tokens: of galaxies with high SFRs/luminosities to the CSFRD/total IR luminosity decreases much flatter. This discrepancy reflects the tension between the SFRFs of the EAGLE reference model and IR constraints. The later imply larger number densities of objects with SFR ∼ 10–100 M ⊙ yr −1 (Section 4.1 ) at z 2, and the disagreement with the L100N1504-Ref run increases with time. In Section 6 we will see the important role that feedback plays on keeping the number of these extremely high star-forming objects low at these redshifts. 5 THE CONTRIBUTION OF HALOES WITH DIFFERENT MASSES TO THE SFRF AND CSFRD In this section we present the contribution of haloes with various masses to the CSFRD (Fig. 4 ), the number density of haloes of different masses at different redshifts (Fig. 5 ) and their contribution on the SFRF (Fig. 6 ) in the EAGLE L100N1504-Ref run. Figure 4. CSFRD contribution of haloes with different masses in EAGLE. Below redshift 5 objects with masses M halo = 10 11–12 M ⊙ dominate through their high efficiencies besides their low numbers (Fig. 5 ). Figure 5. Left-hand panel: evolution of the number of haloes with different masses in the L100N1504-Ref. Haloes with low masses are numerous even at high redshift while higher mass objects (e.g. M halo ∼ 10 11–13 M ⊙ ) form with high rate up to redshift z ∼ 1.5. Right-hand panel: percentage of star-forming haloes at different masses. Haloes with M halo ∼ 10 11–12 M ⊙ are typically star forming at all redshift. Figure 6. The contribution of dark matter haloes to the SFRF (black stars) for redshifts z ∼ 8.0 (top left-hand panel), z ∼ 4.0 (top right-hand panel), z ∼ 2.0 (bottom left-hand panel) and z ∼ 0.1 (bottom right-hand panel). Galaxies with SFR ≥ 1 M ⊙ yr −1 reside in large haloes M halo ∼ 10 11–12 M ⊙ even at z ∼ 4.0. These haloes represent only ∼1 per cent of the total star-forming population at this era. In the local Universe the number of massive haloes M halo ≥ 10 11 M ⊙ is significantly higher than that of z ∼ 4. They dominate almost entirely the SFRF at SFR ≥ 0.1 M ⊙ yr −1 . Behroozi, Wechsler Conroy ( 2013 ) and Moster, Naab White ( 2013 ) argued that haloes near 10 12 M ⊙ are the most efficient at forming stars at all redshifts with the baryon conversion efficiency ( M ⋆ / M baryon ) dropping rapidly at both higher and lower masses. In addition, the stellar to halo mass ratio also peaks at 10 12 M ⊙ (Behroozi et al. 2013 ). However, in the paradigm of hierarchical structure formation, small haloes form earlier than larger ones, which need some time to emerge. In Fig. 4 we see that at z ≥ 5 the CSFRD is dominated by relatively small haloes of mass M halo = 10 9–10 M ⊙ . 5 The left-hand panel of Fig. 5 reveals that the number of objects of this mass interval is high. In addition, the right-hand panel of the same figure, where we present the percentage of star-forming haloes at different masses (i.e. n haloes, SFR > 0 / n haloes, total ), shows that a large percentage (>50 per
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