For a long time, open clusters (OCs) have been used to trace the kinematical, dynamical, and chemical evolution of the galaxy (Allen et al., 1998; Minchev et al., 2014; Bobylev et al., 2019). Since OCs span a wide range of ages and chemical compositions and mostly lie in the galactic plane, they are identified as tracers of the galactic disk (Luck et al., 2011; Toyouchi and Masashi, 2014; Joshi and Malhotra, 2023). As the ages and chemical compositions of OCs can be determined with a higher precision in comparison to the field stars, they are believed to be better tracers of the temporal and chemical evolution of the galactic properties (Netopil, 2016; Magrini et al., 2017; Donor, 2018; Spina, 2021; Zhang et al., 2021; Netopil, 2022). With over 6,000 OCs discovered in the galaxy so far, we now have a much better understanding of their properties and, as a result, of the composition of the galaxy (Joshi and Malhotra, 2023; Magrini, 2023). In recent years, the number of OCs having metallicity information has increased significantly, with large-scale spectroscopic surveys such as the Gaia-ESO Public Spectroscopic Survey (Magrini et al., 2017), GALAH (Martell et al., 2017), APOGEE (Majewski et al., 2017; Donor, 2020), and the LAMOST survey (Zhong et al., 2020). Furthermore, due to the availability of high-quality photometric and astrometric data from the ESA Gaia mission (Gaia Collaboration et al., 2016), significant improvement has been made in the ability to refine the cluster membership, resulting in a better estimate of age and distance, among other parameters (e.g., Cantat-Gaudin, 2018; Cantat-Gaudin et al., 2020; Dias et al., 2021).

Radial abundance gradient is one of the key constraints to the galactic chemical evolution models. The exact nature of the radial metallicity gradient, reported through various tracers like planetary nebulae, HII region, OB stars, and classical Cepheids, is still not quite conclusive and portrays a diverse picture of the chemical evolution of the galaxy (e.g., Andrievsky, 2002; Daflon and Cunha, 2004; Maciel et al. 2005; Lemasle, 2008; Maciel et al. 2010; Genovali et al. 2014; da Silva, 2023, and references therein). However, having an extensive range in age, distance, and chemical composition, OCs are regarded as a better tracer than other such sources (Chen, 2008; Friel 2013; Magrini. 2023). Various studies have been carried out in the last 2 decades to study the chemical evolution of the galactic disk using OCs (e.g., Friel et al. 2002; Chen et al. 2003; Bragaglia, 2008; Friel et al. 2010; Carrera et al. 2011; Yong et al. 2012a; Frinchaboy et al. 2013a; Reddy et al. 2016; Netopil, 2016; Magrini et al. 2017). However, the main advancement came after the recent release of three large-scale surveys, namely, Gaia-ESO (Randich, 2022), GALactic Archeology with HERMES (Martell et al. 2017), and Apache Point Observatory Galactic Evolution Experiment (Majewski et al. 2017), which resulted in the estimation of more complete and precise chemical compositions of a large number of OCs (Carrera et al. 2019; Donor, 2020; Zhong et al, 2020; Spina, 2021; Zhang et al. 2021; Myers et al. 2022a; Netopil, 2022; Spina et al. 2022; Magrini, 2023). These studies have obtained a single-slope radial metallicity gradient ranging from −0.051 to −0.077 dex/kpc while employing a two-function radial metallicity gradient, and they obtained a steeper slope in the range of −0.054 to −0.081 dex/kpc for the younger and inner region of the clusters and a shallower slope of 0.009 to 0.044 dex/kpc for the older and outer region of the clusters, which is also supported by the inside-out disk formation models. The intersection point or knee point in such two-function slopes also varies between 11 and 12 kpc among different studies. The age–metallicity relation is another important constraint on the theoretical models of the galactic disk and has been studied by various authors using different stellar populations (e.g., Friel 1995; Carraro et al. 1998; Feltzing et al., 2001). Except for a few studies like Edvardsson et al. (1993), Chen et al. (2003), and Zhong et al. (2020), most of the studies found no obvious AMR for the OC population (Friel et al. 2010; Yong et al. 2012b; Netopil, 2016; Magrini et al. 2017; Zhang et al. 2021).

Considering a wide range of galactic chemical evolution parameters among different studies, the prime motive of the present work is to form a more extensive set of OCs having chemical compositions available through recent photometric and spectroscopic surveys, thus extending the sample with a wide range in the age and galactocentric distance. Despite extracting cluster parameters from different sources, hence making a heterogeneous data set, we trust that a statistical analysis on a larger sample of OCs would not lead to any systematic bias in our results. This paper is structured as follows: we describe the data used in the present work in Section 1. The metallicity distribution of OCs is analyzed in Section 2. The cluster age–metallicity relation is examined in Section 3. In Section 4, we investigate various correlations between radial and vertical metallicity gradients with the age and positions of the OCs. Our results are summarized in Section 5.

To understand the chemical evolution of the galaxy, particularly the galactic disk, over the last few billion years, a large and homogeneous sample of OCs with measured metallicity and age is required. For this purpose, we searched the literature for OCs with known metallicity along with other information like position coordinates, radial distances, and age. It may be noted here that we have used the term metallicity for iron abundance [Fe/H] (relative to the solar abundance) throughout this study. Most of the OC metallicity estimates reported prior to 2018 are either based on photometric techniques (Kharchenko, 2013) or low-resolution spectroscopic data (e.g., Netopil, 2016, and references therein). Additionally, over the years, many of the clusters have been studied repeatedly, and thus, metallicity estimates for these clusters are available based on different techniques, spectral resolutions, and data qualities. To create a comprehensive list of OCs with the best available metallicity estimate, we started by collecting all the metallicity estimates along with other related information like the method of estimation (photometric or spectroscopic), spectral resolution, signal-to-noise ratio (SNR), number of member stars used for average metallicity estimation, and the year of reporting from all the major studies published in the last three decades. This resulted in a total of 4,772 metallicity reports for known OCs, Baratella, 2020; Bragaglia, 2008; Caetano, 2015; Carraro, 2004; Carraro G. et al., 2007; Carraro Giovanni et al., 2007; Carraro, 2008; Carrera, 2012; Carrera et al., 2015; Carrera et al., 2019; Casamiquela et al., 2019; Casamiquela et al., 2021; Claria et al., 1989; Clariá, 2003; Clariá, 2008; Conrad, 2014; D’Orazi et al., 2009; De Silva et al., 2007; De Silva, 2015; Dias et al., 2021; Donati et al., 2015a; Donor, 2018; Donor, 2020; Ford et al., 2005; Fossati, 2011; Friel and Boesgaard, 1992; Friel et al., 2002; Frinchaboy, 2004; Frinchaboy, 2013b; Fu et al., 2022; Geisler et al., 2012; Gonzalez and George, 2000; Gratton et al., 1994; Hasegawa et al., 2008; Hill et al., 1999; Jacobson et al., 2008; Jacobson and Eileen, 2013; Krisciunas et al., 2015; Luck 1994; Magrini, 2010; Magrini et al., 2018; Margheim, 2000; Monroe and Catherine, 2010; Myers, 2022b; Netopil et al., 2013; Netopil, 2016; Netopil, 2022; Overbeek et al., 2016; Pasquini et al., 2004; Paunzen et al., 2003; Paunzen, 2010; Pereira et al., 2010; Piatti et al., 1995; Randich, 2022; Reddy et al., 2013; Santos, 2009; Santos, 2012; Schuler, 2003; Sestito et al., 2003; Spina, 2021; Twarog et al., 1997; Vansevicius, 1997; Villanova et al., 2005; Warren and Cole, 2009; Yong et al., 2012a; Začs et al., 2011; Zhong et al., 2020; and the reference therein, which also includes multiple reporting from different studies for some clusters. To avoid duplication of OCs in the list because of the use of different identifiers for a cluster in different studies, we used the astroquery.simbad package to detect and assign a common name to all such duplicates. As a secondary measure, we manually searched and checked all the possible duplicates with a spatial angular distance of less than 0.1° along with a maximum difference of 5 milli-arcsec in the OC’s proper motion. This helped us in detecting and eliminating five more duplicate OC pairs: Berkeley 85–Dolidze 41, COIN-Gaia23–Majaess 65, NGC 1746–NGC 1750, vdBergh-Hagen 72–UBC 491, and vdBergh-Hagen 84–Gulliver 35. Some of the other OC pairs, like UBC 55–FSR 686 and UBC 73–Gulliver 56, have very small separations in phase space but are confirmed as different clusters in previous studies. For example, Piecka et al., 2021 suggested that UBC 55 and FSR 686 are a possible pair of binary clusters, while UBC 73 and Gulliver 56 are also different clusters.

To select the best unique metallicity estimate from multiple reporting for each of the clusters, we selected the metallicity estimates by giving higher priority to spectroscopic studies (compared to the photometric metallicity estimate), followed by the highest spectral resolution, highest SNR, highest number of member stars used to find the average metallicity for the OC, smallest error in the reported metallicity, and latest reporting. This resulted in a final sample of 1,879 unique OCs with the best available metallicity estimates, of which 615 have metallicity estimates based on spectroscopic data (hereafter sample OCS, where “S” stands for spectroscopic) and the remaining 1,264 have metallicity estimates based on the photometric data (hereafter sample OCP, where “P” stands for photometric).

Like metallicity selection, we selected the best-quality astrometric and age data for each cluster from multiple reporting by prioritizing the most recent publication. During the selection, studies that also provide measurement uncertainties were preferred. From our final sample of 1,879 unique clusters, astrometric data (including distance information) are available for all the clusters, while age is available for all but one cluster. However, uncertainty estimates in age and metallicity parameters for all the clusters could not be found; therefore, any weighted statistical analysis cannot be done in the present study.

Adopting the galactocentric distance of the Sun, R_⊙, as 8.15 kpc (Reid, 2019), we calculated the galactocentric distance of the cluster using the following well-known transformation relation: R GC = R ⊙ 2 + d c o s b 2 − 2 R ⊙ d c o s l c o s b , (1)

where d, l, and b are the heliocentric distance, galactic longitude, and galactic latitude, respectively. We also used the rectangular coordinate system (X, Y, and Z), which is defined as X = d cos(b) cos(l), Y = d cos(b) sin(l), and Z = d sin(b). The most distant cluster with metallicity information is at R _GC = 20.38 kpc, and only nine OCs are seen beyond R _GC = 14 kpc. This reveals either a lack of OCs in the outer galactic disk or observational limitations to observe such clusters due to large extinction along the line of sight. Additionally, the number of OCs decreases drastically as we move farther away from the heliocenter. For example, only 22 OCs are located beyond a heliocentric distance of 5 kpc, further suggesting that the drop in OC number with a radial distance is primarily linked to the detection limits (e.g., Joshi, 2016).

The metallicity in our cluster sample ranges from approximately −0.80 to 0.60 dex except for six OCs, namely, NGC 6204, NGC 2129, Trumpler 33, Dolidze 5, NGC 6910, and FSR 932, for which the adopted [Fe/H] based on our selection criteria are −1.05, −1.53, −1.54, −1.94, −1.96, and −2.17, respectively. For all the six clusters, the adopted metallicities are based on spectroscopic data. For NGC 6204 and Trumpler 33, metallicity estimates are adopted from Conrad (2014), which provided the metallicity estimates based on a spectral resolution of 7,500, while for NGC 2129, Dolidze 5, NGC 6910, and FSR 932, metallicity estimates are adopted from Fu et al. (2022), which provided metallicity estimates based on data from the LAMOST survey with a spectral resolution of 1,800. For NGC 2129 and NGC 6910, Zhong et al. (2020) provided independent spectroscopic metallicity estimates of −1.426 ± 0.856 and −1.97, respectively, based on data from the LAMOST survey with a spectral resolution of 1,800. For all of these six clusters, NGC 6204, NGC 2129, Trumpler 33, Dolidze 5, NGC 6910, and FSR 932, Dias et al. (2021) provided independent photometric metallicity estimates of 0.096 ± 0.004, −0.07 ± 0.01, 0.145 ± 0.016, −0.033 ± 0.033, 0.035 ± 0.008, and −0.142 ± 0.008, respectively. For NGC 6204, Netopil (2016) and Paunzen et al. (2010) also provided photometric metallicities of 0.02 and −0.14 ± 0.10, respectively. The wrong identification of cluster member stars to estimate the cluster’s average metallicity appears to be one of the main reasons for the large differences between the available spectroscopic and photometric metallicities for these six clusters. Finding the exact reason for this discrepancy is beyond the scope of this study. However, considering the unexpectedly lower metallicity and the large difference when compared to available photometric estimates for these six clusters, we exclude these six clusters from further analysis in this study. The final catalog of 1,879 OCs used in this study is provided in a machine-readable format in Table 1. Among the 1,879 clusters, 609 have metallicity estimates based on spectroscopic data (sample OCS), and the remaining 1,264 have metallicity estimates based on photometric data (sample OCP).

The metallicity functions for the sample OCP, OCS, and OCs (OCP + OCS) are shown in Figure 1. For all three cases, the Gaussian distribution fits are also drawn. The OC sample has a mean metallicity of −0.018 ± 0.004 with a sample standard deviation (σ) of 0.188. The sample of OCP has a slightly higher mean metallicity with [Fe/H] = −0.021 ± 0.005 compared to the sample of OCS, which has a mean [Fe/H] = −0.099 ± 0.007. Both OCP and OCS span an almost similar range in [Fe/H] and also have similar sample standard deviations. The small but significant difference between the mean metallicity of the sample OCP and OCS may be the result of two factors: 1) systematic offsets in the photometric metallicity estimates and 2) bias in the sample selection. Because of the unavailability of photometric data for all the cases, it is not possible to directly check for the systematic offsets in the estimated metallicities. However, as sample OCP consists of photometric metallicity estimates from many studies that provide metallicity estimates based on different sets of photometric data along with theoretical isochrones, a systematic offset in all or the majority of these studies is not expected. To examine whether bias in the sample selection is the reason behind this offset, we draw the distribution of sample OCP and OCS in the X–Y plane in the heliocentric frame in the bottom panel of Figure 2. Here, the Sun is located at (X, Y) = (0, 0) where positive X points toward the galactic center (GC) and positive Y points toward the north galactic pole. The distribution readily suggests that the OCP clusters are located more toward the GC than the clusters in OCS. This is clearer from the top panel of the figure where the density distributions of the sample OCP and OCS along X are provided. Here, the distribution for sample OCS is more negatively skewed with a skewness of −0.23, compared to sample OCP which has a skewness of −0.15, and it is understood to be due to the presence of more clusters in the anti-GC direction in sample OCS than in the sample OCP.

The age–metallicity relation (AMR) in the galactic disc is crucial to constrain the chemical evolution models, and star clusters offer an important advantage in the studies of the evolution of the galaxy because they provide a time sequence for investigating the changes that occur in our galaxy over the period of time. The large temporal range in the age and metallicity for the OCs provides useful insights related to the chemical evolution history of the galaxy and also presents a useful constraint on the various theoretical models of the disk (Friel 1995). Over the last 20 years, many studies that focus on this relation use either nearby stars (Carraro et al. 1998; Feltzing et al. 2001) or OCs (Netopil, 2016; Magrini et al. 2017; Döner, 2023). As noted in many earlier studies, there is no obvious AMR for the OC population (e.g., Friel et al. 2010; Yong et al. 2012b; Zhang et al. 2021), while some of the studies find a weak AMR (Edvardsson et al. 1993; Chen et al. 2003; Zhong et al. 2020). However, the large sample of OCs having metallicity measurements in the present study is re-employed to understand this relation in some detail.

The AMR in our sample of clusters is shown in Figure 3. The distribution readily suggests that for clusters with log(age/yr)⪅8.4, the average metallicity of clusters is near to the solar metallicity and does not change significantly over time. However, for log(age/yr)⪆8.4, the clusters’ average metallicity follows a slightly decreasing trend with an increase in log(age/yr). To find the exact age–metallicity gradients and the age turn-off point at which the metallicity gradient changes, we fitted the data with a combination of two linear regressions (i.e., stepped linear regression) in the following form: F e / H = m 1 × log a g e / y r + b 1 , log a g e / y r ≤ C , (2) F e / H = m 2 × log a g e / y r + b 2 , log a g e / y r > C , (3)

where C is the point of intersection, b₁ and b₂ are the [Fe/H]-axis intercepts, and m₁ and m₂ are slopes for the two functions. The coefficients of the fitted regressions (along with the point of intersection C and corresponding standard errors) were determined using iterative least square estimation by treating b₁, m₁, C, and m₂ as variables while assuming b₂ = (m₁ ×C + b₁). Based on the distribution in Figure 3, we assumed the initial values of b₁, m₁, C, and m₂ as 0, 0, 8.5, and −0.02, respectively. Estimated values of coefficients from each iteration were adopted as inputs for the next iteration. Along with minimizing the mean error, we also repeated the iterations until the difference between the estimated coefficients and the corresponding adopted coefficients was less than 10^–5. In addition, for each of the iterations, we also checked the distribution of the fitted metallicity residual (i.e., the observed metallicity value minus the predicted model value) as a function of log(age/yr) and found that for the final iteration, the slope and the intercept to this distribution were less than 10^–5. The final fitted function to our OC data is shown as the red line in Figure 3. The coefficients of the fitted functions are also provided in the legend of Figure 3 in the following forms: b₁, m₁, C, and m₂. Based on the sample OC, the two linear functions intersect at log(age/yr) = 8.378 ± 0.093 (i.e., an age of approximately 240 Myr), and the age–metallicity gradients are given as follows: d F e / H d ⁡ log a g e / y r = 0.014 ± 0.011 , log a g e / y r ≤ 8.378 ± 0.093 (4) d F e / H d ⁡ log a g e / y r = − 0.159 ± 0.021 , log a g e / y r > 8.378 ± 0.093 (5)

For log(age/yr) > 8.378 ± 0.093, the decrease in [Fe/H] with an increase in log(age/yr) with a slope of d [ F e / H ] d ⁡ log ( a g e / y r ) = − 0.159 ± 0.021 is equivalent to −0.031 ± 0.006 dex/Gyr. The negative slope between age and metallicity suggests that the metallicity in the interstellar medium of the galaxy gradually increased with time until approximately 240 Myrs ago. In Table 2, we compare our derived AMR slope with earlier studies that were carried out using OCs, although with a significantly smaller sample (Pancino, 2010; Zhong et al. 2020). Our present estimate is quite consistent with these studies. However, for log(age/yr) ≤ 8.378 ± 0.093, a very slightly increasing trend in [Fe/H] is seen with the increase in log(age/yr). Although it surprisingly suggests that the formation site of the younger cluster is relatively metal-poor compared to the intermediate age clusters, a slope of 0.014 at almost 1-σ level is too small to make any definite conclusion. Overall, a negative slope in AMR is in agreement with the results from previous studies that the metallicity of old-age OCs is lower than that of young and intermediate-age OCs at any given galactocentric distance (e.g., Jacobson et al., 2016; Netopil, 2016; Spina, 2017). Using a homogenous compilation of 172 clusters from the literature, Netopil (2016) investigated the metallicity distribution and found that the clusters younger than 500 Myrs may be characterized by lower metallicities than the older clusters, at least in the region between 7 and 9 kpc from the GC. At the same time, they confirmed a negative gradient for these clusters. However, their sample did not include any clusters younger than 100 Myrs located in the inner galaxy.

As evident from Figure 3, the sample OCS has a relatively lower average metallicity compared to sample OCP at all the ages in the available age span. This, as discussed previously in Section 2, is possibly due to the sample selection bias as sample OCP has more clusters from the GC direction, while sample OCS has more clusters from the anti-GC direction. More interestingly, both samples have a nearly constant spread in metallicity throughout the available age span, suggesting that at both older and recent times, the natal gas at the formation site of the clusters had similar mixture properties. To understand the properties of OCs from different ages, we broadly segregate our sample OC in three different age bins, namely, ≤20 Myrs as young open clusters (YOC), 20–700 Myr as intermediate-age clusters (IOC), and > 700 Myr as old clusters (OOC). Samples YOC, IOC and OOC have 410, 1114 and 349 clusters. Metallicity functions for the sample YOC, IOC, and OOC are shown across the panels in Figure 4. For YOC, IOC, and OOC, the mean values of the [Fe/H] distributions are −0.000 ± 0.009, 0.004 ± 0.005, and −0.111 ± 0.010, respectively, and the corresponding sample standard deviations are 0.186, 0.176, and 0.196, respectively. There is hardly any significant difference in metallicity between YOCs and IOCs. However, slightly higher mean metallicity for the YOC and IOC compared to OOC is apparent, which is well-expected as the clusters belonging to YOC and IOC are understood to have formed from gas and dust in the thin disk of the galaxy that has already been enriched through the earlier generation of stellar formation. Additionally, as seen from the figure, the metallicity functions for the OCs of different age groups are not symmetric and are slightly skewed. The skewness values for YOC, IOC, and OOC samples are −0.175, −0.212, and 0.083, respectively. All three age group OC samples span almost similar ranges in metallicity. The metal-poor clusters in the YOC sample have likely formed from the fall of a metal-poor gas to the younger thin disk along with the succeeding starburst. This in-fall of a metal-poor gas is believed to be due to merging satellite galaxies to the Milky Way (Wyse, 1999), resulting in diluting the metallicity of interstellar material in the galactic thin disk and, subsequently, triggering the formation of a large number of metal-poor clusters. On the other hand, the super solar metallicity clusters in the OOC group may have formed from the highly processed material from the inner region of the galaxy. It is believed that the metal-rich old clusters in the inner region had migrated outward the outer disk over a period of time in order to survive the destruction due to relatively stronger galactic potential in the inner disc (Myers et al., 2022a; Magrini, 2023).

To further understand the reason behind the almost-similar large spread in metallicity distribution for OCs of different age groups, we looked into the distribution of [Fe/H] as a function of the galactic longitude. As shown in the bottom panel of Figure 5, clusters toward the anti-GC direction (i.e., with 90 ^o < l < 270 ^o ) have relatively lower metallicity than the cluster in the GC direction (i.e., with 270 ^o < l < 90 ^o ). The reason behind this asymmetry is that most of the star-forming regions are in the GC direction where the nucleosynthesis process is more active in comparison to fewer star-forming regions present in the anti-GC direction. As a result, metallicity increases as the stellar evolution progresses. The top panel of the figure shows the cumulative distribution functions (CDFs) for the three age groups and suggests that all three age populations span a similar range in the galactic longitude. We further performed the Kolmogorov–Smirnov (KS) test to check if the three CDFs come from the same distribution. The KS test p-value for the OOC and IOC pair is 0.98, for the IOC and YOC pair is 0.87, and for the OOC and YOC pair is 0.50, hence suggesting that all three CDFs follow the same distribution at a minimum of 50% significance level.

In this study, we used the largest sample of 1,879 open clusters to understand the distribution and evolution of metallicity in the galactic disk. The cluster sample was compiled from the literature with available metallicity information along with other information like age, position coordinates, distances, and radial and vertical distances. About 90% of the OCs in our sample are younger than 1 Gyr, with the oldest being about 10 Gyr old. Radially and vertically, about 90% of the clusters in our sample are within a heliocentric distance of 3 kpc, while about 97% of the clusters are within a vertical distance of 500 pc, practically restricting our study to the galactic disk.

The age–metallicity relation provides an important constraint on the theoretical models of the disk and, thus, has been studied multiple times in the past. The study of metallicity evolution for our sample of OCs did not find a strict age–metallicity relation, but a stepped linear evolution of metallicity in the galaxy was observed with a discontinuity at log(age/year) = 8.378 ± 0.093 at the age of approximately 240 Myr. OCs older than 240 Myr follow a decreasing trend in metallicity with an increase in age, with an age–metallicity gradient of − 0.031 ± 0.006 dex/Gyr, which is in agreement with some of the recent studies as well as the galactic evolutionary models. The slightly higher average metallicity in the intermediate age clusters compared to the average metallicity in the young ones agrees with findings in earlier studies (Pancino, 2010; Zhong et al., 2020). Interestingly, the sample of OCs younger than about 240 Myr follows a slightly increasing trend in metallicity with an increase in age. The radial and vertical migration of young OCs in the disk is suspected to be one of the main reasons for this weak correlation between log(age) and [Fe/H] for younger clusters. However, no strong correlation has been found to draw any meaningful conclusion. Despite a large scatter in the age–metallicity relation in our study, it is crucial to observe the slightly different age–metallicity relation for two different samples of clusters, which possibly applied distinct formation constraints on the galactic thin and thick disc in modeling the Milky Way.

It is well-understood that the metallicity in the inner region of the galactic disk is increasing with time (e.g., Reddy, 2003; Haywood et al., 2013, and references therein). Hence, the younger clusters with lower metallicity must have either formed away from the galactic plane or in the anti-GC direction. To see whether the latter is the reason behind lower metallicity in younger clusters, we investigated the distribution of metallicity in the galactic plane by plotting metallicity as a function of the galactic longitude. The OCs in the anti-GC direction do have lower metallicity compared to the OCs in the GC direction, possibly owing to the differences in timelines of gas in-falls and formation of clusters in the GC and anti-GC directions. Our samples of YOCs, IOCs, and OOCs are found to equally populate both the GC and anti-GC directions, hence leaving vertical migration as one of the likely reasons for slightly lower metallicity in younger clusters.

Using our sample of clusters, we further explored the vertical and radial metallicity gradients in the galactic disk. Metallicity was found to follow a stepped variation with vertical distance from the galactic plane. Near the galactic plane, with |Z| < 0.487 ± 0.087 kpc, we estimated the vertical metallicity gradient of −0.545 ± 0.046 dex kpc⁻¹, while for a large vertical distance having 0.487 ± 0.087 < |Z|≲ 1.8 kpc, we found a lower vertical metallicity gradient of −0.075 ± 0.093 dex kpc⁻¹. The lower metallicity gradient at large vertical distances compared to the one at smaller vertical distances agrees with the galactic chemical evolution models. We found that most of the OCs at large vertical distances are older compared to the majority of the clusters located near the galactic plane. This difference in the ages of clusters from the two vertical regions is believed to be the main reason for the flatter vertical metallicity gradient at large vertical distances compared to the steep vertical metallicity gradient at smaller vertical distances.

Similar to the vertical direction, the change in metallicity in the radial direction is also found to follow a stepped linear relation. For a radial distance between approximately 4.0 and 12.8 kpc, we found a radial metallicity gradient d [ F e / H ] d R GC of −0.070 ± 0.002 dex kpc⁻¹, while for a radial distance between approximately 12.8 and 20.5 kpc, we found a much smaller radial metallicity gradient of −0.005 ± 0.018 dex kpc⁻¹. Thus, the OCs in the outer galactic disc are generally more metal-poor than the OCs in the inner galactic disc and in the solar neighborhood. Although a shallower metallicity gradient in the region 12.8–20.5 kpc may be biased due to the relatively smaller number of OCs at larger galactocentric distances, it could also be the result of radial migration of clusters in the galactic disk (Zhang et al., 2021). Using a smaller sample of 295 OCs within a galactocentric distance of 7–15 kpc, Zhong et al. (2020) reported a steeper slope of −0.252 ± 0.039 dex kpc⁻¹. It should also be noted that a significant variation in the slope and the turn-off point in the radial metallicity gradient among different studies comes from the choice of the cluster sample, selected range of R _GC , and unequal vertical heights. Overall, our radial metallicity gradient estimates agree with most of the recent studies (Reddy et al. 2020; Zhang et al. 2021; Myers et al. 2022a).

One of the key questions in the galactic chemical evolution models is the evolution of the radial metallicity gradients over time, and the answer is not determined yet. We, therefore, examined the time evolution of the metallicity gradients, both in radial and vertical directions, with age, by dividing the clusters into three age bins of < 20 Myr, 20–700 Myr, and > 700 Myr. We observed that these gradients are shallower for the oldest age bin, while not much difference was noticeable in the young and intermediate-age clusters. The time evolution of abundance gradients has also been examined in the past, but an unequivocal result has not been found so far. Although Vincenzo et al. (2018) and Minchev et al. (2018) suggested a flatter metallicity gradient with time, there are a few studies like Chiappini et al. (2001) and Mott et al. (2013), which suggested a steepening in gradient over time. However, the variation is only prominent over a longer time scale, and the limited temporal coverage of the present cluster sample, where only a small number of OCs are available beyond the 1 Gyr period, in no way sheds any more light on this discussion. We refer Magrini (2023) for a more detailed discussion on the temporal evolution of the metallicity gradients.

We further studied the variation in the radial metallicity gradient with distance from the galactic plane and found that the radial metallicity gradient linearly increases with an increase in the vertical distance and obtained a radial metallicity gradient slope of d [ F e / H ] d R GC = 0.068 ± 0.016 dex kpc⁻¹ kpc⁻¹ as a function of vertical distance from the galactic plane. This agrees with the galactic evolutionary models, for example, see Toyouchi and Masashi (2014) and references therein. In the case of a thin disk, which has a scale height of approximately 300 pc, the radial metallicity gradient is highly negative even though it linearly increases with the vertical distance from the galactic plane. However, for the thick disk (having a typical scale height of approximately 900 pc), the radial metallicity gradient is slightly high and approaches zero at approximately 1 kpc. Toyouchi and Masashi (2014) suggested that the radial metallicity gradient was positive at the time of formation of the thick disk but subsequently became negative during the transition phase of the disk formation from the thick to thin disk. The gradient became flatter by the time of the formation of the thin disk. This change in the radial metallicity gradient with a vertical distance is believed to be related to the gas in-fall history in the galaxy. A large negative radial metallicity gradient near the galactic plane (i.e., in the thin disk) but a higher gradient in the case of the thick disk (i.e., large vertical distance) can be explained by the shorter and longer time scales, respectively, for the gas in-fall.