The physical origin of positive metallicity radial gradients in high-redshift galaxies: insights from the FIRE-2 cosmological hydrodynamic simulations

Our analysis focuses on the Latte suite galaxies from the FIRE-2 cosmological zoom-in simulations, all modeled as Milky Way-mass isolated galaxy progenitors. The Latte suite comprises eight simulations as listed in Table 1 (see also Wetzel et al., 2023; Garrison-Kimmel et al., 2017, 2019; Samuel et al., 2020; Wetzel et al., 2016; Hopkins et al., 2018). The simulations were conducted using the gizmo code in mesh-less finite-mass (MFM) mode (Hopkins, 2015). These simulated galaxies were evolved down to redshift $z=0$, yielding a main halo mass of $M_{\rm halo}\sim 10^{12}$ M_⊙ at $z=0$. We selected snapshots spanning redshifts $z\sim 0.44-3$, covering the stellar mass range of $M_{\star}\sim 10^{8}$ to $10^{11}{\rm M}_{\odot}$ for central galaxies only. Force softening (Plummer equivalent) values are $\epsilon_{\rm star}=3.2-4.0$ pc for stellar and $\epsilon_{\rm dm}=32-40$ pc for dark-matter particles. The minimum adaptive force softening for gas cells is $\epsilon_{\rm gas,min}=0.4-1.0$ pc. Initial masses of baryonic (gas or star) and dark-matter particles are $M_{\rm baryon}=4200-7100{\rm M}\odot$ and $M_{\rm dm}=21000-39000{\rm M}_{\odot}$, respectively.

FIRE-2 incorporates radiative cooling and heating across a temperature range from 10 to $10^{10}$ K, tracking the abundances of 11 different elements (H, He, C, N, O, Ne, Mg, Si, S, Ca, Fe). The model includes detailed stellar feedback mechanisms, including supernovae (Type II and Ia), stellar winds (from OB and AGB stars), and radiative feedback, to accurately simulate the dynamics and chemical composition of the ISM. These processes, crucial for driving galactic winds and regulating star formation, are based on stellar evolution models with rates and energies derived from starburst99 (Leitherer et al., 1999) and assume a Kroupa (2001) initial mass function. Together, these mechanisms enrich ISM with metals and play a significant role in galaxy evolution through balancing gas heating and cooling.

FIRE-2 features an explicit model for the turbulent diffusion of gas-phase metals (Su et al., 2017; Escala et al., 2018; Hopkins et al., 2018), which addresses the sub-grid scale mixing processes critical for the chemical evolution of galaxies. This mechanism facilitates chemical exchange between particles, enabling a more realistic representation of metal mixing and distribution within the ISM. Bellardini et al. (2021) showed that varying the diffusion coefficient for metal mixing affects the azimuthal variations in gas metallicity in these galaxies, but it does not significantly affect the vertical or radial gradients.

We focus solely on the most massive halo in each galaxy at redshifts $z\sim 0.44-3$. The detailed physical properties of these galaxies are presented in Appendix B.

We define the center of each galaxy as the point within a sphere of radius ranging from 20 down to 1 kpc that consistently exhibits the highest stellar mass density. The stellar mass, gas mass, and SFR, relevant to our calculations, are confined to within 5 kpc of this center. Following Ma et al. (2017), we define a characteristic radius $R_{90}$ as the radius enclosing 90 percent of the total SFR within 5 kpc, with the SFR averaged over a period of 200 Myr.

In Fig. 1, we present three examples of our simulated galaxy sample: m12b at $z\approx 0.44$ (top), m12w at $z\approx 1.42$ (middle), and m12c at $z\approx 2.28$ (bottom). For each individual galaxy, the $z$-axis is defined to be aligned with the total angular momentum of all gas particles within $R_{90}$. The ‘face-on’ view is thus along the $z$-axis, and the ‘edge-on’ view is along a direction perpendicular to the $z$-axis. For each example, the left two columns of Fig. 1 display the face-on gas density map (upper left), edge-on gas density map (upper right), face-on stellar density map (bottom left), and face-on SFR map (bottom right). The $R_{90}$ range is indicated by a white dashed circle in each map. These images illustrate that m12b features a thin disk, m12w a thick disk, and m12c appears irregular.

In the top panels of Fig. 2, we show the face-on metallicity distributions of the three galaxies in Fig. 1. Here the gas-phase metallicity is measured in each pixel (100 pc $\times$ 100 pc), and only pixels with gas mass density $\Sigma_{\rm g}\geq 10{\rm M}_{\odot}\cdot{\rm pc}^{-2}$ are included in the metallicity gradient statistics. This threshold represents the surface density of pixels above which there will be observationally detectable nebular emission lines, indicative of star formation (Orr et al., 2018).

Our analysis focuses on all particle data within the radius interval of 0.25-1$R_{90}$, following Ma et al. (2017), which has shown that the metallicity gradients measured within a more inner range (0-2 kpc) yield qualitatively consistent results. As shown by the red lines in the bottom panels of Fig. 2, the radial metallicity profile can be fitted with a linear function

where $\alpha$ is the metallicity gradient in $\mathrm{dex}\cdot\mathrm{kpc}^{-1}$. Eq. 1 provides a measure of the gradients of total metal in $d\log Z_{\rm g}/dR$.

In this study, positive gradient denotes $\alpha>0$, and we subdivide negative gradients ($\alpha<0$) into “flat” and “strong negative”, where flat gradient denotes $-0.03<\alpha<0$, and strong negative gradient denotes $\alpha<-0.03$.

We note that for galaxies with a well-ordered rotation curve whose metallicity is concentrated at the center (e.g. m12b in Figs. 1 and 2), the metallicity profile may be better modeled by a reciprocal ($d\log Z_{\rm g}/dR\sim 1/R$) rather than linear function, especially when considered over a larger radial distance (see Appendix A for more details). Nonetheless, Eq. 1 is still a good approximate for characterizing metallicity gradients.

We measure the kinematic properties for gas of these galaxies by mimicking the widely used long-slit spectroscopy technique following Ma et al. (2017). To begin with, we put a long slit with a width of 1 kpc at the center along the y-axis (edge-on) direction, as shown in the edge-on gas density images in Fig. 1. A one-dimensional velocity curve is then extracted along the direction of this slit, covering the range $-R_{90}<y<R_{90}$ and -0.5 kpc $<z<$ 0.5 kpc, with all gas particles therein considered in the calculation. We measure the mass-weighted mean velocity of gas in each bin and the 1-$\sigma$ velocity dispersion of total velocity. Three examples are shown in the right column of Fig. 1, m12b at $z=0.44$, m12w at $z=1.42$, and m12c at $z=2.28$, where black points represent the line-of-sight velocity and error bars indicate the velocity dispersion along the slit.

We fit the one-dimensional velocity curve with the following function

which originates from the simple disk model and similar to Eq.(1) in Ma et al. (2017) except that the peculiar velocity $v_{0}$ in the simulation box is placed on the left side. Here $v_{\rm c}$ represents the asymptotic rotation velocity of the gas at large radius. In the right panels of Fig. 1, the red lines are the best-fits for the three examples. On the top left corner of each panel, we provide $v_{\rm c}/\sigma$ for all the gas particles to indicate the disk formation of these galaxies, with $\sigma$ denoting the velocity dispersion of the line-of-sight velocity of all gas particles in the considered range.

We adopt $v_{\rm c}/\sigma\geq 1$ in identifying rotationally supported disk systems. Galaxies with $v_{\rm c}/\sigma<1$ lack well-ordered rotation, and exhibit irregular morphology. And we define a threshold at $v_{\rm c}/\sigma=3$, where galaxies with $v_{\rm c}/\sigma\geq 3$ are classified as thin disks, and galaxies with $1<v_{\rm c}/\sigma<3$ are classified as thick disks.

The velocity curves of m12b at $z=0.44$ can be well fitted by the arctan function, indicating that it possesses a well-ordered rotating thin disk, as evidenced by $v_{\rm c}/\sigma$ reaching 4.72. Meanwhile, m12w at $z=1.42$ can be roughly fitted, suggesting it possesses a thick disk with a $v_{\rm c}/\sigma$ of 2.76. However, m12c at $z=2.28$ returns a very poor fit, with a $v_{\rm c}/\sigma$ value of 0.28, indicating that it is an irregular galaxy. These observations are consistent with the images in Fig. 1.

In this study, we focus on galaxies with a $v_{\rm c}/\sigma$ value within the range of 0.3-8, as those with $v_{\rm c}/\sigma$ values beyond this range typically exhibit characteristics of irregular galaxies, which often show very unstable rotational velocities.

Fig. 2 displays the gas-phase metallicity maps and the radial metallicity distributions with linear fits for each galaxy snapshot in Fig. 1. Galaxy m12b at $z=0.44$ represents a galaxy in the later stages of evolution with a highly ordered rotational thin disk and a strong negative gradient with metals concentrated at the center. Galaxy m12w at $z=1.42$ indicates a mid-stage evolutionary galaxy with a thick disk, characterized by a flat gradient. Galaxy m12c at $z=2.28$ shows an irregular galaxy with a disordered velocity field, displaying a higher metal abundance in the outer regions, which is classified as a positive gradient. See Appendix B for the metallicity gradients of other galaxies in our study. Previously, we mentioned that the results are similar across different regions. In Fig.3, we show that metallicity gradient measurements from 0-1$R_{90}$ and from 0.25-1$R_{90}$ are in excellent agreement with one another, with a correlation coefficient of $k=0.994$.

Intense outflows, rapid gas infall, and mergers in galaxies stir the ISM and drive galaxy-scale gas flows that mix metal-enriched or metal-poor gas. These gas flows move at velocities of hundreds of km s^-1, which can reshape the spatial distribution of gas and metals in a very short time or cause changes in the galaxy’s morphology (Ma et al., 2017; Pandya et al., 2021). Therefore, simulations with ”enhanced” feedback often exhibit flat metallicity gradients, while the absence of such feedback can lead to steeply negative gradients (Gibson et al., 2013). In the simulation m12c at $z=2.28$, perturbations are predominantly caused by a series of minor mergers, as observable in the images. These merger events across the galaxy mix metals in the gas, effectively reversing the gradient. Meanwhile, for m12w at $z=1.42$, the central starburst acts as the main source of feedback, driving metal-enriched gas radially outward and consequently fostering the formation of a flat gradient. On the other hand, in m12b at $z=0.44$ (Fig. 1), the weak feedback (or lower SFR) produces less energy, which allows strong negative gradients to remain stable. In galaxy evolution, different types of dynamical processes (such as mergers, starbursts and associated feedback, accretion, etc.), their intensities, and the interactions among them can lead to changes in their impact on the entire galaxy (Mercado et al., 2021). This dynamic interaction not only influences galactic structure and star formation but also manifests in the observable variations in metallicity distribution across the galaxy. Thanks to the high resolution of FIRE-2, we are able to resolve the movements of galactic winds on very small scales, the turbulence within the ISM, and its effects on radial mixing.

Fig. 2 also illustrates how measurements of radial metallicity gradients in galaxies can be influenced by the choice of center. In fact, when we choose starbursts as the center, flat and positive gradients are more easily observed. It is easy to define the center for thin disk galaxies, while it is more challenging for thick disk or irregular galaxies. As mentioned in Bellardini et al. (2021, 2022), late-stage evolved thin disk galaxies exhibit minor variations in azimuthal angle; however, early-stage galaxies experience additional azimuthal scatter due to gas flows. Feedback mechanisms within the galaxy, such as localized star formation activities, influence azimuthal metal abundance variations and lead to a patchy distribution of metals (as shown in m12c at $z=2.28$ in Fig.2), resulting in observable an larger azimuthal scatter. The impact of these dynamics is particularly significant in galaxies with active star formation or turbulent conditions, where localized events can rapidly alter the metal distribution. These analyses, distinct from radial distributions, provide more information related to local conditions. In this paper, we use the galaxy’s center of mass as the center for measuring metallicity gradients, and we do not discuss other potential centers for measurement extensively.

In the following parts of this section, we first present the Mass-Metallicity Relation (MZR) of our samples in Section 3.2. Next, we explore the relationships of metallicity gradient with stellar mass and sSFR in Section 3.3. In Section 3.4, we examine the correlation between metallicity gradient and the degree of rotational support. Following that, in Section 3.5, we discuss the dependence of metallicity gradient on redshift across all our samples, with a specific focus on m12b. Finally, using m12b as an example, we investigate the formation of positive gradients in Section 3.6.

In Fig. 4, we present the mass-metallicity relation for our simulated galaxies at redshift $z=2$. Following the definition in Ma et al. (2016), the gas-phase metallicity is identified as the mass-weighted mean metallicity of the ISM gas, i.e., all gas particles with temperature below 10⁴ K and $R<R_{\rm vir}$. Generally, this helps distinguish the star-forming regions clearly. Here $Z$ is the total gas-phase metallicity and $Z_{\odot}=0.02$ is the solar metallicity. In Fig. 4, the blue dashed line shows the linear fit

from Ma et al. (2016) for gas-phase metallicity at $z=2$ using FIRE-1 galaxies with a stellar mass range $10^{4}-10^{10}M_{\odot}$. The black circles show the FIRE-1 simulated galaxies A2:0 and A8:0 at $z=2$ in Ma et al. (2017), which expand the mass range to $10^{11}M_{\odot}$. The red circles represent all galaxies from FIRE-2 simulations at redshift $z=2$ studied in this work. Our sample spans a stellar mass range of $M_{\star}\sim 10^{8.5}-10^{10}$M_⊙, including only Milky Way-mass galaxies (at $z=0$). Compared to FIRE-1, FIRE-2 incorporates improved numerical methods and algorithmic advancements, along with a larger set of available simulations. Although our study on the MZR does not cover a broader range of mass than previous published studies, the comparison plotted here is useful to relate our study to the previous analyses by Ma et al. (2016, 2017).

We first examine the relationship between metallicity gradients, stellar mass, and sSFR. The SFR for a given epoch is measured as the average formation rate of young stars over the past 200 Myrs. We display this relationship in Fig. 5 for all the galaxies across the redshift range of $z\sim 0.44-3$. Ma et al. (2017) indicates that redshift changes do not significantly alter the underlying relationship between the metallicity gradient and these galaxy properties, so we do not distinguish between redshifts in this particular study. Although we only use the m12 series galaxies, where there is a direct correlation between the stellar mass and redshift, the relationship between gradient and stellar mass is not independent of redshift. Nevertheless, due to the diverse evolutionary paths of different galaxies, the result still provides valuable insights into the relationships among them. The red line represents the linear fits to the simulated data, while the blue dashed lines show the result from Stott et al. (2014) at redshifts $z\sim 0-2.5$.

From the left panel of Fig. 5, metallicity gradients exhibit a weak negative correlation with stellar mass, indicated by a Pearson correlation coefficient of $r=-0.16$ and $p=0.62$. The correlation between stellar mass and metallicity gradients in our Milky Way-mass galaxies is very weak. However, high mass galaxies still tend to exhibit strong negative gradients, while positive gradients occur more frequently in low mass galaxies. For instance, the occurrence of positive gradients is around $20\%$ for galaxies with masses less than $10^{9}M_{\odot}$, and decreases to about $10\%$ for those in the $10^{9}-10^{10}M_{\odot}$ range. Lower mass galaxies have smaller scales and lower $v/\sigma$, which indicates that (turbulent) mixing is more efficient in them. This leads to the redistribution of metals on a galactic scale (Muratov et al., 2015; Belfiore et al., 2017), thereby more easily resulting in extreme gradients, like positive ones. However, due to the instability of the internal dynamics of galaxies, the average metallicity gradients they exhibit are highly unstable, leading to variable trends at lower masses (even showing an increase). The relation between redshift and stellar mass suggests that as galaxies evolve towards larger mass, they rapidly develop thin, stable disk structures (see, e.g., Stern et al., 2021; Hafen et al., 2022; Gurvich et al., 2023; Hopkins et al., 2023; McCluskey et al., 2024, for more on the emergence of thin disks and its connection to the end of bursty star formation in FIRE), leading to the pronounced steepening of the gradient above $M_{\star}\sim 3\times 10^{10}\rm{M}_{\odot}$. Compared to Stott et al. (2014), our simulation provides a flatter fit, largely due to the correlation between stellar mass and redshift for our galaxies, so the discussion of redshift and metallicity gradients might also apply to stellar mass.

We also observe a strong positive correlation between gradients and sSFR, as reflected by a Pearson correlation coefficient of $r=0.73$ and $p=0.004$, showing an increased frequency of positive gradients at higher sSFR levels. Higher sSFR drives stronger feedback, leading to more vigorous gas flows, which can more effectively promote the redistribution of metals. Typically, strong star formation activity occurs in these galaxies that have more cold gas and are more unstable at high redshift, making them more susceptible to the resulting feedback. This suggests that galactic winds triggered by starbursts which could transport metal-enriched gas outward, or rapid accretion events which drive high sSFR, or just overall turbulence in the galaxy could result in strong mixing or create patchiness, leading to the formation of positive gradient.

From our analysis of the FIRE-2 galaxy sample, we only see subtle dependence of metallicity gradient on stellar mass. Although, we caution that this analysis is performed on the same simulation galaxies over a wide redshift range across their mass assembly history, so there is an inevitable degeneracy between the effects that stellar mass and redshift plays in the evolution of gradients presented here and in Sect. 3.5. In contrast, the correlation between metallicity gradient and sSFR is stronger. This indicates that in galaxies with lower mass (more susceptible to feedback) and active star formation activity (strong feedback), the gas in the ISM is more easily disturbed, leading to the redistribution of metals on a galactic scale, resulting in positive gradients.

In Fig. 6, we illustrate the relationship between the gas-phase metallicity gradient and the degree of rotational support for gas, denoted by $v_{\rm c}/\sigma$. Similar to the analysis for stellar mass and sSFR, the red line represents the linear fit to the simulated data. Additionally, although the redshift of the m12 series galaxies correlates with disk formation, the insights derived from the differences among various galaxies provide substantial reference value for the relationship.

Within the range of $v_{\rm c}/\sigma\sim$ 0.3-8, the gradients exhibit a negative correlation with the degree of rotational support, with a Pearson correlation coefficient of $r=-0.86$ and $p=0.0003$, suggesting that galaxies with thinner disks tend to have stronger negative metallicity gradients. For convenience, all galaxies are classified into three regions according to their gradient and $v_{\rm c}/\sigma$ as shown by the grey dotted lines in Fig. 6.

For $0.3<v_{\rm c}/\sigma<1$, the internal dynamics of galaxies are unstable, making them more susceptible to disturbances caused by strong feedback-driven gas flows, leading to a wide redistribution of metals. Typically, starbursts near the center result in flat or positive gradients, while those further from the center may cause strong negative gradients. In these irregular galaxies, the proportion of positive gradients is relatively high ($\sim 20\%$), while strong negative gradients are much less common. Galaxies with rotationally supported disks have a higher likelihood of exhibiting strong negative gradients, reaching nearly half in thin disk galaxies. Meanwhile, the proportion of positive gradients is decreasing as well, reducing to $\sim 6\%$ in thick disks, and falling to only $\sim 3\%$ in thin disks. As galaxies transition from disordered states to rotational disks, strong feedback progressively weakens, thus diminishing the gas mixing in the ISM dominated by strong feedback, such as gas inflows, outflows and turbulent mixing (Graf & Wetzel, in prep.). Similar to FIRE-1 galaxies in Ma et al. (2017), almost all galaxies with strong negative gradients are likely to be rotationally supported, but not vice versa. Stable disk galaxies inhibit these powerful gas flows across the entire galaxy, while localized, orderly gas exchanges gradually maintain stability and promote the formation of strong negative gradients.

In Fig. 7, the metallicity gradients of our simulated galaxies at $z\sim 0.44-3$ are represented as gray points, while the red line indicates the average for each redshift bin. Our analysis suggests that the majority of the gradients fall within the range from -0.08 to 0.04. The consistent trend in galaxies reveals the diversity of metallicity gradients during evolution, from positive to flat to strong negative gradients, demonstrating the sensitivity of these metals to various feedback mechanisms within the galaxy.

Throughout the chemo-structural evolution of these galaxies, positive metallicity gradients account for a total of $10\%$, a proportion similar to that reported in Pérez-Montero et al. (2016); Carton et al. (2018); Wang et al. (2020). In contrast, Simons et al. (2021) reported a significantly higher proportion of $29\%$ for their emission-line selected galaxy sample at $0.6<z<2.6$. Yet we notice that only X-ray bright active galactic nuclei (AGNs) are removed from their galaxy sample, and AGN ionization can strongly increase the [O iii]$\lambda$5007/[O ii]$\lambda\lambda$3727,3730 line flux ratio in galaxy centers, resulting in artificial positive metallicity gradients. From the numerical simulation side, Gibson et al. (2013) conducted two different sets of simulations; the conservative feedback model (MUGS) showed that galaxies establish very strong negative metallicity gradients at high redshifts, which gradually flatten as the galaxies grow. A similar phenomenon occurs in Acharyya et al. (2024), where they state that the feedback mechanisms employed in the current FOGGIE simulations are overall underpowered. While the ”enhanced” feedback models maintained flat metallicity gradients at high redshifts and evolved to become steeper over time. Based on the feedback model and the burstiness of star formation in the FIRE-2 simulations, our results show a wide scatter in metallicity gradients, indicating that these average metallicity gradients steepen with the evolution of redshift (See also: Ma et al., 2017; Bellardini et al., 2022). Although the trends toward steeper gradients at lower redshifts are similar, the average gradients we observe at higher redshifts not as flat as those reported by Bellardini et al. (2022). The gradient calculations for these high-redshift galaxies are influenced by various factors, including the computational ranges used in this paper ($0-0.25R_{90}$). Furthermore, the inclusion of ELVIS LG-like galaxies in their calculations may also contribute to the observed discrepancies.

Additionally, the proportion of inverted metallicity gradients decreases with lower redshifts, as shown in Fig. 7. As galaxies transition from irregular to ordered disks (at $z\lesssim 1$), the positive gradients tend to decrease. This occurs as strong feedback, which drives the redistribution of metals through powerful gas flows, is gradually suppressed, transforming some positive gradients into flat ones. The same transformation applies to strong negative gradients in irregular galaxies. In the mid-stages of galaxy evolution, more ordered rotating disks prevent strong feedback that spans the entire galactic scale, suppressing the emergence of positive gradients; while radial mixing (turbulence) within the ISM mixes metals, inhibiting the formation of strong negative gradients (Graf & Wetzel, in prep.). At $z<1$, weaker feedback (lower SFR) dominates, and the presence of stronger ordered rotating thin disks inhibits radial mixing in the ISM, leading to a reduction in flat gradients and an increase in negative gradients. Therefore, as metals continue to enrich in thin disk galaxies, their metallicity gradients will further steepen.

In Fig. 8, we display all snapshots of galaxy m12b, including both gradients and sSFR over the last 10 Myrs, showing gradients in red and sSFR in blue. The proportion of positive metallicity gradients is about $\sim 10\%$, which is roughly consistent with observed across all galaxies. This proportion aligns with previous findings, with the trend reflecting a transition from disorder to order (Zhuang et al., 2019).

We observe a clear evolution for these Milky Way-mass progenitors galaxies: at redshifts $z>1.5$, galaxies typically exhibit bursty star formation activity, leading to extremely strong outflows (Muratov et al., 2015, 2017; Anglés-Alcázar et al., 2017; Pandya et al., 2021), which facilitates radial metal mixing in ISM, manifesting in flat and positive gradients. Around $z\sim 1.5$, the average gradient peaks as the internal dynamics and structure of galaxies stabilize. And the relative stability in the physical structure of galaxies supports the formation and maintenance of more stable gradients. From $z\sim 1.5$ to $1$, as the intensity of stellar activities declines, the impact of feedback mechanisms weakens, leading to weaker radial metal mixing or turbulence in the ISM (Graf et al., 2024; Graf & Wetzel, in prep.). Consequently, there is a noticeable steepening in the average metallicity gradients across galaxies. Then $z\sim 1-0.7$, galaxies transition further from disordered states to rotational disks. The SFR decreases from bursty to time-steady (Gurvich et al., 2023), and galactic-scale gas outflows or turbulence are suppressed; the disordered accretion from CGM shifts to orderly form (namely, the virialization of the inner CGM) (Stern et al., 2021), leading to a further steepening in the average metallicity gradients. Below $z<0.7$, dynamics are dominated by weak “fountain flows” (Anglés-Alcázar et al., 2017) and ordered accretion from the CGM. The effective radial redistribution of metals nearly are prevented, stabilizing metallicity at steep negative values around -0.08.

After discussing the evolution of positive metallicity gradients into strong negative gradients, we now explore their formation mechanisms. Our simulations indicate that positive gradients are more likely to occur in smaller galaxies with higher activity and irregular shapes, where strong feedback is more active and more susceptible to complex gas flows.

We observed several samples in Fig. 8 where the peaks of sSFR coincide with the appearance of positive metallicity gradients, suggesting that intense starburst activity can reverse metallicity gradients. This observation supports the hypothesis that high intensity starbursts at the galaxy’s center can drive metal-enriched gas towards the outskirts, altering the overall metal distribution and leading to positive metallicity gradients. The sample shown in m12c of Fig. 1 is a typical example, with a notably active center causing higher metallicity in the outer regions than at the center. Additionally, some samples do not have sSFR peaks coinciding with positive gradients, indicating no strong outflows dominating metal redistribution in these instances, with peaks instead appearing after the positive gradients. In such cases, metal-poor gas accreted into the galaxy’s center dilutes the existing central gas, introducing cold, metal-poor gas that promotes star formation activity. The first phenomenon is commonly referred to as metal-enriched gas outflow, while the second is known as metal-poor gas inflow (Wang et al., 2022).

At cosmic noon, star-forming galaxies are often characterized by intense star bursts and vigorous gas accretion. These processes catalyze sustained and powerful feedback mechanisms within galaxies, including powerful, galaxy-scale outflows driven primarily by supernovae. These feedback effects are crucial for reshaping the ISM by dispersing and mixing metals throughout the galaxy, significantly influencing their structural and chemical properties. Consequently, this active redistribution leads to the formation and frequent occurrence of positive metallicity gradients.

In our study of positive gradients, we often found that many gradients are quite flat, and the extent of these gradients depends on the intensity of strong feedback. When strong feedback is insufficient to reverse the distribution of metal, it could result in flat gradients. The reasons of these flat gradients are similar to those for positive gradients, thus positive gradients may be observed in a smaller area. In Fig. 7, the proportion of flat gradients increases with redshift, suggesting that as galaxies evolve, the weakening of strong feedback and the suppression of galaxy-scale gas flows make many gas flows too weak for positive gradients, yet sufficient for flat gradients. We are not suggesting that all flat gradients originate in the same way as positive gradients. Some may arise from strong turbulence within the galaxy, which merely mixes metals (rather than altering the large-scale metal distribution), leading to the formation of flat gradients.