Population III stars and galaxies a topdown theoretical approach

We shall now briefly summarize the expected theoretical properties governing the first generations of stars and galaxies, i.e. objects that are of primordial composition or very metal-poor.

4.2.1 Primordial star formation In present-day gas, with a heavy-element mass fraction (metallicity) up to ~2%, C+, O, CO and dust grains are excellent radiators (coolants) and the thermal equilibrium timescale is much shorter than the dynamical timescale. Hence large gas reservoirs can cool and collapse rapidly, leading to clouds with typical temperatures of ~10K. In contrast, primordial gas clouds would evolve almost adiabatically, since heavy elements are absent and H and He are poor radiators for T < 104 K. However, molecules such as H2 and HD can form and cool the gas under these conditions. Approximately, it is found that at metallicities Z<Zcr;t = 10-5±1Z0 these molecules dominate the cooling (e.g. Schneider et al. 2002, 2004).

Starting from the largest scale relevant for star formation (SF) in galaxies, i.e. the scale of the DM halo, one can consider the conditions necessary for star formation (e.g. Barkana & Loeb 2001; Ferrara 2007). Such estimates usually rely on timescale arguments. Most importantly, the necessary condition for fragmentation that the cooling timescale is shorter than the free-fall timescale, tcooi ^ tff, translates to a minimum mass Mcrit of the DM halo for SF to occur as a function of redshift. A classical derivation of Mcrit is found in Tegmark et al. (1997); typical values of Mcritt are about 107M0 to 109M0 from z ~ 20 to 5. However, the value of Mcrit is subject to uncertainties related to the precise cooling function and to the inclusion of other physical mechanisms (e.g. ultra-high-energy cosmic rays), as discussed e.g. in the review of Ciardi & Ferrara (2005).

After SF has started within a DM halo, the "final products" may be quite diverse, depending in particular strongly on a variety of radiative and mechanical feedback processes. Schematically, taking fragmentation and feedback into account, one may foresee t Remember that this denotes the total DM mass, not the baryonic mass.

the following classes of objects according to Ciardi et al. (2000): "normal" gaseous galaxies, naked star clusters (i.e. "proto-galaxies" that have blown away all their gas) and dark objects (where no stars formed, or where SF was rapidly turned off due to negative radiative feedback). At very high redshift (z > 10) naked star clusters may be more numerous than gaseous galaxies.

How does SF proceed within such a small "proto-galaxy" and what stars will be formed? Fragmentation may continue down to smaller scales. In general mass of the resulting stars will depend on the fragment mass, accretion rate, radiation pressure and other effects such as rotation, outflows, competitive accretion etc., forming a rich physics that cannot be described here; see e.g. reviews by Bromm & Larson (2004) and Ciardi & Ferrara (2005) and references therein. Most recent numerical simulations following early star formation at very low metallicities agree that at Z < Zcrit the smallest fragments are quite massive and that they undergo a runaway collapse accompanied by a high accretion rate resulting in (very) massive stars, (10-100)M0 or larger, compared with a typical mass scale of —M0 at "normal" (higher) metallicities (cf. Bromm & Larson 2004). This suggests that the stellar initial mass function (IMF) may differ significantly from the present-day distribution at Z < Zcrit = 10~5±1Z0. The value of the critical metallicity is found to be determined mostly by fragmentation physics; in the transition regime around Zcrit the latter may in particular also depend on dust properties (cf. Schneider et al. 2002, 2004).

Determining the IMF at Z < Zcrit observationally is difficult and relies mostly on indirect constraints (e.g. Schneider et al. 2006). The most-direct approaches use the most-metal-poor Galactic halo stars found. From counts (metallicity distributions) of these stars, Hernandez & Ferrara (2001) find indications for an increase of the characteristic stellar mass at very low Z. Similar results have been obtained by Tumlinson (2006), using also stellar abundance patterns. However, no signs of very massive (>130M0) stars giving rise to pair-instability supernovae (see Section 4.2.4) have been found yet (cf. Tumlinson 2006). In Section 4.4 we will discuss attempts to detect Population III stars and to constrain their IMF in situ in high-redshift galaxies.

4.2.2 Primordial stars: properties Now that we have formed individual (massive) stars at low metallicity, what are their internal and evolutionary properties? Basically these stars differ on two main points from their normal-metallicity equivalents: the initial source of nuclear burning and the opacity in their outer parts. Indeed, since Population III stars (or more precisely stars with metallicities Z< 10~9 = 10~7'3Z0) cannot burn on the CNO cycle like normal massive stars, their energy production has to rely initially on the less-efficient p-p chain. Therefore these stars have higher central temperatures. Under these conditions (T > 1081 K) and after the build-up of some amount of He, the 3a reaction becomes possible, leading to the production of some amounts of C. In this way the star can then "switch" to the more-efficient CNO cycle for the rest of H-burning, and its structure (convective interior, radiative envelope) is then similar to that of "normal" massive stars. Given the high central temperature and the low opacity (dominated by electron scattering throughout the entire star due to the lack of metals), these stars are more compact than corresponding Population II and I stars. Their effective temperatures are therefore considerably higher, reaching up to —105 K for M> 100M0 (cf. Schaerer 2002). The lifetimes of Population III stars are "normal" (i.e. —3 Myr at a minimum), since L — M, i.e. since the luminosity increases approximately linearly with the increase of the fuel reservoir. Other properties of "canonical" Population III stellar-evolution models are discussed in detail in Marigo et al. (2001), Schaerer (2002) and references therein.

Figure 4.1. Left: relative output of hydrogen-ionizing photons to UV light, measured in the 1500-A restframe, Qh/Lis00, as a function of metallicity for constant star formation over 1 Gyr. Results for different IMFs, including a Salpeter, Scalo and top-heavier cases, are shown. The shaded area indicates the critical metallicity range where the IMF is expected to change from a "normal" Salpeter-like regime to a more-massive IMF. Right: hardness Q(He+)/Q(H) of the He+-ionizing flux for constant star formation as a function of metallicity (in mass fraction) and for different IMFs. At metallicities above Z > 4 x 10~4 the predictions from our models (crosses), as well as those of Leitherer et al. (1999, open circles), and Smith et al. (2002, open triangles) are plotted. The shaded area and the upper limit (at higher Z) indicate the range of the empirical hardness estimated from H II-region observations. From Schaerer (2003).

Figure 4.1. Left: relative output of hydrogen-ionizing photons to UV light, measured in the 1500-A restframe, Qh/Lis00, as a function of metallicity for constant star formation over 1 Gyr. Results for different IMFs, including a Salpeter, Scalo and top-heavier cases, are shown. The shaded area indicates the critical metallicity range where the IMF is expected to change from a "normal" Salpeter-like regime to a more-massive IMF. Right: hardness Q(He+)/Q(H) of the He+-ionizing flux for constant star formation as a function of metallicity (in mass fraction) and for different IMFs. At metallicities above Z > 4 x 10~4 the predictions from our models (crosses), as well as those of Leitherer et al. (1999, open circles), and Smith et al. (2002, open triangles) are plotted. The shaded area and the upper limit (at higher Z) indicate the range of the empirical hardness estimated from H II-region observations. From Schaerer (2003).

More-sophisticated stellar evolution models including many physical processes related to stellar rotation are now being constructed (cf. Meynet et al. 2006; Ekstrom et al. 2006). Whereas before it was thought that mass loss would be negligible for Population III and very-metal-poor stars, since radiation pressure is very low and pulsational instabilities may occur only during a very short phase, cf. Kudritzki (2002) and Baraffe et al. (2001), fast rotation - due to fast initial rotation and inefficient transport of angular momentum -may lead to mechanical mass loss, when these stars reach critical (break-up) velocity. Rotation also alters the detailed chemical yields, may lead to an evolution at hotter Teff, even to Wolf-Rayet (WR) stars, and may alter the final fate of Population III/very-metal-poor stars, which may in this way even avoid the outcome of becoming a "classical" pair-instability supernova (PISN, cf. below). Many details and the implications of these models on observable properties of metal-free/very-metal-poor populations still remain to be worked out.

4.2.3 Primordial stars and galaxies: observable properties The observable properties of individual Population III and metal-poor stars and of an integrated population of such stars can be predicted using stellar-evolution models, appropriate non-local-thermodynamic-equilibrium (NLTE) stellar atmospheres and evolutionary synthesis techniques; see e.g. Tumlinson et al. (2001), Bromm et al. (2001) and detailed discussions in Schaerer (2002, 2003).

Given the exceptionally high effective temperatures of Population III stars on the zero-age main sequence, such objects emit a larger fraction of the luminosity in the Lyman

Pop III: Salpeter IMF, (1-500)MS

Pop III: Salpeter IMF, (1-500)MS

2000 4000

Figure 4.2. Left: the spectral energy distribution of a very young Population III galaxy including H and He recombination lines. The pure stellar continuum (neglecting nebular emission) is shown by the dashed line. For comparison the SED of the Z = (1/50)Z0 population (model ZL: Salpeter IMF from M0 to 150M0) is shown by the dotted line. The vertical dashed lines indicate the ionization potentials of H, He0 and He+. Note the presence of the unique He II features (shown as thick dashed lines) and the importance of nebular continuous emission. From Schaerer (2002). Right: Temporal evolution of the UV slope ( measured between 1300 and 1800 A from synthesis models of various metallicities and for instantaneous bursts (solid lines) and constant SF (long dashed lines). Full lines show Solar-metallicity models, metallicities between Z = 10-5 and zero (Population III) and intermediate cases of Z = 0.004 and 0.0004. The dotted lines show ( if nebular continuous emission is neglected, i.e. assuming pure stellar emission. Note especially the strong degeneracies of ( in age and metallicity for bursts, the insensitivity of ( to Z for constant SF and the rather red slope for young very-metal-poor bursts. From Schaerer & Pello (2005).

2000 4000

Figure 4.2. Left: the spectral energy distribution of a very young Population III galaxy including H and He recombination lines. The pure stellar continuum (neglecting nebular emission) is shown by the dashed line. For comparison the SED of the Z = (1/50)Z0 population (model ZL: Salpeter IMF from M0 to 150M0) is shown by the dotted line. The vertical dashed lines indicate the ionization potentials of H, He0 and He+. Note the presence of the unique He II features (shown as thick dashed lines) and the importance of nebular continuous emission. From Schaerer (2002). Right: Temporal evolution of the UV slope ( measured between 1300 and 1800 A from synthesis models of various metallicities and for instantaneous bursts (solid lines) and constant SF (long dashed lines). Full lines show Solar-metallicity models, metallicities between Z = 10-5 and zero (Population III) and intermediate cases of Z = 0.004 and 0.0004. The dotted lines show ( if nebular continuous emission is neglected, i.e. assuming pure stellar emission. Note especially the strong degeneracies of ( in age and metallicity for bursts, the insensitivity of ( to Z for constant SF and the rather red slope for young very-metal-poor bursts. From Schaerer & Pello (2005).

continuum and have a much-harder ionizing spectrum than do higher-metallicity stars. For example, a Population III star of 5M0 is still an ionizing source! In other words, stellar populations at low metallicity are characterized by a high ionization efficiency (per unit stellar mass formed) and by a hard spectrum, as illustrated in Figure 4.1. For an unchanged IMF, e.g. Salpeter, the ionizing output normalized with respect to the UV flux density increases by a factor of or more on going from Solar metallicity to Population III. However, this increase may be much more substantial if the IMF favours massive stars at low Z, as argued before.

The predicted integrated spectrum of a very-young zero-age main-sequence (ZAMS) ensemble of Population III stars is shown in Figure 4.2. Its main characteristics are the presence of strong H emission lines (in particular strong Lya, cf. below) due to the strong ionizing flux, He+ recombination lines (especially He II A1640) due to spectral hardness and strong/dominating nebular continuum emission (cf. Schaerer 2002). The strength of Lya can be used to identify interesting Population III or very-metal-poor galaxy candidates (cf. Section 4.3). The detection of nebular He II A1640, if shown to be due to stellar photoionization, i.e. non-active-galactic-nucleus (AGN) origin, would be a very interesting signature of primordial (or very close to primordial) stars. Indeed, as shown on the right of Figure 4.1, very hard spectra are predicted only at Z<10-5 '-6Z0.

It is often heard that Population III, primeval or similar galaxies should be distinguished by bluer colours, e.g. measured in the rest-frame UV, as one would naively expect. Although the colours of stars do indeed get bluer on average with decreasing metallicity, this is no longer the case for the integrated spectrum of such a population, since nebular continuum emission (originating from the HII regions surrounding the massive stars) may dominate the spectrum, even in the UV. This leads to a much-redder spectrum, as shown in Figure 4.2 (left). Taking this effect into account leads in fact to a non-monotonic behaviour of the slope (colour) of the UV spectrum with metallicity, as illustrated in Figure 4.2 (right). This fact, and the dependence of the UV slope on the star-formation history on timescales shorter than 108-109 yr, corresponding to 10%-100% of the Hubble time at z — 6, show that the interpretation of the UV slope (or colour) of primeval galaxies must be performed with great caution.

4.2.4 Final fate

The end stages of very-metal-poor and Population III stars may also differ from those at higher metallicity, with several interesting consequences also for the observational properties of primeval galaxies. In particular such massive stars may at the end of their evolution exhibit such conditions in terms of central temperature and density that the creation of electron-positron pairs occurs, leading to an instability that will completely disrupt the star. This phenomenon is known as a pair-instability supernova (PISN),t and there exists a rich literature about the phenomenon and its many implications. Here we shall only summarize the main salient points and recent findings.

A recent overview of the various "final events" and remnants is found in Heger et al. (2003). PISNs are thought to occur for stars with initial masses of M — (140-260)M0 at very low Z. Owing to their high energy and to non-negligible time dilation, which increases the duration of their "visibility", PISNs are potentially detectable out to very high redshift (e.g. Weinmann & Lilly 2005; Scannapieco et al. 2005; Wise & Abel 2005). Large amounts of gas are ejected, as the event disrupts the star completely. Furthermore, the processed matter contains peculiar nucleosynthesic signatures, which may in principle be distinguished from those of normal SNs (cf. below). Finally PISNs are also thought to be the first dust-production factories in the Universe (cf. Schneider et al. 2004). Thus PISNs may be observable directly and indirectly, which would be very important to confirm or disprove the existence of such massive stars, i.e. to constrain the IMF of the first stellar generations. Currently, however, there is no such confirmation, as we will go on to discuss.

4.2.5 Nucleosynthesis and abundance pattern

Among the particularities of PISNs are the production of large quantities of O and Si, which translate e.g. into large O/C and Si/C abundance ratios potentially measurable in the IGM. More generally one expects roughly solar abundance of nuclei with even nuclear charge (Si, S, Ar,...) and deficiencies in odd nuclei (Na, Al, P, V,...) i.e. a strong so-called odd/even effect, and no elements heavier than Zn, due to the lack of sand r-processes; see Heger & Woosley (2002) for recent predictions.

Results from abundance studies of the most-metal-poor halo stars in the Galaxy do not show the odd/even effect predicted for PISNs. In the face of our current knowledge, in particular on nucleosynthesis, quantitative analysis of the observed abundance pattern thus disfavours IMFs with a large fraction of stars with masses M — (140-260)M0 (Tumlinson 2006). However, the abundance pattern and other constraints are compatible t Sometimes the terms pair-creation SN and pair-production SN are also used.

with a qualitative change of the IMF at Z < 10 4Z0 as suggested by simulations (cf. above).

4.2.6 Dust at high z

Dust is known to be present out to the highest redshifts from damped-Lya absorbers (DLA), from sub-millimetre emission in z ~ 6 quasars (e.g. Walter et al. 2003), from a gamma-ray-burst (GRB) host galaxy at z = 6.3 (Stratta et al. 2007) and possibly also from the spectral energy distribution (SED) of some normal galaxies at z ~ 6 (Schaerer & Pello 2005). We also know that dust exists in the most-metal-poor galaxies, as testified e.g. by the nearby galaxy SBS 0335-052 with a metallicity of ~(1/50)Z0.

Since the age of the Universe at z > 6 is Gyr at most, longer-lived stars cannot be invoked to explain the dust production in primeval galaxies. Among the possible "shortlived" dust producers are SN II, PISN and maybe also WR stars or massive AGB stars. SN II are known dust producers (e.g. SN1987A), albeit maybe not producing enough dust. Efficient dust production is found in explosions of SN II and PISNs (e.g. Todini & Ferrara 2001; Schneider et al. 2004). At zero metallicity PISNs may provide a very efficient mechanism, converting up to 7%-20% of PISN mass into dust.

Evidence for dust produced by SN has been found from the peculiar extinction curve in the BAL QSO SDSS1048+46 at z = 6.2, which is in good agreement with SN dust models (Maiolino et al. 2004). Similar indications have been obtained recently from a GRB host galaxy at z = 6.3 (Stratta et al. 2007). Whether this is a general feature remains, however, to be established. Furthermore, the most important questions, including how common dust is in high-z galaxies, in what quantities and up to what redshift, have not yet been touched upon. Forthcoming IR to sub-millimetre facilities such as Herschel and especially ALMA will allow us to address these important issues.

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