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by the chemical and numerical network, when high densities are reached, and the net star formation can be null.

We see that the total star formation rate is only mildly influenced by the value adopted forZcrit, meaning that population III star formation does not affect the global behaviour

significantly and the bulk of star formation is mainly led by population II-I objects. The reason for that is simply understood in terms of time-scales, as population III objects have a short lifetime (at most_∼106_{yr) and rapidly pollute the medium up to the critical}

Z. Therefore, after the very first bursts, it is much easier to match the condition for standard population II-I star formation, rather than for metal free, population III star formation (see also Figure 7.6).

This is very well seen in Figure 7.4, where we display the metal evolution in the simulations. First metals spread during the final stages of stellar evolution have typical

Z _∼ (10−5 _{− 10}−4_)Z

⊙ and they immediately reach values of Z ∼ (10−4 − 10−3)Z⊙ between redshift z _∼ 16 and z _∼ 15. Therefore, the critical metallicity Zcrit is easily

reached, despite its precise, actual value. The leading element is always oxygen, as it is the most abundant one produced by supernova explosions.

We point out that for higherZcrit the population III regime lasts longer, so one has more

massive star explosions which can pollute the medium up to higher metallicities, before population II-I star formation regime sets in. This results in a quicker Z increase in the very early stages, but, on average, the differences between the two extremes are not exagerately big.

In addition, for what said in the beginning of this section, the simultaneous presence of different star formation regimes is naturally expected since soon after the onset. We check this, plotting the ratio between population III star formation rate, SFRIII, and

population II-I star formation, SFRII−I in the right panel of Figure 7.3. The presence

of spikes is due to divergencies arising when there is no standard star formation (i.e. SFRII−I ∼ 0 M⊙yr−1Mpc−3) and it is, obviously, particularly strong in the high-z tail. None the less, residual, isolated population III bursts are still ongoing at lower redshifts, where on average this regime becomes negligible.

In Figure 7.5, for sake of clarity, we consider only those redshifts at which population III and population II-I star formation are non-zero. In this way we just avoid the divergencies

156 Early structure formation and critical metallicity

Figure 7.4: The plots show metal evolution as function of redshift for theZcrit= 10−3 (upper-left panel), 10−4 (upper-right panel), 10−5 _{(bottom-left panel), and 10}−6_Z

⊙ (bottom-right panel) case. The magenta horizontal

dot-dot-dot-dashed line indicates, in each panel, the critical metallicity; the dotted line is the maximum metallicity; the dot-dashed line is the average metallicity of the spread metals; the solid line is the total metallicity averaged over the whole simulation box and the dashed lines the corresponding individual metallicities: carbon (blue), oxygen (green), magnesium (red), sulphur (purple), silicon (pink), iron (yellow), other metals (cyan).

7.2 Effects ofZcrit on SFR 157

Figure 7.5: The plots are similar to Figure 7.3, but here the ratio between population III star formation rate

(SFRIII) and population II-I star formation rate (SFRII−I) is shown. The critical metallicity for the transition

from population III regime to population II-I regime is assumed to beZcrit= 10−3Z⊙(top-left),Zcrit= 10−4Z⊙

158 Early structure formation and critical metallicity

Figure 7.6: The plots show the quantity Log10(SFRIII/SFRTOT) (left panel) and Log10(SFRIII/SFRII−I) (right

panel) as function of redshift forZcrit = 10−3Z⊙ (solid line), Zcrit = 10−4Z⊙ (dotted line), Zcrit = 10−5Z⊙

(dashed line),Zcrit= 10−6Z⊙(dot-dashed line), as indicated by the legend. The data are the same as in Figure

7.5, averaged and plotted in decimal logarithmic scale.

in the early epochs, where population III star formation is the only regime and SFRII−I is

zero. We see that the contribution from population III star formation is relevant only in the very early phases, when star formation sets in. In this period (corresponding to a ratio greater or equal to unity) star formation is lead by metal-free star formation, according to a top-heavy IMF (see section 7.1). In the four different panels, we see that the main effect of changing Zcrit is altering the duration of population III regime. Indeed, this is slightly

longer in the Zcrit= 10−3Z⊙ case and decreses gradually with Zcrit. For Zcrit= 10−3Z⊙ (top-left panel), population III is relevant for ∆z _≃ 1 (a time interval of _∼ 2_· 107_yr

at z _≃ 16), while for Zcrit = 10−6Z⊙ (bottom-right panel), there is a sudden drop at

z _≃16, immediately after the onset of star formation. This behaviour, the smaller Zcrit,

the earlier the transition from population III to population II-I dominated star formation, is expected, because the time needed to pollute the IGM is shorter.

We also highlight that population III contributions are about 2 or 3 orders of magnitude smaller than population II-I already at redshift z _∼ 12, so the effect on large-scale structure formation can be neglected.

In Figure 7.6, we summarize the discussion showing, for the different critical metallicities adopted, a plot of the average ratio of simultaneous population III and population II-I star formation, SFRIII/SFRII−I (left panel), and a plot of the average ratio of population