Correction to: Prevention is better than cure? Feedback from high specific energy winds in cosmological simulations with Arkenstone (Monthly Notices of the Royal Astronomical Society (2025) 543:2 (1456–1478) DOI: 10.1093/mnras/staf1440)

This is a correction to our paper Prevention is better than cure? Feedback from high specific energy winds in c osmologic al simula- tions with Arkenstone , which was recently published in MN- RAS Volume 543, Issue 2, pp. 1456–1478 (2025). In brief, we cor- rect a coding error in the thermal energy injection during wind- particle recoupling, which introduced an unintentional redshift dependence in the energy loading. With this fixed, we recover similar z = 0 galaxy properties by increasing the global energy loading by a factor of ∼2 −3 and removing the cap at ηE = 1 . The main conclusions of the paper remain unchanged, although some high-redshift results (in particular fig. 13) should now be int erpret ed with caution. We detail the err or, intr oduce new sim- ulations with the err or fix ed, and pr esent the corr ected figur es from these new simulations below. After publication, an error was discovered in the simulation code for the recoupling of wind particles in the circumgalactic medium (CGM), which meant that, at scale factor a , we were accidentally injecting a fact or of a −2 t oo much thermal energy each time a full displacement recoupling occurred (the kinetic energy input was unaffected). While the energy loadings shown in the original fig. 1 were correct at z = 0 , they hid a significantly higher energy loading at higher redshift. With this error correct ed, w e ran test simulations and found that we can achieve similar z = 0 results to our original work, though this r equir es overall energy loadings appr o ximately a fac- t or of tw o higher than those stated in the original paper once the accidental redshift dependence was remov ed. Giv en the com- putational expense inv olv ed in running the full suite we have not re-run every simulation with the corrected code, but we pr esent below r esults fr om a variable energy loading run (with ηE = 0 . 9[ σDM , 1D / 51 km s −1 ] −3 / 2 ≈0 . 9[ M h / 10 11 M ] −1 / 2 ). In Fig. 1 we show the variable energy loading (with a slope of appr o ximately ηE ∝ M −1 / 2 h ) of our new run in light blue (middle line), compared to TNG in black (upper line). For r efer ence we also show the line for the equivalent run as shown in the original fig. 1 (bottom line), though we note this line (as well as the line for TNG) is only true for z = 0 . Figs 2 and 3 show the gas surface density map of the new Arkenstone simulation box, and the ratio of this to the TNG bo x, r espectively. These ar e very similar to the original versions. In Fig. 4 we show the stellar mass function, and in Fig. 5 we show the stellar mass to halo mass (SMHM) relation normalized by the cosmic baryon fraction, both at z = 0 , for TNG, the old, and the new Arkenstone simulations. We can see our new simula- tion in the light blue gives a reasonable match to the observational data M. Bernardi et al. ( 2017 ); P. Behroozi et al. ( 2019 ); S. P. Driver et al. ( 2022 ), with a better match at intermediate masses compared to the old Arkenstone run, but slightly higher stellar masses at the low mass end. We note that, if we had adopted the original energy scaling (i.e. lower ηE normalization) with the corrected code, the predicted stellar masses at z = 0 (particularly in the dwarf regime) would have been much too high –this simulation was started but found to be pr ohibitively e xpensiv e t o run to z = 0 . The updated black hole to stellar mass relation is in Fig. 6 and is compared to the relation from J. Kormendy & L. C. Ho ( 2013 ). We do find a slight difference in our corrected run compared to the old Arkenstone run, although, as discussed in the main paper, the black hole models have not been re-calibrat ed aft er introduc- ing Arkenstone , and the int eraction betw een the models will be studied in future work. In Fig. 7 we show the relationship between stellar mass and stellar half mass radii, and again we see results comparable to ob- servations (P. Behroozi, A. Hearin & B. P. Moster 2022 ). Galaxies are, on average, more compact in Arkenstone than TNG –the same conclusion we reached in the original paper. The gas and baryon fractions at z = 0 , shown in Figs 8 and 9 respectively, and the average C GM temperatur e in Fig. 10 , are (Figure Persented) largely similar in our new Arkenstone run, with only a slight reduction in gas and baryons in lower mass haloes. The corrected Figs 11 and 12 have the same trends as the orig- inal paper, but with the effect of prev entativ e feedback demon- strated more clearly –strengthening our original conclusions. Fig. 11 shows a clear correlation between star formation rate and C GM g as fraction, with galaxies lying below the main sequence having a depleted gaseous halo. The lower inflow (and outflow) rat es compared t o TNG in Fig. 12 also demonstrat e prev entativ e feedback in action, with lower inflowing mass fluxes at smaller radii for both z = 0 and z = 2 . The overestimation of thermal energy injection in our old runs at high redshift means the early behaviour of our new simulations is notably different, with significantly more stars formed at earlier (Figure Persented) times. We show how this impacts the z = 2 SMHM relation in Fig . 13 , wher e we can see a corr esponding overpr oduction of stars in low mass haloes at this redshift, even though the stellar masses ar e r easonable by z = 0 . The gas fractions (Fig. 14 ) and av- er age CGM temper atures (Fig. 15 ) are comparable for the Arken- stone runs, and the relative difference to TNG is unchanged. The early enhancement of star formation in our new Arken- stone run is shown most clearly in the global SFR of our old (Figure Persented) and new simulations in Fig. 16 . We will e xplor e the impact of our changes at high redshift in detail in future w ork. How ev er the strong implication from our new runs is that, for prev entativ e feedback alone, dependence on dark matter velocity dispersion is insufficient t o regulat e high redshift star formation in low mass g alaxies. Ther e ar e sev eral pot ential solutions t o this –early feed- back could be more ejective, for example, or there could be a dependence of wind loadings on metallicity or ISM pr essur e that when considering the impact of pre-supernova feedback) and varies significantly between simulations.