<figure><img src="image_21.png" /><figcaption>**Figure 20.** Left: the mean-stacked azimuthally averaged radial SB profiles of Mg II emission in circular annuli of 10 kpc from the galaxy centres for different stellar mass bins are shown in solid lines as marked in the legend in the right-hand panel. The error bars represent the $1\sigma$ uncertainties from bootstrapping analysis. The Mg II SB profiles from the TNG50 simulation (Nelson et al. 2021) at comparable redshift and stellar masses are shown in dashed lines. The shaded regions represent the $1\sigma$ halo-to-halo variation. Right: the same as in the left-hand panel, but for the median-stacked profiles.</figcaption></figure>

strong increase of the central SB with stellar mass found in the simulation is not reflected in the observed central SB. For the highest stellar mass range, $M_* = 10^{10-12} M_\odot$, Mg II is observed in absorption in the central 10 kpc region. The observed and simulated central SB values are comparable for stellar mass $M_* \approx 10^{9-10} M_\odot$. For lower stellar masses, the simulated SB values are much lower than the observed ones. Secondly, we note that the observed SB profiles are generally flatter than the simulated profiles across stellar masses. The discrepancies between the observed and simulated SB profiles likely arise due to the simplifying assumptions that have gone into the Mg II emission model. These are described in detail in section 2.3 of Nelson et al. (2021) and we discuss some of them here briefly.

First, due to the inability of the TNG50 simulation to resolve physical mechanisms at small scales ($\lesssim 100$ pc) in the ISM, emission from highly ionized H II regions around young stars is neglected. The Mg II emission from the ISM could be non-negligible, particularly in lower mass galaxies with larger young stellar population, and could propagate and scatter into the CGM. This could explain the brighter and more extended Mg II SB profile observed around lower mass ($M_* < 10^9 M_\odot$) galaxies compared to that in the simulation. Secondly, the model assumes that the Mg II emission is optically thin and neglects the impact of resonant scattering. Resonant scattering is expected to redistribute the emergent Mg II emission from smaller to larger radii and thereby to flatten the radial SB profiles (Prochaska et al. 2011b; Byrohl et al. 2021; Mitchell et al. 2021). This could explain why the observed SB profiles are flatter than the simulated ones. Additionally, the model does not take into account the stellar continuum at the Mg II wavelength, which if scattered could lead to flattening of the SB profiles, and dust, which could be an additional source of opacity for photons. Indeed, in the case of Ly$\alpha$ emission, it is found that dust significantly suppresses the flux and that the dust attenuation of the central SB strongly scales with stellar mass (e.g. fig. A5 of Byrohl et al. 2021). This along with the lack of Mg II absorption from the ISM in the models could explain the difference in the central SB between observations and simulations for the most massive galaxies ($M_* \ge 10^{10} M_\odot$).

Overall, the above comparison indicates significant uncertainties in predicting Mg II observations, and motivates the need for better modelling of the ISM physics and radiative transfer effects, also

including a more rigorous dust treatment. Future work will extend the Monte Carlo radiative transfer technique of Byrohl et al. (2021) to the problem of Mg II resonant scattering, including empirically calibrated dust models (Byrohl et al., in preparation). Simultaneously, all cosmological hydrodynamical simulations have limited spatial resolution, which could impact the size and abundance of cool gas clouds that are resolved in the halo (Peeples et al. 2019; Suresh et al. 2019). We also note that the underlying TNG (The Next Generation) galaxy formation model yields specific predictions for the abundance, physical properties, and thus emissivity of halo gas (Truong et al. 2020; Pillepich et al. 2021; Ramesh, Nelson & Pillepich 2023), and other galaxy formation models will produce different results (Fielding et al. 2020; Ayromlou, Nelson & Pillepich 2022; Sorini et al. 2022). Thus, the comparison presented here offers a first analysis, but not a complete one, in comparing metal emission around galaxies in simulations and observations.

From the observational perspective, we note that, as mentioned previously, there maybe a bias against passive galaxies in the sample used for stacking in this work, and the sample is more representative of the star-forming galaxy population. The simulation results, on the other hand, are based on all galaxies and are not restricted to only star-forming galaxies. The highest mass bins in the simulation are dominated by more passive galaxies, which combined with the specific SFR showing a positive correlation with the Mg II halo extent in the simulation (see fig. 8 of Nelson et al. 2021), could lead to a smaller Mg II halo extent than in the observations. Next, the observed stacks are obtained in a line-of-sight velocity window and could be affected by projection effects, whereas the simulation results are based on gas that is gravitationally bound to the central halo. In the future, after the Mg II scattering problem is addressed with the methodology of Byrohl et al. (2021), we would be able to obtain spatially resolved spectra from the TNG50 simulation, and more faithfully reproduce the observations using the same velocity integration window. Finally, Mg II, being a resonant line, can be detected in emission and in absorption against the background stellar continuum, with part of the absorption infilled by redshifted emission (i.e. P Cygni-like profiles; see e.g. Prochaska et al. 2011b; Erb et al. 2012; Martin et al. 2012). We have not attempted to decompose the Mg II emission and absorption from the ISM in this work, which
<figure><img src="image_22.png" /><figcaption>**Figure 20.** Left: the mean-stacked azimuthally averaged radial SB profiles of Mg II emission in circular annuli of 10 kpc from the galaxy centres for different stellar mass bins are shown in solid lines as marked in the legend in the right-hand panel. The error bars represent the $1\sigma$ uncertainties from bootstrapping analysis. The Mg II SB profiles from the TNG50 simulation (Nelson et al. 2021) at comparable redshift and stellar masses are shown in dashed lines. The shaded regions represent the $1\sigma$ halo-to-halo variation. Right: the same as in the left-hand panel, but for the median-stacked profiles.</figcaption></figure>

strong increase of the central SB with stellar mass found in the simulation is not reflected in the observed central SB. For the highest stellar mass range, $M_* = 10^{10-12} M_\odot$, Mg II is observed in absorption in the central 10 kpc region. The observed and simulated central SB values are comparable for stellar mass $M_* \approx 10^{9-10} M_\odot$. For lower stellar masses, the simulated SB values are much lower than the observed ones. Secondly, we note that the observed SB profiles are generally flatter than the simulated profiles across stellar masses. The discrepancies between the observed and simulated SB profiles likely arise due to the simplifying assumptions that have gone into the Mg II emission model. These are described in detail in section 2.3 of Nelson et al. (2021) and we discuss some of them here briefly.

First, due to the inability of the TNG50 simulation to resolve physical mechanisms at small scales ($\le 100$ pc) in the ISM, emission from highly ionized H II regions around young stars is neglected. The Mg II emission from the ISM could be non-negligible, particularly in lower mass galaxies with larger young stellar population, and could propagate and scatter into the CGM. This could explain the brighter and more extended Mg II SB profile observed around lower mass ($M_* < 10^9 M_\odot$) galaxies compared to that in the simulation. Secondly, the model assumes that the Mg II emission is optically thin and neglects the impact of resonant scattering. Resonant scattering is expected to redistribute the emergent Mg II emission from smaller to larger radii and thereby to flatten the radial SB profiles (Prochaska et al. 2011b; Byrohl et al. 2021; Mitchell et al. 2021). This could explain why the observed SB profiles are flatter than the simulated ones. Additionally, the model does not take into account the stellar continuum at the Mg II wavelength, which if scattered could lead to flattening of the SB profiles, and dust, which could be an additional source of opacity for photons. Indeed, in the case of Ly$\alpha$ emission, it is found that dust significantly suppresses the flux and that the dust attenuation of the central SB strongly scales with stellar mass (e.g. fig. A5 of Byrohl et al. 2021). This along with the lack of Mg II absorption from the ISM in the models could explain the difference in the central SB between observations and simulations for the most massive galaxies ($M_* \ge 10^{10} M_\odot$).

Overall, the above comparison indicates significant uncertainties in predicting Mg II observations, and motivates the need for better modelling of the ISM physics and radiative transfer effects, also

including a more rigorous dust treatment. Future work will extend the Monte Carlo radiative transfer technique of Byrohl et al. (2021) to the problem of Mg II resonant scattering, including empirically calibrated dust models (Byrohl et al., in preparation). Simultaneously, all cosmological hydrodynamical simulations have limited spatial resolution, which could impact the size and abundance of cool gas clouds that are resolved in the halo (Peeples et al. 2019; Suresh et al. 2019). We also note that the underlying TNG (The Next Generation) galaxy formation model yields specific predictions for the abundance, physical properties, and thus emissivity of halo gas (Truong et al. 2020; Pillepich et al. 2021; Ramesh, Nelson & Pillepich 2023), and other galaxy formation models will produce different results (Fielding et al. 2020; Ayromlou, Nelson & Pillepich 2022; Sorini et al. 2022). Thus, the comparison presented here offers a first analysis, but not a complete one, in comparing metal emission around galaxies in simulations and observations.

From the observational perspective, we note that, as mentioned previously, there maybe a bias against passive galaxies in the sample used for stacking in this work, and the sample is more representative of the star-forming galaxy population. The simulation results, on the other hand, are based on all galaxies and are not restricted to only star-forming galaxies. The highest mass bins in the simulation are dominated by more passive galaxies, which combined with the specific SFR showing a positive correlation with the Mg II halo extent in the simulation (see fig. 8 of Nelson et al. 2021), could lead to a smaller Mg II halo extent than in the observations. Next, the observed stacks are obtained in a line-of-sight velocity window and could be affected by projection effects, whereas the simulation results are based on gas that is gravitationally bound to the central halo. In the future, after the Mg II scattering problem is addressed with the methodology of Byrohl et al. (2021), we would be able to obtain spatially resolved spectra from the TNG50 simulation, and more faithfully reproduce the observations using the same velocity integration window. Finally, Mg II, being a resonant line, can be detected in emission and in absorption against the background stellar continuum, with part of the absorption infilled by redshifted emission (i.e. P Cygni-like profiles; see e.g. Prochaska et al. 2011b; Erb et al. 2012; Martin et al. 2012). We have not attempted to decompose the Mg II emission and absorption from the ISM in this work, which
would mainly affect the central SB, but this could be explored in the future. All of the above factors, along with the modelling uncertainties, contribute to the differences we find between the observed and simulated Mg II SB profiles.

Although the observed and simulated Mg II SB profiles in different stellar mass bins do not match quantitatively, there are some trends that are qualitatively similar in the observational and simulation results. The size or extent at a fixed SB level of the Mg II haloes increases with stellar mass in both the observations and simulation. The extent of the Mg II emission also correlates with the environment in both cases. The observed Mg II SB profile is more extended around group galaxies, whereas the half-light radii of the simulated Mg II haloes increases with the local galaxy overdensity due to contributions from nearby satellites.

## 5.3 Physical implications of stacked line emission

There are several physical mechanisms that could explain the extended Mg II and [O II] emission detected around the galaxies through the stacked analysis. One possible scenario is that the ionizing photons (ionization potentials of Mg II and [O II] are 15 and 13.6 eV, respectively) escape from the stellar discs of the galaxies, likely via outflows as indicated by the P Cygni-like Mg II profile in the central region, and ionize the cool gas in the haloes (e.g. Chisholm et al. 2020). Another possibility is that the UV background and/or low levels of star formation in the extended disc or disc-halo interface acts as a local source of ionizing radiation. The presence of more extended [O II] emission along the disc of the galaxy (Section 4.1.4) could support this scenario, since it would be less likely for ionizing photons produced in the inner part of the galaxy to escape along the disc. Lastly, gravitational interactions or galactic outflows could lead to shocks, which in turn could produce the required ionizing photons (e.g. Heckman, Armus & Miley 1990; Pedrini et al. 2022). It is likely that a combination of the different mechanisms contributes to the average extended emission. Observations of additional emission lines (e.g. [O III], Hα, and [N II]) are required to distinguish between the different mechanisms.

Constraints on the physical mechanisms and gas conditions can also be obtained by comparing the average Mg II- and [O II]-emitting halo gas. The [O II] emission is brighter than the Mg II emission, as also found in observations of individual galaxies in the literature (e.g. Rubin et al. 2011; Feltre et al. 2018; Leclercq et al. 2022). Based on observations of star-forming galaxies at $z = 0.7-2.4$ and predictions from photoionization models of Gutkin, Charlot & Bruzual (2016), Feltre et al. (2018) found that the [O II] to Mg II emission line ratio increases with metallicity and varies between ≈3 and ≈40. As can be seen from Fig. 21, the [O II] to Mg II SB ratio from the stack of the full sample is a factor of ≈40 in the central 10 kpc, decreases with increasing distance from the centre and remains constant around ≈3 over 20–50 kpc, before tentatively declining further out. This constant ratio could indicate that the Mg II emission in the inner region of the halo does not originate solely from scattering of ionizing photons produced in the stellar disc, but could have a non-negligible *in situ* component through collisional ionization similar to the [O II] emission. The resulting Mg II photons can subsequently undergo scattering in the outer halo, leading to a flatter SB profile.

Indeed, as noted in Section 4.1, it can be seen from Fig. 21 that the Mg II SB profile is shallower than the [O II] SB profile on average. This suggests that the resonant Mg II emission is more likely to be affected by dust and radiative transfer effects compared to the non-resonant, collisionally excited [O II] emission, leading to the observed flattening. Studies of individual systems with coverage of both the

<figure><img src="image_22.png" /><figcaption>**Figure 21.** The top panel compares the Mg II and the [O II] SB profiles. The mean- and median-stacked azimuthally averaged radial SB profiles of Mg II emission in circular annuli of 10 kpc from the galaxy centres for the full sample are shown in light blue and dark blue, respectively. Similarly, the mean- and median-stacked SB profiles of [O II] emission are shown in pink and red, respectively. The error bars represent the $1\sigma$ uncertainties from bootstrapping analysis. The bottom panel shows the ratio of the SB of [O II] to Mg II, in grey for the mean profiles and in black for the median profiles.</figcaption></figure>

lines in the literature have also found that the Mg II SB profiles are flatter than the [O II] ones (Zabl et al. 2021; Leclercq et al. 2022). Currently, there are no studies that have compared the Mg II and [O II] halo emission around galaxies in cosmological simulations. Such a comparison would place useful constraints on the possible physical mechanisms leading to the extended Mg II and [O II] emission around galaxies.

Next, we can obtain an estimate of the electron density using the ratio of the intensities of the [O II] doublet lines, $\lambda3729/\lambda3727$, which varies between 0.35 in the high density limit and 1.5 in the low density limit (Osterbrock 1989). We fit the [O II] emission line extracted from the median-stacked cube of the full sample (see Fig. 2) with a double Gaussian profile (with the wavelength difference between the two Gaussian components fixed to that of the [O II] doublet). We find that the ratio of the intensity of the doublet lines is $1.3 \pm 0.1$ in the central 10 kpc region and marginally increases to $1.5 \pm 0.4$ in the outer annulus region between 30 and 40 kpc, suggesting that the density is declining with increasing distance into the halo. Following Sanders et al. (2016), we estimate that the above [O II] doublet ratios imply that the average electron density at $z \approx 1$ is $\lesssim 100 \text{ cm}^{-3}$. This is similar to what has been found for star-forming field galaxies at $z \approx 1-1.5$ (Harshan et al. 2020; Davies et al. 2021).

The intrinsic flux ratio of the Mg II emission doublet lines, $\lambda2796/\lambda2803$, would be 2 if the excitation is dominated by collisions, and would be $\approx 1$ if the excitation is dominated by photon absorption (Sigut & Pradhan 1995; Prochaska et al. 2011b). While the stacked spectrum in the central $\approx 10$ kpc region shows Mg II in both emission and absorption, the spectra in the outer region (10–30 kpc) show Mg II emission and no prominent absorption signatures (see Fig. 2), suggesting that the Mg II gas in the halo is likely to be optically thin. From double Gaussian fits (with the wavelength difference between the two Gaussian components fixed to that of the Mg II doublet) to the stacked Mg II emission lines, the flux ratio is $1.5 \pm 0.1$ and $1.7 \pm 0.2$ in the annular region between 10–20 and 20–30 kpc, respectively. The ratio being close to 2 suggests that the extended Mg II emission could indeed be produced in part through collisional excitation *in situ*. The Mg II gas in the halo could then absorb and scatter the
would mainly affect the central SB, but this could be explored in the future. All of the above factors, along with the modelling uncertainties, contribute to the differences we find between the observed and simulated Mg II SB profiles.

Although the observed and simulated Mg II SB profiles in different stellar mass bins do not match quantitatively, there are some trends that are qualitatively similar in the observational and simulation results. The size or extent at a fixed SB level of the Mg II haloes increases with stellar mass in both the observations and simulation. The extent of the Mg II emission also correlates with the environment in both cases. The observed Mg II SB profile is more extended around group galaxies, whereas the half-light radii of the simulated Mg II haloes increases with the local galaxy overdensity due to contributions from nearby satellites.

## 5.3 Physical implications of stacked line emission

There are several physical mechanisms that could explain the extended Mg II and [O II] emission detected around the galaxies through the stacked analysis. One possible scenario is that the ionizing photons (ionization potentials of Mg II and [O II] are 15 and 13.6 eV, respectively) escape from the stellar discs of the galaxies, likely via outflows as indicated by the P Cygni-like Mg II profile in the central region, and ionize the cool gas in the haloes (e.g. Chisholm et al. 2020). Another possibility is that the UV background and/or low levels of star formation in the extended disc or disc-halo interface acts as a local source of ionizing radiation. The presence of more extended [O II] emission along the disc of the galaxy (Section 4.1.4) could support this scenario, since it would be less likely for ionizing photons produced in the inner part of the galaxy to escape along the disc. Lastly, gravitational interactions or galactic outflows could lead to shocks, which in turn could produce the required ionizing photons (e.g. Heckman, Armus & Miley 1990; Pedrini et al. 2022). It is likely that a combination of the different mechanisms contributes to the average extended emission. Observations of additional emission lines (e.g. [O III], H$\alpha$, and [N II]) are required to distinguish between the different mechanisms.

Constraints on the physical mechanisms and gas conditions can also be obtained by comparing the average Mg II- and [O II]-emitting halo gas. The [O II] emission is brighter than the Mg II emission, as also found in observations of individual galaxies in the literature (e.g. Rubin et al. 2011; Feltre et al. 2018; Leclercq et al. 2022). Based on observations of star-forming galaxies at $z = 0.7–2.4$ and predictions from photoionization models of Gutkin, Charlot & Bruzual (2016), Feltre et al. (2018) found that the [O II] to Mg II emission line ratio increases with metallicity and varies between $\approx 3$ and $\approx 40$. As can be seen from Fig. 21, the [O II] to Mg II SB ratio from the stack of the full sample is a factor of $\approx 40$ in the central 10 kpc, decreases with increasing distance from the centre and remains constant around $\approx 3$ over 20–50 kpc, before tentatively declining further out. This constant ratio could indicate that the Mg II emission in the inner region of the halo does not originate solely from scattering of ionizing photons produced in the stellar disc, but could have a non-negligible *in situ* component through collisional ionization similar to the [O II] emission. The resulting Mg II photons can subsequently undergo scattering in the outer halo, leading to a flatter SB profile.

Indeed, as noted in Section 4.1, it can be seen from Fig. 21 that the Mg II SB profile is shallower than the [O II] SB profile on average. This suggests that the resonant Mg II emission is more likely to be affected by dust and radiative transfer effects compared to the non-resonant, collisionally excited [O II] emission, leading to the observed flattening. Studies of individual systems with coverage of both the

<figure><img src="image_23.png" /><figcaption>**Figure 21.** The top panel compares the Mg II and the [O II] SB profiles. The mean- and median-stacked azimuthally averaged radial SB profiles of Mg II emission in circular annuli of 10 kpc from the galaxy centres for the full sample are shown in light blue and dark blue, respectively. Similarly, the mean- and median-stacked SB profiles of [O II] emission are shown in pink and red, respectively. The error bars represent the $1\sigma$ uncertainties from bootstrapping analysis. The bottom panel shows the ratio of the SB of [O II] to Mg II, in grey for the mean profiles and in black for the median profiles.</figcaption></figure>

lines in the literature have also found that the Mg II SB profiles are flatter than the [O II] ones (Zabl et al. 2021; Leclercq et al. 2022). Currently, there are no studies that have compared the Mg II and [O II] halo emission around galaxies in cosmological simulations. Such a comparison would place useful constraints on the possible physical mechanisms leading to the extended Mg II and [O II] emission around galaxies.

Next, we can obtain an estimate of the electron density using the ratio of the intensities of the [O II] doublet lines, $\lambda3729/\lambda3727$, which varies between 0.35 in the high density limit and 1.5 in the low density limit (Osterbrock 1989). We fit the [O II] emission line extracted from the median-stacked cube of the full sample (see Fig. 2) with a double Gaussian profile (with the wavelength difference between the two Gaussian components fixed to that of the [O II] doublet). We find that the ratio of the intensity of the doublet lines is $1.3 \pm 0.1$ in the central 10 kpc region and marginally increases to $1.5 \pm 0.4$ in the outer annulus region between 30 and 40 kpc, suggesting that the density is declining with increasing distance into the halo. Following Sanders et al. (2016), we estimate that the above [O II] doublet ratios imply that the average electron density at $z \approx 1$ is $\lesssim 100 \text{ cm}^{-3}$. This is similar to what has been found for star-forming field galaxies at $z \approx 1–1.5$ (Harshan et al. 2020; Davies et al. 2021).

The intrinsic flux ratio of the Mg II emission doublet lines, $\lambda2796/\lambda2803$, would be 2 if the excitation is dominated by collisions, and would be $\approx 1$ if the excitation is dominated by photon absorption (Sigut & Pradhan 1995; Prochaska et al. 2011b). While the stacked spectrum in the central $\approx 10$ kpc region shows Mg II in both emission and absorption, the spectra in the outer region (10–30 kpc) show Mg II emission and no prominent absorption signatures (see Fig. 2), suggesting that the Mg II gas in the halo is likely to be optically thin. From double Gaussian fits (with the wavelength difference between the two Gaussian components fixed to that of the Mg II doublet) to the stacked Mg II emission lines, the flux ratio is $1.5 \pm 0.1$ and $1.7 \pm 0.2$ in the annular region between 10–20 and 20–30 kpc, respectively. The ratio being close to 2 suggests that the extended Mg II emission could indeed be produced in part through collisional excitation *in situ*. The Mg II gas in the halo could then absorb and scatter the
intrinsic light, decreasing the flux ratio from the intrinsic value of 2. Detailed kinematic modelling of the spatially resolved emission would help to test such a scenario.

Next, we discuss and compare the dependence of the metal-enriched halo gas, as probed through emission and absorption lines, on redshift, stellar mass, and environment. Both the Mg II and [O II] SB profiles are brighter and more extended at $1 < z \le 1.5$ compared to at $0.7 \le z \le 1.0$. It is interesting to note that the covering fractions of the more diffuse halo gas probed using Mg II and C IV absorption within the virial radius of galaxies are found to be larger at $z > 1$ compared to at $z \le 1$, indicating a more extended metal-enriched halo at higher redshifts (Lan 2020; Dutta et al. 2021). This dependence of the halo gas on redshift, found independently using emission and absorption probes, could be arising from the higher SFR, ionizing radiation, or cool gas density at higher redshifts. Indeed, after matching the samples in SFR, we find that the metal SB profiles in the two redshift bins become consistent within the uncertainties, indicating that this dependence could be mainly driven by the redshift evolution of SFR.

Furthermore, the extents of the Mg II and the [O II] emission evolve with stellar mass, increasing by a factor of ≈2 from $M_* = 10^{7-8}$ to $10^{10-12} M_\odot$ at a fixed SB limit. While the central SB of Mg II emission does not show any significant dependence on stellar mass, the central SB of [O II] emission increases by a factor of ≈3 going from $M_* = 10^{7-8}$ to $10^{10-12} M_\odot$. The increase in emission line extent with stellar mass is consistent with absorption line studies finding that more massive galaxies show on average larger equivalent width and covering fraction of Mg II absorbing halo gas (e.g. Rubin et al. 2018; Dutta et al. 2021). The more massive galaxies could be populating their haloes with larger amount of metals, e.g. through outflows.

Another complementary result between emission and absorption line studies is the dependence of the gas distribution on the galaxy environment. The metal line SB profiles, [O II] to a greater extent than Mg II, are brighter and more extended around group galaxies compared to around single galaxies. Consistently, overdense group environments have been shown to be associated with stronger and more prevalent Mg II absorption, on average, compared to single galaxies (e.g. Bordoloi et al. 2011; Nielsen et al. 2018; Fossati et al. 2019b; Dutta et al. 2020, 2021). These studies propose that this could be due to tidal or ram-pressure stripping, as also suggested by detections of extended [O II] emission around individual galaxies in group environments in this work.

# 6 SUMMARY AND CONCLUSIONS

We have presented a study of the extended metal emission around galaxies, traced by the rest-frame optical Mg II and [O II] doublet lines, using MUSE IFU data from two large, blind galaxy surveys, MAGG and MUDF. To probe the average metal line emission around galaxies, we have conducted a stacking analysis of the MUSE 3D data totalling ≈6000–7000 h of ≈600 galaxies over the stellar mass range of $10^{6-12} M_\odot$ and over the redshift range of $0.7 \le z \le 1.5$. To check whether the metal emission traces the halo, we have compared the average metal line emission with the average stellar continuum emission in control windows. We have investigated the dependence of the average Mg II and [O II] emission around galaxies on redshift, stellar mass, environment, and orientation. In addition, we have searched for extended Mg II and [O II] line emission in a sample of group galaxies using CUBEx. Finally, we have compared our results with those obtained from observations in the literature and the TNG50 simulation. Below we summarize the key results from this study.

(i) Significant Mg II and [O II] line emission is detected out to ≈30 and ≈40 kpc, respectively, from the galaxies on average in the stacked NB images and SB radial profiles. This metal emission is radially more extended than the average stellar continuum emission, which extends up to ≈15 kpc, and therefore it traces the metal-enriched halo gas. The [O II] emission is more centrally peaked, while the Mg II emission profile is shallower. The [O II]/Mg II SB ratio is ≈40 in the central region and decreases to ≈3 beyond 20 kpc. The total luminosity of the average Mg II and the [O II] emission at $z \approx 1$ from the halo region (≈15–30 kpc) is ≈6 × $10^{39}$ erg s⁻¹ and ≈2 × $10^{40}$ erg s⁻¹, respectively.

(ii) The Mg II and [O II] emission around galaxies becomes brighter and more extended at higher redshifts. In particular, the Mg II and [O II] SB profiles are intrinsically brighter by a factor of ≈2–3 and more radially extended at the observed SB limit by a factor of ≈1.3 at 1.0 < z ≤ 1.5 than at 0.7 < z ≤ 1.0. Our control analysis indicates that this redshift evolution in the metal emission could be related to galaxies having higher SFR at $z > 1$, which could be leading to a higher local radiation field and gas density.

(iii) The extent of the Mg II and [O II] emission around galaxies shows an increasing trend with the stellar mass of the galaxies. The SB profiles become more radially extended by a factor of ≈2 on going from the lowest stellar mass bin ($10^{7-8} M_\odot$) to the highest stellar mass bin ($10^{10-12} M_\odot$). The [O II] emission in the central region also becomes brighter by a factor of ≈3, while the central Mg II emission does not show any strong dependence on stellar mass. The dependence of the metal emission on stellar mass could be due to the larger metal enrichment in the haloes of more massive galaxies because of stronger feedback.

(iv) The Mg II SB profile around a sample of group galaxies, identified through a FoF technique, is brighter by a factor of ≈1.4 on average within 30 kpc, while the [O II] SB profile is more extended by a factor of ≈1.6 compared to that around a sample of isolated galaxies that is matched in stellar mass and redshift. This enhancement could be due to interactions in the group environment, as also indicated by observations of extended [O II] emission around individual galaxies in groups.

(v) For a subsample of ≤60 galaxies at inclination ≥30° in the MUDF with deep HST imaging and morphological parameters, the [O II] SB profile is brighter over ≈30–40 kpc and more extended by a factor of ≈1.3 along the major axis of the disc compared to that along the minor axis. No significant dependence on orientation is found for the Mg II emission. However, these results need to be verified using a larger galaxy sample with morphological measurements.

(vi) Extended (≈10–50 kpc) [O II] emission is detected around ≈32 per cent and ≈40 per cent of galaxies in group environments (comprising three or more galaxies) in MAGG and MUDF surveys, respectively. Further, extended [O II] emission connecting seven galaxies in a $z = 1.0$ group is detected across ≈200 kpc in the MUDF survey. Extended (≈30–40 kpc) Mg II emission is detected only around two active galaxies (quasars) in the sample (≈1 per cent). Environmental processes (tidal or ram-pressure stripping) or outflows could be responsible for the extended metal line emission detected around the galaxies in overdense group environments.

(vii) There are differences in the stacked Mg II radial SB profiles obtained from our study and those obtained using TNG50 simulations. Specifically, unlike the simulated profiles, the central SB of the observed profiles do not show a strong increasing trend with stellar mass, and the observed profiles are flatter. Two key modelling assumptions – neglecting resonant scattering and the impact of dust – likely drive these differences. However, there is an overall agreement
intrinsic light, decreasing the flux ratio from the intrinsic value of 2. Detailed kinematic modelling of the spatially resolved emission would help to test such a scenario.

Next, we discuss and compare the dependence of the metal-enriched halo gas, as probed through emission and absorption lines, on redshift, stellar mass, and environment. Both the Mg II and [O II] SB profiles are brighter and more extended at $1 < z \le 1.5$ compared to at $0.7 \le z \le 1.0$. It is interesting to note that the covering fractions of the more diffuse halo gas probed using Mg II and C IV absorption within the virial radius of galaxies are found to be larger at $z > 1$ compared to at $z \le 1$, indicating a more extended metal-enriched halo at higher redshifts (Lan 2020; Dutta et al. 2021). This dependence of the halo gas on redshift, found independently using emission and absorption probes, could be arising from the higher SFR, ionizing radiation, or cool gas density at higher redshifts. Indeed, after matching the samples in SFR, we find that the metal SB profiles in the two redshift bins become consistent within the uncertainties, indicating that this dependence could be mainly driven by the redshift evolution of SFR.

Furthermore, the extents of the Mg II and the [O II] emission evolve with stellar mass, increasing by a factor of ≈2 from $M_* = 10^{7-8}$ to $10^{10-12} M_\odot$ at a fixed SB limit. While the central SB of Mg II emission does not show any significant dependence on stellar mass, the central SB of [O II] emission increases by a factor of ≈3 going from $M_* = 10^{7-8}$ to $10^{10-12} M_\odot$. The increase in emission line extent with stellar mass is consistent with absorption line studies finding that more massive galaxies show on average larger equivalent width and covering fraction of Mg II absorbing halo gas (e.g. Rubin et al. 2018; Dutta et al. 2021). The more massive galaxies could be populating their haloes with larger amount of metals, e.g. through outflows.

Another complementary result between emission and absorption line studies is the dependence of the gas distribution on the galaxy environment. The metal line SB profiles, [O II] to a greater extent than Mg II, are brighter and more extended around group galaxies compared to around single galaxies. Consistently, overdense group environments have been shown to be associated with stronger and more prevalent Mg II absorption, on average, compared to single galaxies (e.g. Bordoloi et al. 2011; Nielsen et al. 2018; Fossati et al. 2019b; Dutta et al. 2020, 2021). These studies propose that this could be due to tidal or ram-pressure stripping, as also suggested by detections of extended [O II] emission around individual galaxies in group environments in this work.

# 6 SUMMARY AND CONCLUSIONS

We have presented a study of the extended metal emission around galaxies, traced by the rest-frame optical Mg II and [O II] doublet lines, using MUSE IFU data from two large, blind galaxy surveys, MAGG and MUDF. To probe the average metal line emission around galaxies, we have conducted a stacking analysis of the MUSE 3D data totalling ≈6000–7000 h of ≈600 galaxies over the stellar mass range of $10^{6-12} M_\odot$ and over the redshift range of $0.7 \le z \le 1.5$. To check whether the metal emission traces the halo, we have compared the average metal line emission with the average stellar continuum emission in control windows. We have investigated the dependence of the average Mg II and [O II] emission around galaxies on redshift, stellar mass, environment, and orientation. In addition, we have searched for extended Mg II and [O II] line emission in a sample of group galaxies using CUBEx. Finally, we have compared our results with those obtained from observations in the literature and the TNG50 simulation. Below we summarize the key results from this study.

(i) Significant Mg II and [O II] line emission is detected out to ≈30 and ≈40 kpc, respectively, from the galaxies on average in the stacked NB images and SB radial profiles. This metal emission is radially more extended than the average stellar continuum emission, which extends up to ≈15 kpc, and therefore it traces the metal-enriched halo gas. The [O II] emission is more centrally peaked, while the Mg II emission profile is shallower. The [O II]/Mg II SB ratio is ≈40 in the central region and decreases to ≈3 beyond 20 kpc. The total luminosity of the average Mg II and the [O II] emission at $z \approx 1$ from the halo region (≈15–30 kpc) is ≈6 × $10^{39}$ erg s⁻¹ and ≈2 × $10^{40}$ erg s⁻¹, respectively.

(ii) The Mg II and [O II] emission around galaxies becomes brighter and more extended at higher redshifts. In particular, the Mg II and [O II] SB profiles are intrinsically brighter by a factor of ≈2–3 and more radially extended at the observed SB limit by a factor of ≈1.3 at 1.0 < z ≤ 1.5 than at 0.7 < z ≤ 1.0. Our control analysis indicates that this redshift evolution in the metal emission could be related to galaxies having higher SFR at $z > 1$, which could be leading to a higher local radiation field and gas density.

(iii) The extent of the Mg II and [O II] emission around galaxies shows an increasing trend with the stellar mass of the galaxies. The SB profiles become more radially extended by a factor of ≈2 on going from the lowest stellar mass bin ($10^{7-8} M_\odot$) to the highest stellar mass bin ($10^{10-12} M_\odot$). The [O II] emission in the central region also becomes brighter by a factor of ≈3, while the central Mg II emission does not show any strong dependence on stellar mass. The dependence of the metal emission on stellar mass could be due to the larger metal enrichment in the haloes of more massive galaxies because of stronger feedback.

(iv) The Mg II SB profile around a sample of group galaxies, identified through a FoF technique, is brighter by a factor of ≈1.4 on average within 30 kpc, while the [O II] SB profile is more extended by a factor of ≈1.6 compared to that around a sample of isolated galaxies that is matched in stellar mass and redshift. This enhancement could be due to interactions in the group environment, as also indicated by observations of extended [O II] emission around individual galaxies in groups.

(v) For a subsample of ≤60 galaxies at inclination ≥30° in the MUDF with deep HST imaging and morphological parameters, the [O II] SB profile is brighter over ≈30–40 kpc and more extended by a factor of ≈1.3 along the major axis of the disc compared to that along the minor axis. No significant dependence on orientation is found for the Mg II emission. However, these results need to be verified using a larger galaxy sample with morphological measurements.

(vi) Extended (≈10–50 kpc) [O II] emission is detected around ≈32 per cent and ≈40 per cent of galaxies in group environments (comprising three or more galaxies) in MAGG and MUDF surveys, respectively. Further, extended [O II] emission connecting seven galaxies in a $z = 1.0$ group is detected across ≈200 kpc in the MUDF survey. Extended (≈30–40 kpc) Mg II emission is detected only around two active galaxies (quasars) in the sample (≈1 per cent). Environmental processes (tidal or ram-pressure stripping) or outflows could be responsible for the extended metal line emission detected around the galaxies in overdense group environments.

(vii) There are differences in the stacked Mg II radial SB profiles obtained from our study and those obtained using TNG50 simulations. Specifically, unlike the simulated profiles, the central SB of the observed profiles do not show a strong increasing trend with stellar mass, and the observed profiles are flatter. Two key modelling assumptions – neglecting resonant scattering and the impact of dust – likely drive these differences. However, there is an overall agreement
in trends between the observational and simulation results given the many complex physical processes at play.

This work demonstrates that we are now able to probe the CGM around normal star-forming galaxies directly in emission using the power of deep and large IFU surveys such as MAGG and MUFD. We have presented here the first characterization of the average metal-emitting halo gas around galaxies at $0.7 \le z \le 1.5$. The stacking results found in this work complement studies of the more diffuse metal-enriched halo gas probed in absorption around $z < 2$ galaxies (Dutta et al. 2020, 2021). A combination of these two different approaches in the future, for a general galaxy population and also for individual systems, will lead to richer constraints on galaxy formation models.

Based on the stacking analysis in this work, the average [O II] doublet ratio in the halo (≈10–40 kpc annular region) suggests average electron densities $\le 100 \text{ cm}^{-3}$, while the Mg II doublet ratio and the [O II]/Mg II ratio in the halo point towards *in situ* collisional ionization, with subsequent scattering of the Mg II photons, both playing an important role in the origin of the extended emission. Detailed modelling of the spatially resolved morphokinematics of the extended metal emission is required to place more robust constraints on the potential physical mechanisms and gas conditions. Large galaxy surveys with 4-metre Multi-Object Spectrograph Telescope (4MOST; de Jong et al. 2019), Dark Energy Spectroscopic Instrument (DESI; DESI Collaboration 2016), Hobby-Eberly Telescope (HET; Gebhardt et al. 2021), Multi-Object Optical and Near-infrared Spectrograph (MOONS; Cirasuolo et al. 2014), the Prime Focus Spectrograph (PFS; Tamura et al. 2016), and the WHT Enhanced Area Velocity Explorer (WEAVE; Jin et al. 2023), deep observations of individual systems with Enhanced Resolution Imager and Spectrograph (ERIS; Davies et al. 2018), JWST (Gardner et al. 2006), KCWI (Morrissey et al. 2018), and MUSE (Bacon et al. 2010), and with future instruments such as Extremely Large Telescope (ELT)/High Angular Resolution Monolithic Optical and Near-infrared Integral field spectrograph (HARMONI; Thatte et al. 2021), Magellan Infrared Multi-Object Spectrograph (MIRMOS; Konidaris et al. 2020), and VLT/BlueMUSE (Richard et al. 2019), will allow us to obtain multiple diagnostics and interpret the physical mechanisms driving the extended emission.

## ACKNOWLEDGEMENTS

We thank the reviewer for their helpful comments. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Framework Programme (grant agreement no. 757535) and by Fondazione Cariplo (grant no. 2018-2329). DN acknowledges funding from the Deutsche Forschungs-gemeinschaft (DFG) through an Emmy Noether Research Group (grant number NE 2441/1-1). SC gratefully acknowledges support from the Swiss National Science Foundation grant PP00P2 190092 and from the ERC under the European Union's Horizon 2020 Framework Programme (grant agreement no. 864361). PD acknowledges support from the NWO grant 016.VIDI.189.162 ('ODIN') and from the European Commission's and University of Groningen's CO-FUND Rosalind Franklin program. This work is based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme IDs 197.A-0384, 065.O-0299, 067.A-0022, 068.A-0461, 068.A-0492, 068.A-0600, 068.B-0115, 069.A-0613, 071.A-0067, 071.A-0114, 073.A-0071, 073.A-0653, 073.B-0787, 074.A-0306, 075.A-0464, 077.A-0166, 080.A-0482, 083.A-0042, 091.A-0833, 092.A-0011, 093.A-

0575, 094.A-0280, 094.A-0131, 094.A-0585, 095.A-0200, 096.A-0937, 097.A-0089, 099.A-0159, 166.A-0106, 189.A-0424, 094.B-0304, 096.A-0222, 096.A-0303, 103.A-0389, and 1100.A-0528. Based on observations with the NASA/ESA Hubble Space Telescope obtained, from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS 5-26555. Support for Program numbers 15637 and 15968 was provided through grants from the STScI under NASA contract NAS 5-26555. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC Operations grant ST/K003267/1, and Durham University. DiRAC is part of the National E-Infrastructure. This research has made use of the following PYTHON packages: NUMPY (Harris et al. 2020), SCIPY (Virtanen et al. 2020), MATPLOTLIB (Hunter 2007), and ASTROPY (Astropy Collaboration 2013).

## DATA AVAILABILITY

The MUSE data used in this work are available from the European Southern Observatory archive (https://archive.eso.org). The MUSE ESO P3 level data of the MAGG survey are available at https://archive.eso.org/scienceportal/home?data_collection=197.A-0384&publ_date=2022-11-14. The HST data used in this work are available from the MAST archive (https://mast.stsci.edu). The IllustrisTNG simulations, including TNG50, are publicly available and accessible at www.tng-project.org/data (Nelson et al. 2019a).

## REFERENCES

Arrigoni Battaia F., Hennawi J. F., Prochaska J. X., Oñorbe J., Farina E. P., Cantalupo S., Lusso E., 2019, MNRAS, 482, 3162

Astropy Collaboration, 2013, A&A, 558, A33

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Augustin R., Péroux C., Hamanowicz A., Kulkarni V., Rahmani H., Zanella A., 2021, MNRAS, 505, 6195

Ayromlou M., Nelson D., Pillepich A., 2022, preprint (arXiv:2211.07659)

Bacon R. et al., 2010, in McLean I. S., Ramsay S. K., Takami H., eds, Proc. SPIE Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III. SPIE, Bellingham, p. 773508

Bacon R. et al., 2021, A&A, 647, A107

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Berg M. A. et al., 2023, ApJ, 944, 101

Bertin E., Arnouts S., 1996, A&AS, 117, 393

Bertone S., Schaye J., 2012, MNRAS, 419, 780

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Borisova E. et al., 2016, ApJ, 831, 39

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Bruzual G., Charlot S., 2003, MNRAS, 344, 1000

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Byler N., Dalcanton J. J., Conroy C., Johnson B. D., Levesque E. M., Berg D. A., 2018, ApJ, 863, 14
in trends between the observational and simulation results given the
many complex physical processes at play.

This work demonstrates that we are now able to probe the CGM
around normal star-forming galaxies directly in emission using the
power of deep and large IFU surveys such as MAGG and MUFD. We
have presented here the first characterization of the average metal-
emitting halo gas around galaxies at 0.7 $\le$ z $\le$ 1.5. The stacking
results found in this work complement studies of the more diffuse
metal-enriched halo gas probed in absorption around z < 2 galaxies
(Dutta et al. 2020, 2021). A combination of these two different
approaches in the future, for a general galaxy population and also for
individual systems, will lead to richer constraints on galaxy formation
models.

Based on the stacking analysis in this work, the average [O II] doublet ratio in the halo (≈10–40 kpc annular region) suggests average electron densities $\le$100 cm$^{-3}$, while the Mg II doublet ratio and the [O II]/Mg II ratio in the halo point towards *in situ* collisional ionization, with subsequent scattering of the Mg II photons, both playing an important role in the origin of the extended emission. Detailed modelling of the spatially resolved morphokinematics of the extended metal emission is required to place more robust constraints on the potential physical mechanisms and gas conditions. Large galaxy surveys with 4-metre Multi-Object Spectrograph Telescope (4MOST; de Jong et al. 2019), Dark Energy Spectroscopic Instrument (DESI; DESI Collaboration 2016), Hobby-Eberly Telescope (HET; Gebhardt et al. 2021), Multi-Object Optical and Near-infrared Spectrograph (MOONS; Cirasuolo et al. 2014), the Prime Focus Spectrograph (PFS; Tamura et al. 2016), and the WHT Enhanced Area Velocity Explorer (WEAVE; Jin et al. 2023), deep observations of individual systems with Enhanced Resolution Imager and Spectrograph (ERIS; Davies et al. 2018), JWST (Gardner et al. 2006), KCWI (Morrissey et al. 2018), and MUSE (Bacon et al. 2010), and with future instruments such as Extremely Large Telescope (ELT)/High Angular Resolution Monolithic Optical and Near-infrared Integral field spectrograph (HARMONI; Thatte et al. 2021), Magellan Infrared Multi-Object Spectrograph (MIRMOS; Konidaris et al. 2020), and VLT/BlueMUSE (Richard et al. 2019), will allow us to obtain multiple diagnostics and interpret the physical mechanisms driving the extended emission.

ACKNOWLEDGEMENTS

We thank the reviewer for their helpful comments. This project has
received funding from the European Research Council (ERC) under
the European Union's Horizon 2020 Framework Programme (grant
agreement no. 757535) and by Fondazione Cariplo (grant no. 2018-
2329). DN acknowledges funding from the Deutsche Forschungsge-
meinschaft (DFG) through an Emmy Noether Research Group (grant
number NE 2441/1-1). SC gratefully acknowledges support from
the Swiss National Science Foundation grant PP00P2 190092 and
from the ERC under the European Union's Horizon 2020 Framework
Programme (grant agreement no. 864361). PD acknowledges support
from the NWO grant 016.VIDI.189.162 ('ODIN') and from the
European Commission's and University of Groningen's CO-FUND
Rosalind Franklin program. This work is based on observations
collected at the European Organisation for Astronomical Research
in the Southern Hemisphere under ESO programme IDs 197.A-
0384, 065.O-0299, 067.A-0022, 068.A-0461, 068.A-0492, 068.A-
0600, 068.B-0115, 069.A-0613, 071.A-0067, 071.A-0114, 073.A-
0071, 073.A-0653, 073.B-0787, 074.A-0306, 075.A-0464, 077.A-
0166, 080.A-0482, 083.A-0042, 091.A-0833, 092.A-0011, 093.A-

0575, 094.A-0280, 094.A-0131, 094.A-0585, 095.A-0200, 096.A-0937, 097.A-0089, 099.A-0159, 166.A-0106, 189.A-0424, 094.B-0304, 096.A-0222, 096.A-0303, 103.A-0389, and 1100.A-0528. Based on observations with the NASA/ESA Hubble Space Telescope obtained, from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS 5-26555. Support for Program numbers 15637 and 15968 was provided through grants from the STScI under NASA contract NAS 5-26555. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC Operations grant ST/K003267/1, and Durham University. DiRAC is part of the National E-Infrastructure. This research has made use of the following PYTHON packages: NUMPY (Harris et al. 2020), SCIPY (Virtanen et al. 2020), MATPLOTLIB (Hunter 2007), and ASTROPY (Astropy Collaboration 2013).

DATA AVAILABILITY

The MUSE data used in this work are available from the European Southern Observatory archive (https://archive.eso.org). The MUSE ESO P3 level data of the MAGG survey are available at https://archive.eso.org/scienceportal/home?data_collection=197.A-0384&publ_date = 2022-11-14. The HST data used in this work are available from the MAST archive (https://mast.stsci.edu). The IllustrisTNG simulations, including TNG50, are publicly available and accessible at www.tng-project.org/data (Nelson et al. 2019a).

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This paper has been typeset from a TeX/LATEX file prepared by the author.