Cosmic Chemical Evolution with an Early Population of Intermediate Mass Stars
Elisabeth Vangioni, Joseph Silk, Keith A. Olive, Brian D. Fields
aa r X i v : . [ a s t r o - ph . C O ] O c t Cosmic Chemical Evolution with an Early Population ofIntermediate Mass Stars
Elisabeth Vangioni
Institut d’Astrophysique de Paris, UMR 7095 CNRS, University Pierre et Marie Curie, 98bis Boulevard Arago, Paris 75014, France
Joseph Silk
Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH,and Institut d’Astrophysique, 98 bis Boulevard Arago, Paris 75014, France
Keith A. Olive
Theoretical Physics Institute, School of Physics and Astronomy,University of Minnesota, Minneapolis, MN 55455 USA andBrian D. Fields
Departments of Astronomy and of Physics, University of Illinois, Urbana, IL 61801, USA
ABSTRACT
UMN-TH-2923/10TPI-MINN-10/30October 2010We explore the consequences of an early population of intermediate mass starsin the 2 – 8 M ⊙ range on cosmic chemical evolution. We discuss the implicationsof this population as it pertains to several cosmological and astrophysical observ-ables. For example, some very metal-poor galactic stars show large enhancementsof carbon, typical of the C-rich ejecta of low-mass stars but not of supernovae;moreover, halo star carbon and oxygen abundances show wide scatter, whichimply a wide range of star-formation and nucleosynthetic histories contributedto the first generations of stars. Also, recent analyses of the He abundance inmetal-poor extragalactic H II regions suggest an elevated abundance Y p ≃ . Y p = 0 . He, this offset may suggest aprompt initial enrichment of He in early metal-poor structures. We also discussthe effect of intermediate mass stars on global cosmic evolution, the reionizationof the Universe, the density of white dwarfs, as well as SNII and SNIa rates at 2 –high redshift. We also comment on the early astration of D and Li. We con-clude that if intermediate mass stars are to be associated with Population IIIstars, their relevance is limited (primarily from observed abundance patterns) tolow mass structures involving a limited fraction of the total baryon content ofthe Universe. 3 –
1. Introduction
One of the outstanding questions concerning the first epoch of star formation is thestellar mass distribution of Population III stars. Most often, Pop III stars are assumed tobe very massive (40 - 100 M ⊙ ) or supermassive ( >
100 M ⊙ ). Tracing chemical abundancepatterns through cosmic chemical evolution allows one to test theories employing massivePop III stars. For example, the abundance patterns seen in extremely iron-poor stars donot support the hypothesis that the first stars had masses between 140 −
250 M ⊙ andend as pair-instability supernovae (Venkatesan et al. et al. ⊙ )stars, which dominate at a redshift z ∼ et al. ⊙ with steep declines at both larger and smaller masses(Yoshii & Saio 1986). Primordial CMB regulated-star formation also leads to the productionof a population of early intermediate mass stars at low metallicity (Smith et al. 2009).On the observational side, there is abundant evidence for an early contribution fromIM stars. Intermediate mass stars have particular effects on chemical abundance patterns.Unlike their massive counterparts that end as core-collapse supernovae, these stars producevery little in the way of heavy elements (oxygen and above), but produce significant amountsof carbon and/or nitrogen and above all helium. Indeed, there is evidence that the numberof carbon enhanced stars increases at low iron abundances (Rossi et al. et al. et al. et al. ⊙ is needed (Abia et al. et al. , Mg/ Mg, consistent with pollution from core col- 4 –lapse supernovae, to high values of the Mg ratios indicating the presence of AGB productionof the heavy Mg isotopes. Core collapse supernovae produce almost exclusively Mg, whilethe observations of Yong et al. (2003a) show enhancements (relative to predictions basedon standard chemical evolution models) in both , Mg. AGB stars were also concluded tobe the source of the high , Mg/ Mg ratios seen in the globular cluster NGC 6752 with[Fe/H] = -1.62 (Yong et al. et al. (2001);Fenner et al. (2003).Determining the identity and nature of the first stars is a primary goal in any attempt tounderstand the physics of the first billion years of the universe. Cosmic chemical evolutionarymodels enable one to test many of the hypotheses for Pop III stars (Ciardi & Ferrara 2005).The bulk of the existing work in this area considers either massive stars (M >
40 M ⊙ ) orvery massive stars (M >
100 M ⊙ ). However, given the indications discussed above for anearly population of intermediate mass stars, it seems crucial to examine the consequencesfor cosmic chemical evolution with IM Pop III stars.The paper is organized as follows: In section 2, we discuss some of the expected conse-quences for a population of intermediate mass stars. These include a) the effective promptinitial enrichment of helium, which we compare to recent determinations of primordial he-lium (Izotov & Thuan 2010; Aver et al. et al. (2001). This model employs abimodal star formation rate (SFR) which supplements a normal IMF and SFR, with one en-hanced with IM stars. In section 4, we introduce a cosmic chemical evolutionary model basedheavily on the hierarchical models developed in Daigne et al. (2006) and Rollinde et al. (2009). We present our results in section 5. Discussion and concluding remarks are given insection 6. 5 –
2. Consequences of an early population of intermediate mass stars2.1. The primordial helium abundance
Among the successes of the WMAP determination of cosmological parameters is theaccurate determination of the baryon density, Ω B h or equivalently the baryon-to-photonratio η ≡ n b /n γ = 10 − η ; Komatsu et al. (2009, 2010) find η = 6 . ± . . (1)As a consequence, it has become possible to treat standard big bang nucleosynthesis (BBN)as a zero-parameter theory (Cyburt et al. He, He, Li (Cyburt et al. et al. et al. et al. et al. et al. He,and Li, we find varying degrees of concordance, none of which are perfect. Deuterium istypically credited as being responsible for the concordance between BBN and the cosmicmicrowave background determination of η . At the current value of η (eq. 1), the deuteriumabundance is predicted to be D/H = 2 . ± . × − . This can be compared with theabundance of deuterium measured in quasar absorption systems. The weighted mean valueof seven systems with reliable abundance determinations is D/H = (2 . ± . × − (Pettini et al. lower than the observed mean and this(slight) discrepancy will serve as a constraint below.The discrepancy between the predicted abundance of Li and the value found in halodwarf stars is well documented (Cyburt et al. η = 6 . Li/H = (5 . +0 . − . ) × − which is considerably higher than most observational deter-minations (Spite & Spite 1982; Spite et al. et al. et al. et al. et al. et al. (2010) finds Li/H = (1 . ± . × − . We comment below on thepossible effects of astration in chemical evolution models on the lithium abundance.Among the light elements, helium has the most accurately predicted primordial abun-dance. In addition, it is relatively insensitive to the baryon density and at η = 6 .
19, thehelium mass fraction is Y p = 0 . ± . . (2) 6 –The standard BBN results obtained in Coc and Vangioni (2010) are similar to those givenabove (Y = 0 . ± . . ± . × − , Li/H = (5 . ± . × − ).On the observational side, the determination of the helium abundance in extragalacticHII regions is fraught with difficulties (Olive & Skillman 2001). Over the last 15 years, im-provements in the analysis has led to a systematically higher He abundance. Izotov, Thuan, & Lipovetsky(1994) and Peimbert, Peimbert, & Ruiz (2000) introduced a ‘self-consistent’ method for de-termining the abundance of He simultaneously with the determination of the physical pa-rameters associated with the HII region. They found Y p = 0 . ± .
005 and 0 . ± . Y p = 0 . ± . et al. (2007) where higherhelium mass fractions were obtained 0 . ± . . ± . Y p = 0 . ± . ± . et al. (2010) found a similarly high value of Y p = 0 . ± . η . Given, the short baselineof this data set, it may be argued that a weighted mean of the helium results is warrantedrather than the commonly used regression of Y vs O/H as in the case of all results quotedabove. The weighted mean found in Aver et al. (2010) is Y p = 0 . ± . , (3)and one could be tempted to claim a slight discrepancy between the predicted and derived He abundance.If the central value of Y p is indeed 0.256, rather than invoking non-standard BBN or anon-standard cosmological history, it may be possible to argue for a prompt initial enrichmentof He by an early population of stars. While the helium data responsible for Y p is at relativelylow metallicity, the most metal-poor HII region used in the analysis leading to Eq. (3) isabout 1/20 of solar metallicity. There is, therefore, a reasonable possibility that some helium 7 –was produced early in the star formation history of pre-galactic structures. Here, we considerspecific models of chemical evolution which may be responsible for such a prompt initialenrichment of He remaining at the same time consistent with a multitude of evolutionaryconstraints.
When WMAP first reported their result for a large optical depth due to electron scatter-ing (Kogut et al. τ e = 0 . ± .
04 implied a redshift of reionization, z r ≈ et al. et al. τ e = 0 . ± . z r = 10 . ± .
2. This change is significant as itgreatly relaxes the constraints imposed on the models. First, reionization at the relativelylate redshift of 11 allows more time for structures and stars to form, and more importantlyat the later time, more baryons are incorporated in structures (in the hierarchical structureformation picture), and this decreases the ionizing flux per star needed for reionization.The early epoch of reionization is one of the driving forces behind the identificationof Pop III stars with supermassive stars. However, it has been argued that the numberof very massive Pop III stars needed for reionization would produce metal enrichments inconflict with observations (Venkatesan et al. et al. et al. M & ⊙ can contribute to reionizing the IGMby a redshift of 11. While it has been shown that massive stars (in the range 40-100 M ⊙ )are fully capable of reionizing the IGM in a bimodal model of star formation (Daigne et al. One can make a phenomenological case from galaxy evolution for an IM star-dominatedIMF at z > ∼ . The arguments are individually refutable but the cumulative effect is certainlysuggestive. • Comparison of the cosmic star formation rate with the rate of stellar mass assembly,inferred from integrating the luminosity function over various bands, reveals a dis-crepancy at z > ∼ z . The discrepancy is such that one apparently requires a reduced ratio of stellar mass to luminosity in star-forming galax-ies. This is achievable if the IMF has an excess of intermediate mass stars at theseepochs. No universal power law fit is acceptable at z > ∼ . et al. (2008a). A similar discussion also leads to a preferred SFR at z > ∼ ∼ et al. • Comparison of the rate of luminosity evolution of massive early-type galaxies in clustersat 0 . < z < .
83 to the rate of their color evolution requires that the IMF isweighted towards more massive stars at earlier epochs. A specific interpretation isthat the characteristic stellar mass ( ∼ . ⊙ today) had a value of ∼ ⊙ at z ∼ • The evolution of the galaxy stellar mass–star formation rate relationship for star-forming galaxies constrains the stellar mass assembly histories of galaxies. Simulationsincluding gas accretion reproduce a tight correlation but the evolution with redshiftdisagrees with the data. The simulations generally prefer a constant specific starformation rate ˙ M ∗ /M ∗ . The specific star formation rate is high at z > ∼
2, remains highto z ∼
7, but is low today (Gonzalez et al. z ) to z ∼ et al. (2009) find that the flux ratio H-alpha/FUV shows strong correlations with the surface-brightness in H-alpha and the Rband: Low Surface Brightness (LSB) galaxies have lower ratios compared to High SurfaceBrightness galaxies. The most plausible explanation for the correlations are systematic vari-ations of the upper mass limit and/or slope of the IMF at the upper end. Massive galaxiesin the local universe have an IMF that is preferentially enhanced in massive stars relative tolow mass galaxies.It seems that a case can be made that galaxies which form stars rapidly, specificallymassive galaxies at high redshift and their nearby counterparts, possess an IMF that isrelatively top-heavy (or bottom-light). We can speculate that essentially all vigorously star-forming systems at high redshift may similarly possess an IMF enriched in intermediate massstars. These at least are the building blocks that in our model provide the sources of thebulk of ionizing photons at z as high as ∼
10 and play a role in the recycling of processedgas. D trans It is well known that massive Pop III stars have a very specific impact on the nucle-osynthesis budget of the early Universe. In this context, it is useful to incorporate stellarhalo observations, specifically from extremely metal-poor stars (EMPS, [Fe/H] < − < −
4) and hyper-metal poor stars (HMPS, [Fe/H] < − et al. et al. D trans = log(10 [ C/H ] + 0 . × [ O/H ] ) (4)which clearly reveals the nucleosynthetic imprint of Pop III stars. This function has thegreat advantage of being able to connect aspects of cosmological evolution with the C/Oabundances in low mass stars. In this context, carbon-enhanced metal-poor stars or carbon-rich ultra-metal-poor stars (CEMPS and CRUMPS) seem to indicate an overabundance ofcarbon (and oxygen) at early stages of evolution. CEMPS represent about 20 percent ofthe metal poor stars. Recent studies considering multi-zone chemical evolution models showthat only models with increased C yields or an initial top-heavy IMF in the IM star massrange provide good fits of observations in the Milky Way (Mattsson 2010). Note that thesemodels also predict a nitrogen enhancement which will be considered below. Therefore, fromthe nucleosynthesis viewpoint it is interesting to consider IM stars as Pop III candidates,since they are producers of both C and He.Finally, observations of metal absorption features in the intergalactic medium (IGM)give important constraints on models of the formation and evolution of the earliest structures.Recent measurements of C in the IGM (Kramer et al. z = 6. This seems to clearly indicate an increase in the star formation rate at thisredshift able to produce carbon. Again, IM stars are good candidates for explaining thistrend. Note that we also predict that IGM material could have a high C/O ratio; indeed, wecan obtain insight into this ratio from observations, though presently, it is difficult to obtainreliable C/O ratios from ionized abundance data (namely CIV and OVI). In the course of standard stellar evolution, nitrogen is produced through He burning.Primary nitrogen is also synthesized in massive stars in the H burning layer via fresh carboncoming from the He burning core. In intermediate-mass stars, nitrogen is produced togetherwith carbon. Hot bottom-burning plays a dominant role for the synthesis of N and theamount of nitrogen produced depends on the efficiency and the duration of nuclear burning.At lower metallicity, the production of nitrogen is favored over carbon. There are indeedsystems at low metallicity, such as 47 Tuc and M71, which show large nitrogen enhancements(Harbeck et al. et al. et al. et al. > ⊙ ). Unfortunately, this element is difficult to observe.Indeed, the best measurements come from the CN BX electronic transition band which isnot generally detected. In this context, it is difficult to confront the calculated evolution ofthis element with available observations. However, it is interesting to note that N is observedin the few CEMPS as shown below.Magnesium is produced predominantly in Type II supernovae where it is formed in thecarbon and neon burning shells in massive stars. The dominant isotope formed in SNII is Mg. The neutron-rich isotopes Mg and Mg are produced in the outer carbon layerthrough α capture on neon. The yield of the heavier isotopes scales with the metallicity inthe carbon layer and as a result, very little of these isotopes are produced at low metallic-ity. In contrast, significant amounts of , Mg are produced during hot bottom-burning inthe asymptotic giant branch phase in IM stars (Boothroyd, Sackmann, & Wasserburg 1995).These stars are hot enough for efficient proton capture processes on Mg leading to Al (whichdecays to the heavier Mg isotopes). The neutron-rich isotopes are also produced duringthermal pulses of the helium burning shell. Here, α capture on Ne (which is produced from α capture on N) lead to both Mg and Mg. The latter process is very important for ≈ ⊙ (Karakas & Latanzzio 2003). Several observations (Shetrone 1996; Yong et al. et al. et al. et al. The best current limits on the halo old white dwarf population come from a combinationof interpreting the MACHO and EROS microlensing events with improved white dwarfatmosphere modeling (Torres et al. et al. (2000)). For comparison, our IM Pop III componentgives a white dwarf mass fraction very comparable to the standard one ; it differs only by15 % (see Figure 3 below).
Among the important constraints imposed on the models of cosmic chemical evolutionare the rates of supernovae (SN). These are intimately linked to the choice of an IMF andSFR and represent an independent probe of the star-forming universe. While Type II ratesdirectly trace the star formation history, there is a model-dependent time delay between theformation (and lifetime) of the progenitor star and the Type Ia explosion. Since existingdata is available only for relatively low redshifts, we discuss the predicted SN rates in thecontext of three different models and give some constraints related to the SNIa rate comingfrom the IM star mode.Our early IM stellar population hypothesis inevitably produces many SN at high red-shift. The predicted SFR and SN rates are presented below. The SFR rate corrections (fordust, luminosity function etc) are notoriously unreliable at z > ∼ z ∼
10) makes a significant contribution. The SN Iarates provide a potentially more robust discriminant. However we note here that three issueshelp reconcile our SN rate predictions with observations of SNIa at z > ∼ . Most importantly,the selection efficiently of SNIa, in the absence of near infrared selection, dives rapidly tozero at high redshift (beyond z ∼ . et al. (2010), the extrapolationof the efficiency to z = 2 implies a steep drop (to only a fraction of a percent). Moreoverthe SNIa precursors are predominantly in low mass galaxies, which contain sub-luminousSNIa, by as much as 0 . et al. < − . et al. et al.
3. Standard chemical evolution model
There are only a few basic ingredients to a standard (non-cosmological) galactic evolu-tion model. These include: the specification of an IMF, usually assumed to be a power lawof the form φ ( m ) ∼ m − x ; a star formation rate, which may be proportional to some power ofthe gas mass fraction or a specified function of time; a specification of stellar properties suchas lifetimes and elemental yields. More complex models will include infall of gas from theIGM, and outflows from stellar induced winds. Certain observations such as the metallicitydistribution in low mass stars may call for the prompt initial enrichment of metals which canbe accomplished using bi-modal models of chemical evolution in which a standard mode (e.g.a Salpeter IMF and a SFR proportional to the gas fraction) is supplemented with a shallowIMF providing predominantly massive stars over a brief period of time (or metallicity). Inthis section, we will show that this approach cannot work for the prompt enrichment of He as the most massive stars would produce heavy elements very early and thus would notenhance the ratio of He to metals. In other words, the enrichment of helium would occurtoo late and would not explain the enhancement in low metallicity regions.In contrast, bi-modal models which are augmented with a population of intermediatemass stars (with mass between 2 and 8 M ⊙ ), can indeed provide an enrichment of heliumat low metallicity in simple galactic chemical evolution models. While the model presentedin this section cannot directly be extended to a model of cosmic chemical evolution, it doesprovide some insight to the needed bimodality involving IM stars that will carry over intoa more sophisticated model based on hierarchical structure formation as in Daigne et al. (2006).In Fields et al. (2001), we constructed chemical evolution models which led to signifi-cant D astration at low metallicity and also had significant white dwarf production. Thesemodels were based on a bimodal construction where the ‘massive’ mode consisted of IMstars. Here we consider the effect of such models on He production at low metallicity.We illustrate results with the simple closed-box model of Fields et al. (2001), whichneglects both infall and outflow of baryons. Baryonic cycling through stars is determined bythe creation function C ( m, t ) d N ⋆ = C ( m, t ) d m d t, (5) 14 –which describes the mass distribution of new stars and the total star-formation rate Ψ( t ) = R C ( m, t ) dm . We adopt a “bimodal” creation function C ( m, t ) = ψ ( t ) φ ( m ) + ψ ( t ) φ ( m ) , (6)each term of which represents a distinct star-formation mode.In the first term of eq. (6) we encode an early burst of IM star formation; to do this weadopt the star formation rate ψ = x burst M B τ e − t/τ , (7)with a burst timescale τ = 100 Myr. The parameter x burst controls the fraction of thebaryonic mass M b which is processed in the burst; we will show results for different valuesof this parameter, but clearly we must have x burst ≤
1. Since our focus is on IM stars, theIMF for this mode is a power-law (Salpeter) form: φ ( m ) ∝ m − . , for m ∈ [2 M ⊙ , M ⊙ ].The second term in eq. (6) describes normal star formation. Again, following Fields et al. (2001), we adopt the classic form ψ = λg ( t ) M gas , with λ = 0 . − , and a smoothingfactor g ( t ) = 1 − e − t/ . which ensures that star formation begins in the bursting IMmode, which then smoothly goes over to the standard mode. The normal-mode IMF isof the Salpeter form φ ( m ) ∝ m − . , but now with m ∈ [0 . M ⊙ , M ⊙ ]. Both IMFs arenormalized in the usual way R m φ ( m ) dm = 1.In Fig. 1, we show the evolution of the He mass fraction, Y as a function of the oxygenabundance (relative to solar oxygen). Curves are shown for different values of the burstmass fraction x burst in eq. (7). In the case of normal star formation (i.e., when x burst = 0and the IM mode is absent), as O increases we see He rise from its primordial value, butundershoots the low-metallicity data. That normal star formation fails to match the datatraces back to nucleosynthesis patterns in high-mass stars, which dominate the productionof O and of new He in this scenario. Specifically, for high-mass stars, the ejecta have∆ Y / ∆ Z O ∼
1, i.e., comparable masses of new He and of O (Woosley &Weaver 1995). Thusat low metallicity Z O ≪ Z O , ⊙ ∼ .
01, we have ∆ Y ≪ .
01, whereas the data seem to require∆ Y obs ≃ .
01. This not only explains the problem with this simple scenario, but also suggeststhe solution: invoke a stellar population which has substantially different helium and metalnucleosynthesis.Indeed, Fig. 1 shows that as we turn on the bursting IM mode via x burst >
0, there is anabrupt rise in He at low O abundances, with a larger rise for larger x burst . As anticipated, thisrise now allows for the predictions to match the data, with good fits for x burst ∼ − He mass fraction in several bimodal models of chemical evolution. Curvesshow different fractions x burst (eq. 7) of baryons processed through the burst phase. Thedata point is representative of the helium data in low metallicity extragalactic HII regions.for IM stars at low metallicity in the m = (4 M ⊙ , M ⊙ ) we have ∆ Y / ∆ Z O ∼ (50 , et al.
16 –(2001) and discussed above, such a scenario also has substantial consequences, includingother element abundances, white dwarfs, and Type Ia supernovae. To examine all of theseissues in a more realistic manner requires a chemical evolution model in a cosmologicalcontext.
4. A cosmological chemical evolution model4.1. Generalities
The study of star formation in a cosmological context requires the inclusion of i) a modelof dark matter structure formation, and ii) accretion and outflow of baryonic matter withrespect to existing and forming structures.We have developed a detailed model of cosmological chemical evolution (Daigne et al. et al. f P S ( M, z ). The model included mass (baryon) exchange between the IGM and ISM,and between the ISM and stellar component. In this study we assume that the minimummass of dark matter halos for star-forming structures is 10 M ⊙ .Once the model is specified, we can follow many astrophysical quantities such as: theglobal SFR, the optical depth, the supernova (SN) rates and the abundances of individualelements (Y, D, Li, Fe, C, N, O, Mg abundances) which are used to tackle specific questionsrelated to early star formation and the reionization epoch. In this study, we consider twodistinct modes of star formation: a normal mode of Pop II/I and a massive or intermediatemass mode of Pop III stars.Throughout this paper, a primordial power spectrum with a power law index n = 1is assumed and we adopt the cosmological parameters of the so-called concordance model(Komatsu et al. m = 0 .
27, Ω Λ = 0 . h = 0 .
71 and σ = 0 . As in the simple model described in section 3, the models considered are bimodal. Eachmodel contains a normal mode with stellar masses between 0.1 M ⊙ and 100 M ⊙ , with a near 17 –Salpeter IMF ( x = 1 .
6) (hereafter called model 2).We fit the SFR history of Pop II/I stars to the data compiled in Hopkins & Beacom(2006) (from z = 0 to 5), and to the recent measurements at high redshift by Bouwens et al. (2010) and Gonzalez et al. (2010b). These observations place strong constraints on thePop II/I SFR. The fit for the SFR, ψ ( z ), is based on the mathematical form proposed inSpringel and Hernquist (2003) ψ ( z ) = ν a exp( b ( z − z m )) a − b + b exp( a ( z − z m )) . (8)The amplitude (astration rate) and the redshift of the SFR maximum are given by ν and z m respectively, while b and b − a are related to its slope at low and high redshifts respectively.The normal mode is fitted using: ν II / I = 0 . ⊙ yr − Mpc − , z m II / I = 2 . a II / I = 1 . b II / I = 1 .
1. The SFR of this mode peaks at z ≈ ⊙ (hereafter model 3), assuming an IMF with slope 1.3. Some fraction of the IM starsbecome SNIa. The SFR parameters are the following: ν IIIa = 3 M ⊙ yr − Mpc − , z m IIIa = 10, a IIIa = 1 . b IIIa = 1 .
1. The redshift peak is chosen so that the IM stars are born in timeto affect low-metallicity abundances, and the normalization is chosen to allow a substantialeffect on He.For comparative purposes, we also consider a massive component with stars between 36- 100 M ⊙ with an IMF slope of 1.6, which terminate as Type II supernovae (SNII) (hereaftermodel 1). The SFR parameters are the following: ν IIIb = 0 . ⊙ yr − Mpc − , z m IIIb =22 . a IIIb = 4 and b IIIb = 3 .
3. For a detailed description of the model see Rollinde et al. (2009) and Daigne et al. (2006). Note that both models 1 (massive) and 3 (IM) include thenormal mode (model 2).In Fig. 2, we show the adopted SFR for each of the three cases considered. As onecan see, the normal mode is chosen to fit the observations also plotted in the figure. Asthe data extend only up to z ≈
8, there is essentially no constraint on the massive modewhich dominates at z &
20. Data at z > ∼ et al. (2010)).Fig. 2 also shows that the IM mode represents a significant processing of baryons. Thepeak of the IM star formation rate is about a factor ∼
10 higher than the peak of the normalstar formation rate, and a factor ∼ higher than the massive Pop III star formation rate. 18 –On the other hand, the IM star formation peak lasts for about a factor ∼
10 less time thanthe normal star formation rate. Thus we expect that roughly comparable amounts of baryonswill be processed through these two modes. In contrast, a much smaller fraction of baryonsare processes through the massive Pop III mode. One should recall, however, that in ourmodel many baryons always remain the IGM and never reside in galaxies nor are processedthough stars.Fig. 2.— The cosmic star formation rate (SFR) as a function of redshift. The data (solidblack points) are taken from Hopkins & Beacom (2006). Dashed black points come fromBouwens et al. (2010) and from Gonzalez et al. (2010b). The blue solid line represents thestandard SFR with a Salpeter IMF and a mass range: 0.1 < M/M ⊙ < < M/M ⊙ < < M/M ⊙ < ∼
10% of allbaryons. This occurs at z ∼
10. The star fraction then drops as the IM stars die off, thenrises with normal star formation. Thus we see that in our model, about 10% of the baryonsare processed through the IM mode. In contrast, we see that the massive Pop III mode onlyprocesses about ∼ − of all baryons.Fig. 3.— Different mass fractions as a function of redshift. The flat solid black line (top ofthe figure) represents the total baryons in the Universe. The IGM fraction is shown by thedashed black curve, the galactic fraction is shown by the growing solid blue curve. The massfraction of stars is plotted for the three models considered (red curves): solid line for model2 (normal mode), dashed line for the model 1 (with massive Pop III stars) and the dottedline for model 3 (with IM stars). The lifetimes of intermediate mass stars (0 . < M/ M ⊙ <
8) are taken from Maeder and Meynet(1989) and from Schaerer (2002) for more massive stars. Old halo stars with masses below 20 – ∼ . ⊙ have a lifetime long enough to be observed today. They are assumed to inheritthe abundances of the ISM at the time of their formation. Thus, their observed abundancesreflect, in a complex way (due to exchanges with the IGM), the yields of all massive starsthat have exploded earlier.The yields of stars depend on their mass and their metallicity, but not on their status(i.e. Pop II/I or Pop III). Some Pop II/I stars are massive, although in only a very smallproportion since we use a slightly steeper than Salpeter IMF. Pop III stars are all massivestars. We use the tables of yields (and remnant types) given in van den Hoek & Groenewegen(1997) for intermediate mass stars ( < ⊙ ), and the tables in Woosley &Weaver (1995) formassive stars (8 < M/ M ⊙ <
40 ). An interpolation is made between different metallicities(Z=0 and Z=10 − , − , − , − , Z ⊙ ) and we extrapolate the tabulated values beyond 40 M ⊙ .
5. Results
Having specified the models under consideration, we can now systematically considerthe consequences of our particular choices for Pop III stars. For most of the results whichfollow, we will compare three distinct model choices. 1) model 2 alone, ie, only Pop II/Istars; 2) model 3, a bimodal model including the normal mode (model 2) plus the IM modeof Pop III stars ; 3) model 1, a bimodal model including the normal model (model 2) plusthe massive mode of Pop III stars.
Having set the SFR in our model, we now compute the electron scattering optical depthfor our choice of IMF. The evolution of the volume filling fraction of ionized regions is givenby: d Q ion ( z )d z = 1 n b d n ion ( z )d z − α B n b C ( z ) Q ( z ) (1 + z ) (cid:12)(cid:12)(cid:12)(cid:12) d t d z (cid:12)(cid:12)(cid:12)(cid:12) , (9)where n b is the comoving density in baryons, n ion ( z ) the comoving density of ionizing photons, α B the recombination coefficient, and C ( z ) the clumping factor. This factor is taken fromGreif & Bromm (2006) and varies from a value of 2 at z ≤
20 to a constant value of 10 for z <
6. The escape fraction, f esc , is set to 0.2 for both Pop III and PopII/I . The numberof ionizing photons for massive stars is calculated using the tables given in Schaerer (2002). 21 –Finally, the Thomson optical depth is computed as in Greif & Bromm (2006): τ = cσ T n b Z z dz ′ Q ion ( z ′ ) (1 + z ′ ) (cid:12)(cid:12)(cid:12)(cid:12) d t d z ′ (cid:12)(cid:12)(cid:12)(cid:12) , (10)where z is the redshift of emission, and σ T the Thomson scattering cross-section.In Figure 4, we plot the integrated optical depth from z = 0 to z . The red bandrepresents the observed results from WMAP7 (Komatsu et al. ∼ . − . , which provides considerable flexibility in accountingfor reionization. While the ratio of ionizing photons from a 6 M ⊙ star vs that of a 20 M ⊙ star is small, one has many additional stars in the IM scenario relative to the number in themassive mode. We next consider the evolution of the abundances of He, CNO, Fe and Mg as a functionof the redshift and/or the metallicity. We also show the evolution of D and Li due to earlyastration.We begin with the evolution of the He abundance. In the left panel of Fig. 5, we showthe analogue of Fig. 1 for the bimodal models based on hierarchical structure formation.Plotted is the He mass fraction, Y , vs. [O/H]. The solid blue curve corresponds to themodel with only a Pop II/I contribution. This result is indistinguishable from that producedby models including the massive Pop III contribution (not shown). This can be understoodas the bulk of the He and oxygen are derived from the same stars in the two models. Inboth cases, the helium abundance begins at the BBN primordial value and remains ratherflat until the oxygen abundance is roughy 1/10th of solar. In contrast, as shown by theblack dotted curve, in the IM Pop III model, He is produced early in IM stars with littleor no accompanied oxygen. As a result, the He mass fraction begins to grow at very low[O/H] and for the model parameters chosen, plateaus at value close to Y ≈ . et al. et al. (2010)). The red dashed line correspondsto model 1 (with Massive Pop III stars), the blue solid line to model 2 (the normal mode)and the black dotted line to model 3 (with IM stars).prompt initial enrichment of He in low metallicity galaxies. Note however, that due to thesize of the error bar associated with the observations, we cannot exclude the possibility thatno enrichment occurred, leaving models 1 and 2 viable.It is helpful to compare the helium–oxygen trend in Fig 5(a) with the simple closed boxresults in Fig. 1. The latter shows results for different fractions x burst of baryons processedthrough the IM mode. As noted above, our full hierarchical model cycles about 10% of allbaryons through IM stars; thus Fig. 5(a) should be compared to the x burst = 0 . He evolution.In the right panel of Fig. 5, we show the corresponding evolution of the He abundancewith redshift. The dashed red curve corresponds to the massive Pop III mode. Once again,the standard model and the massive Pop III model show nearly identical histories. We do seehowever, a modest increase in the helium mass fraction at high redshift due to the massive 23 –Fig. 5.—
Left:
Evolution of the helium mass fraction as a function of [O/H] (relative to thesolar value). The solid blue line corresponds to the both models: 2 (standard model) and 1(with a massive Pop III mode). The dotted black curve corresponds to model 3 ( with IMPop III stars). The red point comes from Aver et al. (2010).
Right:
Evolution of the heliummass fraction as a function of redshift . The red dashed line corresponds to the Massive PopIII model , the blue solid line to the standard model, and the black dotted one to the IMPop III model.Pop III mode. This is diluted by further infall as structures continue to grow. In the IMPop III model, there is a significant enhancement in the helium mass fraction around z ∼ Li; note that thevertical axes have zero offset in order to more clearly distinguish the model predictions. Ineach case, there is little difference between the standard model and the massive Pop IIImodel. Intermediate mass stars on the other hand are known to deplete D/H (Fields et al. Li astration factor is the same as for D/H and in this case moves the BBN value closer tothe abundance determined in halo stars. However, an abundance of ∼ × − is still veryfar from the observed plateau value between 1 and 2 × − .Consider now the abundance evolution of CNOMg together with their abundance ratios. 24 –Fig. 6.— Left:
As in Fig. 5 showing the evolution of the deuterium abundance as a functionof [O/H],
Right: showing the evolution of the deuterium abundance with redshift. Note thatthe vertical axis is offset from zero, in order to more clearly show the (relatively small) effecton D.Figures 8 and 9 display the abundance evolution with z . As in all of the previous figures,each of the following figures shows three curves corresponding to a model with no Pop IIIcontribution (solid blue curve), a model with a massive Pop III component (red dashedcurve) and a model with an IM Pop III component (black dotted curve). The evolutionarybehaviour of these model choices is well understood. Normal mode stars produce a moderateabundance of heavy elements at high redshift from the IMF-suppressed massive stars in thatmode. The same stars, nevertheless are effective at low redshift and produce the bulk ofmetals observed in the Milky Way. The Massive Pop III component produces C, O and Mgat high redshift, though these abundances are diluted at low redshift by infall as structurescontinue to grow. The IM stellar component produces a rather specific nucleosyntheticsignature: essentially C and N.Figures 10 and 11 show the evolution of the abundance ratios as a function of redshift.As one might expect, at lower redshifts, the IM star Pop III component produces the highest[O/Fe], [C/Fe] , [N/Fe]. The evolution of [Mg/Fe] corresponds to Mg coming from massivestars and the highest value comes from the massive population III component. The ratio ofthe neutron-rich isotopes to Mg remains small in the Pop III model dominated by massivestars, but this ratio can become large ( O (1)) in the IM Pop III model. Also shown in these 25 –Fig. 7.— Left:
As in Fig. 5 showing the evolution of the lithium abundance as a function of[O/H] .
Right: showing the evolution of the lithium abundance with redshift.Fig. 8.— As in Fig. 5 for Carbon (
Left ), and Nitrogen (
Right ).figures are the abundance ratios seen in several CEMPS.Surprisingly, the [C/O] ratio shown in Figure 12 is high in this model as oxygen is 26 –Fig. 9.— As in Fig. 5 for Oxygen (
Left ) and Magnesium (
Right ).also primarily produced in more massive stars whose role is diminished in this model atintermediate redshifts. In contrast, the massive Pop III component reaches very high ratiosof [C/Fe] and [O/Fe]. Only the massive Pop III model is capable of reproducing the [O/Fe]abundance ratios observed in these stars. Similarly, the IM model has difficulty in achieving[C/Fe] ratios as high as the two HE stars with [C/Fe] ≈ trans defined above in eq. (4).Figure 13 shows the D trans parameter as a function of the metal enrichment. Black circlescome from a compilation of Frebel et al. (2007). We see that this representation allows oneto clearly distinguish the effects of the different choices of stellar mass ranges: the normalmode fits the bulk of standard stellar data. The massive mode can explain the few CRUMPS(Rollinde et al. − < [Fe / H] < − > −
3, IM stars give D trans & −
1. In Figure 1 of Frebel et al. (2007), a specific stellar population is found exactly there: C rich stars. It is very interestingto note that only the IM component is able to explain this part of the diagram. Indeed, 27 –Fig. 10.—
Left:
As in Fig. 5, the evolution of the [C/Fe] ratio (relative to the solar value) asa function of redshift.
Right:
Idem for [O/Fe] ratio. Observational data (horizontal dashedlines) represent measured abundances in the following very iron poor halo stars: CS 22949-037 (Depagne et al. et al. et al. ∼ −
20% fall in the C-richred box fit by IM stars. To the extent that the data in the figure faithfully trace the ensembleof star-forming histories in the early universe, we would then estimate that Pop III IM starsform at ∼ −
20% of our model rate. Since our IM model has ∼
10% of baryons processedthrough this mode, the C-rich stars would in turn imply that ∼ −
2% of baryons participatein IM star formation.Thus we see that C-rich halo stars seem to demand some early IM star formation.Moreover, the large scatter in C and O abundance patterns over the full metal-poor halostar population demand that no single nucleosynthesis (and thus star-forming) history willsuffice. Indeed, given that C-rich stars are outliers to the main trend, the IM populationappears to be probably sub-dominant, acting only in low mass galactic structures at high z. 28 –Fig. 11.— As in Fig. 10 for the [N/Fe] and [Mg/Fe] ratios.Fig. 12.— As in Fig. 10 for the [C/O] ratio.
In Figure 14, at high redshift, we show the resulting evolution of the Type II SN ratealong with the data at relatively low redshift. The GOODS data for core collapse supernovae 29 –Fig. 13.— As in Fig. 5, the evolution of the D trans parameter (transition discriminant D trans - see eq. (4)) as a function of [Fe/H] . The black circles come from the compilation ofFrebel et al. (2007). The red box corresponds to the region corresponding to C rich stars.have been placed in two bins at z = 0 . ± .
2, and z = 0 . ± . et al. (2004, 2008)).Their results (which have been corrected for the effects of extinction) show SNII rates whichare significantly higher than the local rate (at z = 0; Cappelaro et al. et al. z .The SN Type II rate is directly related to the overall SFR and therefore to the astration rate ν and the slope of the SFR at high redshift.The data at low z is well described by the models. This result is independent of ourchoice of the mass range for Pop III since massive Pop III stars will only contribute to theSN rate at very high redshift and our IM Pop III stars produce no SNII. However, the modelpredicts much higher SN rates at higher redshift. Indeed, the SN Type II rate peaks ata redshift z ≈ z . It will beinteresting to see whether future data will be able to probe the SN rate at higher redshift. 30 –Fig. 14.— Evolution of the SNII rate as a function of redshift. The observed rates aretaken from Cappelaro et al. (1999); Capellaro et al. (2005); Dalhen et al. (2004, 2008);Botticella et al. (2008); Bazin et al. (2009); Li et al. (2010). The evolution is the same forall three models.These elevated rates may be detectable in spite of the expected increase in dust extinctiondue to the early production of metals. Our calculation of the Type Ia SN rate depends on two additional assumptions beyondthe specification of the models present in the previous section. The Type Ia rate will dependon the fraction of low and IM mass stars which end up as SNIa, as well as the time delaybetween formation and explosion. Furthermore, it is not clear that either of these quantitiesare universal constants. That is, they may vary with redshift, metallicity, or the size of thestructure the stars are formed in. We have assumed that the SNIa rate is proportional tothe IM star SFR (2 − M ⊙ ). The coefficients adopted are ǫ = 0.02 and 0.01 for the models 31 –2, 1 and 3 respectively.In Fig. 15, we show the SNIa rate contrasted with the observational data. As in the casefor Type II supernovae, at high redshift, the data (also taken from GOODS; Dalhen et al. z = 0 .
4, 0.8, 1.2, and 1.6, each with a spreadof ± .
2. Other data references are given in the caption. We see that, in contrast to the caseof SNII, the evolution of the SNI rate is very different for the two models with and withoutIM stars. Adding the IM stellar mode implies a high SNIa rate at high redshift. The positionof this bump depends on the time delay of the SNIa.Fig. 15.— Evolution of the SNI rate as a function of redshift. The observed rates are takenfrom Cappelaro et al. (1999); Reiss (2000); Hardin et al. (2000); Dalhen et al. (2004);Pain et al. (2002); Madgwick et al. (2003); Tonry et al. (2003); Strogler et al. (2004);Blanc et al. (2004); Li et al. (2010); Perrett et al. (2010). The red solid curve correspondsto the both models 1 (normal mode) and 2 (with Massive Pop III stars). The black dottedcurve corresponds to model 3 (with IM stars).
Left:
The assumed time delays for IM starsin model 2 and model 3 are 2.5 and 3.4 Gyr (including the lifetime of stars) respectively, andthe fraction of the white dwarfs which become SNIa are ǫ = 2 and 1 per cent, respectively. Right:
The time delay for IM stars to become SNIa in model 3 is reduced to 0.5 Gyr and ǫ is 2 per cent for both models.Due to large uncertainties concerning the time delay, we present two cases (Maoz et al. et al. ǫ of IM stars becoming SNIa is reducedas discussed in section 2.7.In the upper panel Fig. 16, the SNI/SNII ratio is plotted as a function of the redshiftfor models 1 and 3. In the lower panel of the figure both SNIa and SNII rates are plotted,as in 14 and 15. The IM stellar mode predicts that the bulk of SNIa occur at hight redshift,though this results depends on the time delay of these SN. However, at such a high redshiftthe selection efficiently drops rapidly towards zero (Perrett et al. (2010)) and we cannotexclude the existence of this SNIa component. In the future it would be interesting to haveobservational insight into low mass galaxies, which could contain sub-luminous SNIa. Analternative, if these sub luminous SNIa are not observed we could put strong constraints onthe early helium abundance in the primitive structures.It is interesting to note the interplay between the IM constraints from halo star carbonabundances and from and Type Ia SNe. Namely, at the end of § require an early cosmic IM star population,but the relative rarity of such C-rich stars also seems to imply the IM population was sub-dominant, perhaps accounting for ∼ −
20% of early star formation. Note that if we applythis same ∼ −
20% factor to the IM predictions for Type IA SNe in Figs. 15 and 16,the predictions would be brought into agreement with the observations. Similarly, we couldargue the other direction, demanding that the IM fraction be small enough to agree withthe Type Ia SN observations; this would again give ∼ −
20% of our all-IM Pop III model,and thus would agree with the rough statistics suggested by the counts of C-rich metal poorstars. This rough concordance may be coincidental but is nonetheless both encouraging andintriguing.
6. Discussion
By definition, as the first stars formed in a metal-free environment, Pop III stars existedand played a role in our past history. However, the identity and mass distribution of thesestars is largely unknown. We expect that they played an important role in re-ionizing theUniverse at high redshift, as well as laid the chemical seeds for future generations of stars(population II/I). We also know that a Salpeter IMF, typical of population I with a mass 33 –Fig. 16.— Evolution of the ratio of SNIa and SNII event rates as a function of redshift. (toppanel) for model 1 and model 3. In the bottom panel, the rates plotted of SNI and SNII aspresented in 14 and 15. The delay of SNIa is taken as 3.4 Gyr.range of 0.1 - 100 M ⊙ is not capable of producing a sufficient optical depth for reionizationor of producing the specific abundance patterns in EMPs. Very massive stars ( >
100 M ⊙ )also fail in producing the observed abundance patterns, though they are certainly capableof reionizing the Universe. A top-heavy IMF for Pop III was studied in the cosmologicalcontext in Daigne et al. (2006); Rollinde et al. (2009) and while successful in many aspects,is not capable of producing the (albeit weak) evidence for an enhancement in He at lowmetallicity over BBN predictions or the lagre carbon enhancements which are made manifestin the parameter D trans . To the best of our knowledge, IM stars as candidates for Pop IIIhave not been studied in the cosmological context.We have shown that an early generation of IM stars is indeed capable of providing aneffective prompt initial enrichment of He. We have also shown, perhaps surprisingly, thatthese stars normalized in abundance to the required He enrichment, are more than capableof providing a sufficient number of ionizing photons to the early IGM. Also as a bonus, IM 34 –stars can provide the large abundance ratios of C, N, O, and Mg relative to Fe in EMP stars.However, our results indicate that one cannot simply assume a homogeneous and well-mixedIGM and/or ISM as smaller structures grow to large galaxies and clusters of galaxies. TheCNO abundance that this model predicts at metallicities between − < [Fe/H] < − D trans represents a measure of carbonand oxygen produced in prior generations of stars. As discussed earlier, the data show twodistinct populations: the bulk of the data show increasing D trans with [Fe/H] and is very wellmodeled by either a standard or top-heavy IMF; and a second population with very large D trans between − < [Fe/H] < −
3. The latter is well explained by our Pop III IM stellarmode. How can one model explain both populations?It is perhaps too naive to expect a homogeneous model as the type we have beendescribing to explain this discrepancy. Indeed one can imagine that the impact of thegeneration of IM stars was effective only early on in the building of higher mass objects inthe hierarchical structure formation scenario. That is, this generation was active only in thesmallest scale structures, here taken to be typically 10 M ⊙ . These structures and the lowmass stars and remnants left behind were in some cases incorporated into the halos of largerobjects to become galaxies. Others remain as low mass dwarfs. In this way, one can perhapsexplain the bulk of the observations of low and increasing D trans in stars formed in largerscale objects involving a larger baryon fraction, while those stars with large D trans would beexplained by the impact of IM stars in the smallest structures formed. Indeed, using bothcarbon data on metal-poor stars, and Type Ia SN observations, we roughly estimate that aPop III IM mode operates at ∼ −
20% of our model rate. Since our IM mode processesabout 10% of baryons, this in turn implies that ∼ −
2% of baryons participate in IM starformation.In this interpretation, the prompt initial enrichment of He, which is observed largely indwarf irregular galaxies, was also impacted by IM stars as these objects were evidently notincorporated into larger scale structures. In the context of the light element abundances, it isinteresting to note further that some of the stars which show large carbon enhancements alsoshow deficiencies in Li. Furthermore, there is increasing evidence (Sbordone et al. < −
3. In Sbordone et al. (2010), it is argued that the depletion (which shows considerabledispersion below the plateau) at low metallicity may have been due to stellar astration. Themodel discussed here (given the above interpretation) can account for most of the astrationseen in these stars. The model cannot, however, account for the discrepancy between the 35 –BBN prediction at the WMAP baryon density and the Spite plateau value as speculatedin Piau et al. (2006). Note that the depletion in D/H is probably not an issue, as theabsorption systems with measured D/H are presumably larger scale structures for which ourabundance patterns would not be expected to apply.Unfortunately, neither of the two Pop III models delivers entirely satisfactory results.While the massive mode, is capable of producing sufficiently high ratios of [C,O,Mg/Fe] toexplain the observations of extremely iron-poor stars, the high ratios occur almost instantlyafter the first stars are born, and thus require these stars to be born at that time at very highredshift. This model also has difficulty in explaining the high [N/Fe] or [C/O] ratios seen.As a result, the massive Pop III model cannot explain the high values of D trans seen in somestars. The model cannot account for the effective prompt initial enrichment of He nor canit be used to account for the astration of Li below the Spite plateau. On the other hand,the IM model for Pop III underproduces [O/Fe] and because of the large amounts of C andN produced cannot explain the bulk of the values of D trans observed, but the top panel datais explained due to the overabundances of C,N. Indeed, the overproduction of these elementswould preclude the homogeneous and well-mixed treatment of gas in ever increasingly largescale structures.Another distinctive feature of the IM Pop III model is the prediction for the rate ofType Ia supernovae at high redshift. This model naturally predicts a large increase in theType Ia rate if the efficiency for supernovae is constant and the time delay is not small. It isrelevant to speculate that a small high mass tail in the IM population could lead to possibleGRBs in the redshift range 10-20. This would fill the “GRB desert” between Pop II and theusual high redshift Pop III stars.The work of KAO was supported in part by DOE grant DE–FG02–94ER–40823 atthe University of Minnesota. Plus PICS CNRS/USA. We are indebted to F. Daigne for hispermanent help. Thanks very much to Anna Frebel for the use of her data table compilation.Thanks also to Yannick Mellier and Reynald Pain for their precious help regarding the SNIarate observations. REFERENCES
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