tokens: discrepancies are caused by differences in how ρ SFR is calculated. A good example of this problem can be illustrated by comparing our estimate of ρ SFR at z ≃ 10 with the results of Oesch et al. ( 2014 ). The headline result from Oesch et al. ( 2014 ) is that log 10 (ρ SFR ) = −3.25 ± 0.35 at z ≃ 10 (lower data point in Fig. 9 ), which is in poor agreement with the value of derived here. However, it is worth noting that the value of log 10 (ρ SFR ) = −3.25 ± 0.35 was calculated by summing the contribution of the five z ≃ 10 candidates found by Oesch et al. ( 2014 ), rather than integrating their estimated z ≃ 10 LF to a consistent UV luminosity limit. Interestingly, Oesch et al. ( 2014 ) also calculate an alternative value of log 10 (ρ SFR ) = −2.80 ± 0.11 (upper data point in Fig. 9 ), based on assuming luminosity evolution of the LF (as adopted here) and integrating to our adopted limit of M 1500 = −17.7. This estimate of ρ SFR is in excellent agreement with both our new determination at z ≃ 10, and our best-fitting linear ρ SFR – z relation. Finally, it is interesting to compare our new observational estimate of the high-redshift evolution of ρ UV with the predictions of recently published models of galaxy evolution. Our data points are plotted against the predictions of seven such models in Fig. 10 . It is important to acknowledge that some of these predictions are at least partly based on hydrodynamic simulations, while others are semi-analytic models, some of which have been effectively tuned to reproduce the UV LF at moderately high redshift (e.g. z ≃ 6). Thus, in a sense, this comparison is not completely fair, and cannot be simply regarded as specifically favouring one form of model over another. Nevertheless, some important general trends can be deduced. In particular, the Illustris (Genel et al. 2014 ) and Munich (Henriques et al. 2015 ) models, while clearly capable of reproducing many (often quite complex) aspects of galaxy evolution, both clearly underpredict ρ UV at redshifts higher than z ≃ 7. We stress that this discrepancy is already clear by z ≃ 8 (where the measured value of ρ UV is well established) and is simply confirmed and strengthened by our new results at z ≃ 9 and ≃ 10. The challenge, then, for such models is to be able to produce star formation activity which extends to higher redshifts than currently predicted. Indeed, the only model shown here that systematically overpredicts ρ UV is that of Behroozi Silk ( 2015 ). We note that the overprediction of raw observed ρ UV at redshifts z ≃ 5–6 by the Illustris and Khochfar et al. simulations is not really a fundamental problem, as both of these models do not include the impact of dust obscuration. Figure 10. Our new measurement of the evolution of the UV luminosity density (ρ UV ) and inferred star-formation rate density (ρ SFR ) at z > 5, compared with the predictions of a range of models and simulations from the literature. The model predictions are as follows:
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