How Massive Single Stars End Their Life

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How Massive Single Stars End their Life

A. Heger Department of Astronomy and Astrophysics, Enrico Fermi Institute, The University of Chicago, 5640 S. Ellis Ave, Chicago, IL 60637

C. L. Fryer Theoretical Astrophysics, MS B288, Los Alamos National Laboratories, Los Alamos, NM 87545

S. E. Woosley Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064

N. Langer Astronomical Institute, P.O. Box 80000, NL-3508 TA Utrecht, The Netherlands and

D. H. Hartmann Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978

ABSTRACT How massive stars die – what sort of explosion and remnant each produces – depends chiefly on the masses of their helium cores and hydrogen envelopes at death. For single stars, stellar winds are the only means of mass loss, and these are chiefly a function of the metallicity of the star. We discuss how metallicity, and a simplified prescription for its effect on mass loss, affects the evolution and final fate of massive stars. We map, as a function of mass and metallicity, where black holes and neutron stars are likely to form and where different types of supernovae are produced. Integrating over an initial mass function, we derive the relative populations as a function of metallicity. Provided single stars rotate rapidly enough at death, we speculate upon stellar populations that might produce gamma-ray bursts and jet-driven supernovae. Subject headings: massive stars, supernovae, stellar remnants, neutron stars, black holes, gamma-ray bursts, collapsars

1. Introduction If so, one can calculate realization frequencies for stellar explosions and remnants of various kinds The fate of a massive star is governed chieﬂy and estimate how these might have evolved with by its mass and composition at birth and by the time. history of its mass loss. For single stars, mass loss Such estimates are fraught with uncertainty. occurs as a result of stellar winds for which there The litany of complications is long and requires exist semi-empirical estimates. Thus, within cur- discussion ( 6). No two groups presently agree, rently existing paradigms for the explosion, the in detail, on§ the ﬁnal evolution of any massive star fate of a star of given initial mass and compo- (including its explosion energy, remnant mass, and sition is determined (the Russell-Vogt theorem).

1 rotation rate) and the scaling of mass loss with star remnant turning it, within one day, into a metallicity during diﬀerent evolutionary stages is black hole. We thus distinguish black holes that widely debated. Still it is worthwhile to attempt are produced promptly or “directly” from those an approximate table of histories. We would like made by fall back. to know, within the comparatively well under- ?) has estimated that the helium core mass stood domain of stars that do not experience mass where black hole formation by fall back ensues exchange with a companion and for a particu- is about 8 M (a .25 M main sequence star) lar set of assumptions regarding mass loss and and that direct black hole formation occurs for he- explosion, what sort of supernova each star pro- lium cores over 15 M (40 M main sequence star duces and what sort of bound remnant, if any, it with no mass loss). These numbers are uncertain leaves. If possible, we would also like some indi- ( 6.2), but are representative choices. It is as- cation of which massive stars might make gamma- sumed§ that a baryonic remnant mass of over 2.0 ray bursts. M will produce a black hole.

In this paper we construct such a table of stel- While the helium core mass governs the ex- lar fates and remnants. In 2 we describe our plosion mechanism, the hydrogen envelope is § assumptions regarding mass loss, explosion mech- largely responsible for determining the spectrum anism(s), and remnant properties, and in 6 dis- (at peak) and light curve of common Type II su- § cuss the uncertainties. Section 4 delineates the pernovae. Stars with massive hydrogen envelopes sorts of stellar explosions and collapses we want when they die will be Type IIp; low mass en- to distinguish, and in 5 we discuss the resulting velopes will give Type IIL and IIb; etc. ( 4). § realizations of different outcomes as a function of An exception are supernovae of Types Ib and§ Ic metallicity in the galaxy. whose light curves do depend sensitively on the helium core mass since all the hydrogen envelope 2. Assumptions has been removed. The light curves of Types IIb, Ib, Ic, and 87A-like explosions are also sensitive 2.1. Stellar Models and Paradigms to the amount of 56Ni made in the explosion. The stellar models used in this paper were taken from ???)and?). These papers treat the evolu- 2.2. Mass loss tion of massive stars in the range 9 to 300 M cal- The principal physics connecting the final evo- culated without rotation from birth on the main lution of a star to its metallicity is its mass loss. sequence to death, either as iron-core collapse su- Low metallicity stars have less mass loss and have pernovae (helium core masses at death less than bigger helium cores and hydrogen envelopes when about 65 M ) or pair instability supernovae (he- they die. To a lesser extent, metallicity also affects lium core masses at death greater than 65 M and whether the presupernova star is a red or blue su- up to about 135 M ). The effects of mass loss were pergiant (?). included in those studies as discussed in 2.2. § For main sequence stars and red supergiants We shall presume here that the explosion mech- the mass loss rates employed in the studies cited anism, however it may operate, and the remnant above were taken from ?). For Wolf-Rayet stars, properties are determined by the mass of the he- a mass-dependent mass loss rate (?) was assumed lium core when the star dies. (Perhaps the carbon using the scaling law established by ??), but low- oxygen core mass is a better discriminant, but sys- ered by a factor 3 (?). Wind-driven mass loss is tematics of the two are very similar). As the mass believed to be metallicity dependent and a scal- of the helium core increases, so does its binding ing law √Z has been suggested for hot stars energy and entropy. Because of its higher entropy, (??). ?)∝ assumed that the same scaling law holds a larger helium core also has, on the average, a for Wolf-Rayet stars (?) and blue and red super- larger iron core mass, and a shallower density gra- giants as well. “Metallicity” is assumed here to be dient around that core (?). Consequently such the initial abundance of heavy elements, especially stars are harder to explode (??). Even in “suc- of iron, not the abundances of new heavy elements cessful” explosions where a strong outward shock like carbon and oxygen in the atmospheres of WC is born, mass may later fall back onto a neutron

2 and WO stars ( 6.1). assumed to be stronger in higher mass stars, so § In very massive stars above 60 M , the epsilon the metallicity at which these transitions occur mechanism for pulsational driven∼ mass loss sets in decreases with mass. But beyond 100 M , this ∼ and enhances the mass loss during central hydro- limit may rise again due to high enough initial gen burning. Opacity-driven pulsations also be- mass or the significant role of evolution phases come important, if not dominant, at high metallic- with lower mass loss rates (e.g., a WNL phases; ity (?). At very low metallicity on the other hand, see ?). ?) have shown that primordial stars should not At low metallicities, there is also a range of have significant mass loss due to pulsations. This masses for massive stars that leave behind no rem- suggests significant evolution in the mass loss of nant whatsoever. These are the pair-instability very massive stars with metallicity (Figs. ??–??). supernovae. If the helium core exceeds 65 M , corresponding to a 140 M initial mass∼ for stars 3. Remnant Properties without mass loss,∼ the pulsational pair instability (?) becomes so violent that the star is disrupted Fig. ?? shows the expected remnant types as entirely. When the helium core mass at the end a function of mass and initial “metallicity” for of central carbon burning exceeds 135 M for the above assumptions. In preparing Fig. ??,it non-rotating stars (initial mass of ∼260 M with- is assumed that stars below 9M do not form ∼ ∼ out mass loss), photo-disintegration in the cen- massive enough cores to collapse, that they end ter leads to collapse to a very massive black hole their lives as white dwarfs. Just above this mass (& 100 M ), once again forming a black hole di- lies a narrow range, 9 10 M , where degener- ∼ − rectly (??). However, as the metallicity increases, ate oxygen-neon cores are formed that either col- mass loss shifts the regime of pair-instability su- lapse due to electron capture (???????)andmake pernovae to higher initial masses. At still higher a neutron star or lose their envelopes and make metallicities, these supernovae do not occur at all white dwarfs (?????). Above 10 M core col- (?) because the progenitor stars are pulsationally ∼ lapse is the only alternative. unstable. Wherever this transition between white dwarf formation and iron core collapse lies, it should de- 4. Supernovae pend very little on metallicity and thus appears as a vertical line in Fig. ??. At low metallicities, 4.1. Supernovae of Type IIp and IIL the boundaries for black hole formation are also It has long been recognized that massive stars defined entirely by the initial stellar mass since produce supernovae (?). In this paper, we assume there is a one to one correspondence between ini- the following progenitor properties for the differ- tial stellar mass and final helium core mass. ent core collapse supernova types: For stars of higher metallicity, mass loss becomes increasingly important resulting in smaller helium cores for a given initial mass. If the star SN Type pre-SN stellar structure loses its entire hydrogen envelope (to the right of IIp..... 2M Henvelope the green line in Figs. ??–??), its rate of mass & loss increases significantly (e.g., ??) producing IIL..... 2M Henvelope . much smaller helium cores at collapse. This ef- Ib/c.... noH envelope fect underlies the abrupt change in the otherwise vertical boundaries between neutron star, fallback black hole and direct black hole formation. For The lower and upper limits of main sequence very massive stars, the remnant of the collapsing mass that will produce a successful supernova star depends sensitively on the metallicity. Above (“M-lower” and “M-upper”) — one with a strong 40 M , low metallicity stars form black holes di- outgoing shock still intact at the surface of the rectly, while at higher metallicities black holes of star — has long been debated. On the lower smaller mass are produced by fall back until, ul- end, the limit is set by the heaviest star that will timately, only neutron stars are made. Winds are eject its envelope quiescently and produce a white

3 dwarf. Estimates range from 6 to 11 M with 4.2. Type Ib and Ic Supernovae smaller values characteristic of calculations that A complication is that Type Ib/c SNe with employ with a large amount of convective over- masses above 4-5 M , which may be the most com- shoot mixing (??) and the upper limit determined mon ones to come from single stars, also have dim by whether helium shell flashes can eject the enve- displays even if they are still powerful explosions lope surrounding a neon-oxygen core in the same (?), i.e., the progenitor stars’ cores are not so way they do for carbon-oxygen cores ( 3). It may massive that they encounter significant fallback. also slightly depend on metallicity (?§). Here we In this paper, we do not differentiate these types will adopt 9 M for M-lower. of supernovae from our set of normal supernovae. The value of M-upper depends on details of the Our assumptions regarding the different types of explosion mechanism and is even more uncertain supernovae are summarized in the table below: ( 6.2). ?)estimate40M , but calculations of explosion§ even in supernovae as light as 15 M give widely varying results. It is likely that stars up Type Ib/c explosion to at least 25 M do explode, by one means or He core mass display energy another, in order that the heavy elements be pro- at explosion duced in solar proportions. The number of stars between 25 and 40 M is not large. Here we have & 15 M direct collapse none† taken what some may regard as a rather large 15 8M weak dim† ∼ − value, M-upper equals 40 M (Fig. ??). 8 5M strong possibly dim ∼ −5M strong bright For increasing metallicity mass loss reduces the . hydrogen envelope at the time of core collapse. A †if not rotating small hydrogen envelope (. 2M ) can’t sustain a long plateau phase in the light curve, and only Type IIL supernovae or, for very thin hydrogen layers, Type IIb supernovae result (??). It is also Clearly, mass loss is a key parameter and both necessary for Type IIL supernovae that the radius high metallicities (and high initial masses) are re- be large (?) and helpful if the 56Ni mass is not too quired to produce Type Ib/c supernovae in sin- small. The minimum metallicity for Type IIL su- gle stars. ?) find that for solar metallicity the limit for non-rotating stars is 34 M .These pernovae in single stars, is set by the requirement ∼ that the mass loss needs to be strong enough to re- supernovae can be weak and their later fallback move enough of the hydrogen envelope (Fig. ??). will produce BH remnants. As with the Type II In single stars Type IIL/b SNe are formed only black-hole forming supernovae, we anticipate that 56 in a thin strip where the hydrogen envelope is al- this fallback, in particular of the Ni lost this most but not entirely lost. ?) finds that Type way, may weaken the brightness of the supernova IIL supernovae are currently about 10 % - 20 % as display, similar to the case of weak Type II SNe. frequent as Type IIp. 4.3. Nickel-deficient Supernovae For increasing metallicity this domain shifts to lower initial mass. Below a certain minimum The light curve of most supernovae is a con- metallicity we do not expect Type IIL supernovae sequence of two energy sources - shock-deposited from single stars at all. Indeed, those stars that energy and radioactivity, especially the decay of form at the lowest (possible) metallicities will be 56Ni to 56Fe. There are cases however, where so massive that they frequently form black holes the radioactive component may be weak or ab- by fall back and have not very luminous super- sent. If the hydrogen envelope is still present, a novae. This will be particularly true if the stars bright supernova may still result with the bright- explode as blue supergiants but lack radioactivity. ness depending on the explosion energy (?), but the light curve lacks the characteristic radioactive “tail” (e.g., ???). If the hydrogen envelope is is gone (Type Ib/c), the consequences for the light curve are more dramatic and the supernova may

4 4 be for practical purposes invisible. that at sufficiently low metallicity (Z 10− Z ) . Four cases of nickel-deficient supernovae may very massive stars may retain most of their mass be noted. through the end of central helium burning, forming a massive helium core (???). 1) Stars in the mass range 9 to 11 M . Such For zero-metallicity stars above 100 M (he- ∼ stars have steep density gradients at the lium cores & 42 M ; ???) stars encounter the the edge of degenerate cores. The shock wave pair instability after central carbon burning (e.g., from core collapse heats very little material ??). Between 100 M and 140 M (helium ∼ ∼ to greater than 5 109 K and very little core mass . 65 M ) the instability results in vio- × (.0.01M ) 56Ni is ejected (?) lent pulsations but not complete disruption. The implosive burning is not energetic enough to ex- 56 56 2) Stars which make Ni but where the Ni plode the star. Depending on the mass of the star falls back into the remnant. This occurs and the strength of the initial pulse, subsequent for more massive stars with the threshold pulses follow after . 1yrto & 10, 000 yr. These mass dependent upon both the presuper- pulsations continue until the star has lost so much nova structure and the explosion mechanism mass, or decreased in central entropy, that it no and energy. The boundary here is somewhat longer encounters the pair instability before form- fuzzy because of the operation of mixing in ing an iron core in hydrostatic equilibrium. Since conjunction with fallback. The lower limit the iron core mass is large and the entropy high, for this regime is probably slightly larger such star probably finally make black holes. than that for BH formation by fallback, the The typical energy of these pulses can reach a upper limit is where BHs are formed directly few 1051 erg and easily expels the hydrogen en- without initiating a supernova, i.e., 10 M . velope, which is only loosely bound, in the first helium core mass 15 M (stellar masses . pulse (?) – when these stars finally collapse they 30 M M 40 M without mass loss). . . are thus hydrogen-free. Subsequent pulses may 3) Pair-instability supernovae with helium core eject the outer layers of the helium core as well. masses in the range 65 to . 85 M . Pair- Though the kinetic energy of these pulses may be instability supernovae, which probably only well in excess of normal supernovae, they are less existed in the early universe can have light bright since they lack any 56Ni or other radioac- curves ranging from very faint if they have tivities that could power an extended light curve. lost their hydrogen envelopes and eject no However, the collision of shells ejected by multiple 56Ni to exceptionally brilliant if the converse pulses could lead to a bright display. is true (helium core & 100 M ; ??). For stars between 140 and 260 M (helium cores of 64 to ∼133 M ) the∼ pair-instability 4) Pulsational pair-instability supernovae with is violent∼ enough∼ to completely disrupt the star helium core masses in the range & 40 to in the first pulse (???). Explosion energies range 65 M . This instability occurs after cen- 51 53 from 3 10 erg to . 10 erg and the ejected tral carbon burning but before the collapse. ∼ × 56Ni mass ranges from zero to & 50 M at the Though each pulse can have up to several high-mass end (?). Above 260 M , the stars 51 10 erg, only the outer layers of the star are directly collapse to a black∼ hole (?? ). Rotation 56 expelled and contain no Ni (see below). would of course affect these mass limits.

4.4. Pair-instability supernovae 4.5. Very energetic and asymmetric su- Very massive stars (M 100 M ) still form pernovae & in the present galaxy (??), but above 60 M , 4.5.1. Jet-powered supernovae nuclear-powered and opacity driven pulsations≈ occur that increase the mass loss (-andκ- A jet-driven supernova (JetSN) is a grossly mechanisms). Recently, ?) have shown that both asymmetric supernova in which most of the en- mechanisms are suppressed in extreme Pop III ergy comes from bipolar outﬂow from a central stars. Therefore it seems reasonable to assume object. Though such supernovae may occur in as-

5 sociation with gamma-ray bursts (GRBs), not all energy initial type time-scale jet-powered supernovae will have sufficiently rela- budget BH mass tivistic ejecta to make such a hard display. The class of jet-powered supernovae is thus a broad one I short low small having GRB progenitors as a subset. II long low small Jet-Driven supernovae can be formed with or III long high large without hydrogen envelopes (??;Fig.??). The hydrogen-free JetSNe are closely related to GRBs. The results can be summarized as: Whether such stars produce JetSNe or GRBs (or both) depends upon the rotation and the explosion Type I and II collapsars without a hydrogen mechanism. Until we understand both better, we • envelope can make ordinary GRBs, though can not distinguish between the two. those of Type II will tend to be longer. 4.5.2. Gamma-ray bursts and collapsars Type II and III collapsars without a hydro- • genenvelope–maybeevenwith–canmake The currently favored model for the forma- very long GRBs (in their rest frame). tion of gamma-ray bursts assumes that a narrowly beamed (θ . 10◦) highly relativistic jet (Γ > 100) All three types can make bright jet-powered leaves a compact “engine” and produces γ-rays ei- • supernovae if a hydrogen envelope is present. ther by internal shocks or by running into some ex- ternal medium (?). Currently two classes of GRBs Though we have described them as GRB pro- are distinguished: long and short bursts (?). It is genitors, collapsars probably produce a variety of assumed that the short class might originate from outbursts from X-ray flashes to jet-driven super- binary neutron stars (?), the long class could be novae. Calculations to reliably show which stars produced by the collapse of the core of a massive make GRBs as opposed to just black holes are star (e.g., ?). In the present work we adopt this presently lacking (though see ?). Here we will as- assumption, focus on the long class of GRBs, and sume that collapsars are made by some subset of use “GRB” synonymous for this class. those stars that make black holes (Fig. ??). The term “collapsar” is used to describe all It is agreed however, that collapsars can only massive stars whose cores collapse to black holes form GRBs if the star has lost its hydrogen en- and which have sufficient angular momentum to velope prior to collapse. Mass loss depends both form a disk. There are three possible varieties. on the stellar mass and metallicity and as both increase, the star uncovers more and more of its I collapsars that form black holes “directly” hydrogen envelope. The green curve in Figs. ?? during the collapse of a massive core. Al- and ?? denotes the boundary between stars which though the star collapses and initially forms retain some of their hydrogen envelope and those a proto-neutron star, it is unable to launch a that lose all of their hydrogen through mass loss. supernova shock and eventually (after 1s) ∼ Above 30 M , mass loss from winds become collapses to form a black hole (??). important,∼ and as the initial mass of the star II collapsars that form black holes by fallback increases, lower and lower metallicities are re- after an initial supernova shock has been quired to retain the hydrogen envelope. Between 100 140 M , pulsational instabilities are able to launched (?). The explosion is too weak to − eject much of the star, and the subsequent drive off the hydrogen layers of the star, even at fallback of material causes the neutron star zero metallicities. This boundary, which deter- in the core to collapse and form a black hole. mines where stars lose their hydrogen envelopes marks the lower bound for GRB producing col- III collapsars which do not form proto-neutron lapsars. The upper bound is set by those stars stars at all, but instead quickly collapse into that collapse to form black holes. massive black holes which grow through accretion (?). These collapsars lead to the formation of massive ( 300 M ) black holes. ∼

6 5. Stellar Populations through direct collapse. If the mass limit at which weak supernovae oc- With our evaluation of the possible fates of mas- cur decreases from 25 M down to 20 M , the frac- sive stars from 4, we estimate the distribution tion of neutron stars and typical Type IIp super- of compact remnants§ and of observable outbursts novae at low metallicities drops below 70 %. The produced by these single stars. The results will fraction of stars that form weak IIp supernovae be uncertain. Not only do the predictions depend and black holes increases to compensate this de- sensitively on the regions outlined in Figs. ??–??, crease. Table 1 summarizes the population frac- but also on the initial mas function (IMF) and its tions for different assumptions for the IMF and evolution. for the lower limit of the stellar core mass (i.e., In Fig. ??, we plot the fraction of massive stars lower limit of the initial mass for hydrogen-covered forming neutron stars (solid line) and black holes stars) resulting in fallback black hole formation. (dotted line)assumingaSalpeterIMF(?). At As mentioned above, here we assume that this cor- low metallicities, roughly 20 % of massive stars responds to the maximum stellar/core mass form- form black holes, and roughly 75 % form neutron ing strong SNe. stars. Half of those black holes form through fall- In Panel A of Fig. ??, we show the distribution back, the other half through direct collapse. Only of Type II supernovae. Most ( 90 %) single mas- 4 % of black holes form massive (>200 M ) black sive stars produce Type II SNe∼ (solid line). Most holes. 1 % of massive stars form pair-instability of these produce normal Type IIp SNe (dashed supernovae (leaving behind no remnant whatso- line). Roughly 10 % of all massive stars produce ever). As the metallicity increases, the fraction of weak Type IIp SNe (dot-dashed line). As the stars producing black holes first increases slightly metallicity approaches solar, some fraction of mas- (as the pair-instability mechanism is shut off) and sive stars will produce Type IIL SNe. In Panel then decreases near solar metallicity as most mas- B, we plot the Type Ib/c SNe distribution. Sin- sive stars lose so much mass that they collapse gle stars will not produce Type Ib/c SNe until to form neutron stars instead of black holes. At the metallicity gets large enough to drive strong these high metallicities, all black holes are formed winds. At first, most Type Ib/c SNe will be through fallback. Note that direct collapse black produced by “weak” explosions that form black holes are larger than fallback black holes and black holes by fallback (dot-dashed line), but as the holes will be larger, on average, at low metallicity. metallicity rises, an increasing fraction of “strong” In addition, if the black hole kick mechanism is Ib/c SNe is produced (long dashed line). Pair- powered by the supernova explosion, direct black instability SNe only occur at low metallicities and, holes will not receive kicks and these large black for our choice of IMF, both pulsational and non- holes will tend to have small spatial velocities. pulsational pair instability supernovae each con- There is increasing evidence that the IMF is stitute only about 1 % of all massive stars. When more skewed toward massive stars (relative to a using the IMF by ?) the pair SNe rates increase Salpeter IMF) at low metallicities (e.g., ???). To by a factor 3(thin lines). Note that in Panel B include these effects, we have used the IMF for of Fig. ?? the∼ pair SNe rate is scaled by a factor Population III by ?). The thin lines in Fig. ?? 10. show the change in the distribution of black holes Fig. ?? shows the distribution of GRBs and Jet- and neutron stars using the ?) IMF with the fol- SNe (explosions arising from collapsars). Since in lowing parameters: m =1.5, m = 50, κ =0.5, p1 p2 the frame of the present paper we cannot well dis- α = β =1.35 (see ? for details). We employ this tinguish between GRBs and JetSNe and, lacking IMF up to a metallicity that corresponds to the a better understanding of rotation, these rates are last occurrence of (non-pulsational) pair instabil- upper limits only. The solid line in Fig. ?? re- ity supernovae (Fig. ??). Note that at low metal- flects the total fraction of massive, single stars that licities, where the IMF is skewed toward massive could produce GRBs or JetSNe. The dotted line stars, the fraction of massive stars that form black denotes the fraction of massive stars that could holes is nearly twice as large as that predicted by a produce GRBs. To produce GRBs, the massive Salpeter IMF. Most of these black holes are formed star must lose all of its hydrogen envelope, but

7 still collapse to form a black hole. Hence, there other mass loss mechanisms and temperature and is a narrow window of metallicities which allow mass regimes, we have insufficient observational GRB production in single stars. Because pulsa- data or theoretical mass loss models to make pre- tional instabilities are able to eject the hydrogen cise predictions of a massive star’s destiny. This is envelope of stars even at zero metallicities, some one reason we do not give precise values for metal- GRBs could be formed at low metallicities. As licity along the axes in Figs. ?? – ??. in Fig. ??, the thin lines denote the differences Though there is general consensus that reduc- caused by using the ?) IMF at low metalicities. ing the initial metallicity of a massive star will To determine a distribution of evolutionary out- increase its mass when it dies, the scaling of mass comes versus redshift, we not only need to know loss with Z during different stages of the evolu- the metallicity dependence of stellar winds, but tion is controversial. We have made the simplest we also need to know the metal distribution and possible assumption, that mass loss rates scale ev- spread as a function of redshift. This cosmic age- erywhere as the square root of initial metallicity, metallicity relation is likely to have large spreads essentially as the square root of the iron abun- and a weak trend (?), as is also the case for this dance. This is almost certainly naive. ?) argue for 0.69 relation within the Milky Way (??). These de- a scaling Z for stars with Teff > 25, 000 K and 0.64 pendencies are difficult to determine because on Z for B-supergiants with Teff < 25, 000 K. ?) a more global galactic or cosmological scale met- argued for a Z0.5 scaling in WN and WC stars, but als may be redistributed so that, e.g., most of the for WC stars at least they had in mind the abun- metals even for low metallicity stars could be pro- dance of carbon in the atmosphere of the star, not duced in stars of metallicity. However, to give a the initial metallicity. On theoretical grounds, ?) flavor of possible redshift effects, we assume that discusses a universal scaling for mass loss in hot the metallicity axis in Figs. ??–?? is indeed log- stars that goes at Z0.5 but which has a threshold arithmic and use the metallicity redshift distribu- below which the mass loss declines more sharply. tion assumed by ?): ?) distribution versus redshift For red supergiants, even the mass loss at so- with a Gaussian spread using a 1 σ deviation set lar metallicity is not well determined. At higher − to 0.5 in the logarithm of the metallicity. With stellar masses the mass loss from luminous blue these assumptions we can determine the distribu- variables and WR stars also constitutes a major tion of neutron stars (thick solid line), black holes source of uncertainty as do pulsationally-induced (thick dotted line), Type II SNe (thin solid line), and rotationally-induced outflows (see above). Type Ib/c SNe (thin dotted line), pair supernovae (thin dashed line) as a function of redshift (or look- 6.2. Uncertainty in the explosion mecha- back time; Fig. ??). This suggests a trend in the nism populations of massive star outcomes versus redshift. The mechanism whereby the collapse of the iron core in a massive star results in a strong 6. Uncertainties and possible consequences explosion has been debated for decades. The current paradigm is based on a neutrino pow- 6.1. Uncertainties in mass loss ered “hot bubble” formed just outside the young proto-neutron star, but even the validity of this Our mass loss rates explicitly include only ra- paradigm is debated along with its specific predic- diatively driven mass loss, though the exact na- tions (????). The role of rotation and magnetic ture of the Wolf Rayet star mass loss is unknown. fields is also contentious (????; 6.3). We do not include pulsational ejection and similar § Our intuition here has been guided by para- eruptions or by excretion disks in rapidly rotat- metric surveys in which the explosion is simu- ing stars (“Ω-limit”; ?). The magnitude of these lated using a piston. The numerous uncertain- mass loss mechanisms depends upon the compo- ties are thus mapped into choices of the piston’s sition of the star. For hot stars both the abso- location and motion. These parameters are con- lute value and the metallicity-dependence of wind- strained by the requirement that the explosion driven mass loss are reasonably well understood not eject too much neutron-rich material (hence and theoretically modeled (??). For most of the

8 a minimum mass interior to the piston) and that is absent. the kinetic energy of the explosion measured at Nevertheless Fig. ?? does suggest that the lines infinity be 1051 erg. Though a single event, SN separating black hole formation by fall back from 1987A occurred for a representative helium core neutron stars in Figs. 1 - 4 should be interpreted mass (6 M ) and had a measured kinetic energy only as indicating trends. They may not be as at infinity of 1 1.5 1051 erg (???). The re- smooth or as monotonic as indicated. quirement that∼ supernovae− × typically make 0.1 ∼ M of 56Ni also means that the piston cannot be 6.3. Uncertainty in the effects of rotation situated too far out or produce too weak an explosion. There are also more subtle conditions - that Rotation can enhance the mass loss in stars and the mass cut frequently occur in a location where a spread in initial rotation can smear out the tran- past (successful) calculations of the explosion have sitions between the different mass and metallic- found it, that the distribution of remnant masses ity regimes. We have not considered cases where resemble what is observed for neutron stars, that rotationally enhanced mass loss might be impor- the integrated ensemble of abundances resemble tant. In such cases the limiting mass for loss of the Population I in our galaxy, and so on. hydrogen envelope could be lowered and, at the same time, the mass of the helium core increased Fig. ?? shows the remnant masses for a sur- (??). The higher mass loss would tend to lower vey of explosions in solar metallicity stars that ne- the metallicity for divisions between Type II and glects mass loss. The progenitor stars described Type Ib/c supernovae as well is the divisions be- in ?) were exploded using a piston located at the tween strong, weak and no supernova explosions. edge of the “iron core”. The iron core was defined The higher helium core masses with increase the by the location of an abrupt jump in the neutron metallicity divisions between strong, weak, and no excess (electron mole number = =049). A Ye . supernova explosions. The total change will de- constant kinetic energy at infinity (1 2 1051 erg) . pend on the competition of the larger helium core was assumed (see also ?). In fact, the× explosion masses and enhanced mass loss rate. energy will probably vary with mass. ?) calculates that the explosion energy will actually weaken as If the core is rotating rapidly at collapse, ro- the mass of the helium core increases. Thus fall tation may also influence the explosion mecha- back could have an even earlier onset and more nism and especially the possibility of making a dramatic effects than Fig. ?? would suggest. GRB. Also pair-creation supernovae could be significantly affected by rotation, in particular the The apparent non-monotonic behavior in Fig. ?? lower mass limit for direct black hole formation is largely a consequence of the choice of where the (??). Early calculations that followed angular mo- piston was sited. The neutronized iron core may mentum in massive stars (e.g., ?????) all found have a variable mass that depends on details of sufficient angular momentum retained in the core oxygen and silicon shell burning (?). The den- to reach critical rotation (“break-up velocity”) be- sity gradient around that core can also be highly fore the final central burning phases. More recent variable. Thus enforcing a constant kinetic energy calculations by ??) find presupernova core rota- at infinity does not always lead to a predictable tion rates in massive stars that would lead to sub- variation of remnant mass with initial mass. More millisecond neutrons stars just around break-up if recent unpublished calculations by ?), also of zero angular momentum were conserved perfectly dur- metallicity stars, place the piston at an entropy ing the collapse. Calculations by ??); Maeder & jump (dimensionless entropy S/ = 4) rather NAkB Meynet, priv. com. (2000) indicate core rotation than a jump. This choice, which is more con- Ye rates after central helium burning similar to those sistent with explosion models, assumes that an found by ?). explosion develops when the accretion rate declines rapidly. The rapid decline is associated Recently ?) has discussed a “dynamo” mecha- with the density (and entropy) discontinuity near nism based on the interchange instability that al- the base of the oxygen burning shell. Such a pre- lows the estimation of magnetic torques to be in- scription gives more nearly monotonic results and, cluded in models for stellar evolution. Preliminary in particular the bump around 17 M in Fig. ?? calculations by ??) that include these torques find

9 a presupernova angular momentum equivalent to analysis, but there are a number of constraints 5 - 10 milliseconds – still somewhat faster than that should be considered. First, an increasing observed young pulsars, but too slow for collap- number of JetSNe and weak supernovae explosions sars. If the estimates of magnetic torques by ?) are being discovered (???). Although there is an are valid then single stars are unlikely to produce observational bias against the discovery of weak collapsars and rotation is probably not a factor supernovae and they are much dimmer than Jet- in the explosion of common supernovae. Never- SNe, they may still dominate the sample of stars theless, in Fig. ?? we indicate the regimes where more massive than 25 M . Clearly, good statistics the structure of the star, excluding the question of (and correct analysis of the systematics) are nec- sufficient rotation, is favorable for collapsars and essary to determine the relative ratio of jet-driven GRBs. andweakSNe.Withsuchstatistics,wemaybe able to place constraints on the rotation of massive 7. Conclusions and Observational Tests stellar cores. If the IMF becomes more top-heavy at low We have described, qualitatively, the likely fates 4 metallicity (. 10− Z ; ??) the number of core of single massive stars as a function of metallicity. collapse supernovae (mostly Type IIp) and GRBs Our results suggest various trends in the obser- (if occurring in single stars) should significantly vations of these objects which may be subject to increase at high redshift. If the current estimates observational tests. of a characteristic mass of 100 M for primordial stars (???) is correct we∼ should expect a large Normal Type Ib/c SNe are not produced by fraction of pair SNe and very massive black holes • single stars until the metallicity is well above (or Type III collapsars) at zero metallicity, as well solar. Otherwise the helium core mass at as an increase of massive black holes from stars in death is too large. This implies that most the 60–140 M region. Type Ib/c SNe are produced in binary systems where the binary companion aids in re- moving the hydrogen envelope of the collaps- We thank Bruno Leibundgut for discussions ing star. about supernova classifications and Thomas Janka, Ewald Müller, and Wolfgang Hillebrandt for many Although less extreme than Type Ib/c SNe, helpful conversations regarding the explosion • single stars also do not produce Type IIL mechanism. This research has been supported by SNe at low metallicities. Similar to Type the NSF (AST 02-06111), the SciDAC Program of Ib/c SNe, Type IIL SNe from single stars are the DOE (DE-FC02-01ER41176), the DOE ASCI probably “weak” SNe until the metallicity Program (B347885). AH is supported in part by exceeds solar, also implying that Type IIL the Department of Energy under grant B341495 SNe are produced in binaries. to the Center for Astrophysical Thermonuclear Flashes at the University of Chicago and acknowl- If GRBs are produced by single star collapse • edges supported by a Fermi Fellowship of the En- (perhaps unlikely given the constraints on rico Fermi Institute at The University of Chicago. angular momentum), single stars only make The work of CF was funded by a Feynman Fel- up a small subset of GRB progenitors at lowship at LANL. higher metallicities. It is more likely that binary systems form GRBs. Such systems will occur more frequently at low metallicities (?). Jet-driven supernovae from single stars are • likely to be much more common than GRBs from single stars.

It is diﬃcult to make direct comparisons to ob- servations without including binary stars in our

10 Table 1: Remnant and supernova population yields for diﬀerent metallicities, IMFs, and mass limits.

Zero Metallicity Solar Metallicity lim lim lim lim Object high MFBH low MFBH high MFBH low MFBH IMFSal IMFNU IMFSal IMFNU IMFSal IMFSal Remnants NS 75 56 66 50 87 75 BH 23 36 32 43 13 25 MBH 0.9 3.0 0.9 3.0 0 0 Supernovae IIpStrong755666507770 IIp Weak 12 8.9 21 16 0 6.9 IIL 0 0 0 0 6.4 6.4 Ib/c Strong 0 0 0 0 9.2 5.1 Ib/c Weak 0 0 0 0 7.6 12 Other Outbursts Puls. Pair 1.4 4.7 1.4 4.7 0 0 Pair SNe 1.4 4.6 1.4 4.6 0 0 Jet SNe 24 39 33 46 13 25 GRBs 1.4 3.4 1.4 4.7 7.8 12

Note: For solar metallicity we use the IMF by ? (?;IMFSal), for zero metallicity we additionally supply the results for the IMF by ? (?;IMFNU). We give the results two diﬀerent lower mass limits for fallback lim black hole formation (MFBH): high corresponds to 25 M and low to 20 M (?).