WHAT ARE MACHOS? LIMITS ON STELLAR OBJECTS AS THE DARK MATTER OF OUR HALO Katherine Freese, Brian Fields, and David Graff ∗ talk presented by Katherine Freese at the International Workshop on Aspects of Dark Matter in Astro and Particle Physics, Heidelberg, Germany, July 1998 University of Michigan, Department of Physics 9 Ann Arbor, MI 48109-1120 9 9 Abstract 1 ThenatureoftheMassiveCompactHaloobjectsseeninmicrolensing n experiments and interpreted as dark matter in the Halo of our Galaxy a remains a mystery. Arguments are presented that these events are prob- J ably not ordinary stellar or substellar objects, i.e., theyare probably not 3 faint stars, brown dwarfs, white dwarfs, or neutron stars. On theoretical 1 groundsoneisthenpushedtoeitherexoticexplanationsora“no-Macho” Halo (in which the Machos reside elsewhere than in the Halo). Indeed a 1 nonbaryoniccomponent in theHalo seems to berequired. v 8 7 1 Introduction 1 1 0 The Halo of our Galaxy is made of as yet unidentified dark matter. One of 9 the outstanding questions in astrophysics is the nature of this dark matter. 9 Microlensing experiments were designed to look for (10 7−1)M candidates, − / ⊙ h probably baryonic. These objects are called MACHOs, or Massive Compact p HaloObjects. However,notonlyistheissueof“Whatisthedarkmatter?”still - unresolved by the microlensing experiments, but additional new puzzles have o r arisen. I will argue for my personal conviction that t s 1)Mostofthe dark matterinthe GalacticHalomustbenonbaryonic, a and : v 2) The nature and origin of the Machos that have been interpreted i as being in the Halo are currently not at all understood. X Until recently, stellar candidates for the dark matter in galaxies were ex- r a tremely popular. However, in the last few years most of these candidates have been either ruled out or shown to have serious problems. Using Hubble Space Telescope and parallax data (with some caveats mentioned in the text), we showed that faint stars and brown dwarfs contribute no more than 1% of the mass density of the Galaxy. Recent microlensing events interpreted as being in theHalohaveabestfitmassof∼0.5M ,sothatwhitedwarfshavebeentaken ⊙ seriously as dark matter candidates. However,stellar remnants including white dwarfsandneutronstarsareshowntobeextremelyproblematicasdarkmatter candidates. Itis a combinationof mass budgetissues andchemicalabundances that lead to the problems: A significant fraction of the baryons of the universe would have to be cycled through the white dwarfs (or neutron stars) and their main sequence progenitors; however, in the process, an overabundance of car- bon and nitrogen is produced, far in excess of what is observed both inside the Galaxy and in the intergalactic medium. Hence white dwarfs, brown dwarfs, faint stars, and neutron stars are either ruled out or extremely problematic as ∗[email protected]; [email protected]; [email protected] 1 dark matter candidates. Thus the puzzle remains, What are the 14 MACHO eventsthathavebeeninterpretedasbeingintheHalooftheGalaxy? Aresome of them actually located elsewhere, such as in the LMC itself? These questions are currently unanswered. 1.1 Microlensing Experiments The MACHO (Alcock et al. [1996], [1997a]) and EROS (Ansari et al. [1996]) experiments have attempted to find the dark matter of our Galactic Halo by monitoring millions ofstars in the neighboringLargeMagellenicCloud (LMC), which is approximately (45-60) kpc away; they have monitored stars in the Small Magellenic Cloud (SMC) as well. When a Macho crossesthe line of sight betweenastarintheLMCandus,theMacho’sgravitymagnifiesthelightofthe backgroundstar. Thebackgroundstargetstemporarilybrighterandthendims back down. The Macho acts as a lens for the background star. The duration of the event scales as ∆t ∝ √m, where m is the mass of the Macho and v is v the velocity perpendicular to the line of sight. Thus there is a degeneracy in the interpretation of the data between m and v. To break the degeneracy, one has to assume a galactic model, e.g., one has to assume that the lenses are in the Halo of our Galaxy. The three events in the first year MACHO data had a typical timescale of 40 days, which corresponds (with the above assumption) to a best fit mass for the Machos of ∼0.1M . With reanalysis and more data, ⊙ four years of data yield 14 events of longer duration, 35-150 days (T. Axelrod [1997]; this is the Einstein diameter crossing time). Thus the new best fit mass is roughly m∼0.5M . ⊙ Fromtheexperiments,onecanestimatewhatfractionoftheHaloismadeof Machos. UsingisothermalspheremodelsfortheGalaxywiththetwoyeardata, the Macho group estimated that 50% (+30%,-20%) of the Halo could be made of Machos. However, this estimate depends sensitively on the model used for the Galaxy. Gates, Gyuk, and Turner [1996] ran millions of models and found that the number of models vs. Halo mass fraction peaks at Machos comprising (0-30)% of the Halo, with virtually no models compatible with a 100% Macho Halo. Hence there is evidence that a nonbaryonic component to the Halo of our Galaxy is required (see also the contribution in this volume by Marc Moniez of the EROS group). Microlensing experiments have ruled out a large class of possible baryonic dark matter components. As described in the contribution by Marc Moniez, substellar objects in the mass range 10 7M all the way up to 10 2M are − − ⊙ ⊙ ruledout by the experiments. In this talk I willdiscuss the heavierpossibilities in the range 10 2M to few M . − ⊙ ⊙ 2 Baryonic Candidates In this talk I will concentrate on baryonic candidates. Hegyi and Olive [1986] ruled outlarge classesof baryoniccandidates. See alsothe workof Carr[1994]. Until recently the mostplausible remaining possibilities for baryonicdark mat- ter were –Red Dwarfs (0.2M > mass >0.09M ). These are stars just massive enough ⊙ ⊙ to burn hydrogen; they shine due to fusion taking place in the core of the star. 2 Thus these are very faint stars. –Brown Dwarfs (mass < 0.09M ). These are sub-stellar objects that cannot ⊙ burn hydrogen. They are too light to have fusion take place in the interior. –White Dwarfs (mass ∼ 0.6M ). These are the end-products of stellar evolu- ⊙ tion. In this talk, I will present limits on red dwarfs (Graff and Freese 1996a), browndwarfs(GraffandFreese1996b),andwhite dwarfs(Graff,Laughlin,and Freese [1998]; Fields, Freese, and Graff [1998]; Fields, Freese, and Graff [1999]) as candidates for baryonic dark matter. 3 Faint Stars and Brown Dwarfs Until recently, people noticed that the number of stellar objects grows with decreasingstellarmass;hencetherewasspeculationthattheremightbealarge number of faint stars or brown dwarfs that are just too dim to have been seen. However,asIwillarguethesecandidates(modulocaveatsbelow)havenowbeen ruled out as dark matter candidates. Faint stars and brown dwarfs constitute no more than a few percent of the mass of our Galactic Halo. 3.1 Faint Stars: FirstweusedHubbleSpaceTelescopedata(Bahcall,Flynn,Gould,andKirhakos 1994)to limit the mass density inreddwarfsto less than1%ofthe Halo(Graff and Freese 1996a). The data of Bahcall et al (1994) from HST examined a small deep field and measured the relative magnitudes of stars in the V and I bands. We used the six stars that were seen with 1.7 < V −I < 3 to limit the density of red dwarfs in the Halo. First we obtained the distances to these stars,whichare shownin Figure 1. One cansee that the surveyis sensitive out to at least 10 kpc. Note that the closest stars are likely disk contaminants and not included in our final analysis. We obtained estimates of the stellar masses of these objects from stellar models of Baraffe et al (1996); the masses are in the range 0.0875M - 0.2M . For the 6 stars⊙in the HS⊙T data with 1.7 < V −I < 3, we thus obtained a Halo red dwarf mass density. We then compared this red dwarf mass density withvirialestimatesoftheHalodensitytoseewhatfractioniscomposedofred dwarfs. WetookalocalHalomassdensityofρ ∼9×10 3M /pc3. Bahcalletal o − ⊙ (1994)hadmadethiscomparisonbyassumingthatthereddwarfshadproperties of stars at the edge of the high metallicity main sequence; these authors found that red dwarfs contribute less than 6% of the Halo density. However, Halo red dwarfs are low metallicity objects, and we were thus motivated to redo the analysis as outlined above. A ground-based search for halo red dwarfs by Boeshaar, Tyson, and Bernstein (1994) found a much smaller number. We felt thatacarefulreinterpretationoftheBahcalletal(1994)datawasinorder. Our result is that Red dwarfs with 1.7 < V −I < 3 (i.e., mass 0.0875 < M/M < ⊙ 0.2), make up less than 1% of the Halo; our best guess is that they make up 0.14% - 0.37% of the mass of the halo. Subsequent examination of the Hubble Deep Field by Flynn, Gould, and Bahcall [1996] and work by Mera, Chabrier, andSchaeffer[1998]reiteratedthatlow-massstarsrepresentanegligiblefraction of the Halo dark matter. 3 3.2 Brown Dwarfs: With these stronglimits onthe contributionoffaint starsto the Galactic Halo, we then obtained a Mass Function of these same red dwarfs in order to be able to extrapolate to the browndwarfregime;in this waywe were able to limit the contribution of brown dwarfs as well. We obtained the mass function from the following relation: MassFunction=(dM /dm)×LuminosityFunction. (1) V Here, the Mass Function (hereafter MF) is the number density of stars with mass between m and m+dm, and the Luminosity Function (hereafter LF) is the number density of stars in a magnitude rangeM →M+dM (note that M refers to magnitude while m refers to mass). The luminosity function is what is observed; we used parallax data taken by the US Naval Observatory (Dahn et al 1995) who found 114 halo stars. We went from this observed luminosity function to the desired mass function via stellar models of M (m) obtained by V Alexandre et al. [1996]. The parallax data (Dahn et al 1995) are shown in Figure 2. This is an H- R diagram of nearby stars with measured parallax. The filled circles are high metallicity disk stars. The open circles are red dwarfs which are known to be in the Halo because of their low metallicities and high velocities. It is these 114 Halo stars that we used to get a mass function. We always took the most “conservative”case,i.e.,thesteepestMFtowardslowmass;thiscasewouldgive the largest number of brown dwarfs and low mass red dwarfs. For this reason, we considered a number of metallicities and used the lowest realistic value of Z =3×10 4. Thereis apotentialcomplicationinthatsomeofthe starsinthe − survey may actually be unresolvedbinaries. If so, the observedlight is the sum of the light from two stars. Then one may overestimate the mass of the star if one assumes the light is from a single star. We considered three models for binaries. The most extreme of these is that all the stars are really in binaries, with equal masses for the two stars in the binary system. Then the luminosity of each star is really half as big as if it had been a single star, each star has a smaller mass, and one obtains a steeper mass function towards low mass. This model is unphysical but simple, and we used it to illustrate an extreme for the largest number of stars at low mass that can be obtained from this data set. Figure 3 shows the mass functions that we obtained, for the case of no binaries andthe extreme caseof100%binaries. Inthese plotswemultiplied the vertical axis by m2 for simplicity of interpretation. With this factor of m2, a mass function (MF) thatis decreasingto the left converges,anMFthat is increasing to the left diverges, while an MF that is flat diverges only logarithmically. In figure 3a,the case ofno binaries,we cansee that the MF ×m2 decreasesto the left (convergent); in Figure 4c, the case of 100% binaries, the MF ×m2 is flat (diverges logarithmically). Hence Figure 3 summarizes our results for the mass function for faint stars heavier than 0.09M . ⊙ Now,in orderto proceedwith anextrapolationofthis reddwarfmass func- tion past the hydrogenburning limit into the reddwarf regime,we need a brief theoreticalinterlude. Star formationtheoryindicates that, asone goesto lower masses, the MF rises no faster than a power law. The theories of Adams and Fatuzzo (1996), Larson (1992), Zinnecker (1984), and Price and Podsiadlowski (1995), while based on different physical principles, all find this same upper limit. Hence we looked for the power law describing the red dwarf mass func- tionatthe lowestmasses,andthenuse this samepowerlaw to extrapolateinto the brown dwarf regime. We took the mass function to scale as MF ∝m−α. (2) 4 Then the total mass in the Halo is 0.09M⊙ m = m×MF ×dm. (3) tot Z 0 If α > 2, then the total mass diverges. If α = 2, then the total mass diverges only logarithmically. If α<2, then the total mass converges. We found α≤2, (4) forallmodels. Morespecifically,fortheextremecaseof100%binaries,wefound α=2,i.e.,eachorderofmagnitudeofmassrangecontainsanequaltotalmass. Evenfor a lowerlimit ∼m ,the totalmassin browndwarfsis lessthan 3% moon of the Halo mass. For all other models, including the case of no binaries, we find α < 2, and brown dwarfs consitute less than a percent of the Halo mass. Similar results were found by Mera, Chabrier, and Schaeffer [1996]. Dalcanton et al. [1994] found similar results by looking for a reduction in apparent equivalent width of quasar emission lines; such a reduction would be caused by compact objects such as brown dwarfs. ThetwoyearMACHOmicrolensingdatahavealsoshownthat,forstandard Halo models as well as a wide range of alternate models, the timescales of the eventsarenotcompatiblewithapopulationofstarslighterthan0.1M (Gyuk, ⊙ Evans, and Gates [1998]). Caveats: How might one avoid these conclusions? First, star formation theory might be completely wrong. Alternatively, there might be a spatially varying initial mass function so that brown dwarfs exist only at large radii and not in our locality, so that they were missed in the data (Kerins and Evans [1998]). 3.3 Punchline: ThebasicresultofthisworkisthatthetotalmassdensityoflocalPopulationII RedDwarfsandBrownDwarfsmakesuplessthan1%ofthelocalmassdensity ofthe Halo;infact, these objects probablymakeupless than0.3%ofthe Halo. 4 Mass Budget Issues This section (based on work by Fields, Freese, and Graff [1998]) is general to all Halo Machos, no matter what kind of objects they are. 4.1 Contribution of Machos to the Mass Density of the Universe: There is a potential problem in that too many baryons are tied up in Machos and their progenitors (Fields, Freese, and Graff). We begin by estimating the contributionofMachostothemassdensityoftheuniverse: Microlensingresults (Alcocket al. 1997a)predictthatthetotalmassofMachosintheGalacticHalo out to 50 kpc is M =(1.3−3.2)×1011M . (5) Macho ⊙ Now one can obtain a “Macho-to-light” ratio for the Halo by dividing by the luminosity of the Milky Way (in the B-band), L ∼(1.3−2.5)×1010L . (6) MW ⊙ We obtain (M/L) =(5.2−25)M /L . (7) Macho ⊙ ⊙ 5 FromtheESOSliceProjectRedshiftsurvey(Zuccaetal. [1997]),theluminosity density of the Universe in the B band is LB =1.9×108h L Mpc−3 (8) ⊙ where the Hubble parameter h=H0/(100kmsec−1Mpc−1). If we assume that the M/L which we defined for the Milky Way is typical of the Universe as a whole, then the universal mass density of Machos is ρMacho =(M/L)MachoLB =(1−5)×109h M Mpc−3. (9) ⊙ The corresponding fraction of the critical density ρ ≡ 3H2/8πG = 2.71 × c 0 1011h2M Mpc−3 is ⊙ Ω ≡ρ /ρ =(0.0036−0.017)h 1. (10) Macho Macho c − We will now proceed to compare our Ω derived in Eq. (10) with the Macho baryonic density in the universe, Ω , as determined by primordial nucleosyn- B thesis. Recently,the statusofBigBangnucleosynthesishasbeenthe subjectof intensediscussion,promptedbothbyobservationsofdeuteriuminhigh-redshift quasar absorption systems, and also by a more careful examination of consis- tency anduncertaintiesin the theory. To conservativelyallowfor the full range of possibilities, we will therefore adopt Ω =(0.005−0.022) h 2. (11) B − We can see that Ω and Ω are roughly comparable within this na¨ıve Macho B calculation. Thus,ifthe GalactichaloMachointerpretationofthe microlensing resultsiscorrect,Machosmakeupanimportantfractionofthebaryonicmatter of the Universe. Specifically, the central values in eqs. (10) and (11) give Ω /Ω ∼0.7. (12) Macho B However, the lower limit on this fraction is considerably smaller and hence less restrictive. TakingthelowestpossiblevalueforΩ andthe highestpossible Macho value for Ω , we see that B Ω 1 1 Macho ≥ h≥ . (13) Ω 6 12 B The only way to avoid these conclusions is to argue that the luminosity density in eqn. (8)is dominated by galaxieswithout Machos,so that the Milky Way is atypically rich in Machos. However, this is extremely unlikely, because most of the light contributing to the luminosity density L comes from galaxies similartoours. EvenifMachosonlyexistinspiralgalaxies(2/3ofthegalaxies) within one magnitude of the Milky Way, the value of Ω is lowered by at Macho most a factor of 0.17. 4.2 Comparison with the Lyman-α Forest We can compare the Macho contribution to other components of the baryonic matter of the universe. In particular, measurements of the Lyman-α (Lyα) forestabsorptionfrominterveninggasinthelinesofsighttohigh-redshiftQSOs indicate that many, if not most, of the baryons of the universe were in this forest at redshifts z >2. It is hard to reconcile the large baryonic abundance estimated for the Lyα forest with Ω obtained previously (Gates, Gyuk, Macho Holder,&Turner[1997]). AlthoughmeasurementsoftheLyαforestonlyobtain 6 the neutral column density, careful estimates of the ionizing radiation can be made to obtain rough values for the total baryonic matter, i.e. the sum of the neutral and ionized components, in the Lyα forest. For the sum of these two components, Weinberg et al. ([1997]) estimate ΩLyα ∼0.02h−3/2. (14) Thisnumberisatpresentuncertain. Forexample,itassumesanunderstanding of the UV background responsible for ionizing the IGM, and accurate deter- mination of the quasar flux decrement due to the neutral hydrogen absorbers. Despite these uncertainties, we will use Eq. (14) below and examine the impli- cations of this estimate. We cannow requirethat the sumof the Macho energydensity plus the Lyα baryonic energy density do not add up to a value in excess of the baryonic density from nucleosynthesis: Ω (z)+Ω (z)≤Ω ; (15) Macho Lyα B thisexpressionholdsforanyepochz. Unfortunately,theobservationsofMachos and Lyα systems are available for different epochs. Thus, to compare the two onemustassumethatthere hasnotbeenatradeoffofgasintoMachosbetween the era of the Lyman systems (z ∼ 2−3) and the observation of the Machos at z = 0. That is, we assume that the Machos were formed before the Lyα systems. Although Eq. (15) offers a potentially strong constraint, in practice the un- certainties in both Ω and in Ω make a quantitative comparison difficult. Lyα B Nevertheless, we will tentatively use the numbers indicated above. We then have (Ω =0.007−0.04)+(Ω =0.06)≤(Ω =0.02−0.09) forh=1/2, Macho Lyα B (16) and (Ω =0.004−0.02)+(Ω =0.02)≤(Ω =0.005−0.02) forh=1. (17) Macho Lyα B Theseequationscanbesatisfied,butonlyifoneusesthemostfavorableextremes in both Ω and Ω , i.e., for the lowest possible values for Ω and the Macho B Macho highest possible values for Ω . B Recentmeasurementsof KirkmanandTytler ([1997]) ofthe ionizedcompo- nentofaLymanlimitsystematz=3.3816towardsQSOHS1422+2309estimate an even larger value for the mass density in hot and highly ionized gas in the intergalactic medium: Ω ∼ 10 2h 1. If this estimate is correct, then Eq. hot − − (15) becomes even more difficult to satisfy. Onewaytoavoidthis massbudgetproblemwouldbeto arguethatthe Lyα baryons later became Machos. Then it would be inappropriate to add the Lyα plus Macho contributions in comparing with Ω , since the Machos would be B just part of the Lyα baryons. However, the only way to do this would be to make the Machos at a redshift after the Lyα measurements were made. Since these measurements extend down to about z ∼ 2−3, the Machos would have to be made at z < 2. However, this would be difficult to maneuver. A large, previouslyunknownpopulation ofstellar remnantscould nothave formedafter redshift 2; we would see the light from the stars in galaxy counts (Charlot and Silk [1995]) and in the Hubble Deep Field (Loeb [1997]). Until now we have only considered the contribution to the baryonic abun- dance from the Machos themselves. Note: see also the discussion by Fukugita, Hogan, and Peebles [1997]. Below we will consider the baryonic abundance of 7 the progenitorstars as well, in the case where the Machos are stellar remnants. When the progenitor baryons are added to the left hand side of Eq. (15), this equation becomes harder to satisfy. However, we wish to reiterate that mea- surements of Ω are at present uncertain, so that it is possibly premature to Lyα concludethatMachosareatoddswiththeamountofbaryonsintheLyαforest. 5 Machos as Stellar Remnants: White Dwarfs or Neutron Stars In the last section on the mass budget of Machos, we assumed merely that they were baryonic compact objects. In this section (based on work by Fields, Freese, and Graff [1998]): we turn to the specific possibility that Machos are stellarremnantswhitedwarfs,neutronstars,orblackholes. Themostcomplete microlensing data indicate a best fit mass for the Machos of roughly 0.5M . ⊙ Hence there has been particular interest in the possibility that these objects are white dwarfs. I will discuss problems and issues with this interpretation: in particular I will discuss the baryonic mass budget and the pollution due to white dwarf progenitors. 5.1 Mass Budget Constraints from the Macho Progeni- tors: Ingeneral,whitedwarfs,neutronstars,orblackholesallcamefromsignificantly heavierprogenitors. Hence, the excessmassleft overfromthe progenitorsmust be added to the calculation of Ω ; the excess mass then leads to stronger Macho constraints. PreviouslywefoundthatanybaryonicMachosthatareresponsible for the Halo microlensing eventsmust constitute a significantfractionof allthe baryons in the universe. Here we show that, if the Machos are white dwarfs or neutronstars,their progenitors,while onthe mainsequence, areanevenlarger fraction of the total baryonic content of the universe. The excess mass is then ejected in the form of gas when the progenitors leave the main sequence and become stellar remnants. This excess mass is quite problematic, as there is a lot of it and it is chemically enriched beyond what is allowed by observations. If all the Machos formed in a single burst (the burst model), then (for dif- ferent choices of the initial mass function) we can determine the additional contributionofthe excess gasto the mass density ofthe universe. Typically we find the contribution of Macho progenitors to the mass density of the universe to be Ω =4Ω =(0.016−0.08)h 1. (18) prog Macho − (As an extreme minimum, we find an enhancement factor of 2 rather than 4). From comparisonwith Ω , we can see that a very large fraction of the baryons B of the universe must be cycled through the Machos and their progenitors. In fact, the central values of all the numbers now imply Ω ∼3Ω , (19) prog B whichisobviouslyunacceptable. OneisdriventothelowestvaluesofΩ rmMacho and highest value of Ω to avoid this problem. B 5.2 Galactic Winds The white dwarf progenitor stars return most of their mass in their ejecta, i.e., planetary nebulae composed of processed material. Both the mass and the 8 compositionofthematerialarepotentialproblems. Aswehaveemphasized,the cosmic Macho mass budget is a serious issue. Here we see that it is significant evenwhenoneconsidersonlytheMilkyWay. Theamountofmassejectedbythe progenitors is far in excess of what can be accomodated by the Galaxy. Given the M of Eq.(5), a burst model requires the total mass of progenitors in Macho the Galactic Halo (out to 50 kpc) to have been at least twice the total mass in remnant white dwarfs, i.e., M ≥2M =(2.4−5.8)×1011M . The gas prog Macho ⊙ that is ejected by the Macho progenitors is collisionaland tends to fall into the Disk of the Galaxy. But the mass of the ejected gas M =M −M ∼ gas prog Macho M is at least as large as the mass (∼ 1011M ) of the Disk and Spheroid Macho ⊙ of the Milky Way combined. Thus the gas ejected by the Macho progenitors exceeds the mass of the Disk and Spheroid. We see that the Galaxy’s baryonic massbudget—includingMachos—immediatelydemandsthatsomeoftheejecta be removed from the Galaxy. This requirement for outflow is intensified when one considers the compo- sition of the stellar ejecta. It will be void of deuterium, and will include large amounts ofthe nucleosynthesisproducts of (1−8)M white dwarfprogenitors, ⊙ notably: helium, carbon, and nitrogen (and possibly s-process material). A possible means of removing these excess baryons is a Galactic wind. In- deed, as pointed out by Fields, Mathews, & Schramm ([1997]), such a wind maybeavirtue,ashotgascontainingmetalsisubiquitousintheuniverse,seen in galaxy clusters and groups, and present as an ionized intergalactic medium thatdominatestheobservedneutralLyαforest. Thus,itseemsmandatorythat many galaxies do manage to shed hot, processed material. Such a wind may be driven by some of the white dwarfs themselves (Fields, Freese, and Graff [1999]). Some of the white dwarfs may accrete from binary red giant companions and give rise to Type I Supernovae, which serve as an energy source for Galactic winds. However, excess heavy elements such as Fe may be produced in the process (Ruiz–Lapuente [1998]). 5.3 On Carbon and Nitrogen Theissueofcarbon(Gibson&Mould[1997])and/ornitrogenproducedbywhite dwarf progenitors is the greatest difficulty faced by a white dwarf dark matter scenario. Stellar carbon yields for zero metallicity stars are quite uncertain. Still, according to the Van den Hoek & Groenewegen (1997) yields, a star of mass 2.5M will produce about twice the solar enrichment of carbon. If a ⊙ substantial fraction of all baryons pass through intermediate mass stars, the carbon abundance in this model will be near solar. Then overproduction of carbon can be a serious problem, as emphasized by Gibson & Mould ([1997]). They noted that stars in our galactic halo have carbon abundance in the range 10 4 − 10 2 solar, and argued that the gas − − which formed these stars cannot have been polluted by the ejecta of a large populationofwhitedwarfs. Thegalacticwindsdiscussedintheprevioussection could remove carbon from the star forming regions and mix it throughout the universe. However, carbon abundances in intermediate redshift Lyα forest lines have recently been measured to be quite low. Carbon is indeed present, but only at the∼10 2 solarlevel,(Songaila&Cowie[1996])forLyαsystemsatz ∼3with − column densities N ≥ 3×1015cm 2. Furthermore, in an ensemble average of − systems within the redshift interval 2.2≤ z ≤ 3.6, with lower column densities (1013.5cm 2 ≤ N ≤ 1014cm 2), the mean C/H drops to ∼ 10 3.5 solar (Lu, − − − Sargent, Barlow, & Rauch [1998]). In order to maintain carbon abundances as low as 10 2 solar, only about − 9 10 2 of all baryons can have passed through the intermediate mass stars that − were the predecessorsof Machos. Such a fraction can barely be accommodated by our results in section4.1 for the remnantdensity predicted fromourextrap- olation of the Macho group results, and would be in conflict with Ω in the prog case of a single burst of star formation. Wenotethatprogenitorstarslighterthan4M overproduceCarbon;whereas ⊙ progenitorstarsheavierthan4M mayreplacethecarbonoverproductionprob- ⊙ lemwithnitrogenoverproduction(Fields,Freese,andGraff[1999]). Theheavier stars may have a process known as Hot Bottom Burning, in which the temper- ature at the bottom of the star’s convective envelope is high enough for nucle- osynthesis to take place, and carbon is processedto nitrogen (Lattanzio [1989], RenziniandVoli[1981],VandenHoek andGroenewegen(1997),Lattanzioand Boothroyd [1997]). In this case one gets a ten times solar enrichment of ni- trogen, which is far in excess of the the observed nitrogen in damped Lyman systems. In conclusion, both C and N exceed what’s obersved. Note that it is possible (although not likely) that carbon never leaves the whitedwarfprogenitors,sothatcarbonoverproductionisnotaproblem(Chabrier, private communication). Carbon is produced exclusively in the stellar core. In order to be ejected, carbon must convect to the outer layers in the “dredge up” process. Since convection is less efficient in a zero metallicity star, it is possible that no carbon would be ejected in a primordial star. In that case, it wouldbe impossible to place limits onthe density ofwhite dwarfsusingcarbon abundances. We have here assumed that carbon does leave the white dwarf progenitor stars. 5.4 Neutron Stars The first issue raised by neutron star Macho candidates is their compatibility with the microlensing results. Neutron stars (∼1.5M ) and stellar black holes (>∼1.5M ) are more massive objects, so that one wou⊙ld typically expect longer ⊙ lensing timescales than what is currently observed in the microlensing experi- ments (best fit to ∼ 0.5M ). As discussed by Venkatesan, Olinto, & Truran ⊙ ([1999]),onemustpositthatastheexperimentscontinuetotakemeasurements, longer timescale events should begin to be seen. In this regard, it is intriguing that the first SMC results (Palanque-Delabrouille et al. [1998]; Alcock et al. [1997c]) suggest lensing masses of order ∼2M . ⊙ However,the same issues of mass budget and chemical enrichment arise for neutronstarsasdidforwhitedwarfs,onlytheproblemsareworse. Inparticular, thehighermassprogenitorsofneutronstarsejectevenmoremass,sothatΩ prog isevenbiggerthanforthecaseofwhitedwarfs. Theejectaarehighlymetalrich andwouldneedagreatdealofdilution(asmuchasforthecaseofwhitedwarfs) in order to avoid conflict with observations. However, most of the baryons in the universe have already been used to make the progenitors (even more than for the case of white dwarfs); there are no baryons left over to do the diluting. 5.5 Mass Budget Summary: If Machos are indeed found in halos of galaxies like our own, we have found that the cosmological mass budget for Machos requires Ω /Ω ≥ 1hf , Macho B 6 gal where f is the fraction of galaxies that contain Machos, and quite possi- gal bly Ω ≈ Ω . Specifically, the central values in eqs. (10) and (11) give Macho B Ω /Ω ∼ 0.7. Thus a stellar explanation of the microlensing events re- Macho B quires that a significant fraction of baryons cycled through Machos and their progenitors. If the Machos are white dwarfs that arose from a single burst of 10