R. Schneider et al- First Stars, Very Massive Black Holes, and Metals

8/3/2019 R. Schneider et al- First Stars, Very Massive Black Holes, and Metals

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FIRST STARS, VERY MASSIVE BLACK HOLES, AND METALS

R. Schneider,1 A. Ferrara,1 P. Natarajan,2,3 and K. Omukai1,4

Received 2001November 16; accepted2002 January 30

ABSTRACT

Recent studies suggest that the initial mass function (IMF) of the first stars (Population III) is likely to havebeen extremely top-heavy, unlike what is observed at present. We propose a scenario to generate fragmenta-tion to lower masses once the first massive stars have formed and derive constraints on the primordial IMF.We estimate the mass fraction of pair-unstable supernovae (SN), shown to be the dominant sources of thefirst heavy elements. These metals enrich the surrounding gas up to %104 Z, when a transition to efficientcooling-driven fragmentation producingd1 M clumps occurs. We argue that the remaining fraction of thefirst stars ends up in %100 M VMBHs (very massive black holes). If we further assume that all these VMBHsare likely to end up in the centers of galactic nuclei constituting the observed supermassive black holes(SMBHs), then %6% of the first stars contributed to the initial metal enrichment and the IMF remained top-heavy down to a redshift z % 18:5%. Interestingly, this is the epoch at which the cool metals detected in theLy forest at z % 3 must have been ejected from galaxies. At the other extreme, if none of these VMBHs hasas yet ended up in SMBHs, we expect them to be either (1) en route toward galactic nuclei, thereby accountingfor the X-raybright off-center sources detected locally by ROSAT, or (2) the dark matter candidate compos-ing the entire baryonic halos of galaxies. For case 1 we expect all but a negligible fraction of the primordialstars to produce metals, causing the transition at the maximum possible redshift ofe22.1, and for case 2,$3 105, a very negligible fraction of the initial stars produce the metals and the transition redshift occurs atzfe5:4. In this paper, we present a framework (albeit one that is not stringently constrained at present) thatrelates the first episode of star formation to the fate of their remnants at late times. Clearly, further progressin understanding the formation and fragmentation of Population III stars within the cosmological contextwill provide tighter constraints in the future. We conclude with a discussion of several hitherto unexploredimplications of a high-massdominated star formation mode in the early universe.

Subject headings: black hole physics cosmology: theory galaxies: formation intergalactic medium

On-line material: color figures

1. INTRODUCTION

Recent studies have started to tackle the formation and

collapse of the first cosmic structures (often referred to asPopulation III objects) through numerical simulations(Abel et al. 1998; Bromm, Coppi, & Larson 1999; Bromm etal. 2001; Abel, Bryan, & Norman 2000) based on hierarchi-cal scenarios of structure formation. These studies haveshown that gravitational collapse induces fragmentation ofpregalactic units with an initial baryonic mass %105 M intosmaller clumps with a typical mass of 103 M, which corre-sponds to the Jeans mass set by molecular hydrogen cool-ing. However, a considerable mass range (102104 M) forthe clumps seems plausible.

Tracking the subsequent gravitational collapse of thesemetal-free clumps is a very challenging problem, as itrequires the simultaneous solution of hydrodynamics and of

(cooling lines) radiative transfer (Omukai & Nishi 1998;Nakamura & Umemura 1999; Ripamonti et al. 2001). Pre-liminary attempts and several physical arguments indicatethat these clumps do not fragment into smaller units as the

evolution progresses to higher densities. Independent stud-ies (Hernandez & Ferrara 2001) comparing the observednumber of metal-poor stars with that predicted by cosmo-logical models also imply that the characteristic stellar masssharply increases with redshift. Hence, there are grounds tobelieve that the first stars were very massive.

The evolution of massive, metal-free stars is currentlysubject to a rapidly growing number of studies (Fryer 1999;Fryer, Woosley, & Heger 2001; Heger & Woosley 2001) thatrejuvenate earlier activity (Fowler & Hoyle 1964; Carr,Bond, & Arnett 1984; El Eid et al. 1983; Fricke 1973; Fulleret al. 1986). As we discuss in detail later in this paper, starsmore massive than about 260 M collapse completely toblack holes, therefore not contributing to the metal enrich-ment of the surrounding gas. Similar arguments apply tostars in a lower mass window (30140 M), which are alsoexpected to end their evolution as black holes. Hence, ifsupernovae from more standard progenitors (stellar massesin the range 840 M) are neither formed efficiently noroccur in negligible numbers, it appears that the initial cos-mic metal enrichment had to rely on the heavy-element yieldfrom the so-called pair-unstable supernovae (SN), whoseexplosion leaves no remnant. This conclusion can poten-tially be tested by studying peculiar elemental abundances,for example, of heavy r-process elements (Oh et al. 2001).

Metallicity is thought to noticeably affect the fragmenta-tion properties of a gravitationally unstable gas. For exam-ple, Bromm et al. (2001) have shown that the evolution of acollapsing protogalaxy depends strongly on the level of gaspreenrichment. These authors argue that a critical metallic-

1 Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Flor-ence,Italy.

2 Department of Astronomy, Yale University, New Haven, CT 06520-8101.

3 Yale Center for Astronomy and Astrophysics, Yale University, NewHaven, CT 06511.

4 Division of Theoretical Astrophysics, National Astronomical Observ-atory, Mitaka, Tokyo181-8588, Japan.

The Astrophysical Journal, 571:3039, 2002 May 20

# 2002.The American AstronomicalSociety. All rightsreserved.Printedin U.S.A.

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ity %104 Z exists such that above that value vigorousfragmentation into relatively low mass (%10 M) clumpstakes place, differently from what is discussed above undermetal-free conditions.

The key question, then, concerns the interplay betweenthe properties of the initial mass function (IMF) and themetal enrichment of the gas. To better illustrate this, let usideally suppose that the first stars are all formedas sug-gested by numerical simulationswith masses above theSN mass threshold, thus leading to the formation of blackholes. Then, because metals are completely swallowed bythe latter, the gas retains its primordial composition andstar formation continues in the high-massbiased mode. Asolution to this star formation conundrum must evi-dently exist, as at present stars form with a much lower char-acteristic mass (%1 M).

In this paper, we describe in detail a possible solution tothis conundrum utilizing various constraints: metal abun-dance patterns in clusters, the mass density of supermassiveblack holes, off-nuclear galactic X-ray sources, and to amore speculative extent, the nature of a particular class(optically hidden) of gamma-ray bursts; we attempt to inferthe main properties of the early stages of cosmic starformation.

2. FRAGMENTATION MODES

In this section, we focus on the first episode of star forma-tion and discuss the relevant cooling criteria and timescalesin detail. We work within the paradigm of hierarchical colddark matter (CDM) models for structure formation,wherein dark matter halos collapse and the baryons in themcondense, cool, and eventually form stars. Once a halo ofmass M collapses at redshift of zc, the baryons are shock-heated to the virial temperature given by

Tvir 104:5lM2=38 1 zc

10

K ; 1

where M8 M=108 h1 M and l is the molecular weight.If Tvire104 K [or equivalently Me1091 zc

3=2

h1 M], the baryonic gas cools because of the excitation ofthe hydrogen Ly line. In the absence of metals, as expectedfor the very first episode of star formation, objects withTvird104 K can cool only through the collisional excitationof molecular hydrogen. Hereafter in this work, we refer tothe former objects as Ly-cooling halos and to the latter asPopulation III objects.

The first stars form once the gas cools. The typical IMFof this first generation of stars is still highly uncertain. Sev-eral authors have tackled this crucial issue through theoreti-cal (Rees 1976; Rees & Ostriker 1977; Silk 1977, 1983;Haiman, Thoul, & Loeb 1996; Uehara et al. 1996) andnumerical approaches (Omukai & Nishi 1998; Nakamura &Umemura 1999, 2001; Abel et al. 2000; Bromm et al. 1999;Omukai 2000, 2001; Ripamonti et al. 2001). Recent multidi-mensional simulations of the collapse and fragmentation ofprimordial gas within Population III objects show prelimi-nary indications that the IMF could be either top-heavywith typical masses of the order ofe102 M (Abel et al.2000; Bromm et al. 2001) or bimodal with peaks at %102

and %1 M (Nakamura & Umemura 2001). Note that thesenumerical treatments cannot address the issue of the massspectrum. Therefore, it is important to understand what

physical processes set the scales of fragment masses andhence the stellar mass spectrum.

It is obvious that much hinges on the physics of cooling,primarily the number of channels available for the gas tocool and the efficiency of the process (Rees & Ostriker1977). In general, cooling is efficient when the cooling timetcool 3nkT=2n; T is much shorter than the free-falltime tff 3=32G

1=2, i.e., tcool5 tff, where n() is the gasnumber (mass) density and n; T is the net radiative cool-ing rate (ergs cm3 s1). This efficiency condition impliesthat the energy deposited by gravitational contraction can-not balance the radiative losses; as a consequence, tempera-ture decreases with increasing density. Under suchcircumstances, the cloud cools and then fragments. At anygiven time, fragments form on a scale that is small enoughto ensure pressure equilibrium at the corresponding temper-ature, i.e., the Jeans length scale,

RF % J / cstff / n=21 ; 2

where the sound speed cs RT=l1=2, T / n1, where is

the adiabatic index. Since cs varies on the cooling timescale,the corresponding RF becomes smaller as Tdecreases. Simi-

larly, the corresponding fragment mass is the Jeans mass,

MF / nRF / n

=21 ; 3

with 2 for filaments and 3 for spherical fragments(Spitzer 1978). This hierarchical fragmentation processcomes to an end when cooling becomes inefficient because(1) the critical density for LTE is reached or (2) the gasbecomes optically thick to cooling radiation; in both cases,at that juncture tcooletff. At this stage, the temperature can-not decrease any further, and it either remains constant (ifenergy deposition by gravitational contraction is exactlybalanced by radiative losses) or increases. The necessarycondition to stop fragmentation and start gravitational con-traction within each fragment is that the Jeans mass doesnot decrease any further, thus favoring fragmentation intosubclumps. From equation (3), this implies the condition

e2 1

; 4

which translates into e4=3 for a spherical fragment ande1 for a filament. Thus, a filament is marginally stableand contracts quasi-statically when tcool % tff and the gasbecomes isothermal. Finally, when tcool4tff or the frag-ments become optically thick to cooling radiation,the temperature increases as the contraction proceedsadiabatically.

2.1. Fragmentation of Metal-free CloudsIn this subsection, we follow the evolution of metal-free

primordial clumps during the fragmentation process. Theseresults are based on the model of Omukai (2001). The gaswithin the dark matter halo is given an initial temperatureof 100 K, and the subsequent thermal and chemical evolu-tion of the gravitationally collapsing cloud is followednumerically until a central protostellar core forms.

The gas within the dark matter halo gets shock-heated tothe virial temperature Tvir, which is typically4100 K. How-ever, after a short transient phase (irrelevant for the presentanalysis), the evolutionary track in the (n, T) plane shown inFigure 1 (top curve, top panel) provides a good description

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of the thermal evolution of the gas. The metal-free gas isable to cool down to temperatures of a few hundred kelvinregardless of the initial virial temperature. This is the mini-mum temperature at which molecular line cooling becomeseffective.

In this analysis, external sources of heating are notincluded (i.e., external UV background or cosmic micro-wave background [CMB] radiation). This is because at red-shifts prior to reionization, the UV background field isrelatively weak and inhomogeneous (Ciardi, Ferrara, &Abel 2000), and hence we do not expect it to be important.Also, the CMB energy input is negligible for clouds withT > 100 K (or Z < 104 Z), where the first stars presum-ably formed at redshifts z < 30. It might affect the tempera-ture evolution of more metal-rich systems shown in Figure1, but it does not modify the conclusions drawn here.

The gas within halos with Tvir > 104 K starts to coolthrough the hydrogen Ly line. It quickly reaches a temper-ature of%8000 K, and at this stage, the fraction of molecu-lar hydrogen formed is sufficient to activate H2rovibrational line cooling. Thereafter, the gas within a Ly-cooling halo follows the same thermal evolution as the gaswithin Population III objects. Independent of the virial tem-perature, the thermal evolution of the gas rapidly convergesto the (n, T) track corresponding to Z 0 (the zero-metal-licity track) shown in Figure 1. The temperature of the gasdecreases with increasing density, thus favoring fragmenta-tion into subclumps.

As the number density increases, it reaches the criticalvalue ncr % 103 cm3, and the corresponding Jeans mass is

%104 M (open circle in the top panel of Fig. 1). The coolingtime at this critical point becomes comparable to the free-fall time as a consequence of the H2 levels being populatedaccording to LTE [regime in which the cooling raten; T / n] and no longer according to non-LTE (NLTE)[regime in which n; T / n2]. The temperature then startsto rise slowly.

At this stage, the stability of the fragments toward furtherincrease in the density needs to be investigated according toequation (4) above. The bottom panel of Figure 1 shows thedensity dependence of (see eq. [2]) for each metallicitytrack. For a metal-free gas, lies in the range 0 < 1 < 13,implying that further fragmentation is unlikely to occurunless the fragments are spherical. Although the gravita-tional evolution will probably favor a tendency towardspherical symmetry, this is not likely to occur until the cen-tral density has reached high (%108 cm3) values as seenfrom simulations (e.g., Abel et al. 2000).

The only two deviations from the above range occur (seeFig. 1, bottom panel) around n 1010 and 1016 cm3. Theformer is a result of the thermal instability due to three-bodyH2 formation (Silk 1983; Haiman et al. 1996). However, thisinstability is quite weak and does not lead to fragmentation(Abel et al. 2000). The latter (at n 1016 cm3) is caused byH2 collision-induced emission. This instability is also weakand probably unimportant.

It is important to stress that, even if the fragments arenearly spherical, fragmentation will be modest and is likelyto result only in a low-multiplicity stellar system. As thedensity increases, quasi-static contraction takes place(n 1020 cm3) until the fragments become optically thickto H2 lines, tcool4tff, and adiabatically collapse to increas-ingly higher central densities and temperatures. At thisstage, > 4=3 and a central hydrostatic core (stellar core;filled circle in Fig. 1, top panel) is formed, with mass %103

M (Omukai & Nishi 1998).We stress again that as long as the gas is metal free, this

sequence of events and conclusions hold independent of thehalo virial temperature, i.e., for Population III objects aswell as for Ly-cooling halos. In Figure 2, we show the evo-lution with temperature of the ionization fraction and of thefraction of molecular hydrogen for typical Ly-coolinghalos of mass M 108 M at three different redshifts,z 15, 20, and 25. We find that the evolution of these frac-tions is independent of the mass (or, equivalently, Tvir) andvirialization redshift. Molecule formation in the postshockflow that follows the virialization of the gas within a darkmatter halo has been recently investigated by Uehara &Inutsuka (2000). If the gas is fully ionized, molecules formthrough nonequilibrium recombination, leading to overallfractions that are much higher than in the expanding homo-geneous universe. As a consequence of enhanced H2 andHD fractions, the gas rapidly cools to well below 104 K andfragments. Molecular chemistry is important also for starformation in halos with Tvir > 104 K as assessed by Susa etal. (1998) and Oh & Haiman (2002). They find that initialatomic line cooling leaves a large residual free electron den-sity that allows molecule formation up to a universal frac-tion of xH2 10

3. The newly formed molecules cool thegas further to $100 K, and the gas fragments on mass scalesofa few100 M.

Once the critical density for H2 (ncr % 103 or 105 cm3 for

HD, if this is assumed to be the main coolant) has beenreached, LTE conditions for the level populations disfavor

Fig. 1.Top: Evolutionof thetemperature as a function of thehydrogennumber density of protostellar clouds with the same initial gas temperaturebut varying metallicities Z 0; 106; 104; 102; 1 Z (Zincreasing fromtop to bottom curves). The dashed lines correspond to the constant Jeansmass for spherical clumps; open circles indicate the points where fragmen-tation stops; filled circles mark the formation of hydrostatic cores. This fig-ure is reproduced from Fig. 1 of Omukai (2000) for illustration after somemodifications. Bottom: The adiabatic index as a function of the hydrogennumber density for the curves shown in the top panel. Dotted (dashed )linescorrespond to 1 ( 4=3);open andfilled circles as above.

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further cooling and fragmentation. At this stage, fragmentshave masses comparable to the Jeans mass corresponding tothe point (ncr, Tcr) and virialize, following the evolutiondescribed above. Therefore, independent of the initial virialtemperature, fragments are formed with typical masses%103 104 M

.

Each fragment is characterized by a central core of 103

M surrounded by a large envelope of gravitationally unsta-ble gas. The core grows in mass because of gas accretionfrom the envelope. The mass of the formed stars depends onthe accretion rate as well as on the fragment mass (Larson1999). In the absence of metals, radiation pressure cannotcounterbalance mass accretion onto the core (Ripamonti etal. 2001; Omukai & Inutsuka 2001), and the mass of theresulting star is comparable to that of the original fragment,i.e.,d103 M. We will return to this crucial issue in x 2.3. Ofcourse, if the parent cloud is rotating, angular momentum,if not dissipated, might prevent the collapse of the entirecloud. However, for the arguments relevant to this paper, it

is sufficient that the overall efficiency is of a few percent, thusyielding a few hundred solar mass stars out of the %104 Mfragments predicted by Figure 1. The question that needs tobe addressed now is what mechanism can finally lead to thetransition to a conventional mode of star formation, i.e., toa standard IMF, and what are the necessary conditions forthis to occur.

2.2. Fragmentation of Metal-enriched Clouds

We now consider the effects of the presence of heavy ele-ments on the fragmentation process. The discussion pre-sented in this section is based on the analysis by Omukai(2000) (see the original paper for details). Figure 1, repro-

duced from Omukai (2000), shows the effects of metalenrichment on the (n, T) tracks for the same initial condi-tions and different values of the mean metallicity.

In general, clouds with lower metallicity tend to bewarmer because of their lower radiative cooling ability. Aslong as the clouds are transparent, cooling and fragmenta-tion occur. Clouds with a mean metallicity Z % 106 Zfollow the same evolution as that of the gas with primordialcomposition in the (n, T) plane. However, at Ze104 Z,H2 formation on grain surfaces enhances cooling at lowdensity. Dust grains are well known to condense out theejecta of SNe (see Todini & Ferrara 2001 and referencestherein). When the LTE-NLTE transition occurs for H2, thecloud can still cool (although less efficiently) because of O iline cooling. At densities greater than 106 cm3, heating dueto H2 formation becomes larger than compressional work,i.e., > 1, and the temperature starts to increase until ther-mal emission from grains due to energy transfer betweengas and dust dominates the cooling. This occurs at a densityn % 1010 cm3, where the temperature drops to %100 K anda new fragmentation phase occurs. This shows up in the bot-tom panel of Figure 1 as the large dip in the evolution. Theminimum fragment mass is reached at the point indicatedby the open circle, when the density is %1013 cm3 and thecorresponding Jeans mass is of the order 102 M. Finally,as the density increases, the gas becomes opaque to dustthermal emission, fragmentation stops, and compressionalheating causes the fragments to contract adiabatically( > 4=3). Therefore, a critical metallicity ofZcr % 104 Zcan be identified, which marks the transition point betweenmetal-free and metal-rich gas evolution.

When the metallicity is Z > 104 Z, at density d104

cm3 cooling is driven by O i, C i, and CO line emission.When the NLTE-LTE transition for the level populationsof CO occurs, fragmentation stops and the temperatureincreases because of H2 formation. The larger concentrationof dust grains (assumed here to be proportional to the meanmetallicity) leads to a significant thermal emission that isresponsible for cooling the gas and starting a new phase offragmentation. This stops when Tgrain T, and thereafterthe fragments contract quasi-statically until they becomeoptically opaque to dust emission and adiabatic contractionoccurs. Because of the enhanced ability to cool, fragmenta-tion stops at lower temperatures and densities for highermetallicity clouds (see open circles in the bottom panel ofFig. 1). However, the Jeans mass corresponding to the mini-mum fragmentation scale is always 102 M MF 1 M for the metallicity range 104 Z=Z 1, severalorders of magnitude smaller than for a cloud with nometals.

At the onset of adiabatic contraction, when becomeslarger than 4/3, an initial hydrostatic core (transient core)forms with a mass %102 M, regardless of the metallicityof the gas. This transient core is fully molecular and isabsent when the gas is metal free. The temperature of thetransient core increases as its mass increases because ofaccretion of surrounding gas. Eventually, the temperaturereaches about 2000 K, where H2 dissociation begins. Thissoftens the equation of state until the dissociation is almostcomplete. Then, falls below 4/3 in the density range 10161020 cm3. Note that the thermal evolution after H2 dissoci-ation (i.e., n > 1016 cm3) is the same independent of theinitial composition of the gas. After once again exceeds4/3, a hydrostatic core (so-called stellar core) forms. Its

Fig. 2. Fractional abundance of H2 (solid lines) and ionization frac-tions (dashed lines) as a function of gas temperature. The three cases plottedare for a halo of mass M 108 M at three different virialization redshiftsz 15; 20; 25 [virial temperatures of Tvir 2:2; 6:9; 17 104 K]. As canbe seen in the figure, the evolution appears to be independent of the virialtemperature of the halo.

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physical characteristics are independent of metallicity(n % 1022 cm3; M % 103 M; Omukai 2000).

2.3. Formation of Protostars

Protostars, whose mass is initially very low (about 103

M), grow in mass by accretion of the envelope material.The final mass of stars is then determined not only by themass of the fragments, but also by when accretion stops.

The accretion rate onto the protostar is related to the soundspeed (and therefore, temperature) of the protostellar cloudby the relation _MM c3s=G(Stahler, Shu, & Taam 1980).

As seen in Figure 1, the temperature of protostellarclouds decreases with metallicity. Therefore, the mass accre-tion rate is higher for protostars formed from lower metal-licity gas. If dust is present in the accretion flow, accretiononto the massive protostar becomes increasingly difficultowing to the radiation pressure onto the dust. In present-day interstellar gas, accretion onto stars more massive than30 M is inhibited by this mechanism (Wolfire & Cassinelli1987). In gas with lower metallicity, the mass bound isexpected to be higher because of the higher accretion rateand lower radiation force. In particular for metal-free gas

this mechanism does not work. Therefore, without dust,accretion is likely to continue until the ambient gas supply isexhausted (Ripamonti et al. 2001; Omukai & Inutsuka2001).

In conclusion, the presence of metals not only enablesfragmentation down to smaller mass scales 102 M, butalso breaks the one-to-one correspondence between themass of the formed star and that of the parent fragment byhalting the accretion through radiation force onto the dust.

3. THE STAR FORMATION CONUNDRUM

According to the scenario proposed above, the first starsthat form within Population III and Ly-cooling halos outof gas of primordial composition tend to be very massive,with masses %102103 M. It is only when metals changethe composition of the gas that further fragmentationoccurs, producing stars with significantly lower masses. It isat this stage that we expect a transition to occur from a top-heavy IMF toward a more conventional IMF with a widerange of masses, such as the one observed locally (Scalo1998; Kroupa 2001).

A growing body of observational evidence points to anearly top-heavy IMF (see Hernandez & Ferrara 2001 andreferences therein). Compelling arguments for an early top-heavy IMF can also be made from observations on variousscales: (1) the early enrichment of our Galaxy required tosolve the so-called G dwarf problem, (2) the abundance pat-terns of metals in the intracluster medium (ICM), (3) theenergetics of the ICM, (4) the nondetection of metal-freestars, and (5) the overproduction of low-mass stars at thepresent epoch and metals at z $ 2 5 for the submillimeter-derived star formation histories using Submillimeter Com-mon-User Bolometric Array (SCUBA) detections for astandard IMF can be resolved with an early top-heavyIMF.

For instance, the ICM metal abundances measured fromChandra and XMM spectral data are higher than expectedfrom the enrichment by standard IMF SN yields in clustergalaxy members, which can be explained by a top-heavyearly IMF. Furthermore, the observed abundance anoma-

lies (e.g., oxygen) in the ICM can be explained by an earlygeneration of Population III SNe (Loewenstein 2001).There is observational evidence from the abundance ratiopatterns of [Si/Fe], [Mg/Fe], [Ca/Fe], and [Ti/Fe] in theextremely metal poor double-lined spectroscopic binary CS22876032 in the halo of our Galaxy (Norris, Beers, &Ryan 2000) for enrichment by a massive, zero-metallicitysupernova in comparison with the theoretical models ofWoosley & Weaver (1995). These issues, highly suggestiveof top-heavy early star formation, have recently motivateda series of numerical investigations of the nucleosynthesisand final fate of metal-free massive stars (Heger & Woosley2001; Fryer et al. 2001; Umeda & Nomoto 2002). In theirrecent paper, Heger & Woosley (2001) delineate three massranges characterized by distinct evolutionary paths:

1. Me260 M .The nuclear energy release from thecollapse of stars in this mass range is insufficient to reversethe implosion. The final result is a very massive black hole(VMBH) locking up all heavy elements produced.

2. 140 MdMd260 M.The mass regime of thepair-unstable supernovae (SN). Precollapse winds andpulsations result in little mass loss; the star implodes to a

maximum temperature that depends on its mass and thenexplodes, leaving no remnant. The explosion expels metalsinto the surrounding ambient ISM.

3. 30 MdMd140 M.Black hole formation is themost likely outcome, because either a successful outgoingshock fails to occur or the shock is so weak that the fallbackconverts the neutron star remnant into a black hole (Fryer1999).

Stars that form in the mass ranges 1 and 3 above fail toeject most of their heavy elements. If the first stars havemasses in excess of 260 M (in agreement with numericalfindings), they invariably end their lives as VMBHs (in thefollowing we will refer to VMBHs as black holes of a hun-dred solar mass or so) and do not release any of their synthe-sized heavy elements. However, as we have shown, as longas the gas remains metal free, the subsequent generations ofstars will continue to be top-heavy. This star formationconundrum can be solved only if a fraction of the first gen-eration of massive stars have massesd260 M. Under suchcircumstances, these will explode as SN and enrich the gaswith heavy elements up to a mean metallicity ofZe104 Z, and as per arguments outlined in x 2 (see Fig.1), thereafter causing a shift over to an IMF that is similarto the local one. In what follows, we further explore theimplications of the above scenario and derive the conditionsfor the solution of the conundrum.

3.1. Abundance of VMBHs and Metals

As a consequence of the picture proposed above, VMBHsare an inevitable outcome. We now compute the expectedmass density of metals and the mass density of remnantVMBHs produced in such a first episode of star formation.For a collapsed dark matter halo of total mass M, the asso-ciated baryonic mass is assumed to be MB=M (whereB=M is simply the baryon fraction). Following the resultsof numerical simulations at different resolutions (Bromm etal. 2001; Abel et al. 2000), we assume that %12 of the totalavailable gas is utilized in star formation, the rest remainingin diffuse form.



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The relative mass fractions of SN and VMBH progeni-tors are parameterized as

M fM

2

B

M

fM ; 5

MBH 1 fM

2

B

M

1 fM ;

where M (MBH) is the total mass that ends up in SN(VMBHs) and M* is the mass processed into stars. Thus,only a fraction f of the formed stars can contribute to gasmetal enrichment. The metal yields for the dominant ele-ments have been computed using the results of Heger &Woosley (2001) and are plotted in Figure 3 as a function ofthe mass of the progenitor star. The bulk of the yield iscontributed by O16, and the mass of metals ejected can bewritten as

MZ %M

2 10 M

M

200 M; 6

where we have taken %200 M as a fiducial mass for SNprogenitors. Next, the further assumption is made that met-

als are ejected from the parent galaxy into the IGM and thattheir cosmic volume filling factor is close to unity, thereforeuniformly polluting the IGM. This comes from the resultsof Madau, Ferrara, & Rees (2001, hereafter MFR01) andMori, Ferrara, & Madau (2002), in which it is shown thatfor reasonable values of the star formation efficiency, metalbubbles produced by (standard SNe II in) protogalaxiesthat result from 2 peaks of the density power spectrum atredshift 10 do overlap. Indeed, the kinetic energy releasedby SN is much higher than for ordinary SNe II (see Fig.2), hence making our assumption even more solid. The tem-perature of the hot gas is expected to be somewhat higherthan estimated by MFR01; however, because of the higherredshifts and consequent stronger inverse Compton cool-

ing, ejected metals have enough time to cool by z % 3.

As long as the average metallicity is below the criticalvalue, i.e., Zcr 104 Z, we argue that the IMF remainstop-heavy and the redshift-dependent critical density ofmetals contributed by all SN at redshifts greater than zcan be computed as

Zz 1

cr

Z1z

dz0Z

Mminz0

dM nM; z0 MZ ; 7

where n(M, z) is the number density of halos per unit masspredicted by the Press-Schechter formalism, and the inte-gration is performed from Mmin(z), which is the minimummass that can cool within a Hubble time at the specified for-mation redshift z, i.e., tcoolM; zdtHz (see Ciardi et al.2000). We adopt a cosmological model with the followingparameters to compute the abundance of halos: M 0:3, 0:7, h 0:65, and B 0:047 (latest predictions frombig bang nucleosynthesis; see Burles, Nollett, & Turner2001), and use the COBE-normalized power spectrum forfluctuations as described in Efstathiou, Bond, & White(1992).

From equation (7),we can estimate the transition redshiftzfat which the mean metallicity is 10

4 Z,

Zzf

Zzf

B% 104 Z ; 8

for various values of the fraction f. The results are plottedin Figure 4 along with the corresponding critical densityVMBH contributed by the VMBHs formed, which is given

Fig. 3.Metal yields of the main elements synthesized in metal-freeSN according to Heger & Woosley (2001). The upper solid line corre-sponds to the total yield ejected, and the dashed line indicates the kineticenergy of the explosion. [See the electronic edition of the Journal for a colorversion of this figure.]

Fig. 4.Top-heavy to normal IMF transition redshift, zf, as a functionof SN progenitor mass fraction and the mass density contributed byVMBHs VMBH. Top: The computed critical density of VMBH remnants iscompared to the observed value for SMBHs (upper dashed line). Bottom:The computed critical density of VMBH remnants is compared to the con-tribution to from the X-raybright, off-center ROSAT sources (lowerdashed line) and to the abundance predicted assuming that the baryonicdark matter in galaxy halos is entirely contributed by VMBHs ( upperdashed line). The observations on VMBH constrain the value for f. For agiven f, the corresponding value for the transition redshift can be inferredby the zf curve. [See the electronic edition of the Journal for a color version ofthis figure.]



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by

VMBHzf 1 f

crit

Z1zf

dz0Z

Mminz0

dM nM; z0 M :

9

In x 4, several assumptions as to the fate of these VMBHs atlate times is examined in an attempt to obtain constraints onthe value off from current observations.

4. OBSERVATIONAL CONSTRAINTS

The objective now is to set some limits on f, the fractionof stars formed that result in SN, providing the first met-als, that are eventually responsible for the shift to a normalIMF. In order to compare the predicted critical density ofVMBH remnants to present observational data, we mustmake further assumptions about the fate of these VMBHsat late times.

The mass density contributed by remnant supermassiveblack holes (SMBHs), 0SMBH, can be estimated observatio-nally5 from the demography of local galaxies (Magorrian et

al. 1998; Merritt & Ferrarese 2001). There are two extremepossibilities (bounding cases for the values of f) concern-ing the relation between the inferred mass density ofSMBHs and VMBHs: case A: VMBHzf

0SMBH (all

VMBHs have, during the course of galaxy mergers, in factbeen used to build up the SMBHs detected today); and caseB: VMBHzf

0VMBH 6

0SMBH; there is no relation

between the detected SMBHs and the early VMBHs, imply-ing that SMBHs have grown primarily by gas accretion.

Thus, in case A, we assume that all VMBHs are able tosink to the center of host systems to merge within a Hubbletime, giving birth to the SMBHs in the nuclei of galaxiesthat we see today. Note that this is in fact unlikely (asexplained later); nevertheless, this argument provides an

extreme bound.It is important to point out here that in the current pro-posed theoretical models for the mass accretion history ofblack holes, the mass density seen locally today in SMBHscan be built either predominantly by mergers or by accre-tion. In phenomenological models that attempt to tie in thecurrent high-redshift observations of the space density andluminosity function of quasars with that of the local spacedensity of black holes, wherein it is assumed that quasarsare (1) powered by BHs and (2) optically bright for a periodof%106107 yr (Haiman & Loeb 1998; Haehnelt, Natarajan,& Rees 1998; Kauffmann & Haehnelt 2000), either picture(mergers/accretion) can adequately explain the mass assem-bly of the remnant SMBHs.

This permits both cases A (wherein SMBHs grow primar-ily via mergers of VMBHs during galaxy assembly) and B(wherein SMBHs grow primarily by accretion and 0SMBH isunrelated to VMBH) to be plausible extreme cases. Consid-eration of cases A and B will provide bounds on the valuefor f. For a given f, the corresponding value for the tran-sition redshift can be found on the zf curve shown inFigure 4.

We note here that VMBHs in the mass range expectedfrom the first episode of metal-free star formation (a fewhundred solar masses) are likely to be ubiquitous. UsingInfrared Space Observatory (ISO) observations, Gilmore &

Unavane (1998) have convincingly argued that low-massstars (in fact, hydrogen-burning stars of any mass) do notprovide a substantial portion of the dark matter inferred inthe halos of galaxies. In combination with the mass limitsobtained on potential dark matter candidates from theMACHO (Alcock et al. 2001) and EROS (Lasserre et al.2000) experiments (microlensing studies) in our Galaxy,low-mass objects with masses under 10 M are ruled out,thereby making VMBHs (%100 M BHs) in halos (case B)plausible dark matter candidates.

For case A, we can simply equate 0VMBH to the measuredmass density in SMBHs found from the demography ofnuclei of nearby galaxies (Magorrian et al. 1998; Gebhardtet al. 2001) indicated by the horizontal line in Fig. 4 (top

panel). The most recent value reported by Merritt & Ferrar-ese (2001) is 0SMBH 10

4 h B, which for h 0:65 andB 0:047 yields 0SMBH 3:05 10

6. From the toppanel of Figure 4, we see that this gives f % 0:06. The cor-responding value for the transition redshift can be found onthe zfcurve on the same plot, yielding a value zf % 18:5. Thisconstraint implies that all but a small fraction of the massinvolved in the first episode of star formationapproxi-mately 6%went into objects outside the mass range140 M < M < 260 M, yielding remnant black holeswith mass 10500 M . The scenario corresponding to caseA therefore implies that zf, the transition redshift from top-heavy to normal IMF, occurred at %10. This value for zf isconsistent with the estimate from MFR01 for the redshift atwhich the metals in the Ly forest need to have beenreleased to explain their absorption line widths measured atz % 3 (their cool temperature requires ejection at muchhigher redshift).

Let us now look at the other extreme case, B, wherein theassembled SMBHs in galactic centers have formed primar-ily via accretion and are unrelated to VMBHs. This leads usto two further possibilities: (1) VMBHs would still be in theprocess of spiraling into the centers of galaxies because ofdynamical friction but are unlikely to have reached the cen-ters within a Hubble time because of the dynamical frictiontimescale being long (Madau & Rees 2001), or (2) VMBHscontribute the entire baryonic dark matter in galactic halos.

Pursuing scenario 1, at best some fraction of theseVMBHs (for instance, those in gas-rich regions of gas-richsystems) might appear as off-center accreting sources thatshow up in the hard X-ray wave band. Such sources haveindeed been detected both by ROSAT(Roberts & Warwick2000) and more recently by Chandra in nearby galaxies(M84: Jones 2001; NGC 720: Buote 2001).

In a survey of archival ROSATHRI data to study the X-ray properties of the nuclei of 486 optically selected brightnearby galaxies (Ho, Fillipenko, & Sargent 1995), Roberts& Warwick (2000) found a large number of off-center X-raysources. The X-ray sources detected within the opticalextent of these galaxies were classified either as nuclear ornonnuclear (and therefore off-center) depending on whetherthe source was positioned within 2500 of the optical nucleus.They detect a nuclear source in over 70% of the galaxysample and a total of 142 off-center sources. Roberts &Warwick (2000) find that the nonnuclear sources follow asteep, near power-law X-ray luminosity distribution in the1036 1040 ergs s1, which leads to an LX=LB ratio of

LX

LB 1:1 1039 ergs s11010 L

1 : 105 The superscript 0 denotes the present-day value.



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The median luminosity of the nonnuclear sources isfound to be a factor of$10 lower than that of the nuclearsources. However, they estimate the incidence rate of off-center sources with LX ! 1038:3 ergs s1 (which corre-sponds to the Eddington luminosity for a 1.4 M neutronstar) to be %0.7 per 1010 L galaxy. The existence of accret-ing VMBHs might also help explain the following observa-tion. The far-IR (FIR) excess detected with DIRBE at 60and 100 lm has been tentatively interpreted as an extraga-lactic background with integrated intensity of 44 9 nWm2 sr1 in the range 60100 lm (Finkbeiner, Davis, &Schlegel 2000). The energy required to produce such a FIRbackground could derive from a highly obscured popula-tion of accreting VMBHs at moderate redshifts (for an alter-native to this, see explanation of scenario 2 below).

In order to estimate the mass density contributed by theseVMBHs, we can compare the mass in VMBHs to that of theSMBH in a typical galaxy of luminosity, say 1010 L for caseB. Most of the VMBHs are likely to be en route to galacticcenters. Note, however, that not all the inspiraling VMBHswill be accreting and X-ray bright; many of these could, infact, be low radiative efficiency advection-dominated accre-tion flows (ADAFs), and therefore be too faint to bedetected by ROSAT or Chandra, or not accreting at all ifthey do not happen to be in gas-rich regions of the galaxy.Thus, using the following argument we can obtain a lowerlimit on the abundance of VMBHs.

The mass of the central SMBH hosted by a galaxy with aluminosity Lgalaxy 1010 L (assumed to be the fiducial gal-axy for these purposes) in the Bband is given by (Merritt &Ferrarese 2001)

MSMBH 103Mbulge 10

3Lgalaxy;

where the mass-to-light ratio in the B band is taken to be1 M=L, and the galaxy luminosity is essentially domi-nated by the bulge luminosity. Hence, the mass of the cen-

tral SMBH is MSMBH % 107 M. Now, we use theluminosity of the ROSAT off-center sources (Roberts &Warwick 2000) and use the fact that they find % 0.7 off-cen-ter sources with luminosity !1038.3 ergs s1 per 1010 L gal-axy to estimate the mass of VMBHs in the fiducial galaxy. Ifwe assume that these VMBHs have a typical mass of %300M, their Eddington luminosity is

LEdd 4:3 1040 MVMBH

300 M

ergs s1 :

Thus, VMBHs appear to be radiating at sub-Eddingtonluminosities, the average rate (given by eq. [10]) being %3%of the Eddington value. This is consistent with the observedluminosities of the nuclear sources in the sample, whichRoberts & Warwick (2000) find to be radiating at severelysub-Eddington rates.

Therefore, we expect the typical accreting VMBH mass ina 1010 L galaxy to be about 210 M. Little is known aboutthe spatial distribution of such objects. How can we takeinto account the fact that only a fraction of the sources arelikely to be accreting? Since the detected ROSAToff-centersources are within the optical radius of the galaxies, thenumber of nonaccreting VMBHs in the halos of these gal-axies can be large. One can obtain a simple estimate of thisnumber by pursuing the following argument. Assume thatVMBHs, being collisionless particles, closely trace the darkmatter (which we take to obey a NFW profile; Navarro,

Frenk, & White 1997) and that the ratio of virial to opticalradius is %15 for a 1010 L disk galaxy (Persic, Salucci, &Stel 1996). These hypotheses require that we scale up thetotal mass in VMBHs by a factor of %10, which givesMVMBH 2:1 103 M. Now, the ratio MVMBH=MSMBH is%2:1 104, implying that VMBH 2:1 104

0SMBH

6:4 1010, which in turn gives f % 1 (see dashed line inbottom panel of Fig. 4) and zfe22:1.

Now we explore scenario 2 of case B, the instance whenVMBHs constitute the entire baryonic dark matter contentof galaxy halos (but do not contribute to the disk dark mat-ter). It is important to point out here that cosmologicalnucleosynthesis arguments require both baryonic and non-baryonic dark matter (Pagel 1990). Essentially, this is due tothe fact that the mass density contributed by baryons, B, iswell in excess ofV, the contribution to the mass density byvisible baryons.

Using the luminosity-dependent relation of visible todark matter for spirals (Persic et al. 1996) for a fiducial gal-axy of1010 L, we find

Mvis

MDM% 0:05 ;

where Mvis is the visible mass and MDM MbDM M

nbDM is

the total dark matter mass, given as a sum of a baryonic anda nonbaryonic component. The total baryonic mass is afractionB=M of the total mass of the system, e.g.,

Mvis MbDM

B

MMvis MDM :

From these two equations and assuming a NFW densityprofile, we estimate the total baryonic dark matter contentas

MbDM 1M 1Mvis 2:33Mvis ;

moreover, 90% of this mass resides outside the opticalradius and can be contributed by VMBHs,

MVMBH

MSMBH

2:1 Mvis103 Mvis

2:1 103 ; 11

implying

VMBH 2:1 103 SMBH 6:4 10

3 : 12

Incorporating this constraint into Figure 4 (bottom panel),we find f % 3:15 105 and zfe5:4. Note that this sce-nario does not violate the constraint on the overproductionof background light (see Carr 1998; Bond, Carr, & Hogan1991; Wright et al. 1994). In fact, some fraction of theobserved near-IR DIRBE excess could be produced byVMBHs. In a recent estimate of the cosmic background at1.25 and 2.2 lm (corresponding to the J and K bands,respectively) using the Two Micron All Sky Survey(2MASS) and the DIRBE results, Cambresy et al. (2001)also find an excess (significantly higher than the integratedgalaxy counts in the Jand K bands), suggesting the contri-bution of other sources. Population III stars and theirVMBH remnants (accreting at very high redshifts) postu-lated here are likely candidates.

According to case B, the average metal abundance at red-shift $5.4 should be Zcr 104 Z, marking the transition



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from a top-heavy IMF to a standard power-law IMF. Thisdoes not necessarily violate the observed metal abundancesin damped Ly systems, Z % 103, as it is not yet clear towhat extent the IGM metallicity is spatially uniform at theseintermediate redshifts.

Therefore, case B is poorly constrained by the data, asscenarios 1 and 2 give large ranges for f and zf:3:15 105 < f < 1 a n d 5:4 < zf < 22:1. Consistently,case A gives a limit on f and zfoff 0:06 and zf 18:5.

The actual data do not allow us at present to stronglyconstrain the two quantities above, but they provide inter-esting bounds on the proposed scenario. These ranges alsohave implications for the expected detection rate of SNebeyond zf with future instruments like the Next GenerationSpace Telescope (NGST) (Marri & Ferrara 1998; Marri,Ferrara, & Pozzetti 2000).

5. DISCUSSION

We have proposed a scenario to solve a puzzling star for-mation conundrum: the first stars are now thought to bevery massive and hence to lock their nucleosynthesis prod-ucts into a remnant (very massive) black hole. Thishigh-massbiased star formation mode continues as longas the gas remains metal free. During this phase, metalenrichment can occur only if a fraction f of the stars havemass in the window leading to pair-unstable SNe(140 M < M < 260 M), which disperse their heavy ele-ments into the surrounding gas. Such metals enrich the gasup to Zcr % 104 Z, when a transition to efficient cooling-driven fragmentation producing d1 M clumps occurs atredshift zf. We argue that the remaining fraction of the firststars end up in %100 M VMBHs. By analyzing the evolu-tionary fate of such objects, we argue that in case A theycould end up in the SMBHs in the centers of galactic nuclei;in case B, (1) they could be en route to the center and henceidentified with the X-raybright, off-center ROSATsources,or (2) they could constitute the entire baryonic dark mattercontent of galaxy halos. These possibilities are used toobtain constraints on the two quantities: f $ 0:06 andzf $ 18:5 for case A, and f % 105 to 1 andzf % 5:4 22:1 for case B. The value Zcr % 104 Z foundhere is admittedly somewhat uncertain. For this reason wehave investigated how the above results might be affected bya different choice, e.g., assuming Zcr % 105 Z. Indeed,lower values ofZcr imply that less efficient metal enrichmentis required in order to change to a more conventional starformation mode. Thus, comparable values for zf are found,but the corresponding values for f tend to be systemati-cally smaller, being f

% 0:6% for case A and in the range

3:15 105 < zf < 0:98 for case B.Several uncertainties remain in the comparison of the

inferred density of VMBHs to local observations. Forexample, it is not obvious if SMBHs could at all form out ofVMBHs. Dynamical friction can effectively drag VMBHstoward the center of the host system, at least within a dis-tance of$100 pc (Madau & Rees 2001). Unless most of theenergy is radiated away in gravitational waves, it could bedifficult for a VMBH cluster to coalesce into a single unit.Furthermore, accretion onto isolated VMBHs could be tooinefficient to explain most of the off-center sources observedby ROSAT and Chandra. Higher accretion rates might beactivated by the tidal capture/disruption of ordinary stars.

The question remains if the frequency of such an event is infact sufficiently high to explain the data.

In spite of the many difficulties and uncertainties dis-cussed here, our study represents a first attempt to link thefirst episode of cosmic star formation activity to present-dayobservational evidence of their fossil remnants.

A top-heavy IMF for the early episodes of star formationin the universe might have other interesting observationalconsequences; we speculate further on them later. Thekinetic energy released during the thermonuclear explosionspowered by pair instability are %102 larger than those ofordinary Type II SNe. This might cause the interaction withthe circumstellar medium to be as strong as predicted forhypernovae (Woosley & Weaver 1982). However, theseexplosions do not lead to the ejection of strongly relativisticmatter (Fryer et al. 2001) and therefore cannot power agamma-ray burst (GRB).

In Population III progenitors of VMBHs, the estimatedangular momentum is sufficient to delay black hole forma-tion and the system might develop triaxial deformations(Fryer et al. 2001). If the instabilities have enough time togrow, the core might break into smaller fragments thatwould then collapse and merge to form the central VMBH.If not, the star might still develop a barlike configuration.Both these scenarios lead to a significant emission of gravi-tational waves (Schneider et al. 2000; Fryer, Holz, &Hughes 2002). Furthermore, significant emission of gravita-tional radiation can occur as a result of the inspiral andmerger of VMBHs onto the SMBHs in the center of hostsystems (Madau & Rees 2001).

Once the VMBHs have formed, accretion continuesthrough a disk at a rate that can be as large as 10 M s

1

(Fryer et al. 2001). Magnetic fields might drive an energeticjet that can produce a strong GRB through the interactionwith surrounding gas. The properties of these PopulationIII GRBs would be considerably different from their morerecent (z < 5) counterparts; depending on the uncertaininteraction of the jet with the surrounding matter, the burstswould be probably longer [101 z s], and the peak ofemission, which in the rest frame is in -rays, would beshifted into X-rays. Indeed, BeppoSAX has revealed theexistence of a new class of events, the so-called X-ray flashesor X-rayrich GRBs, which emit the bulk of their energy inX-rays (L. Piro 2001, private communication). Further-more, since Population III GRBs explode at very high red-shifts, it is likely that their optical afterglow might beheavily absorbed by the intervening gas. These systemsmight be the natural candidates for the significant number(about 40% of GRBs for which fast follow-up observationswere carried out) of GRBs that do not show an opticalcounterpart, the so-called GHOST (GRB hiding opticalsource transient) or dark GRBs. Other explanations ascribethe failed optical detection to dust extinction within the hostsystem, but the ultimate nature of GHOSTs is still highlydebated (Lazzati, Covino, & Ghisellini 2002; Djorgovski etal. 2001).

Finally, the energetic jets generated by GRB engines pro-duce, by photon-meson interaction, a burst of TeV neutri-nos while propagating in the stellar envelope (Meszaros &Waxman 2001). We investigate this aspect in a companionpaper (Schneider, Guetta, & Ferrara 2002) in which we usethe constraints set by the AMANDA-B10 experiment onthe total integrated flux of TeV neutrinos from PopulationIII GRBs.



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We are grateful to P. Coppi, K. Nomoto, and M. Rees forcomments and suggestions. We wish to thank V. Brommand L. Piro for discussions. We thank the referee for his/herthoughtful comments. This work is partially supported

(R. S.) by the Italian CNAA (project 16/A); K. O. issupported by Research Fellowships of the Japan Societyfor the Promotion of Science for Young Scientists,grant 6819.

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