Cambridge,MA02138;[email protected] 3Seehttp://swift.gsfc.nasa.gov 1 2 The organization of the paper is as follows. In 2 we rate at z > 15 could be larger by one order of magnitude § describeourcosmicstarformationmodel,inparticularde- than the p∼urely atomic cooling case discussed here. termining the Pop III mode at the highest redshifts. The resulting GRB redshift distribution is calculated in 3, § together with a discussion of plausible GRB progenitors. Finally, we address the implications of our results in 4. § 2. STARFORMATIONMODESATHIGHREDSHIFTS We note that GRBs are expected to exist at redshifts z > 7 even in the absence of any true Pop III contribu- tio∼n. This isdue to the rapidenrichmentofthe IGMwith heavyelementsdispersedbythefirstsupernovae(SNe)be- ginningatz >20(e.g.,Loeb&Haiman1997;Madau,Fer- rara,&Rees∼2001;Brommetal. 2003;Furlanetto&Loeb 2003; Scannapieco, Schneider, & Ferrara 2003). Once a given region of the universe has been enriched beyond a criticalmetallicity,Zcrit 10−3.5Z⊙,themodeofstarfor- ∼ mation is predicted to shift from high-mass Pop III stars to the lower-mass Pop I and II cases (e.g., Omukai 2000; Bromm et al. 2001a; Schneider et al. 2002; Bromm & Loeb 2003b; Mackey, Bromm, & Hernquist 2003; Schnei- der et al. 2003). The mass fraction of super-critical gas is rapidly growingtowardlower redshift, and GRBs could be formed in the conventional way from metal-enriched Pop I and II progenitors at high-z. In the following dis- cussion, we first construct the total cosmic star formation rate (SFR), and subsequently decompose the total SFR into separate Pop I/II and Pop III components. 2.1. Star Formation History Ourmodelforthe totalcosmicSFRcloselyfollowsthat of Bromm & Loeb (2002), and we here only briefly de- scribe the key assumptions. The abundance and merger history of the cold dark matter (CDM) halos is described by the extendedPress-Schechterformalism(Lacey& Cole 1993). WeassumethattheIGMhasatwo-phasestructure, consisting of neutral and ionized hydrogen phases. The reionization of the IGM was likely an extended process, occurringover6<z <20(e.g.,Cen2003;Wyithe&Loeb 2003a;Sokasian e∼t al∼. 2004;Furlanetto & Loeb 2005). To Fig. 1.—Cosmiccomovingstarformationrate(SFR)inunitsof bracketthe possibilities, we consider tworeionizationred- M⊙ yr−1 Mpc−3, as a function of redshift. We assume that cool- shifts, z 7 and 17, where z corresponds to an ing inprimordial gas is due to atomic hydrogen only, and the star ionizatiorneiofinll≈ing fraction by volumreeionof 50%. In each formationefficiencyisη∗=10%. (a)Latereionization(zreion≈7). ∼ Solid line: Total comoving SFR. Dotted lines: Contribution tothe case, reionization is spread out over a range in redshifts, total SFR from Pop I/II and Pop III for the case of weak chem- ∆z/(1+z) 1. ical feedback. Dashed lines: Contribution to the total SFR from ≃ Within eachphaseofthe IGM,starsareableto formin Pop I/II and Pop III for the case of strong chemical feedback. (b) two different ways. The first mechanism pertains to pri- Early reionization (zreion ≈ 17). We adopt the same convention for the lines as in panel (a). In all cases, Pop III star formation mordial, metal-free, gas. Such gas undergoes star forma- isrestricted tohigh redshifts,but extends over asignificant range, tionprovidedthatitaccretesontoadarkmatterhalowith ∆z∼10−15. a sufficiently deep gravitational potential well or equiva- lently a mass above a minimum value. For the neutral For the ionized medium, on the other hand, the min- medium,thisminimummassissetbytherequirementthat imum threshold mass is given by the Jeans mass, since thegaswillbeabletocool. Radiativecoolingbymolecular the infall of gas and the subsequent formation of stars re- hydrogen(H2) allows star formation in halos with a virial quiresthat the gravitationalforce ofthe dark matter halo temperature Tvir > 500 K, while atomic cooling domi- be greater than the opposing pressure force on the gas. nates for haloswit∼h T >103.9 K.Since H canbe easily After reionization, the IGM is photo-heated to tempera- vir 2 photo-dissociated by pho∼tons below the Lyman-limit, its tures >104K, leading to a dramatic increase in the Jeans significanceinthe cosmicstarformationhistoryisunclear mass.∼We model the suppression of gas infall according (e.g. Bromm & Larson 2004 and references therein), and to results from spherically-symmetriccollapse simulations so we only show results without H cooling in this paper. (see Bromm & Loeb 2002 for details). In calculating the 2 We note, however, that in the limiting case of negligible late reionization case (z 7), we employ the predic- reion ≈ H photodissociation feedback, the cosmic star formation tion by Thoul & Weinberg (1996) that gas infall is com- 2 3 pletely suppressed in halos with circular velocities v < Assuming that the formation of GRBs follows closely c 35 km s−1. For the early reionization case (z 17∼), the cosmic star formationhistory with no cosmologically– reion however,we use the recentworkby Dijkstra et al. (≈2004), significanttimedelay(e.g,Conseliceetal. 2005),wewrite showingthattheinfallsuppressionduetophoto-ionization for the number of all GRB events per comoving volume heatingcouldbemuchlesssevereinthe high-redshiftuni- per time, regardless of whether they are observed or not: verse. Specifically,weassumethatinthislattercaseinfall ψGtrRueB(z)=ηGRB×ψ∗(z), where ψ∗(z)is the cosmic SFR, is completely suppressedonly in haloswith circularveloc- as calculated in 2. The efficiency factor, ηGRB, links the § ities v < 10 km s−1. formation of stars to that of GRBs, and is in principle a c Withi∼n our model, the second mechanism to form stars function of redshift as well as the properties of the under- occurs in gas that has experienced a previous burst of lying stellar population. The stellar initial mass function starformation,andisthereforealreadysomewhatenriched (IMF) is predicted to differ fundamentally for Pop I/II with heavy elements. Such gas, residing in a halo of mass and Pop III (e.g., Bromm & Larson 2004 and references M , can undergo induced star formation triggered by a therein). The GRB efficiency factor will depend on the 1 mergerwithasufficientlymassivecompanionhaloofmass fraction of stars able to form BHs, and consequently on M2 > 0.5M1. We finally assume that stars form with an theIMF(see§3.2). Here,weassumethatηGRB isconstant efficiencyofη∗ 10%,independentofredshiftandregard- with redshift for PopI/II star formation, whereas Pop III less ofwhether∼the gasis primordialorpre-enriched. This stars may be characterized by a different efficiency. efficiency yields roughly the correct fraction of Ω found The numberofburstsdetectedbyanygiveninstrument B in stars in the present-day universe. Figure 1 shows the depends on the instrument-specific flux sensitivity thresh- resulting total star formation histories. It is evident that old and on the poorly-determined isotropic-luminosity therearetwodistinctepochsofcosmicstarformation,one function (LF) of GRBs (see, e.g., Schmidt 2001; Sethi & at z 3, and a second one at z 8 for late reionization, Bhargavi 2001; Norris 2002). In order to ascertain what wher∼eas there is only a single, ex∼tended peak at z 5 for Swift is expected to find, we modify the true GRB event early reionization. ∼ rate as follows: 2.2. Population III Star Formation To determine the fraction of the total SFR contributed ∞ bthyePaotpomIIiIcsctaorosl,inwgethharveeshtooldidefonrtiftyhethfiorssethtaimloes.thIantacdrodsis- ψGobRsB(z)=ηGRBψ∗(z)ZLlim(z)p(L)dL . (1) tion, we require that the collapse takes place in a region of the IGMwhich is not yetenrichedwith heavyelements from previous episodes of star formation. Here, we adopt theformalismdevelopedinFurlanetto&Loeb(2005)who Here, p(L) is the GRB LF with L being the intrinsic, derived the redshift-dependent probability that a newly isotropic-equivalent photon luminosity (in units of pho- collapsed halo forms out of pristine gas (see their Fig. 2). tons s−1). If f denotes the sensitivity threshold of a lim This probability crucially depends on the efficiency with given instrument (in photons s−1 cm−2), then the mini- whichthenewlycreatedmetalsaredispersedintotheIGM mum luminosity is: via SNdrivenwinds. Tobracketthe rangeofpossibilities, we consider the cases of weak and strong chemical feed- back,correspondingtowindsexperiencinglargeandsmall radiative losses, respectively4. L (z)=4πd2f (1+z)α−2 , (2) As can be seen in Figure 1, Pop III star formation is lim L lim limited to the highest redshifts, but in each case extends over a substantial range in redshift: ∆z 10 for strong ∼ chemical feedback, and ∆z 15 for weak feedback. The ∼ PopIII histories are rather similar for both early and late whered is the luminositydistance toa sourceatredshift L reionization. The suppression of gas infall for the early z,and α the intrinsic high-energy spectralindex (Band et reionization case (with v < 10 km s−1), would have a al. 1993). For definiteness, we assume α=2, which gives c much more pronounced effe∼ct on halos that cool via H , a reasonable fit to the observed burst spectra (see Band 2 because of their shallower potential wells. et al. 1993 for a detailed discussion). We here use the samelognormalLFandthe sameparametersasdescribed 3. GRBREDSHIFTDISTRIBUTION in Bromm & Loeb (2002). Next we will predict the GRB redshift distribution for In Bromm & Loeb (2002), we predicted that 25% of ∼ flux-limited surveys, distinguishing between the contribu- allburstsobservedbySwiftwouldoriginateatz 5. This ≥ tions fromPopI/II andPopIII starformation. In partic- estimate wasbasedona flux thresholdofflim =0.04pho- ular, we will focus on the existing Swift satellite, which is tonss−1cm−2. Basedonthefirstfewmonthsofactualob- capable of making the most detailed determination of the servations by Swift, the sensitivity limit has recently been GRB redshift distribution to date. revised upward to flim = 0.2 photons s−1 cm−2, compa- rable to the older BATSE experiment (e.g., Berger et al. 2005). Usingthisrevisedfluxlimit,wepredictthat 10% 3.1. Population I/II Contribution ∼ of all Swift GRBs will originate at z 5. ≥ 4Theweakandstrongfeedbackcases correspondtoKw1/3=1/3and1inequation(4)ofFurlanetto&Loeb(2005). 4 year detectable by Swift. In Figure 2, we show the Swift GRB rate, associated with Pop I/II star formation. For bothearlyandlate reionization,the observeddistribution is expected to peak around z 2. This distribution is ∼ broadly consistent with the first GRB redshifts, still lim- ited in number, measured during the first months of the Swift mission (Berger et al. 2005). We now turn to the possible contribution to the high redshift GRB rate from Pop III stars. 3.2. Population III Contribution We beginbyassumingthatPopIII starformationgives riseto GRBs with the same(constant)efficiency as is em- piricallyderivedforPopI/IIstars. AsisevidentfromFig- ure 2, only for the case of weak chemical feedback is Swift expectedto detectafewburstsderivingfromPopIII pro- genitors over the 5 yr lifetime of the mission. Whether ∼ reionizationoccurredearlyor late,on the other hand, has only a small effect on the predicted rates. It is quite pos- sible, on the other hand, that Swift will not detect any Pop III GRBs at all. Regardless of the uncertain contri- bution from Pop III stars, however, the prediction that 10% of all Swift bursts originate at z 5 is rather ro- ∼ ≥ bust. This fractionis due to PopI/II progenitorsthatare knownto produce GRBs, and those shouldexist at z 5. ≥ Adopting the same η for Pop III as for Pop I/II, GRB however, could be significantly in error. To examine the fundamentaldifferencebetweenthestellarpopulations,we needtogobeyondthephenomenologicalapproachpursued sofaranddiscussthepropertiesofplausibleGRBprogen- itors in greater physical detail. 3.2.1. Collapsar Engine Existing evidence implies that long-duration bursts are related to the death of a massive star, leading to the for- mation of a BH (see review by Piran 2004). The pop- ular collapsar model assumes that an accretion torus is temporarily formed around the black hole, and that the Fig. 2.—PredictedGRBrateobservedbySwift. Shownistheob- gravitational energy released during the accretion is able servednumberofburstsperyear,dNGobRsB/dln(1+z),asafunction to power a strong explosion (e.g., Woosley 1993; Lee & ofredshift. AllratesarecalculatedwithaconstantGRBefficiency, η(aG)RLBa≃te2r×eio1n0i−za9tibounrs(tzsreMion⊙−1≈,u7s)i.ngDtohtetecdoslminiecs:SFCRosntfrroibmutFioign.t1o. Radadmitiiroenza-Rl ureizqu20ir0e5m).enFtosrhtahveecotollabpesamrteotrbeesyuoltnidntahGeRfoBr-, the observed GRB rate from Pop I/II and Pop III for the case of mation of a BH. We will discuss these next, and will then weak chemical feedback. Dashed lines: Contribution to the GRB explorewhetherasubsetofPopIIIstarscouldsuccessfully ratefromPopI/IIandPopIIIforthecaseofstrongchemicalfeed- launch a GRB under the collapsar scenario. back. (b)Earlyreionization(zreion≈17). Thelineshavethesame To successfully produce a GRB with a collapsar, three meaningasinpanel(a). Filledcircle: GRBratefromPopIIIstars if these were responsible for reionizing the universe at z ∼ 17 (see basic requirements have to be fulfilled (see, e.g., Zhang & text). TheGRBratesfromPopIIIprogenitorsareveryuncertain; Fryer 2004; Petrovic et al. 2005): theycouldbezero,or,intheotherextreme,displayanenhancement (i) The progenitor star has to be sufficiently massive to byuptooneorderofmagnitudeabovethebaselineratesshownhere result in the formation of a central BH. Collapse to a BH (seetextfordetails). could occur either directly for initial masses of the pro- Over a particular time interval ∆tobs in the observer genitor > 40M⊙, or in a delayed fashion by fallback of frame, the observednumber of GRBs originating between the eject∼a following a failed SN explosion for progenitor redshifts z and z+dz is masses 25 < M∗ < 40M⊙ (e.g., Heger et al. 2003). The number of∼BH for∼ming stars resulting from a given total dNGobRsB =ψobs (z) ∆tobs dV , (3) stellarmass,heredenotedbyηBH,willdependonthestel- dz GRB (1+z) dz lar IMF which in turn is predicted to differ between the Pop I/II and Pop III cases. where dV/dz is the comoving volume element per unit For simplicity, we assume that the IMF in both cases redshift (see Bromm & Loeb 2002). As a final step, we consists of a power-law with the standard Salpeter value, normalize the GRB formation efficiency per unit mass in dN/dm m−2.35, but with different values for the lower Pop I/II stars to η 2 10−9 GRBs M−1. This and upp∝er mass limits, M and M respectively. For GRB ⊙ low up ≃ × choice results in a predicted number of 90 GRBs per Pop I/II stars, we take these to be: Mlow = 0.1M⊙ and ∼ 5 Mup = 100M⊙. The Pop III IMF, on the other hand, identify progenitor systems for collapsar–driven GRBs is still very uncertain (see, e.g., Bromm & Larson 2004). that fulfill both conditions (ii) and (iii). The basic prob- The upper mass limit can be conservatively estimated to lem is that the removal of the extended H-envelope is ac- be Mup 500M⊙ (Bromm& Loeb 2004),whereas for the companied by the loss of angular momentum in the core ∼ lower limit, we consider two possibilities: Mlow 30M⊙ (e.g., Petrovic et al. 2005). We will explore this problem ∼ (e.g., Tan & McKee 2004)and 100M⊙ (e.g., Abel et al. next,firstforsingle-starprogenitors,andthenforbinaries. ∼ 2002; Bromm et al. 2002). In general, 3.2.2. Single-star Progenitor Mupm−2.35dm In massive Pop I/II stars, radiation driven winds can η = MBH , (4) leadtovigorousmassloss,wherethe mainsourceofopac- BH RMup m−1.35dm ity is provided by metal lines (e.g., Kudritzki & Puls Mlow 2000). Empirically, the existence of Wolf-Rayet (WR) R stars proves that Pop I/II stars can indeed experience where MBH 25M⊙. For the Pop I/II case, this re- ≃ catastrophic mass loss, leading to the removal of the en- sults in ηBH 1/(700M⊙). The Pop III lower mass limit ≃ tire hydrogen-, and, in extreme cases, even of the helium- exceeds the threshold for BH formation in either case, M >M . NoteveryPopIIIstar,however,willleavea envelope. The violent mass loss, however, is accompanied low BH BH behind. In the narrowmass range of 140 260M⊙, by the effective removal of angular momentum from the PopIIIstarsarepredictedtoundergoapa∼ir-inst−abilitysu- remaining pre-collapse core, rendering the creation of a pernova (PISN) explosion (e.g., Fryer, Woosley, & Heger collapsar impossible. 2001; Heger et al. 2003). A PISN will lead to the com- For massive Pop III stars, radiatively driven winds are plete disruption of the star, such that no compact rem- predictedtobeunimportant(e.g.,Kudritzki2002;Krtiˇcka nant will be left behind. For the Pop III case, the expres- & Kuba´t 2005). Alternatively, mass loss could occur as sion results in ηBH 1/(80M⊙) for Mlow = 30M⊙, and a result of stellar pulsations (through the ǫ mechanism). ηBH 1/(300M⊙) fo≃r Mlow =100M⊙. Thus, the BH for- Simplified, linear calculations, however, indicate that this mati≃onefficiencyislargerforPopIIIcomparedtoPopI/II mechanism is not important below 500M⊙ (Baraffe, ∼ by up to one order of magnitude, depending on the lower Heger, & Woosley 2001). There still remains an unex- mass limit. plored possibility that Pop III stars could experience sig- (ii) The progenitor star has to be able to lose its hydro- nificantmasslossdrivenbyradiationpressureonHe+ions, gen envelope in order for the relativistic outflow to pene- where the opacity is provided by bound-free transitions. trate through and exit the star (e.g., Zhang et al. 2004). Alternatively,processedmaterialfrompreceedingepisodes This requirement derives from the observed burst dura- ofnuclearburning could be transportedto the stellarsur- tions, t < 100 s, providing an estimate for the lifetime of face by convection, rotationally-induced mixing, and dif- the cent∼ralGRB engine. The jet cantherefore only travel fusion, thus enriching the atmosphere to Z > 10−4Z⊙ at a distance of r ct 50R⊙ before being slowed down to which point line–driven mass loss is predic∼ted to set in non-relativistic∼speed∼s. Massive stars with hydrogen en- (Kudritzki 2002; Marigo, Chiosi, & Kudritzki 2003). Re- velopesgrowtoalargesizeduringtheirlaterevolutionary cently, it hasbeen suggestedthat WR type winds, in con- phases. For example, red supergiants can reach radii of nection with rapid rotation and the approach to the Ed- up to 103R⊙ (e.g., Kippenhahn & Weigert 1990). The dington limit, could possibly lead to significant mass loss effectiv∼eness of mass loss crucially depends on metallicity evenforverylow-metallicitystars(Vink&deKoter2005). (e.g., Kudritzki 2002), and on whether the star is isolated Themostlikelyexpectation,however,isthatisolatedmas- or part of a binary system. Below, we will discuss both sive PopIII stars are not able to shed much mass priorto effects further. their final collapse. (iii)Theprogenitorstarhastocontainacentralcorewith Thus itappearslikelythatthe majorityofmassive,sin- sufficientangularmomentumtoallowanaccretiondiskto glestarprogenitors,bothforPopI/IIandIII,cannotgive form around the growing BH. Important aspects of stel- risetoacollapsar-drivenGRB,althoughfordifferentphys- lar structureandevolutioncanbe understoodby dividing ical reasons. We note, however, that the progenitor for the star into a compact core, and an extended outer en- the collapsar engine is still very uncertain. In addition to velope (e.g., Kippenhahn & Weigert 1990). Depending on the binary scenario (see below), massive, rapidly rotating the evolutionarystage,aradiativecoreissurroundedbya single stars have recently been considered (e.g., Yoon & convectiveenvelope,orviceversa. Thepre-collapsestellar Langer 2005; Woosley & Heger 2005). Our main results, corehasa massM , radiusR ,angularvelocityω ,andis basedon the cosmic PopIII SFR and the IMF-dependent c c c characterizedby a specific angularmomentum j R2ω . BH fraction, however, holds in this case as well. We next Assuming that the collapse to a BH conservesspce≃cificcanc- turn our attention to binary-star progenitors. gular momentum, the condition for an accretion torus to formaroundagrowingBHinthecenterwithmassM is 3.2.3. Binary-star Progenitor BH centrifugal support for materialorbiting at the last-stable Close binary systems provide a promising avenue to si- radius. Thisconditioncanbe expressedasj >j ,with c min multaneously meet the requirements of strong mass loss j =√6GM /c 3 1016cm2s−1 (e.g.,Po∼dsiadlowski combined with the retention of sufficient angular momen- min BH ≃ × et al. 2004). tum in the collapsing core (e.g., Lee, Brown, & Wijers Recent results obtained with sophisticated stellar evo- 2002; Izzard, Ramirez-Ruiz, & Tout 2004). For Pop I/II, lution codes that include the effects of magnetic torques a binary pathway to a collapsar–driven GRB has already (e.g., Spruit 2002) have demonstrated the difficulty to been suggested (e.g., Fryer et al. 1993). The basic idea is 6 that a close binary system, experiencing Roche-lobe over- during the red giant phase: R > r > a . We esti- RG L i flow (RLOF) when the primary evolves off the main se- mate the Pop III radius during the giant∼phase, which is quence, will go through a common-envelope (CE) phase, smaller than that of a Pop I star of equal mass, to be during which the hydrogen envelope of the primary can R 300R , where R is the main-sequence radius. RG MS MS ∼ be removed without seriously draining away the spin of Massive Pop III stars obey a simple mass-radius relation the remaining helium core (for a recent review, see Taam (Bromm et al. 2001b): M R2 . The maximum sep- ∝ MS & Sandquist 2000). During the CE phase, the binary will aration for RLOF and therefore a CE phase to occur is spiralclosertogether,andthecorrespondinglossoforbital thus energywillheatthe envelopewithagivenefficiency,often M 1/2 assumed to be very high: αCE ≃ 1.0 (Taam & Sandquist ai,max ≃103R⊙(cid:18)102M⊙(cid:19) . (5) 2000). The frictional energy release during the in-spiral The minimum possible binaryseparation,a , onthe phase has been shown to be sufficient to unbind the hy- i,min other hand, will determine the extent of the inspiral pro- drogen envelope. cess and therefore of the accompanying frictional heating For a progressively tightening binary, the spin of each of the hydrogen envelope as well as the tidal spinning up component is tidally coupled to the orbital motion: ω c ∼ of the helium core. We approximately assume that the ω . Sincetheheliumcoreisspunupagainbecauseofthe orb minimumseparationisgivenbytwicetheradiusofamas- spin-orbit coupling, it is able to retain sufficient angular sive Pop III star during the main–sequence phase (which momentum to fulfill the j >j requirement. c min ∼ is only weakly dependent on mass): ai,min 10R⊙. If we ≃ 3.2.4. GRB Formation Efficiency further assume that the initial separations are distributed withequalprobabilityperlogarithmicseparationinterval, Ingeneral,wecanexpresstheGRBformationefficiency as they are for Pop I/II binaries (e.g., Abt 1983; Hea- for Pop III stars as: η η η η η , where GRB ≃ BH bin close beaming cox 1998; Larson 2003), dN/dlna const., and that the ηbin isthebinaryfraction,ηclose thefractionofsufficiently largest possible binary separation∝is given by the Jeans close binaries to undergo RLOF, η 1/50–1/500 beaming ≃ lengthforthetypicalconditionsinaprimordialgascloud, the beaming factor, where we conservatively assume that λ 1pc(e.g.,Brommetal. 2002,Bromm&Loeb2004), Pop III bursts are collimated by the BH central engine to J ≃ weestimatethefractionofallPopIIIbinariesthataresuf- the same angle as Pop I/II progenitors (the inferred colli- ficientlyclosetoexperienceaCEphasetobeη 30%. mation angles by Frail et al. 2001; Panaitescu & Kumar close ∼ In summary, η for Pop III stars is very uncertain, 2001, are indeed comparable to those of radio jets from GRB andcouldbe zeroin casethat no PopIII binariesexisted. the much more massive BHs in galactic nuclei). We have On the other hand, one may argue that the binary prop- already discussed η , and how Pop III star formation is BH erties for Pop III had been similar to Pop I/II, in cases characterized by an enhancement of up to one order of where Pop III star formation takes place in more massive magnitude because of the higher fraction of BH–forming host systems that could give rise to a stellar cluster, or at progenitors. leastmultiplestars. Suchaclusteredenvironmentisoften ItiscurrentlynotknownwhetherPopIIIstarscanform suggested to explain the formation and the properties of binaries, and if so, what the corresponding binary frac- binaries in present-day galaxies (e.g., Larson 2003). As- tion will be (e.g., Saigo, Matsumoto, & Umemura 2004). suming that the Pop III binary properties are similar to In present-day star formation, the incidence of binaries is PopI/II, we find a significant enhancement in η due to high,with 50%ofallstarsoccurringinbinariesorsmall BH ∼ thedifferenceintheIMFbetweenthepopulations. Wecan multiple systems (e.g., Duquennoy & Mayor 1991). Cur- then place an upper limit on the GRB rate from Pop III rentthree-dimensionalsimulations ofthe formationofthe stars by multiplying the baseline rates in Figure 2 by a first stars still lack the resolution to resolve the possible factor of 10. This would result in Pop III GRB rates fragmentation of a collapsing cloud into tight binaries or ∼ as large as 10 bursts detected by Swift per year for multiple stellar cores on scales < 100 AU. Although we ∼ the case of weak chemical feedback. Such very high rates cannot yet conclusively address t∼he formation of close bi- can already be excluded, since Swift has only identified naries, there is evidence from numerical simulations that two GRBs from z > 5 as of yet, GRB 050814 at z 5.3 binary or multiple clump formation is rather common on ≃ (Jakobsson et al. 2∼005) and GRB 050904 at z 6.3 (An- larger scales (>0.1 pc). In simulations where the collaps- ≃ tonelli et al. 2005;Haislip et al. 2005;Kawaiet al. 2005). ing gashadac∼quiredahighdegreeofangularmomentum, For strong chemical feedback, on the other hand, we pre- and where the collapse led to a disk-like configuration, dict rates of less than one burst detected per year, even pre-stellar clumps commonly occurred in binary or mul- if the BH efficiency were increasedby one order of magni- tiple systems (e.g., Bromm et al. 1999, 2002; Bromm & tude, and such a Pop III contribution cannot be excluded Loeb2003a,2004). Thusmotivated,ourbestguessisthat with the current constraints from Swift. η < 0.5. More work, in particular involving improved bin nume∼ricalsimulations,isrequiredtoconstrainthis crucial 3.3. Constraints from Reionization quantity further. ProvidedthatPopIIIstarformationdoesincludeafrac- If massive Pop III stars led to an early reionization of tion of binaries, we can use the collapsar requirements to the universe atz 17,as may be requiredby the WMAP ∼ obtain an estimate for the maximum binary separation, data(Kogutetal. 2003),wecanobtainanestimateforthe ai,max, prior to the CE inspiral phase, as follows. Assum- corresponding Pop III SFR at zreion and for the possible ing for simplicity that a Pop III binary has equal mass accompanying GRB rate, as follows. cwoimllpoonnlyentosc,ctuhrewRhoecnhethraedsiutasrisorvLer∼flo0w.s5aiit.sARoCcEhephloabsee ionPizoipngIIIphstoatrosnws ipthermsoalsasresm∼>as1s00oMve⊙r tphreoidruce2∼1016026Hy–r ∼ × 7 lifetime (e.g., Bromm et al. 2001b). We can then esti- tightPopIIIbinariesdonotexist)and 10timestheem- mate that 3 105M⊙ in Pop III stars are required to pirically inferred value for Pop I/II (du∼e to the increased ∼ × produce 5 ionizing photons for every hydrogen atom fraction of BH–forming progenitors among Pop III stars). in a com∼oving Mpc3. This number is sufficient to com- Recently, Gorosabel et al. (2004) and Natarajan et al. pensate for recombinations at the mean cosmic density. (2005)predictedtheexpectedredshiftdistributionoflong- Assuming further that the burst of Pop III star forma- duration GRBs, assuming they trace the cosmic star for- tion is spread over a fraction ǫ of the Hubble time at mation history, with various phenomenological prescrip- z 17, ∆t 4 107(ǫ/0.2) yr, the comoving tionsforthe dependence onmetallicity. Indifference from reion SF ∼ ∼ × Pop III SFR able to reionize the universe at that redshift thesestudies,weisolatethezero-metallicity(PopIII)stars is: SFRreion 7.5 10−3/(ǫ/0.2) M⊙ yr−1 Mpc−3. The and treat them as potential GRB progenitors based on a ∼ × extremelyrapidgrowthofthecollapsedfractionofbaryons physical model. with redshift implies a value of ǫ 1; however, the mini- It is of great importance to constrain the Pop III star ≪ mum value of ǫ is 0.1 because even within a single dark formation mode, and in particular to determine down to ∼ matterhalo,starformationcannotbesynchronizedtobet- which redshift it continues to be prominent. The extent ter than the dynamical time which amounts to ǫ 0.1 for of the Pop III star formation will affect models of the ini- ∼ a virial density contrast of 200. tial stages of reionization (e.g., Wyithe & Loeb 2003a,b; ∼ In Figure 2, we show the GRB rate which would corre- Ciardi, Ferrara, & White 2003; Sokasian et al. 2004; spond to SFR for ǫ=0.2 when the constant Pop I/II Yoshida et al. 2004; Alvarez, Bromm, & Shapiro 2006) reion GRB efficiency factor is used, resulting in 0.1 GRBs and metal enrichment (e.g., Mackey et al. 2003; Furlan- ∼ per year. Under this conservative assumption, Swift is etto & Loeb 2003, 2005; Scannapieco et al. 2003; Schaye not expected to detect, within its expected 5 year mission et al. 2003; Simcoe, Sargent, & Rauch 2004), and will lifetime, any bursts connected to the Pop III stars that determine whether planned surveys will be able to effec- were responsible for an early reionization of the universe. tively probe Pop III stars (e.g., Scannapieco et al. 2005). Again, the prospects for detection would be significantly The constraints on Pop III star formation will also de- improved if the Pop III GRB efficiency is boosted due to termine whether the first stars could have contributed a the increased fraction of BH–forming progenitors. significantfractiontothecosmicnear-IRbackground(e.g., Santos,Bromm,& Kamionkowski2002;Salvaterra& Fer- 4. SUMMARYANDCONCLUSIONS rara 2003; Dwek, Arendt, & Krennrich 2005; Kashlinsky Figure 2 leads to the robust expectation that 10% of 2005;Madau&Silk2005;Fernandez&Komatsu2006). If ∼ all Swift bursts should originate at z >5. This prediction PopIII binarieswerecommon,Swift mightbe the firstin- isbasedonthelikelyexistenceofPop∼I/IIstarsingalaxies strumentto detectPopIII starsfromgalaxiesatredshifts that were already metal–enriched at these high redshifts. z >7. AdditionalGRBscouldbetriggeredbyPopIIIstars,with ∼ ahighlyuncertainefficiency. Assumingthatlong-duration GRBsareproducedbythecollapsarmechanism,aPopIII WethankVickyKalogeraandSteveFurlanettoforhelp- star with a close binary companion provides a plausible ful discussions. VB thanks the Institute for Theory and GRB progenitor. We have estimated the Pop III GRB Computation at the CfA where partof this work was car- efficiency, reflecting the probability of forming sufficiently riedout. 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ApJ,inpress PreprinttypesetusingLATEXstyleemulateapjv.04/03/99 HIGH-REDSHIFT GAMMA-RAY BURSTS FROM POPULATION III PROGENITORS Volker Bromm 1 and Abraham Loeb2 ApJ, in press ABSTRACT Detection of gamma-ray bursts (GRBs) from redshifts z > 7 would open a new window into the earliest epoch of cosmic star formation. We construct separate∼star formation histories at high redshifts for normal(PopI and II) stars, andfor predominantly massive (PopIII) stars. Basedon these separate 6 histories, we predict the GRB redshift distribution to be observed by the Swift mission. Regardless 0 of whether Pop III progenitors are able to trigger GRBs, we find that a fraction 10% of all bursts ∼ 0 detected by Swift will originate at z > 5. This baseline contribution is due to Pop I/II star formation 2 which must have extended out to hig∼h redshifts in rare massive galaxies that were enriched by heavy n elements earlier than the typical galaxies. In addition, we consider the possible contribution of Pop III a progenitors to the observable GRB rate. Pop III stars are viable progenitors for long-duration GRBs J which are triggered by the collapsar mechanism, as long as they can lose their outer envelope through 0 mass transfer to a companion star in a close binary. We find that the likelihood of Pop III binaries to 1 satisfy the conditions required by the collapsar mechanism could be enhanced significantly relative to Pop I/II binaries. If Pop III binaries are common, Swift will be the first observatory to probe Pop III 2 star formation at redshifts z >7. v ∼ 3 Subject headings: binaries: general — cosmology: theory — gamma rays: bursts — stars: formation 0 3 1. INTRODUCTION Gou et al. 2004; Inoue, Omukai, & Ciardi 2005; Ioka 9 & M´esza´ros 2005) at redshifts z > 7, beyond the cur- 0 The first stars in the universe, so-called Population III rent horizon of galaxy and quasar s∼urveys. GRBs are the 5 (hereafter Pop III), formed out of metal-free gas at the brightest electromagnetic explosions in the universe (for 0 end of the cosmic dark ages or redshifts z > 10 (for re- recent reviews, see, van Paradijs, Kouveliotou, & Wijers / views, see, e.g., Barkana & Loeb 2001; Brom∼m & Larson h 2000;M´esza´ros2002;Piran2004)andtheiremissionisde- 2004; Ciardi & Ferrara 2005; Glover 2005). These stars p tectable out to z >10. The detectability of their gamma- - are predicted to have been predominantly very massive o with M∗ >100M⊙ (Bromm, Coppi, & Larson1999,2002; rayemission(Lam∼b&Reichart2000)allowssimultaneous r monitoring of a major portion of the sky, while the de- Abel, Br∼yan, & Norman 2002; Nakamura & Umemura t s 2001), and to have left a mark on the thermal and chem- tectability of their afterglow (Ciardi & Loeb 2000) allows a todeterminetheirhighredshiftfromtheappearanceofthe ical evolution of the intergalactic medium (IGM). First, : v their predictedhighsurfacetemperatures (e.g.,Bond,Ar- intergalactic Lyα absorption trough in the infrared (Loeb Xi nett, & Carr 1984) implies that they may have been effi- 2003;Barkana&Loeb2004). Thepopularcollapsarmodel forthecentralengineoflong-durationGRBs(MacFadyen, cient sources of ionizing photons (e.g., Tumlinson & Shull r Woosley, & Heger 2001 and references therein), involves a 2000; Bromm, Kudritzki, & Loeb 2001b; Schaerer 2002). the collapse of a massive star to a black hole (BH). This A contribution from Pop III stars to the reionization of modelnaturallyexplains the observedassociationoflong- the IGM may be required to account for the large optical duration GRBs with star-forming regions (e.g., Fruchter depth to Thomson scattering inferred by the Wilkinson et al. 1999; Djorgovski et al. 2001; Bloom, Kulkarni, & Microwave Anisotropy Probe (WMAP; Kogutet al. 2003) Djorgovski2002a)and the Type Ib/c supernova signature duringitsfirstyearofoperation(e.g.,Cen2003;Wyithe& on the spectra of rapidly decaying afterglow lightcurves Loeb2003a,2003b). Second,sincethestellarevolutionary timescaleformassivePopIIIstarsisshort 106yr,there- (e.g.,Bloomet al. 2002b;Hjorthetal. 2003;Mathesonet ∼ al. 2003; Stanek et al. 2003). sulting initialenrichmentoftheIGMwithheavyelements Becauseoftheirhighcharacteristicmasses,PopIIIstars could have occurred rather promptly (e.g., Mori, Ferrara, could potentially lead to high redshift GRBs. The re- &Madau2002;Bromm,Yoshida,&Hernquist2003;Wada cently launched Swift satellite3 (Gehrels et al. 2004) is & Venkatesan2003;Yoshida, Bromm,& Hernquist 2004). ideally suited to utilize this novel window into the high- Gamma-Ray Bursts (GRBs) offer unique prospects for redshift universe. In the following sections we address the probing the cosmic star formation (Totani 1997; Wijers underlying question: which fraction of high-redshift bursts et al. 1998; Blain & Natarajan 2000; Porciani & Madau could originate from Pop IIIprogenitors? Theactualfrac- 2001; Bromm & Loeb 2002; Hernquist & Springel 2003; tion and distribution of high-z GRBs to be measured by Mesinger, Perna, & Haiman 2005; Natarajan et al. 2005) Swift,mightreflecttheabsenceorpresenceofthepotential as well as the IGM (Loeb 2003; Barkana & Loeb 2004; Pop III contribution. 1DepartmentofAstronomy,UniversityofTexas,Austin,TX78712; [email protected] 2DepartmentofAstronomy,HarvardUniversity,Cambridge,MA02138;[email protected] 3Seehttp://swift.gsfc.nasa.gov 1 2 The organization of the paper is as follows. In 2 we rate at z > 15 could be larger by one order of magnitude § describeourcosmicstarformationmodel,inparticularde- than the p∼urely atomic cooling case discussed here. termining the Pop III mode at the highest redshifts. The resulting GRB redshift distribution is calculated in 3, § together with a discussion of plausible GRB progenitors. Finally, we address the implications of our results in 4. § 2. STARFORMATIONMODESATHIGHREDSHIFTS We note that GRBs are expected to exist at redshifts z > 7 even in the absence of any true Pop III contribu- tio∼n. This isdue to the rapidenrichmentofthe IGMwith heavyelementsdispersedbythefirstsupernovae(SNe)be- ginningatz >20(e.g.,Loeb&Haiman1997;Madau,Fer- rara,&Rees∼2001;Brommetal. 2003;Furlanetto&Loeb 2003; Scannapieco, Schneider, & Ferrara 2003). Once a given region of the universe has been enriched beyond a criticalmetallicity,Zcrit 10−3.5Z⊙,themodeofstarfor- ∼ mation is predicted to shift from high-mass Pop III stars to the lower-mass Pop I and II cases (e.g., Omukai 2000; Bromm et al. 2001a; Schneider et al. 2002; Bromm & Loeb 2003b; Mackey, Bromm, & Hernquist 2003; Schnei- der et al. 2003). The mass fraction of super-critical gas is rapidly growingtowardlower redshift, and GRBs could be formed in the conventional way from metal-enriched Pop I and II progenitors at high-z. In the following dis- cussion, we first construct the total cosmic star formation rate (SFR), and subsequently decompose the total SFR into separate Pop I/II and Pop III components. 2.1. Star Formation History Ourmodelforthe totalcosmicSFRcloselyfollowsthat of Bromm & Loeb (2002), and we here only briefly de- scribe the key assumptions. The abundance and merger history of the cold dark matter (CDM) halos is described by the extendedPress-Schechterformalism(Lacey& Cole 1993). WeassumethattheIGMhasatwo-phasestructure, consisting of neutral and ionized hydrogen phases. The reionization of the IGM was likely an extended process, occurringover6<z <20(e.g.,Cen2003;Wyithe&Loeb 2003a;Sokasian e∼t al∼. 2004;Furlanetto & Loeb 2005). To Fig. 1.—Cosmiccomovingstarformationrate(SFR)inunitsof bracketthe possibilities, we consider tworeionizationred- M⊙ yr−1 Mpc−3, as a function of redshift. We assume that cool- shifts, z 7 and 17, where z corresponds to an ing inprimordial gas is due to atomic hydrogen only, and the star ionizatiorneiofinll≈ing fraction by volumreeionof 50%. In each formationefficiencyisη∗=10%. (a)Latereionization(zreion≈7). ∼ Solid line: Total comoving SFR. Dotted lines: Contribution tothe case, reionization is spread out over a range in redshifts, total SFR from Pop I/II and Pop III for the case of weak chem- ∆z/(1+z) 1. ical feedback. Dashed lines: Contribution to the total SFR from ≃ Within eachphaseofthe IGM,starsareableto formin Pop I/II and Pop III for the case of strong chemical feedback. (b) two different ways. The first mechanism pertains to pri- Early reionization (zreion ≈ 17). We adopt the same convention for the lines as in panel (a). In all cases, Pop III star formation mordial, metal-free, gas. Such gas undergoes star forma- isrestricted tohigh redshifts,but extends over asignificant range, tionprovidedthatitaccretesontoadarkmatterhalowith ∆z∼10−15. a sufficiently deep gravitational potential well or equiva- lently a mass above a minimum value. For the neutral For the ionized medium, on the other hand, the min- medium,thisminimummassissetbytherequirementthat imum threshold mass is given by the Jeans mass, since thegaswillbeabletocool. Radiativecoolingbymolecular the infall of gas and the subsequent formation of stars re- hydrogen(H2) allows star formation in halos with a virial quiresthat the gravitationalforce ofthe dark matter halo temperature Tvir > 500 K, while atomic cooling domi- be greater than the opposing pressure force on the gas. nates for haloswit∼h T >103.9 K.Since H canbe easily After reionization, the IGM is photo-heated to tempera- vir 2 photo-dissociated by pho∼tons below the Lyman-limit, its tures >104K, leading to a dramatic increase in the Jeans significanceinthe cosmicstarformationhistoryisunclear mass.∼We model the suppression of gas infall according (e.g. Bromm & Larson 2004 and references therein), and to results from spherically-symmetriccollapse simulations so we only show results without H cooling in this paper. (see Bromm & Loeb 2002 for details). In calculating the 2 We note, however, that in the limiting case of negligible late reionization case (z 7), we employ the predic- reion ≈ H photodissociation feedback, the cosmic star formation tion by Thoul & Weinberg (1996) that gas infall is com- 2 3 pletely suppressed in halos with circular velocities v < Assuming that the formation of GRBs follows closely c 35 km s−1. For the early reionization case (z 17∼), the cosmic star formationhistory with no cosmologically– reion however,we use the recentworkby Dijkstra et al. (≈2004), significanttimedelay(e.g,Conseliceetal. 2005),wewrite showingthattheinfallsuppressionduetophoto-ionization for the number of all GRB events per comoving volume heatingcouldbemuchlesssevereinthe high-redshiftuni- per time, regardless of whether they are observed or not: verse. Specifically,weassumethatinthislattercaseinfall ψGtrRueB(z)=ηGRB×ψ∗(z), where ψ∗(z)is the cosmic SFR, is completely suppressedonly in haloswith circularveloc- as calculated in 2. The efficiency factor, ηGRB, links the § ities v < 10 km s−1. formation of stars to that of GRBs, and is in principle a c Withi∼n our model, the second mechanism to form stars function of redshift as well as the properties of the under- occurs in gas that has experienced a previous burst of lying stellar population. The stellar initial mass function starformation,andisthereforealreadysomewhatenriched (IMF) is predicted to differ fundamentally for Pop I/II with heavy elements. Such gas, residing in a halo of mass and Pop III (e.g., Bromm & Larson 2004 and references M , can undergo induced star formation triggered by a therein). The GRB efficiency factor will depend on the 1 mergerwithasufficientlymassivecompanionhaloofmass fraction of stars able to form BHs, and consequently on M2 > 0.5M1. We finally assume that stars form with an theIMF(see§3.2). Here,weassumethatηGRB isconstant efficiencyofη∗ 10%,independentofredshiftandregard- with redshift for PopI/II star formation, whereas Pop III less ofwhether∼the gasis primordialorpre-enriched. This stars may be characterized by a different efficiency. efficiency yields roughly the correct fraction of Ω found The numberofburstsdetectedbyanygiveninstrument B in stars in the present-day universe. Figure 1 shows the depends on the instrument-specific flux sensitivity thresh- resulting total star formation histories. It is evident that old and on the poorly-determined isotropic-luminosity therearetwodistinctepochsofcosmicstarformation,one function (LF) of GRBs (see, e.g., Schmidt 2001; Sethi & at z 3, and a second one at z 8 for late reionization, Bhargavi 2001; Norris 2002). In order to ascertain what wher∼eas there is only a single, ex∼tended peak at z 5 for Swift is expected to find, we modify the true GRB event early reionization. ∼ rate as follows: 2.2. Population III Star Formation To determine the fraction of the total SFR contributed ∞ bthyePaotpomIIiIcsctaorosl,inwgethharveeshtooldidefonrtiftyhethfiorssethtaimloes.thIantacdrodsis- ψGobRsB(z)=ηGRBψ∗(z)ZLlim(z)p(L)dL . (1) tion, we require that the collapse takes place in a region of the IGMwhich is not yetenrichedwith heavyelements from previous episodes of star formation. Here, we adopt theformalismdevelopedinFurlanetto&Loeb(2005)who Here, p(L) is the GRB LF with L being the intrinsic, derived the redshift-dependent probability that a newly isotropic-equivalent photon luminosity (in units of pho- collapsed halo forms out of pristine gas (see their Fig. 2). tons s−1). If f denotes the sensitivity threshold of a lim This probability crucially depends on the efficiency with given instrument (in photons s−1 cm−2), then the mini- whichthenewlycreatedmetalsaredispersedintotheIGM mum luminosity is: via SNdrivenwinds. Tobracketthe rangeofpossibilities, we consider the cases of weak and strong chemical feed- back,correspondingtowindsexperiencinglargeandsmall radiative losses, respectively4. L (z)=4πd2f (1+z)α−2 , (2) As can be seen in Figure 1, Pop III star formation is lim L lim limited to the highest redshifts, but in each case extends over a substantial range in redshift: ∆z 10 for strong ∼ chemical feedback, and ∆z 15 for weak feedback. The ∼ PopIII histories are rather similar for both early and late whered is the luminositydistance toa sourceatredshift L reionization. The suppression of gas infall for the early z,and α the intrinsic high-energy spectralindex (Band et reionization case (with v < 10 km s−1), would have a al. 1993). For definiteness, we assume α=2, which gives c much more pronounced effe∼ct on halos that cool via H , a reasonable fit to the observed burst spectra (see Band 2 because of their shallower potential wells. et al. 1993 for a detailed discussion). We here use the samelognormalLFandthe sameparametersasdescribed 3. GRBREDSHIFTDISTRIBUTION in Bromm & Loeb (2002). Next we will predict the GRB redshift distribution for In Bromm & Loeb (2002), we predicted that 25% of ∼ flux-limited surveys, distinguishing between the contribu- allburstsobservedbySwiftwouldoriginateatz 5. This ≥ tions fromPopI/II andPopIII starformation. In partic- estimate wasbasedona flux thresholdofflim =0.04pho- ular, we will focus on the existing Swift satellite, which is tonss−1cm−2. Basedonthefirstfewmonthsofactualob- capable of making the most detailed determination of the servations by Swift, the sensitivity limit has recently been GRB redshift distribution to date. revised upward to flim = 0.2 photons s−1 cm−2, compa- rable to the older BATSE experiment (e.g., Berger et al. 2005). Usingthisrevisedfluxlimit,wepredictthat 10% 3.1. Population I/II Contribution ∼ of all Swift GRBs will originate at z 5. ≥ 4Theweakandstrongfeedbackcases correspondtoKw1/3=1/3and1inequation(4)ofFurlanetto&Loeb(2005). 4 year detectable by Swift. In Figure 2, we show the Swift GRB rate, associated with Pop I/II star formation. For bothearlyandlate reionization,the observeddistribution is expected to peak around z 2. This distribution is ∼ broadly consistent with the first GRB redshifts, still lim- ited in number, measured during the first months of the Swift mission (Berger et al. 2005). We now turn to the possible contribution to the high redshift GRB rate from Pop III stars. 3.2. Population III Contribution We beginbyassumingthatPopIII starformationgives riseto GRBs with the same(constant)efficiency as is em- piricallyderivedforPopI/IIstars. AsisevidentfromFig- ure 2, only for the case of weak chemical feedback is Swift expectedto detectafewburstsderivingfromPopIII pro- genitors over the 5 yr lifetime of the mission. Whether ∼ reionizationoccurredearlyor late,on the other hand, has only a small effect on the predicted rates. It is quite pos- sible, on the other hand, that Swift will not detect any Pop III GRBs at all. Regardless of the uncertain contri- bution from Pop III stars, however, the prediction that 10% of all Swift bursts originate at z 5 is rather ro- ∼ ≥ bust. This fractionis due to PopI/II progenitorsthatare knownto produce GRBs, and those shouldexist at z 5. ≥ Adopting the same η for Pop III as for Pop I/II, GRB however, could be significantly in error. To examine the fundamentaldifferencebetweenthestellarpopulations,we needtogobeyondthephenomenologicalapproachpursued sofaranddiscussthepropertiesofplausibleGRBprogen- itors in greater physical detail. 3.2.1. Collapsar Engine Existing evidence implies that long-duration bursts are related to the death of a massive star, leading to the for- mation of a BH (see review by Piran 2004). The pop- ular collapsar model assumes that an accretion torus is temporarily formed around the black hole, and that the Fig. 2.—PredictedGRBrateobservedbySwift. Shownistheob- gravitational energy released during the accretion is able servednumberofburstsperyear,dNGobRsB/dln(1+z),asafunction to power a strong explosion (e.g., Woosley 1993; Lee & ofredshift. AllratesarecalculatedwithaconstantGRBefficiency, η(aG)RLBa≃te2r×eio1n0i−za9tibounrs(tzsreMion⊙−1≈,u7s)i.ngDtohtetecdoslminiecs:SFCRosntfrroibmutFioign.t1o. Radadmitiiroenza-Rl ureizqu20ir0e5m).enFtosrhtahveecotollabpesamrteotrbeesyuoltnidntahGeRfoBr-, the observed GRB rate from Pop I/II and Pop III for the case of mation of a BH. We will discuss these next, and will then weak chemical feedback. Dashed lines: Contribution to the GRB explorewhetherasubsetofPopIIIstarscouldsuccessfully ratefromPopI/IIandPopIIIforthecaseofstrongchemicalfeed- launch a GRB under the collapsar scenario. back. (b)Earlyreionization(zreion≈17). Thelineshavethesame To successfully produce a GRB with a collapsar, three meaningasinpanel(a). Filledcircle: GRBratefromPopIIIstars if these were responsible for reionizing the universe at z ∼ 17 (see basic requirements have to be fulfilled (see, e.g., Zhang & text). TheGRBratesfromPopIIIprogenitorsareveryuncertain; Fryer 2004; Petrovic et al. 2005): theycouldbezero,or,intheotherextreme,displayanenhancement (i) The progenitor star has to be sufficiently massive to byuptooneorderofmagnitudeabovethebaselineratesshownhere result in the formation of a central BH. Collapse to a BH (seetextfordetails). could occur either directly for initial masses of the pro- Over a particular time interval ∆tobs in the observer genitor > 40M⊙, or in a delayed fashion by fallback of frame, the observednumber of GRBs originating between the eject∼a following a failed SN explosion for progenitor redshifts z and z+dz is masses 25 < M∗ < 40M⊙ (e.g., Heger et al. 2003). The number of∼BH for∼ming stars resulting from a given total dNGobRsB =ψobs (z) ∆tobs dV , (3) stellarmass,heredenotedbyηBH,willdependonthestel- dz GRB (1+z) dz lar IMF which in turn is predicted to differ between the Pop I/II and Pop III cases. where dV/dz is the comoving volume element per unit For simplicity, we assume that the IMF in both cases redshift (see Bromm & Loeb 2002). As a final step, we consists of a power-law with the standard Salpeter value, normalize the GRB formation efficiency per unit mass in dN/dm m−2.35, but with different values for the lower Pop I/II stars to η 2 10−9 GRBs M−1. This and upp∝er mass limits, M and M respectively. For GRB ⊙ low up ≃ × choice results in a predicted number of 90 GRBs per Pop I/II stars, we take these to be: Mlow = 0.1M⊙ and ∼ 5 Mup = 100M⊙. The Pop III IMF, on the other hand, identify progenitor systems for collapsar–driven GRBs is still very uncertain (see, e.g., Bromm & Larson 2004). that fulfill both conditions (ii) and (iii). The basic prob- The upper mass limit can be conservatively estimated to lem is that the removal of the extended H-envelope is ac- be Mup 500M⊙ (Bromm& Loeb 2004),whereas for the companied by the loss of angular momentum in the core ∼ lower limit, we consider two possibilities: Mlow 30M⊙ (e.g., Petrovic et al. 2005). We will explore this problem ∼ (e.g., Tan & McKee 2004)and 100M⊙ (e.g., Abel et al. next,firstforsingle-starprogenitors,andthenforbinaries. ∼ 2002; Bromm et al. 2002). In general, 3.2.2. Single-star Progenitor Mupm−2.35dm In massive Pop I/II stars, radiation driven winds can η = MBH , (4) leadtovigorousmassloss,wherethe mainsourceofopac- BH RMup m−1.35dm ity is provided by metal lines (e.g., Kudritzki & Puls Mlow 2000). Empirically, the existence of Wolf-Rayet (WR) R stars proves that Pop I/II stars can indeed experience where MBH 25M⊙. For the Pop I/II case, this re- ≃ catastrophic mass loss, leading to the removal of the en- sults in ηBH 1/(700M⊙). The Pop III lower mass limit ≃ tire hydrogen-, and, in extreme cases, even of the helium- exceeds the threshold for BH formation in either case, M >M . NoteveryPopIIIstar,however,willleavea envelope. The violent mass loss, however, is accompanied low BH BH behind. In the narrowmass range of 140 260M⊙, by the effective removal of angular momentum from the PopIIIstarsarepredictedtoundergoapa∼ir-inst−abilitysu- remaining pre-collapse core, rendering the creation of a pernova (PISN) explosion (e.g., Fryer, Woosley, & Heger collapsar impossible. 2001; Heger et al. 2003). A PISN will lead to the com- For massive Pop III stars, radiatively driven winds are plete disruption of the star, such that no compact rem- predictedtobeunimportant(e.g.,Kudritzki2002;Krtiˇcka nant will be left behind. For the Pop III case, the expres- & Kuba´t 2005). Alternatively, mass loss could occur as sion results in ηBH 1/(80M⊙) for Mlow = 30M⊙, and a result of stellar pulsations (through the ǫ mechanism). ηBH 1/(300M⊙) fo≃r Mlow =100M⊙. Thus, the BH for- Simplified, linear calculations, however, indicate that this mati≃onefficiencyislargerforPopIIIcomparedtoPopI/II mechanism is not important below 500M⊙ (Baraffe, ∼ by up to one order of magnitude, depending on the lower Heger, & Woosley 2001). There still remains an unex- mass limit. plored possibility that Pop III stars could experience sig- (ii) The progenitor star has to be able to lose its hydro- nificantmasslossdrivenbyradiationpressureonHe+ions, gen envelope in order for the relativistic outflow to pene- where the opacity is provided by bound-free transitions. trate through and exit the star (e.g., Zhang et al. 2004). Alternatively,processedmaterialfrompreceedingepisodes This requirement derives from the observed burst dura- ofnuclearburning could be transportedto the stellarsur- tions, t < 100 s, providing an estimate for the lifetime of face by convection, rotationally-induced mixing, and dif- the cent∼ralGRB engine. The jet cantherefore only travel fusion, thus enriching the atmosphere to Z > 10−4Z⊙ at a distance of r ct 50R⊙ before being slowed down to which point line–driven mass loss is predic∼ted to set in non-relativistic∼speed∼s. Massive stars with hydrogen en- (Kudritzki 2002; Marigo, Chiosi, & Kudritzki 2003). Re- velopesgrowtoalargesizeduringtheirlaterevolutionary cently, it hasbeen suggestedthat WR type winds, in con- phases. For example, red supergiants can reach radii of nection with rapid rotation and the approach to the Ed- up to 103R⊙ (e.g., Kippenhahn & Weigert 1990). The dington limit, could possibly lead to significant mass loss effectiv∼eness of mass loss crucially depends on metallicity evenforverylow-metallicitystars(Vink&deKoter2005). (e.g., Kudritzki 2002), and on whether the star is isolated Themostlikelyexpectation,however,isthatisolatedmas- or part of a binary system. Below, we will discuss both sive PopIII stars are not able to shed much mass priorto effects further. their final collapse. (iii)Theprogenitorstarhastocontainacentralcorewith Thus itappearslikelythatthe majorityofmassive,sin- sufficientangularmomentumtoallowanaccretiondiskto glestarprogenitors,bothforPopI/IIandIII,cannotgive form around the growing BH. Important aspects of stel- risetoacollapsar-drivenGRB,althoughfordifferentphys- lar structureandevolutioncanbe understoodby dividing ical reasons. We note, however, that the progenitor for the star into a compact core, and an extended outer en- the collapsar engine is still very uncertain. In addition to velope (e.g., Kippenhahn & Weigert 1990). Depending on the binary scenario (see below), massive, rapidly rotating the evolutionarystage,aradiativecoreissurroundedbya single stars have recently been considered (e.g., Yoon & convectiveenvelope,orviceversa. Thepre-collapsestellar Langer 2005; Woosley & Heger 2005). Our main results, corehasa massM , radiusR ,angularvelocityω ,andis basedon the cosmic PopIII SFR and the IMF-dependent c c c characterizedby a specific angularmomentum j R2ω . BH fraction, however, holds in this case as well. We next Assuming that the collapse to a BH conservesspce≃cificcanc- turn our attention to binary-star progenitors. gular momentum, the condition for an accretion torus to formaroundagrowingBHinthecenterwithmassM is 3.2.3. Binary-star Progenitor BH centrifugal support for materialorbiting at the last-stable Close binary systems provide a promising avenue to si- radius. Thisconditioncanbe expressedasj >j ,with c min multaneously meet the requirements of strong mass loss j =√6GM /c 3 1016cm2s−1 (e.g.,Po∼dsiadlowski combined with the retention of sufficient angular momen- min BH ≃ × et al. 2004). tum in the collapsing core (e.g., Lee, Brown, & Wijers Recent results obtained with sophisticated stellar evo- 2002; Izzard, Ramirez-Ruiz, & Tout 2004). For Pop I/II, lution codes that include the effects of magnetic torques a binary pathway to a collapsar–driven GRB has already (e.g., Spruit 2002) have demonstrated the difficulty to been suggested (e.g., Fryer et al. 1993). The basic idea is 6 that a close binary system, experiencing Roche-lobe over- during the red giant phase: R > r > a . We esti- RG L i flow (RLOF) when the primary evolves off the main se- mate the Pop III radius during the giant∼phase, which is quence, will go through a common-envelope (CE) phase, smaller than that of a Pop I star of equal mass, to be during which the hydrogen envelope of the primary can R 300R , where R is the main-sequence radius. RG MS MS ∼ be removed without seriously draining away the spin of Massive Pop III stars obey a simple mass-radius relation the remaining helium core (for a recent review, see Taam (Bromm et al. 2001b): M R2 . The maximum sep- ∝ MS & Sandquist 2000). During the CE phase, the binary will aration for RLOF and therefore a CE phase to occur is spiralclosertogether,andthecorrespondinglossoforbital thus energywillheatthe envelopewithagivenefficiency,often M 1/2 assumed to be very high: αCE ≃ 1.0 (Taam & Sandquist ai,max ≃103R⊙(cid:18)102M⊙(cid:19) . (5) 2000). The frictional energy release during the in-spiral The minimum possible binaryseparation,a , onthe phase has been shown to be sufficient to unbind the hy- i,min other hand, will determine the extent of the inspiral pro- drogen envelope. cess and therefore of the accompanying frictional heating For a progressively tightening binary, the spin of each of the hydrogen envelope as well as the tidal spinning up component is tidally coupled to the orbital motion: ω c ∼ of the helium core. We approximately assume that the ω . Sincetheheliumcoreisspunupagainbecauseofthe orb minimumseparationisgivenbytwicetheradiusofamas- spin-orbit coupling, it is able to retain sufficient angular sive Pop III star during the main–sequence phase (which momentum to fulfill the j >j requirement. c min ∼ is only weakly dependent on mass): ai,min 10R⊙. If we ≃ 3.2.4. GRB Formation Efficiency further assume that the initial separations are distributed withequalprobabilityperlogarithmicseparationinterval, Ingeneral,wecanexpresstheGRBformationefficiency as they are for Pop I/II binaries (e.g., Abt 1983; Hea- for Pop III stars as: η η η η η , where GRB ≃ BH bin close beaming cox 1998; Larson 2003), dN/dlna const., and that the ηbin isthebinaryfraction,ηclose thefractionofsufficiently largest possible binary separation∝is given by the Jeans close binaries to undergo RLOF, η 1/50–1/500 beaming ≃ lengthforthetypicalconditionsinaprimordialgascloud, the beaming factor, where we conservatively assume that λ 1pc(e.g.,Brommetal. 2002,Bromm&Loeb2004), Pop III bursts are collimated by the BH central engine to J ≃ weestimatethefractionofallPopIIIbinariesthataresuf- the same angle as Pop I/II progenitors (the inferred colli- ficientlyclosetoexperienceaCEphasetobeη 30%. mation angles by Frail et al. 2001; Panaitescu & Kumar close ∼ In summary, η for Pop III stars is very uncertain, 2001, are indeed comparable to those of radio jets from GRB andcouldbe zeroin casethat no PopIII binariesexisted. the much more massive BHs in galactic nuclei). We have On the other hand, one may argue that the binary prop- already discussed η , and how Pop III star formation is BH erties for Pop III had been similar to Pop I/II, in cases characterized by an enhancement of up to one order of where Pop III star formation takes place in more massive magnitude because of the higher fraction of BH–forming host systems that could give rise to a stellar cluster, or at progenitors. leastmultiplestars. Suchaclusteredenvironmentisoften ItiscurrentlynotknownwhetherPopIIIstarscanform suggested to explain the formation and the properties of binaries, and if so, what the corresponding binary frac- binaries in present-day galaxies (e.g., Larson 2003). As- tion will be (e.g., Saigo, Matsumoto, & Umemura 2004). suming that the Pop III binary properties are similar to In present-day star formation, the incidence of binaries is PopI/II, we find a significant enhancement in η due to high,with 50%ofallstarsoccurringinbinariesorsmall BH ∼ thedifferenceintheIMFbetweenthepopulations. Wecan multiple systems (e.g., Duquennoy & Mayor 1991). Cur- then place an upper limit on the GRB rate from Pop III rentthree-dimensionalsimulations ofthe formationofthe stars by multiplying the baseline rates in Figure 2 by a first stars still lack the resolution to resolve the possible factor of 10. This would result in Pop III GRB rates fragmentation of a collapsing cloud into tight binaries or ∼ as large as 10 bursts detected by Swift per year for multiple stellar cores on scales < 100 AU. Although we ∼ the case of weak chemical feedback. Such very high rates cannot yet conclusively address t∼he formation of close bi- can already be excluded, since Swift has only identified naries, there is evidence from numerical simulations that two GRBs from z > 5 as of yet, GRB 050814 at z 5.3 binary or multiple clump formation is rather common on ≃ (Jakobsson et al. 2∼005) and GRB 050904 at z 6.3 (An- larger scales (>0.1 pc). In simulations where the collaps- ≃ tonelli et al. 2005;Haislip et al. 2005;Kawaiet al. 2005). ing gashadac∼quiredahighdegreeofangularmomentum, For strong chemical feedback, on the other hand, we pre- and where the collapse led to a disk-like configuration, dict rates of less than one burst detected per year, even pre-stellar clumps commonly occurred in binary or mul- if the BH efficiency were increasedby one order of magni- tiple systems (e.g., Bromm et al. 1999, 2002; Bromm & tude, and such a Pop III contribution cannot be excluded Loeb2003a,2004). Thusmotivated,ourbestguessisthat with the current constraints from Swift. η < 0.5. More work, in particular involving improved bin nume∼ricalsimulations,isrequiredtoconstrainthis crucial 3.3. Constraints from Reionization quantity further. ProvidedthatPopIIIstarformationdoesincludeafrac- If massive Pop III stars led to an early reionization of tion of binaries, we can use the collapsar requirements to the universe atz 17,as may be requiredby the WMAP ∼ obtain an estimate for the maximum binary separation, data(Kogutetal. 2003),wecanobtainanestimateforthe ai,max, prior to the CE inspiral phase, as follows. Assum- corresponding Pop III SFR at zreion and for the possible ing for simplicity that a Pop III binary has equal mass accompanying GRB rate, as follows. cwoimllpoonnlyentosc,ctuhrewRhoecnhethraedsiutasrisorvLer∼flo0w.s5aiit.sARoCcEhephloabsee ionPizoipngIIIphstoatrosnws ipthermsoalsasresm∼>as1s00oMve⊙r tphreoidruce2∼1016026Hy–r ∼ × 7 lifetime (e.g., Bromm et al. 2001b). We can then esti- tightPopIIIbinariesdonotexist)and 10timestheem- mate that 3 105M⊙ in Pop III stars are required to pirically inferred value for Pop I/II (du∼e to the increased ∼ × produce 5 ionizing photons for every hydrogen atom fraction of BH–forming progenitors among Pop III stars). in a com∼oving Mpc3. This number is sufficient to com- Recently, Gorosabel et al. (2004) and Natarajan et al. pensate for recombinations at the mean cosmic density. (2005)predictedtheexpectedredshiftdistributionoflong- Assuming further that the burst of Pop III star forma- duration GRBs, assuming they trace the cosmic star for- tion is spread over a fraction ǫ of the Hubble time at mation history, with various phenomenological prescrip- z 17, ∆t 4 107(ǫ/0.2) yr, the comoving tionsforthe dependence onmetallicity. Indifference from reion SF ∼ ∼ × Pop III SFR able to reionize the universe at that redshift thesestudies,weisolatethezero-metallicity(PopIII)stars is: SFRreion 7.5 10−3/(ǫ/0.2) M⊙ yr−1 Mpc−3. The and treat them as potential GRB progenitors based on a ∼ × extremelyrapidgrowthofthecollapsedfractionofbaryons physical model. with redshift implies a value of ǫ 1; however, the mini- It is of great importance to constrain the Pop III star ≪ mum value of ǫ is 0.1 because even within a single dark formation mode, and in particular to determine down to ∼ matterhalo,starformationcannotbesynchronizedtobet- which redshift it continues to be prominent. The extent ter than the dynamical time which amounts to ǫ 0.1 for of the Pop III star formation will affect models of the ini- ∼ a virial density contrast of 200. tial stages of reionization (e.g., Wyithe & Loeb 2003a,b; ∼ In Figure 2, we show the GRB rate which would corre- Ciardi, Ferrara, & White 2003; Sokasian et al. 2004; spond to SFR for ǫ=0.2 when the constant Pop I/II Yoshida et al. 2004; Alvarez, Bromm, & Shapiro 2006) reion GRB efficiency factor is used, resulting in 0.1 GRBs and metal enrichment (e.g., Mackey et al. 2003; Furlan- ∼ per year. Under this conservative assumption, Swift is etto & Loeb 2003, 2005; Scannapieco et al. 2003; Schaye not expected to detect, within its expected 5 year mission et al. 2003; Simcoe, Sargent, & Rauch 2004), and will lifetime, any bursts connected to the Pop III stars that determine whether planned surveys will be able to effec- were responsible for an early reionization of the universe. tively probe Pop III stars (e.g., Scannapieco et al. 2005). Again, the prospects for detection would be significantly The constraints on Pop III star formation will also de- improved if the Pop III GRB efficiency is boosted due to termine whether the first stars could have contributed a the increased fraction of BH–forming progenitors. significantfractiontothecosmicnear-IRbackground(e.g., Santos,Bromm,& Kamionkowski2002;Salvaterra& Fer- 4. SUMMARYANDCONCLUSIONS rara 2003; Dwek, Arendt, & Krennrich 2005; Kashlinsky Figure 2 leads to the robust expectation that 10% of 2005;Madau&Silk2005;Fernandez&Komatsu2006). If ∼ all Swift bursts should originate at z >5. This prediction PopIII binarieswerecommon,Swift mightbe the firstin- isbasedonthelikelyexistenceofPop∼I/IIstarsingalaxies strumentto detectPopIII starsfromgalaxiesatredshifts that were already metal–enriched at these high redshifts. z >7. AdditionalGRBscouldbetriggeredbyPopIIIstars,with ∼ ahighlyuncertainefficiency. Assumingthatlong-duration GRBsareproducedbythecollapsarmechanism,aPopIII WethankVickyKalogeraandSteveFurlanettoforhelp- star with a close binary companion provides a plausible ful discussions. VB thanks the Institute for Theory and GRB progenitor. We have estimated the Pop III GRB Computation at the CfA where partof this work was car- efficiency, reflecting the probability of forming sufficiently riedout. 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