Correction to: The hot gas distribution, X-ray luminosity, and baryon budget in the L-Galaxies semi-analytic model of galaxy formation

Our paper ‘The hot gas distribution, X-ray luminosity, and baryon budget in the L-Galaxies semi-analytic model of galaxy formation’ was published in MNRAS, Volume 519, Issue 3, pp. 4344–4359, March 2023. When we recheck the codes and results, we find that the description of the infall time-scale of the cool core in equation (12) t_infall = r_core/v₂₀₀ did not correspond to the codes in our calculation. By mistake, the infall time of a cool core in our codes is defined as the same dynamical time-scale of a halo t_dyn = r₂₀₀/v₂₀₀ in equations (9) and (10), rather than the free-fall time-scale at the core radius t_infall = r_core/v₂₀₀.

Since the thermal instability and gas cooling happen within the cool core, it should be more physical to adopt t_infall = r_core/v₂₀₀ instead of t_infall = r₂₀₀/v₂₀₀ in the calculation. When we try to adopt t_infall = r_core/v₂₀₀, it will produce an over-cooling gas flow in massive galaxy groups and clusters by the very short infall time-scale in the cool core of massive clusters compared with the t_dyn. Hereafter, we will use t_dyn to represent r₂₀₀/v₂₀₀ and t_core to represent r_core/v₂₀₀. We will then show the results and the difference.

In section 2.7 of the original paper, we tune the model parameters to fit the stellar and H i gas mass function at z = 0, and also the redshift evolution of cosmic star formation density. In the following part of this erratum, we should note that the model parameters is not recalibrated, and we only show how the model results will be if we adopt t_core instead of t_dyn as the infall time-scale.

First of all, the most important influence by the change of the gas infall time-scale is the gas cooling rate. Similar to the top panel of fig. 4 in the original paper, we show the comparison of the gas cooling rate versus halo mass without the suppression by radio-mode AGN in Fig. 1. The black curve is from the original paper, while the blue dashed curve is the result with t_infall = t_core. For comparison, the red curve from Henriques et al. (2015, hereafter H15) is also included. As shown in Fig. 1, the cooling rate of t_core in massive haloes is obviously higher than that of t_dyn. This change will affect the results of the stellar and gas components in galaxy formation.

1 MASS FUNCTIONS AND STAR FORMATION HISTORY

In Fig. 2, we compare the model results of stellar mass function (hereafter SMF) and H i mass function (hereafter HIMF) at z = 0 with t_dyn and t_core as the gas infall time-scale. We find that high mass end of SMF with t_infall = t_core is a lot higher than t_infall = t_dyn and the HIMF also slightly increases at high mass end. Since the cooling rate increases a lot with t_infall = t_core in massive haloes (see Fig. 1), the cooling flow obviously strengthen the star formation and increase the stellar mass in massive haloes. Thus, the SMF at high mass end is the most obvious and important consequence to be noticed that the model is unrealistic if t_core is adopted as the cooling time-scale in the prescription of gas infall.

In Fig. 3, we compare the star formation history with the two cooling time-scales. Addition to fig. 7 in the original paper, we add the results of the redshift evolution of cosmic star formation density with t_infall = t_core based on MS and MS-II. Compared with the results in the original paper (black curves), we can see that the star formation rates with t_infall = t_core in both MS and MS-II haloes only increase a bit at z ∼ 2, which is still comparable to the observational result.

2 THE SCALING RELATIONS OF X-RAY LUMINOSITY FROM THE HOT GAS

In this part, we will show the results of the scaling relations of X-ray luminosity and temperature from hot gaseous haloes if we adopt t_infall = t_core in the models. In Fig. 4, we overplot the results from the scenario t_infall = t_core in green colour in fig. 12 of the original paper, i.e. the green dashed curves and shaded areas represent the mean values and ±1σ deviations for the model samples. To focus on the comparison between two infall time-scales, we do not include the results from isentropic cool core in Fig. 4 (the blue dashed curves in the original fig. 12).

In Fig. 4, we can see that the scaling relations from both t_infall = t_core and t_infall = t_dyn scenarios are quite similar, which fit the X-ray observational data better than the previous H15 model (see fig. 11 in our original paper). Thus, the first main conclusion in the original summary ‘The new model returns a much better match to X-ray observations compared with the previous model’ does not change if we adopt t_core instead of t_dyn as the infall time-scale.

In the top three panels of Fig. 4, L_X and T_X from two infall time-scales are almost same, as well as the slopes of the L_X-T_X, L_X-M₂₀₀ and T_X-M₂₀₀ relations. Thus the second main conclusion ‘A higher ratio of T_X/T₂₀₀ in smaller haloes and a lower density in the cool core leads to a steeper slope in the L_X-T_X relation’ does not change.

3 THE BARYON BUDGET

We will then show the results related to baryon budget in different components with t_infall = t_core in the models, and compare the results with figs 13 and 15 in the original paper.

The left panel of Fig. 5 is the same plot as the original fig. 13 together with the results from the scenario t_infall = t_core in dashed curves. We can find some changes for each components. For haloes with |$v_{200}\lesssim 100~\rm km~s^{-1}$|⁠, the fraction of disc mass in dashed curve is lower than the original result and the hot gas fraction is comparatively higher, while the fraction of total bounded mass (hot+disc) is still lower than the fraction of unbounded reservoir (the ejected component in the model). The unbounded ionized gas still dominates the baryon fraction in these small haloes. Thus, the third main conclusion ‘the ionized gas in the unbounded reservoir out of halo potential should be one of the main components of the ‘missing baryons’ is still correct if t_core is adopted as the cooling time-scale’.

The right panel of Fig. 5 is same to the original fig. 15 with the dashed curves representing the results from t_infall = t_core in the model. The hot gas fractions in both scenarios show very small difference. Consequently, one of the main conclusion ‘the low temperature intergalactic gas bounded in low mass haloes should be the main components of the ‘missing baryons’ does not change’.

4 SUMMARY

We find a bug in our codes of the calculation, and the dynamical time-scale of an entire halo t_dyn = r₂₀₀/v₂₀₀ is used as the cooling time-scale of the cool core instead of t_core = r_core/v₂₀₀ by mistake. In this erratum, we show the results if t_infall = t_core is adopt in the models, without readjusting the model parameters and physical prescriptions. We find the following main conclusions:

• Using r_core/v₂₀₀ instead of r₂₀₀/v₂₀₀ as the cooling time-scale produces a very short infall time scale for gas cooling in massive haloes, which will cause an over-cooling flow in massive galaxy and clusters. The model consequently over-predicts the stellar mass in massive haloes. Thus, the global properties like mass functions and scaling relations in the original paper are not correct. If we adopt t_infall = t_core, more future work is necessary to recalibrate the model prescriptions and parameters to make the model results consistent with various observations, especially the stellar mass function at high mass end.

• If we just use r_core/v₂₀₀ instead of r₂₀₀/v₂₀₀ as the infall time-scale and keep other prescriptions and parameters unchanged, the current three main conclusions in the original paper ‘(1) Consistent with observations, flatter density profiles in halo centers produce lower X-ray emission than an isothermal sphere; (2) Cool core regions prone to precipitation have higher gas temperature than the virial temperature, and a larger T_X/T₂₀₀ ratio in smaller haloes leads to a steeper slope in the L_X − T_X relation; (3) The ionized gas in the unbounded reservoir and low temperature intergalactic gas in low mass haloes could be the main components of the halo ‘missing baryons’ remain almost unchanged.’

DATA AVAILABILITY

The data and codes in this paper will be shared on reasonable request to the corresponding author.

REFERENCES