THE BARYON CYCLE AT HIGH REDSHIFTS: EFFECTS OF GALACTIC WINDS ON GALAXY EVOLUTION IN OVERDENSE AND AVERAGE REGIONS

We use a modified version of the tree-particle-mesh smoothed particle hydrodynamics (SPH) code GADGET-3, originally described in Springel (2005), in its conservative entropy formulation (Springel & Hernquist 2002). Our conventional code includes radiative cooling by H, He, and metals (Choi & Nagamine 2009), a recipe for star formation and SN feedback, a phenomenological model for galactic winds, and a sub-resolution model for the multiphase ISM (Springel & Hernquist 2003, hereafter SH03). In the multiphase ISM model, star-forming SPH particles contain the cold phase that forms stars and the hot phase that results from SN heating. The cold phase contributes to the gas mass, and the hot phase contributes to gas pressure. Metal enrichment is also taken into account according to the recipe from SH03 (see also Choi & Nagamine 2009), in which the increase in metallicity of star-forming gas particles is related to the fraction of gas in the cold phase, the fraction of stars that turn into SNe, and the metal yield per SN explosion. Although metal diffusion is not explicitly implemented, metals can still be transported outside galaxies by wind particles and can enrich the halos and the IGM.

Since we focus only on $z\gtrsim 6$, before the full reionization, and do not implement on-the-fly radiative transfer of ionizing photons, the UV background is not included in our simulations. One expects this omission to have a larger effect on the overdense regions. To quantify this would require the introduction of additional free parameter(s), because the precise level of the UV background is unknown at present. We therefore refrain from doing so. For the same reason we have neglected the AGN feedback (e.g., Sijacki et al. 2009), which has been predicted to affect the more massive galaxies.

For star formation, we use the "Pressure model" (Choi & Nagamine 2010), which implements the relationship between the surface density and volume density of the gas using the prescription of Schaye & Dalla Vecchia (2008). The characteristic timescale for the SF becomes ${\tau }_{\mathrm{SF}}\sim {{A}}^{-1}{(1{M}_{\odot }{\mathrm{pc}}^{-2})}^{n}{(\gamma P/G)}^{(1-n)/2}$, where ${A}=2.5\pm 0.7\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, n = 1.4 ± 0.15, γ = 5/3 (Kennicutt 1998), and P is the total effective gas thermal pressure (including the contribution from both cold and hot phases). This model reduces the high-z SFR relative to the standard recipe described in SH03. Star formation is triggered when the gas density is above the threshold value ${n}_{\mathrm{crit}}^{\mathrm{SF}}=0.6\,{\mathrm{cm}}^{-3}$ (e.g., Springel 2005; Choi & Nagamine 2010; Romano-Díaz et al. 2011a). The value of ${n}_{\mathrm{crit}}^{\mathrm{SF}}$ is based on the translation of the threshold surface density in the Kennicutt–Schmidt law, SFR$\sim {{\rm{\Sigma }}}_{\mathrm{gas}}^{\alpha }$, where SFR is the disk surface density of star formation, Σ_gas is the surface density of the neutral gas, and α ∼ 1–2, depending on the tracers used and on the relevant linear scales.

We have considered three different galactic outflow models: a constant-velocity wind (CW) model based on the method of SH03 and a variable-velocity wind (VW) model from Choi & Nagamine (2011, hereafter CN11), supplemented with a model without outflows (NW). All of our three wind models share the same thermal feedback as in SH03.

No-Wind model (NW).This model has no kinematic feedback, but maintains thermal feedback by the SNe.

Constant Wind model (CW).The galactic wind has been triggered by modifying some gas particles into "wind" particles. Those were not subject to hydrodynamical forces and have experienced the initial kick from the SNe. All CW particles had the same constant velocity, ${v}_{{\rm{w}}}=484\,\mathrm{km}\,{{\rm{s}}}^{-1}$, and the same mass loading factor, ${\beta }_{{\rm{w}}}\equiv {\dot{M}}_{{\rm{w}}}/{\dot{M}}_{\mathrm{SF}}$, where ${\dot{M}}_{{\rm{w}}}$ is the mass loss in the wind and ${\dot{M}}_{\mathrm{SF}}$ is the SFR. The mass loading factor has been fixed to a value β_w = 2 in agreement with the CW prescription used in CN11.

Variable Wind model (VW).The variable wind model from CN11 has introduced a more flexible subgrid physics compared to the simple recipe of SH03. In this paper, we adopt the 1.5ME wind model described in CN11. Briefly, the model assumes that all gas particles in a given galaxy have the same chance to become part of the wind. The probability that a gas particle becomes a wind particle is based on the values of β_w, galaxy mass, and galaxy SFR. The main parameters are the wind load β_w, defined above, and the wind velocity v_w—both have been constrained by observations that express these two parameters in terms of the host galaxy stellar mass, ${M}_{\star }$, and the galaxy SFR.

The wind velocity is calculated as a fraction of the escape speed from the host galaxy, ${v}_{{\rm{w}}}=\zeta {v}_{\mathrm{esc}}$, where ζ = 1.5 for momentum-driven winds and ζ = 1 for energy-driven winds in the current setting.The empirical relation between galaxy SFR and v_esc becomes

$$\begin{eqnarray}&&\mathrm{SFR}=1.0{\left(\displaystyle \frac{{v}_{\mathrm{esc}}}{130\mathrm{km}{{\rm{s}}}^{-1}}\right)}^{3}{\left(\displaystyle \frac{1+z}{4}\right)}^{-3/2}\,{M}_{\odot }\,{\mathrm{yr}}^{-1},\end{eqnarray} \tag{ 1 }$$

which is consistent with observations (e.g., Martin 2005; Weiner et al. 2009). The mass loading factor, β_w, is assumed to represent the energy-driven wind (${\beta }_{{\rm{w}}}\propto {v}_{\mathrm{esc}}^{-1}$) in the low-density case, $n\lt {n}_{\mathrm{crit}}^{\mathrm{SF}}$, and the momentum-driven wind (${\beta }_{{\rm{w}}}\propto {v}_{\mathrm{esc}}^{-2}$) for $n\gt {n}_{\mathrm{crit}}^{\mathrm{SF}}$. Hence, for the low-density gas, i.e., away from star-forming regions (but inside the galaxy!), we apply the parameters of the energy-driven wind for the gas particles. This procedure requires that simulations compute β_w and v_w using an on-the-fly group finder, which, in our runs, is a simplified version of the SUBFIND algorithm (Springel et al. 2001).

When an SPH particle is converted to a wind particle, it receives a v_w kick and decouples from hydrodynamic forces. The direction of the kicks is chosen to be preferentially perpendicular to the angular momentum of the particle such that, overall, the winds are launched above or below the galactic plane. The wind particles are turned back to normal SPH particles when the ambient gas density becomes lower than $0.1{n}_{\mathrm{crit}}^{\mathrm{SF}}$, or when they have traveled further than 20 kpc h⁻¹, whichever comes first.

The initial conditions have been generated using the constrained realization (CR) method (e.g., Bertschinger 1987; Hoffman & Ribak 1991; Romano-Díaz et al. 2007) and are those used by Romano-Díaz et al. (2011a), being downgraded from 2 × 1024³ to 2 × 512³. A CR of a Gaussian field is a random realization of such a field constructed to obey a set of linear constraints imposed on the field. The algorithm is exact, involves no iterations, and is based on the property that the residual of the field from its mean is statistically independent of the actual numerical value of the constraints (for more details see Romano-Díaz et al. 2011b). The main advantage of such a method is to bypass the sampling problem of highly overdense regions, which are rare and thus require simulation of a large volume ($\gtrsim {\mathrm{Gpc}}^{3}$) of the universe.

The constraints were imposed on a grid of 1024³ within a cubic box of size 20 h⁻¹Mpc to create a DM halo seed of ∼10¹² ${h}^{-1}\,{M}_{\odot }$ collapsing by z ∼ 6, according to the top-hat model. We assume the ΛCDM cosmology with WMAP5 parameters (Dunkley et al. 2009), Ω_m = 0.28, Ω_Λ = 0.72, Ω_b = 0.045, and h = 0.701. The variance σ₈ = 0.817 of the density field convolved with the top-hat window of radius 8h⁻¹ Mpc⁻¹ was used to normalize the power spectrum. The overdensity in the CR models corresponds to ∼5σ with respect to the average density of the universe.

We also evolved the same parent random realization of the density field used to construct the CR runs but without any imposed constraints to represent an average region of the universe. In order to compare the effect of winds in different environments, we have run the unconstrained simulation using the CW and VW models. In the following, we refer to individual runs by the name of the wind model used in the simulation (see Table 1): CW, VW, and NW for constrained runs (CR runs), and UCW and UVW for their unconstrained counterparts (UCR runs).

Table 1.  Summary of the Different Simulation Runs and Their Properties

Name	Initial	Wind	Neffa	Rzoomb	Rinner c	mDMd	mgasd	m⋆d	${\epsilon }_{\mathrm{grav}}$ e	vwf
	Conditions	Model		(h−1 Mpc )	(h−1 Mpc )	(105 ${h}^{-1}\,{M}_{\odot }$)	(${10}^{5}\,{h}^{-1}\,{M}_{\odot }$)	(${10}^{5}\,{h}^{-1}\,{M}_{\odot }$)	(${h}^{-1}\,\mathrm{kpc}$)	(km s−1 )
CW	CR	SH03	2 × 5123	3.5	2.7	37.3	8.88	4.44	0.14	484
VW	CR	CN11	2 × 5123	3.5	2.7	37.3	8.88	4.44	0.14	1−1.5vesc
NW	CR	⋯	2 × 5123	3.5	2.7	37.3	8.88	4.44	0.14	0
UCW	UCR	SH03	2 × 5123	7.0	4.0	37.3	8.88	4.44	0.14	484
UVW	UCR	CN11	2 × 5123	7.0	4.0	37.3	8.88	4.44	0.14	1−1.5vesc

Notes.

^aEffective resolution in the highest refinement (zoom-in) region. ^bComoving radius of the zoom-in region. ^cComoving radius of the central region used to identify halos and galaxies. ^dMass resolution in the DM, gas, and stellar component. ^eComoving gravitational softening length. ^fOutflow velocity used in the galactic wind model.

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Table 2.  Properties of the Halo and Galaxy Samples

Name	Mh, mina	Nh, z = 6b	M⋆, minc	Ng, z = 6d
	(${h}^{-1}\,{M}_{\odot }$)		(${h}^{-1}\,{M}_{\odot }$)
CW	108	6004	3 × 107	509
VW	108	5768	3 × 107	425
NW	108	5960	3 × 107	1969
UCW	108	9135	3 × 107	245
UVW	108	8470	3 × 107	92

Notes.

^aMinimum total halo mass considered. ^bNumber of halos at z = 6. ^cMinimum galaxy stellar mass considered. ^dNumber of galaxies at z = 6.

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The evolution has been followed from z = 199 down to z = 6. Our simulations were run in comoving coordinates and with vacuum boundary conditions. We used the multimass approach and have downgraded the numerical resolution outside the central region using three different levels of resolution in order to reduce the computational time. The highest refinement region has a radius of $3.5\,{h}^{-1}\mathrm{Mpc}$ and an effective resolution of 2 × 512³ in DM and SPH particles. The total mass within the computational box is $6.19\times {10}^{14}\,{h}^{-1}\,{M}_{\odot }$ and the mass of the high-resolution region is $1.45\times {10}^{13}\,{h}^{-1}\,{M}_{\odot }$. Within this region, we obtain particle masses of $3.73\times {10}^{6}\,{h}^{-1}\,{M}_{\odot }$ (DM), $8.88\times {10}^{5}\,{h}^{-1}\,{M}_{\odot }$ (gas), and $4.44\times {10}^{5}\,{h}^{-1}\,{M}_{\odot }$ (stars). The gravitational softening is ${\epsilon }_{\mathrm{grav}}=140\,{h}^{-1}\,\mathrm{pc}$ (comoving), which is about 20 h⁻¹pc in physical units at z = 6.

In order to avoid contamination of heavy particles from the outer refinement levels, we have focused on the central inner spherical region within a radius of $2.7\,{h}^{-1}\,\mathrm{Mpc}$ for our CR simulations, and within 4 h⁻¹Mpc for the unconstrained (UCR) simulations. The size of the inner region in the UCR runs has been chosen by matching the cumulative mass profile with the CR models. The properties of the different simulation runs are summarized in Table 1.

Finally, the CW model is switched on at the initial redshift, while the VW model is run as NW (i.e., without outflows) until z = 12, at which point the winds are switched on. This is done in order to speed up the simulation until the SF starts to rise and the SN feedback becomes important.

We use the group-finding algorithm HOP (Eisenstein & Hut 1998) to identify halos and galaxies. Halos are isolated according to a criterion based purely on particle density—the (local) total particle densities, i.e., DM + baryons, are calculated with an SPH kernel. A halo is defined as the region enclosed within a total iso-density contour of ${{\rm{\Delta }}}_{{\rm{c}}}{\rho }_{\mathrm{crit}}(z)$, where Δ_c = 80 and ρ_crit(z) is the critical density at redshift z. Hence, no geometry of the particle distribution is assumed with this approach. This is a change compared to Romano-Díaz et al. (2011a), who used the standard pure DM definition for the halo, but is exactly as in Romano-Díaz et al. (2014). The benefit of including the baryonic contribution to the density field when identifying halos, while not significantly modifying the resulting halo catalog, is to automatically identify the baryonic component inside each halo. In order to avoid resolution effects, we adopt a minimum mass threshold of ${M}_{{\rm{h}}}={10}^{8}\,{h}^{-1}\,{M}_{\odot }$.

Galaxies are identified with respect to the baryonic density field with the outer boundary corresponding to an iso-density contour of $0.01{n}_{\mathrm{crit}}^{\mathrm{SF}}$, which also differs from that of Romano-Díaz et al. (2011a) but is as in Romano-Díaz et al. (2014). This definition ensures the inclusion of regions that host star-forming gas ($n\gt {n}_{\mathrm{crit}}^{\mathrm{SF}}$), as well as lower density non-star-forming gas ($n\lt {n}_{\mathrm{crit}}^{\mathrm{SF}}$), which is roughly bound to the galaxy.

Following Romano-Díaz et al. (2014), we also exclude galaxies below a minimum stellar mass of $3\times {10}^{7}\,{h}^{-1}\,{M}_{\odot }$, in agreement with recent observations (Ryan et al. 2014), corresponding to ∼70 stellar particles. In order to verify that our simulations are not affected by numerical resolution, we have compared our CW run with the higher-resolution version presented in Romano-Díaz et al. (2014). We found that the two runs are in excellent agreement in terms of galaxy stellar mass functions, SFRs, and metallicities in galaxies, indicating that our simulation runs are numerically converged.

Section 2.2 provided the general description of the wind models implemented in this work. We start by verifying the kinematic properties of these winds, and especially of the VW run. In Figure 1, we plot the resulting velocities of the wind particles in the VW and CW runs. The left panel exhibits the distribution of wind particles as a function of their outflow velocity, v_w, at different redshifts. The vertical dashed line is the value used in the CW model, i.e., 484 km s⁻¹. Even though, overall, the total number of particles in the wind is steadily increasing with time, we observe three interesting trends in the VW model: the number of wind particles corresponding to velocity at the peak of the distribution increases with redshift until z ∼ 8 and falls off thereafter; the average wind velocity increases with time, and the tail of the distribution extends gradually toward higher velocities. Despite this latter increase, we note that, at all redshifts, the majority of wind particles in the VW run have a lower velocity than the constant velocity adopted in the CW model.

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The right panel of Figure 1 displays the relation between the median v_w and stellar mass in galaxies at z = 6 in the VW run. The value of v_w used in the CW model is shown as the horizontal dashed line. Individual galaxies are represented by filled circles with color scaling based on their SFR. The solid black line is the median trend calculated from these objects. The black dotted–dashed and dashed lines are the expected trends for the momentum-driven and energy-driven winds, respectively. They have been calculated from Equation (1), assuming a specific SFR (i.e., sSFR) of 2.5 Gyr⁻¹, in accordance with results shown in Figure 7.

We find that the scaling of wind velocities with stellar mass closely follows the energy-driven case for nearly the entire mass range considered, although the scatter increases toward low masses. This is not entirely surprising since, in the VW model, winds coming from non-star-forming regions ($n\lt {n}_{\mathrm{crit}}^{\mathrm{SF}}$) are assumed to be energy-driven. Given our definition of a galaxy, which includes gas well below the star formation threshold (Section 2.4), these regions usually dominate the total gas content in a given galaxy. Since all gas particles have an equal probability of turning into wind, the majority of wind particles emitted from a galaxy come from those low-density regions and thus produce energy-driven winds, as seen in Figure 1.

We also find that, except for the most massive systems, nearly all galaxies in the VW model have lower median wind velocities than the CW case, in agreement with the velocity distributions presented in the left panel. The most massive objects appear to have stronger winds in the VW case than in the CW case. However, since they constitute the deepest potential wells, these objects are also less affected by winds than the intermediate- and low-mass galaxies. Thus, overall, we expect mechanical feedback from winds in the VW run to increase with time, peak at z ∼ 7–8, and decline afterwards, as shown by the redshift evolution in the left panel. At the same time, this feedback is less efficient than in the CW run at all times. Given the direct coupling between wind and galaxy properties in the VW model, this non-monotonic evolution is accompanied by a similar behavior in galaxy gas content and SFR as we show below. In terms of stellar feedback, the VW model, therefore, represents an intermediate situation between the other two cases, NW and CW.

Figure 2 shows the mass distribution of DM, gas, and stars in all the simulation runs at z = 6 on a scale of 1.3 h⁻¹Mpc (comoving), corresponding to a physical scale of ∼186 h⁻¹ kpc. In the same environment (CR or UCR), no substantial differences are expected in the DM distribution on large scales since they differ only in the physics of galactic outflows implemented. On the other hand, we do observe that the distribution of baryons differs between the runs on progressively smaller spatial scales.

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For a more quantitative analysis, we start by examining the differential HMFs, ${\rm{\Phi }}={dn}/d\mathrm{log}\,{M}_{{\rm{h}}}$, i.e., the number of halos per unit volume per unit logarithmic total halo mass interval, as shown in Figure 3 (upper frame). As expected, the HMFs of the different wind models in a given environment (CR or UCR) are essentially identical over the entire mass range of ${10}^{8}\,{h}^{-1}\,{M}_{\odot }\mbox{--}{10}^{12}\,{h}^{-1}\,{M}_{\odot }$. Slight differences are observed between wind models because our definition of a halo is based on the total mass, which includes baryons (Section 2.4).

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On the other hand, the effect of the overdensity is readily visible from this figure. First, the HMFs for the three CR models are shifted up with respect to the UCR HMFs because of the overdense region sampled by these models. Second, the slopes of the three models are also somewhat shallower than that of the theoretical Sheth–Tormen slope (Sheth & Tormen 1999), as expected around density peaks (e.g., Romano-Díaz et al. 2011b). Third, they extend toward higher masses than do the UCR halos. The HMFs in the UCR runs appear to be in reasonable agreement with the HMF of Sheth & Tormen (1999), except at the low-mass end, where we see some deviation from the theoretical prediction.

We have analyzed the possible causes of this excess of low-mass halos in the UCR simulations over the Sheth–Tormen HMF. First, it could follow from the spurious detection of gas-dominated blobs, which might be identified as low-mass halos by HOP. We have therefore computed the baryon fraction ${f}_{{\rm{b}}}={M}_{\mathrm{baryons}}/{M}_{\mathrm{DM}}$ for each halo in the UCR runs at z = 6, but found that f_b is always below 40%. Second, the difference is still present even when we use only the DM component to find and define our halos. Third, as a complementary test, we have also analyzed the HMFs in a DM-only version of our UCW model (run in a larger volume) presented in Romano-Díaz et al. (2011b) and found a good agreement with the theoretical HMFs from Jenkins et al. (2001) over the entire mass range considered here. For this reason, we are confident that the deviation between our HMFs and the theoretical prediction from Sheth & Tormen (1999) is due to the inclusion of baryonic physics, which is expected to have the most effect on low-mass halos (work in preparation).

The bottom panel of Figure 3 shows the galaxy mass functions (GMFs) for all models as a function of galaxy stellar mass, ${M}_{\star }$, at different redshifts. Here we observe a clear impact of the outflow model on the shape and evolution of the GMF, reflecting the effect of winds on the growth of galaxies. At every redshift, the normalization (amplitude) of the GMF in the NW model is the highest overall among the CR runs, which means that galaxies of a given stellar mass are more abundant in the NW model than in the other two CR runs (CW and VW). However, since the CR runs have the same underlying HMFs, an alternative way to characterize the differences between GMFs is to compare their relative shift at a given number density Φ (i.e., at a given halo mass). In this case, we find that the GMF in the NW model is shifted toward higher stellar masses, meaning that, in a given halo, galaxies have produced more stars in the NW case because of the absence of feedback from winds, unlike in the models including outflows (CW and VW).

In comparison, the effect of winds is prominent in the evolution of the VW and CW GMFs at different redshifts. At z = 11, VW and NW GMFs closely follow each other as expected, since these two models are identical until winds are turned on at z ∼ 12 in the VW run (Section 2.2). With decreasing redshift, the outflows become stronger, which causes both VW and CW GMFs to become shallower, especially at the low-mass end. At z = 6, the VW GMF is more closely related to the CW one, but their slopes differ, which results in a smaller number of low-mass ($\sim {10}^{8}\,{h}^{-1}\,{M}_{\odot }$) galaxies and a larger population of objects at intermediate masses in the VW run. The differences mentioned above are no longer visible at the massive end (${M}_{\star }\gtrsim {10}^{10}\,{h}^{-1}\,{M}_{\odot }$) of the GMFs, where all CR runs agree reasonably well. This means that winds are inefficient in removing baryons from the deepest potential wells and thus affect mostly the low-mass end of the GMFs, in agreement with previous models and observations (e.g., De Young & Heckman 1994; Mac Low & Ferrara 1999; Scannapieco et al. 2001; Benson et al. 2003; Choi & Nagamine 2011).

The evolution of the GMFs in the region of average density (UCW and UVW models) appears to resemble that of their wind-model counterparts (CW and VW) in the CR runs, but is shifted toward lower stellar masses. In particular, we observe a flattening with time of the low-mass end of the UVW GMF compared to the UCW case. However, the main difference between the two environments lies in the low-mass end of the GMFs, which appears to be steeper for UCR than for CR runs. The difference is especially pronounced when comparing CW and UCW runs, which have slopes at the low-mass end of ∼−2 and ∼−1 respectively. Because UCR and CR runs differ only in the presence of the imposed overdensity, it is clear that these trends reflect the difference in the underlying HMFs, as seen in the top panels of Figure 3. This is an important result concerning galaxy evolution in overdense environments at high redshifts, which should have implications for the expected contribution of low-mass galaxies to reionization at $z\gtrsim 6$, since measurements of the faint-end slope of the UV luminosity function at high z indicate a steep trend with a slope of ∼−2 (Dressler et al. 2015; Song et al. 2015), in agreement with the trend we find in the regions of average density.

Next, we analyze the impact of the different prescriptions for galactic wind on the gas content of halos and galaxies. Figure 4 (top) displays the halo gas fraction, ${f}_{\mathrm{gas},{\rm{h}}}={M}_{\mathrm{gas},{\rm{h}}}/{M}_{{\rm{h}}}$ as a function of redshift in four mass bins, from M_h = 10⁸ to ${10}^{12}\,{h}^{-1}\,{M}_{\odot }$ with a bin size of 1 dex. We keep these mass bins constant in time, which means that halos are assigned to a bin based on their total mass at a given redshift. In each panel, solid lines represent the median trend of each model, and shaded regions enclose the 20th and 80th percentiles of the population in each bin.

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For all models, we observe that the evolution of the gas content in halos shows a clear dependence on halo mass. Low-mass halos start with a gas fraction close to the universal baryon fraction, ${f}_{\mathrm{bar},0}={{\rm{\Omega }}}_{{\rm{b}}}/{{\rm{\Omega }}}_{{\rm{m}}}\sim 16 \%$ (dashed line), and exhibit a steeper decline with z than the more massive ones. As halo mass increases, the curve flattens, with the highest-mass bin, $\gtrsim {10}^{11}\,{h}^{-1}\,{M}_{\odot }$, showing little variation in gas fraction, from z = 9 to z = 6, although trends are more noisy in this bin because of the low number of objects at each z. At later times, f_gas,h is in the range of ∼5%–15%, below the universal value f_{bar, 0}. Note that the highest-mass bin does not contain any UCR halos since such massive objects have not yet formed in the region of average density.

The CR runs (CW, VW, and NW) show clear differences from each other, reflecting the impact of the outflow model on the gas content of halos. On average, at each z, gas fractions are highest in the NW model for lower-mass halos, $\lesssim {10}^{10}\,{h}^{-1}\,{M}_{\odot }$, and become lower than in the CW and VW models for the most massive objects, $\gtrsim {10}^{11}\,{h}^{-1}\,{M}_{\odot }$. Although it seems contradictory at first that NW halos have less gas, we find this trend to be accompanied by a similar trend in SFRs. The SF is more efficient and starts earlier in the NW model because of the absence of substantial feedback from galactic outflows. The SFRs are also mass-dependent with very little SF at the low-mass end in all models. As a consequence, since halos in the NW run are better able to retain their gas than halos in the CW and VW runs, more of it gets consumed to form stars in higher-mass objects, which explains the above trend. Such a high efficiency in converting the gas into stars is one of the reasons why the NW model can be ruled out.

Figure 4 (bottom) displays the evolution of the gas fraction, ${f}_{\mathrm{gas},\mathrm{gal}}={M}_{\mathrm{gas}}/({M}_{\mathrm{gas}}+{M}_{\star })$, in galaxies in four mass bins. The lines and shaded areas have the same meaning as in the case for halos (top) but now the galaxies are binned in terms of their stellar mass ${M}_{\star }$ at a given z.

The comparison between the CR models shows a diverse population of objects, whose gas fraction evolves in a much more complex way than in halos. The NW model shows a monotonic decline of f_gas,gal with time, except in the highest-mass bin for $z\gtrsim 9$. By z ∼ 6, the gas fraction is decreasing with increasing mass bin. At the same time, f_gas,gal is independent of mass in the CW model. For the VW model, the final f_gas,gal is also lower for higher galaxy masses. The overall evolution of CW and VW models, however, differs substantially. For almost the entire mass range, the gas fraction stays constant for $z\gtrsim 8$–9, and exhibits a mild decline thereafter. On the other hand, f_gas,gal in the VW model shows a sharp decline for $z\gtrsim 9$, followed by a sharp increase, and saturation. In the highest-mass bin, another sharp decline can be clearly observed.

Overall, by z ∼ 6, the NW galaxies appear to be most gas-poor, followed by VW galaxies and CW ones. Obviously, this trend correlates with the efficiency of feedback in the form of galactic outflows. The weakest feedback is that of the NW model. The CW feedback is strong but fixed in time, while that of the VW is increasing with time, but not monotonically. So averaged over the whole galaxy population, the effect of the VW model falls roughly between that of the CW and NW models, as already mentioned in Section 3.1.

In comparison with the galaxies of Choi & Nagamine (2011), the spread between various models is smaller at z ∼ 5, and ${f}_{\mathrm{gas},\mathrm{gal}}\sim {M}_{* ,\mathrm{gal}}^{-1}$, with f_gas,gal ∼ 0.9 at $\mathrm{log}\,{M}_{* ,\mathrm{gal}}\sim 7$. Our CR models show smaller gas fractions for all galaxies already at z ∼ 6, which is the result of elevated SFR caused by the higher accretion rates and gas supply in the overdense region. This trend persists despite the overdense region, especially at the high-mass end. This is also true in comparison with the models of Thompson et al. (2014). The explanation for the evolution of gas fraction that we observed in the CR models lies in the interplay between the histories of SF and mass accretion onto galaxies (e.g., Romano-Díaz et al. 2014). As we discuss later on, the kinetic luminosity of these winds has a substantial effect on the temperature of the IGM and the halo gas—an effect that lowers accretion rates profoundly.

As is evident from Figure 4, the evolution of gas content in CW and UCW halos and galaxies is nearly identical in all mass bins, except in the mass bin 10¹⁰–${10}^{11}\,{h}^{-1}\,{M}_{\odot }$, where the most massive objects are found in the UCR runs. Since both models use the same outflow prescription, this strongly suggests that, for a given wind model, the overdensity has little effect on the amount of gas inside these halos and galaxies.

When comparing VW and UVW halos, we find that their gas fractions tend to follow similar trends in each mass bin, but with larger relative differences than between CW and UCW runs. This indicates that the VW model couples galaxy evolution with the large-scale environment more strongly than the CW case.

However, addressing the effect of the environment on gas fraction is difficult from a direct comparison between CR and UCR evolution from Figure 4 because objects in the same mass bin can reside in different environments. For example, low-mass galaxies can be found in underdense regions in CR and UCR models, but also as satellites around the massive halos in the overdense region. This effectively causes mixing among objects of similar masses and can thus wash out the differences induced by the presence of the overdensity.

To investigate further the effects of the environment on the gas content in galaxies, it is thus easier to directly divide objects according to their large-scale environment. Figure 5 (top) shows the redshift evolution of gas fractions in galaxies in different density bins for the CR and UCR models that include outflows. The bins are defined based on the smoothed relative density contrast $\delta =\rho /{\bar{\rho }}_{{\rm{b}}}-1$ where ${\bar{\rho }}_{{\rm{b}}}={{\rm{\Omega }}}_{b}{\rho }_{\mathrm{crit}}$ is the universal mean baryonic density. The smoothed galaxy density field ρ has been obtained by convolving the local galaxy densities calculated using an SPH method with a top-hat filter of scale $250\,{h}^{-1}\,\mathrm{kpc}$. Note that we use the universal mean baryonic density ${\bar{\rho }}_{{\rm{b}}}$ in our definition of δ instead of the mean baryonic density inside the simulation box in order to have a common normalization factor for both CR and UCR models. Galaxies are divided between underdense ($\delta \lt 0$, top left panel) and overdense ($\delta \gt 0$, top middle panel) bins and we also show the evolution for the entire galaxy population for comparison (top right panel). Based on our definition of galaxy density, we found no galaxies with $\delta \gt 0$ in the UCR models. The comparison between CR and UCR runs is therefore possible only for galaxies residing in underdense regions.

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The top left panel of Figure 5 shows that the evolution of gas fraction in these galaxies residing in underdense regions follows a similar trend in both CW and UCW models with a modest decline from ∼65%–70% at z = 12 to ∼55% at z = 6. Differences between the two models are not significant given the noise introduced by the small number of galaxies formed in the UCW model. In comparison, the gas fraction in galaxies residing in overdense regions in the CW model exhibits a much steeper decline from z = 10 to z = 6 (top middle panel) due to the accelerated evolution in these regions. The UVW galaxies show a more complicated behavior, but decline as well after z ∼ 8, in tandem with CW. The evolution for the entire galaxy population (top right panel) shows larger differences between CW and UCW due to the mixing of both underdense and overdense environments in the CW case but still shows a similar decreasing trend with redshift and comparable gas fraction levels at all z. The VW and UVW models in the underdense bin exhibit much less correlation than CW and UCW among themselves, as already noted in the previous section.

The similar evolution of gas fraction for CW and UCW galaxies residing in the same environment further confirms that the gas content is mainly affected by the different wind models and not by the presence of the overdensity. The gas fractions in VW and UVW models differ more among themselves, which can be explained by the weaker winds they produce. To more fully understand the reason for this effect, we need to investigate how the galaxy gas fractions depend on the outflow prescription at a given redshift. Figure 5 (bottom) shows the mass-weighted average galaxy gas fractions as a function of galaxy stellar mass in all the simulation runs at z = 10, 8, and 6. Since we are only interested in the average trends, the curves have been smoothed with a boxcar filter of size 0.5 dex in stellar mass to reduce Poisson noise caused by the small number of objects in each mass bin.

We find significant differences among the various wind models at all z, but the main discrepancy can be observed between CW and the other two runs, VW and NW. In particular, there is a clear trend of decreasing gas fraction with increasing stellar mass in both VW and NW, which is not seen in CW. The latter shows nearly constant gas fractions across the entire mass range ${M}_{\star }={10}^{7.5}$–${10}^{11}\,{h}^{-1}\,{M}_{\odot }$. The UCW model also exhibits nearly mass-independent gas fractions at all z, which follows the CW trend as expected. This is in agreement with results shown in the top panels of Figures 5 and 4, although there are clear signs of divergence between the two models for $z\leqslant 8$. These results thus suggest that the likely explanation for the apparent similarities in galaxy gas content between CW and UCW can be attributed, for the most part, to the prescription of constant and strong outflow used in both runs. Since winds scale independently of galaxy properties (mass and SFR) in this outflow model, the gas content inside galaxies varies weakly with stellar mass. As a consequence, the CW and UCW runs produce galaxies with nearly constant gas fractions, which explains the similar behavior observed between the two models despite their different environments.

To construct the SFH for a given galaxy selected at z = 6, we identify the progenitors at earlier redshifts by matching the unique identification numbers (IDs) associated with each particle. The ancestor galaxy is taken to be the progenitor containing the largest number of particles with IDs matching the ones in the descendant galaxy. We repeat this process iteratively to obtain the list of ancestors of the selected galaxy, from z = 6 to z = 12. Figure 6 shows the redshift evolution of galaxy SFRs in different mass bins. Galaxies are assigned to one of the bins based on their stellar mass ${M}_{\star }^{z=6}$ at z = 6, and their SFH is then followed back to z = 12 using the above method. We stress that this mass binning is different from the one in which galaxies are selected by mass at each redshift, as used in Sections 3.3 and 3.6. For this reason, correlating the evolution of SFR and gas fraction cannot be attempted using a straightforward comparison between Figures 4 and 6, because they represent different galaxy populations at each redshift.

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We find a strong dependence of SFHs on stellar mass in all models. Overall, massive galaxies exhibit a strongly rising SFR, while the lowest-mass galaxies maintain flat SFRs on average. These trends are well correlated with the rates of mass accretion onto the galaxies, analyzed in Romano-Díaz et al. (2014). More specifically, in the lowest mass range, $7.5\lt \mathrm{log}\,{M}_{\star }^{z=6}\lt 8.5$, SFRs are essentially constant with z for all models, and lie in the range of ~0.1–$1\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$. The intermediate-mass bins, $8.5\lt \mathrm{log}\,{M}_{\star }^{z=6}\lt 9.5$ and $9.5\lt \mathrm{log}\,{M}_{\star }^{z=6}\lt 10.5$, exhibit an increase in SFR by a factor of ∼7–8 between z = 12 and z = 6. Finally, the most massive galaxies display the strongest increase, roughly a factor of 30 over this redshift interval. Note, however, that small SF levels seen for low-mass galaxies likely result from poorly resolved outflows, with only a few particles for these objects. For this reason, we focus mostly on SFRs in intermediate- and high-mass galaxies in the following.

At high z, the SFRs for the most massive galaxies appear similar among all the CR runs (note that these galaxies are absent from the UCR runs). The rates start to diverge below z ∼ 9, with the CW model becoming the dominant one, followed by the VW and the NW, each lower by a factor of 2–3 by z = 6. For these galaxies, the SFR has reached $\sim {10}^{3}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, bringing them into the observed regime of LBGs at high z (see also Yajima et al. 2015). We also observe a similar trend in the intermediate-mass bins, where SFR in the NW model starts to decrease after z ∼ 8, while models including galactic outflows continue to increase their SFRs. By the end of the simulations, the CW model has the highest median SFR with ~30–$40\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ for $9.5\lt \mathrm{log}\,{M}_{\star }^{z=6}\lt 10.5$, and ~600–$800\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ for $10.5\lt \mathrm{log}\,{M}_{\star }^{z=6}\lt 11.5$. The corresponding median SFRs in the NW run are $\sim 10\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ and $\sim 100\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, and the VW model ends up with intermediate values between the CW and NW runs.

These results indicate that, even at high z, galactic outflows do play an important role in controlling galaxy growth in overdense regions. In the NW run, the absence of these outflows means the absence of a strong feedback that can delay or quench star formation. As a consequence, the peak of star formation in the NW run happens at higher redshifts, $z\gt 6$, as noted above, and thus the available gas supply for SF in galaxies is already consumed by z = 6. Subsequent gas accretion could in principle increase SFRs again at later times in the NW run but, at z = 6, we see that accretion has not yet been able to replenish the gas content in galaxies to maintain high SFRs. For this reason, SFRs are higher in CW and VW models at z = 6 since the feedback from winds in those models acts to effectively delay the peak of star formation activity.

This is in agreement with Choi & Nagamine (2011) and Anglés-Alcázar et al. (2014), which have analyzed galaxy evolution in regions of average density, but lack massive galaxies at these redshifts. However, since galaxy evolution is accelerated in the overdense regions, the peak of SF activity happens at earlier times than in an environment of average density. When comparing CW and VW models, results published in the literature show that the CW SFRs are generally the lowest ones, as measured in simulations at low z ∼ 3–4 (e.g., Choi & Nagamine 2011). However, the cosmic SFR evolution presented in Choi & Nagamine (2011, see their Figure 5) shows that the difference between CW and VW SFRs decreases with increasing redshift at $z\gt 6$, and that these two models eventually reach similar SF levels at high z.

For a more detailed picture of the SF efficiency in different runs, we investigate the specific star formation rate, which represents SFR per unit mass, and essentially indicates the production rate of stellar mass per stellar mass. Figure 7 displays the relation between the median sSFR and stellar mass in galaxies at z = 6 (left panel) and the evolution of sSFR with redshift (right panel) in all runs. Observational data from Labbé et al. (2013) (z = 8), Duncan et al. (2014) (z = 6 and 7), Salmon et al. (2015) (z = 6), and Tasca et al. (2015) (z = 5.5) have been added to both panels. In the left panel, galaxies are binned by stellar mass with intervals of 0.3 dex.

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We observe a nearly constant sSFR with ${M}_{\star }$ in the NW and VW models, with sSFR ∼1.5 and 2.5 Gyr ⁻¹, respectively. At the same time, the CW model shows an overall positive correlation between sSFR and ${M}_{\star }$. This upward turn above the characteristic mass of $\sim {10}^{9}\,{h}^{-1}\,{M}_{\odot }$ is in contradiction with the observational trend shown in Figure 7.

We also find that the sSFR in the CW run falls within the observed range, but the existence of the peak in the mass range of 10⁹–${10}^{10}\,{h}^{-1}\,{M}_{\odot }$ does not agree with the observations of Salmon et al. (2015). On the other hand, for the NW run, the overall trend roughly agrees with the observed one, but the sSFR lies outside the observed range. The best fit to observations is that of the VW model—both the trend with ${M}_{\star }$ and the sSFR range agree, although the median observed fit is slightly shifted away from the model values.

The right-hand panel of Figure 7 shows the evolution of the sSFR with redshift. Solid lines correspond to the median trends for the whole galaxy population. The dashed lines show the evolution only for galaxies with stellar masses in the range 10⁹–${10}^{9.5}\,{h}^{-1}\,{M}_{\odot }$, corresponding approximately to the estimated masses of objects targeted by observers. We find the median evolution of all galaxies to be dominated by the low- and intermediate-mass objects because of a higher number of these galaxies compared to the massive ones. The median sSFRs of all galaxies in the CW and UCW runs are in good agreement—again underlining that gas content and SF in low-mass galaxies are not affected significantly by the overdensity.

The sSFR in the NW run is the highest for $z\gtrsim 7$, where it falls below the VW model. In all models except VW, the sSFR drops by almost an order of magnitude, from $\sim 10\,{\mathrm{Gyr}}^{-1}$ at z = 12 to $\sim 1\,{\mathrm{Gyr}}^{-1}$ at z = 6. The evolution of sSFR in the VW case exhibits a trend similar to the one found for the gas fraction in low-mass galaxies (Figure 4). As we have argued in the previous section, This trend is caused by scaling of the feedback strength with the SFR in the VW run. At high z, outflows quench the SF, which in turn decreases the feedback from the winds and allows an elevated SFR at later times. The evolution of the median sSFR for the whole galaxy samples does not reproduce correctly the observations for $z\lt 8$. The explanation of the mismatch lies in the dominant contribution from low-mass galaxies (${M}_{\star }\lesssim {10}^{9}\,{h}^{-1}\,{M}_{\odot }$) to the global sSFR. When comparing the evolution for galaxies in the observed stellar mass bin (dashed lines), both CW and VW runs, as well as the UCR run, appear to be in good agreement with the observed increase in sSFR with redshift.

Next, we focus on the mass–metallicity relation in halos and galaxies. Figure 8 (left panels) shows the metallicity of gas and stars in halos as a function of the total halo mass at z = 6. The highest metallicities are found in the most massive halos because their star formation starts earlier and they exhibit a higher SFR than lower-mass objects. We observe a rapid increase in the metallicity in the low-mass halos, and it levels off at the intermediate/high-mass end. The CW and VW runs reach close to solar metallicity for ${M}_{{\rm{h}}}\gtrsim {10}^{11}\,{h}^{-1}\,{M}_{\odot }$ by the end of the simulations. For smaller M_h, the CW and VW models display a slow decline in Z, which steepens dramatically below ${M}_{{\rm{h}}}\sim {10}^{10}\,{h}^{-1}\,{M}_{\odot }$ for the VW, and below $\sim {10}^{9}\,{h}^{-1}\,{M}_{\odot }$ for the CW. This "knee" is moving gradually toward higher masses with redshift.

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While halos with M_h ~ 10¹¹–${10}^{12}\,{h}^{-1}\,{M}_{\odot }$ have a median $Z/{Z}_{\odot }\sim 0.6$ (gas) and ∼0.8 (stars), the lower-mass halos, with ~10⁸–${10}^{9}\,{h}^{-1}\,{M}_{\odot }$, show $Z/{Z}_{\odot }\sim 0.01$–0.03 (gas) and ∼0.03 (stars), respectively. Note that the NW model achieves the highest metallicity in all M_h, for both gas and stars. Furthermore, compared with the metallicities of halo gas, stellar metallicities display higher median Z—this means that the gas metallicity is diluted by the cold accretion from the IGM, in agreement with Romano-Díaz et al. (2014).

Galaxy metallicities in the gaseous and stellar components are shown in Figure 8 (right panels). As expected, the metallicity of the NW model exceeds substantially those of CW and VW in both components, due to the metals being locked in galaxies and their immediate vicinity. A possible exception may be the highest-mass bin for the ISM, where CW model shows marginally higher metallicity. The bimodal behavior observed for the halos can be seen here as well. Stars also remain more metal-rich than the gas, again in tandem with the halos. Future observations will constrain these models. We point out that, in Figure 8, we have computed only the average metallicity inside individual galaxies and ignored the scatter in metallicity in a given galaxy.

The temperature maps of the IGM gas, i.e., gas outside galaxies and their host halos, in the inner central region of the simulation box clearly display the growing difference between the wind models with redshift. Figure 9 (left panels) underlines profound differences existing between the CR runs already at z ∼ 10. The NW run lacks gas with $T\gtrsim \mathrm{few}\times {10}^{4}$ K, except for a few spots near the central peak in density corresponding to the growing massive halo. The warmest gas can be found in the large-scale filaments, and it roughly delineates them in all CR models. The gas at a temperature of a few × 10⁴ K is more closely associated with large-scale structures in the VW case, because the feedback from outflows is lower than in the CW run, where this gas "spills out" of the filaments. The rest of the volume hosts gas with $T\lesssim {10}^{4}$ K.

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The redshift evolution of these maps shows gradually heating and cooling regions, with gas at a temperature of a few × 10⁵ K at z = 8, and a few × 10⁶ K at z = 6. By the end of the run, the massive central halo is surrounded by a hot bubble of gas at ∼10⁷ K in CW and VW wind models. Away from the most massive halo, the filament temperature drops, most profoundly in the NW model. By z ∼ 6, the CW gas in nearly the whole volume is heated up to 10⁵–10⁷ K. In this model, the gas at 10⁵–10⁶ K is present in the main filament, and gas at ∼10⁵ K in other filaments. In VW and NW models, the gas outside the filaments remains cold.

Hence, at higher redshifts, z ∼ 10, we observe increasing temperatures of the IGM gas, along the sequence from NW to VW and to CW. With decreasing z, the central bubble heats up, and so do the filaments. The outflows in the CW model are capable of heating up the IGM, while the VW outflows have a dramatically lower impact on the temperature of the IGM at these redshifts, but nevertheless heat it up toward z ∼ 6.

Figure 9 (right panels) shows maps of the metallicity distribution in the IGM gas at similar redshifts for all the CR models. At z = 6, the IGM peak metallicity has reached ∼0.1Z_⊙ inside the central hot bubble and along the main filament corresponding to the regions surrounding the massive central structure in the CW and VW models. The peak metallicity in the NW is a factor of a few lower even though the SFRs are higher in this model at high z. The extended region in the CW model shows a negative metallicity gradient away from the central bubble and the main filament. Still, most of the volume is polluted by metals and has $Z\gtrsim {10}^{-2}{Z}_{\odot }$. The VW exhibits a much lower metallicity outside the filaments, $Z\lesssim {10}^{-3}{Z}_{\odot }$, whereas the NW IGM remains mostly pristine. The reason for this is the absence of outflows, which causes metals to be locked in galaxies and their halos. In comparison, solar metallicities have been reached only within galaxies of the NW model (see Figure 8).

Figure 10 displays the temperature and metallicity maps of the IGM in the UCR runs at z = 6, and can be compared directly with the CW and VW maps in Figure 9, as both figures use the same color scales. Since the UCR runs represent a region of average density and lack massive halos (e.g., Figure 3), both the peak and average IGM temperatures are dramatically lower than in the CR runs. The peak metallicity in the IGM and its average are also lower than in the CR runs. Thus the impact of the overdensity is readily visible from these two figures—the universe of average density remains relatively cool at z ∼ 6.

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A more quantitative comparison between the different runs on the state of the IGM at z = 6 is displayed in Figure 11, which shows the spherically averaged profiles of IGM temperature (top) and metallicity (bottom) from the center of the computational box to the radius R_inner of the inner high-resolution region, where ${R}_{\mathrm{inner}}=2.7\,{h}^{-1}\,\mathrm{Mpc}$ and ${R}_{\mathrm{inner}}=4\,{h}^{-1}\,\mathrm{Mpc}$ for the CR and UCR models respectively. The profiles are computed by averaging the temperature and metallicity of the IGM gas on spherical shells of thickness $50\,{h}^{-1}\,\mathrm{kpc}$.

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Both the temperature and metallicity profiles agree with the qualitative results from Figures 9 and 10. The CR runs have similar IGM temperature within the central $1\,{h}^{-1}\,\mathrm{Mpc}$, corresponding approximately to the size of the imposed constraint, which is visible as a hot bubble on Figure 9. In this central region, the IGM temperature reaches T ∼ 10⁷ K, which is consistent with the virial temperature for a halo of mass ∼10¹² ${M}_{\odot }$, corresponding to the mass of the central halo that forms in the overdense region. On the other hand, the IGM temperature in the UCR runs remains constant with radius at much lower values, around ∼10^3.5–10⁴ K and ∼10^4.5–10⁵ K for the UVW and UCW models respectively. Thus, it appears that shock heating caused by the presence of the massive structure in the overdense region is largely responsible for the elevated IGM temperature within 1 h⁻¹ Mpc in the CR runs. This also explains why the CR runs show similar IGM temperature in the central region, because the differences in temperature due to the different wind models (which are much smaller) get washed out.

The metallicity profiles (Figure 11, bottom) are in general much flatter than the temperature ones. The lowest metallicities are seen in the NW run, followed by the VW and CW models, in agreement with Figure 9. The UCW IGM metallicity is smaller than both CR models including winds (CW and VW) within ∼2 h⁻¹ Mpc and then rises on larger scales to reach levels comparable with the CW run. This increase is associated with the presence of a massive filament in the UCR runs (Figure 10), because a similar rise can be seen in the UCW temperature profile at the same distance from the center.

A supplementary global view of the temperature and metallicity of the gas can be taken from Figure 12, where we show the gas phase diagrams in the temperature–density plane at z = 6 for all gas particles found in the high-resolution region. Gas particles are also colored based on their metallicity. The densities are now normalized by the average baryon density in the high-resolution region, as opposed to using the universal value like we did in Section 3.4. This normalization is thus different between CR and UCR runs since the average density is higher in the overdense region. For this reason, the vertical dashed line, which separates the non-star-forming gas (to its left) from star-forming gas (to its right), is slightly offset in the bottom panels (UCR) from its position in the top panels (CR). We observe the highest metallicities, around solar values, in the star-forming gas that is confined deep within galaxies. One can easily identify the wind gas in the lower right part of the diagrams, because it is present in the VW, CW, UCW, and UVW cases, and is metal-rich, but not in the NW case.

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The fraction of low-density gas polluted with metals (green and red) compared to pristine (blue), and the highest metallicities attained there, depend strongly on the wind model. The metal-rich, low-density gas originates in the galactic outflows, and heats up as a result of the shock-stopping of these high-speed outflows. This gas lies at temperatures of $\sim {10}^{5}$–10⁷ K and densities $\mathrm{log}\,{\rho }_{{\rm{b}}}/{\bar{\rho }}_{{\rm{b}}}\lesssim 4$. Here the baryon density ρ_b is normalized by the average density in the high-resolution box. We note that a large amount of the ∼10⁴ K star-forming gas found in our models at high densities is due to the use of the delayed star formation algorithm, the Pressure model (Section 2.1), and because of the absence of H₂ cooling in our simulations. The amount of heated gas increases substantially from the NW to VW and CW runs. The hot and low-density pristine gas at $T\gtrsim 3\times {10}^{6}$ K in the CR runs consists mostly of virially shock-heated material infalling onto the most massive halo, and, as such, is not observed in the UCR models. The amount of intermediate-metallicity ($Z/{Z}_{\odot }\sim {10}^{-1}$) gas at $T\gtrsim {10}^{6}$ K is steadily increasing in all CR models.

Figure 13 provides the metallicity distribution for different wind models in various gas phases—the IGM, halo gas, and the ISM, as well as the total distribution for gas particles in the high-resolution region. The ISM includes all the gas inside galaxies, the halo gas includes the gas within halos but outside galaxies, and the IGM includes the gas outside the halos. In the IGM panel, we observe that the CW models for CR and UCR exhibit the highest metallicities, basically indistinguishable from each other, with maxima located at log $(Z/{Z}_{\odot })\sim (-0.8)-(-0.7)$. The least efficient injection of metals happens in the NW model (the maximum at log $(Z/{Z}_{\odot })\sim -2.2$), while VW occupies broadly the region between the CW and NW models. It displays a nearly flat top at log $(Z/{Z}_{\odot })\sim (-2)-(-1)$. At the other extreme, the metal distributions in the ISM are basically identical, and the maxima are found between log $(Z/{Z}_{\odot })\sim (-1)$ and 0. The metal distributions in the halo gas are flat-topped for NW and VW models, and show maxima at log $(Z/{Z}_{\odot })\sim -1$ for the UCW and −0.7 for CW. From Figure 13, we conclude that the ISM is polluted by metals in all models. Moreover, there is a large difference in expelling the metals to the halo and the IGM. The CW and UCW models appear to be the most efficient in this process in a given environment.

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To take an alternative view of the evolution of gas, we subdivide the gas phases in a different way. In this section, we alter definitions for the IGM and other gas phases used in the previous section in order to facilitate the comparison with previous works. Figure 14 compares the evolution of various gas phases, namely, diffuse, warm-hot + hot, IGM, and condensed gas. These phases are defined based on the temperature of the gas and the density fluctuation $\delta ={\rho }_{{\rm{b}}}/{\bar{\rho }}_{{\rm{b}}}-1$. For this purpose, we employ the definitions from Davé et al. (1999) and Choi & Nagamine (2011). The "diffuse" gas is defined by $T\lt {10}^{5}$ K and $\delta \lt 1000$, the "hot" gas by $T\gt {10}^{7}$ K, and the "warm-hot" gas by ${10}^{5}\lt T\lt {10}^{7}$ K. The "condensed" phase consists of non-star-forming gas with $T\lt {10}^{5}$ K and $\delta \gt 1000$, and of a star-forming gas as well as stars.

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We observe that the mass fraction of the "condensed" phase is increasing with time for all models, especially for the NW, while the IGM (non-star-forming) fraction decreases. The fraction of "diffuse" filamentary gas is decreasing faster for the CW model than for the VW one. At the same time, the fractions of both the UCW and UVW diffuse gas remain very high at all z, while the condensed fraction stays very low. While in the warm-hot + hot phase the NW and VW evolution are similar, in the condensed and IGM phases it is the VW and CW runs that evolve in tandem.

While the mass fractions in our UCRs and the models of Choi & Nagamine (2011) appear to be reasonably similar, the CR models differ substantially, both from the UCR cases and among themselves. This difference between the CR and the UCR models is expected, because of the overdensity present in the CR runs. But we also observe that the NW model exhibits a much higher fraction of cold gas, as it evolves toward z ∼ 6, and consequently it exhibits smaller fraction of IGM gas. The mass fraction of the condensed phase, which also includes stars, in the NW run reaches ∼50%, while for the VW and CW models it is only ∼32%. The diffuse component shows that the fraction drops to ∼43% in NW, to ∼51% in CW, and to only ∼57% in VW.