The Open Cluster Chemical Abundances and Mapping Survey: VI. Galactic Chemical Gradient Analysis from APOGEE DR17

The goal of the Open Cluster Chemical Abundances and Mapping (OCCAM) survey is to constrain key Galactic dynamic and chemical evolution parameters by the construction and analysis of a large, comprehensive, uniform data set of infrared spectra for stars in hundreds of open clusters. This sixth contribution from the OCCAM survey presents analysis of SDSS/APOGEE Data Release 17 (DR17) results for a sample of stars in 150 open clusters, 94 of which we designate to be"high quality'' based on the appearance of their color-magnitude diagram. We find the APOGEE DR17-derived [Fe/H] values to be in good agreement with those from previous high resolution spectroscopic open cluster abundance studies. Using a subset of the high quality sample, the Galactic abundance gradients were measured for 16 chemical elements, including [Fe/H], for both Galactocentric radius ($R_{GC}$) and guiding center radius ($R_{Guide}$). We find an overall Galactic [Fe/H] vs $R_{GC}$ gradient of $-0.073 \pm 0.002$ dex/kpc over the range of $6<R_{GC}<11.5$ kpc, and a similar gradient is found for [Fe/H] versus $R_{Guide}$. Significant Galactic abundance gradients are also noted for O, Mg, S, Ca, Mn, Na, Al, K and Ce. Our large sample additionally allows us to explore the evolution of the gradients in four age bins for the remaining 15 elements.


INTRODUCTION
Open clusters are key, age-datable tracers that have long been used to explore chemical trends in the Galactic disk. Since the early work of Janes (1979), numerous studies have advanced the field, particularly over the past 15 years (e.g., Sestito et al. 2008;Bragaglia et al. 2008;Friel et al. 2010;Carrera & Pancino 2011;Yong et al. 2012;Frinchaboy et al. 2013;Reddy et al. 2016;Cunha et al. 2016;Netopil et al. 2016;Magrini et al. 2017;Donor et al. 2020;Spina et al. 2021;Netopil et al. 2021), with progress driven by the availability of larger telescopes, the expansion of multifiber spectroscopic capabilities, and, more recently, by large-scale high-resolution spectroscopic surveys, such as, Gaia-ESO (Gilmore et al. 2012), GALactic Archeology with HERMES (GALAH; Martell et al. 2017) and Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017). The APOGEEbased Open Cluster Chemical Abundances and Mapping (OCCAM) Survey has produced a comprehensive, uniformly measured data set of infrared spectra for stars in over a hundred open clusters, with the goal of exploiting the advantages of open clusters for constraining key Galactic dynamic and chemical parameters.
Since our previous open cluster chemical abundance gradient study (Donor et al. 2020, OCCAM-IV, hereafter), which was based on SDSS-IV APOGEE Data Release 16 (DR16; Ahumada et al. (2020)), a few new studies of Galactic abundance gradients have been published, most having incorporated the data from OCCAM-IV. For example, Zhang et al. (2021) use a compilation of LAMOST, APOGEE, and other surveys to constrain the metallicity gradient and acquire a high quality sample of young open clusters. Netopil et al. (2021) also use APOGEE clusters and other studies to characterize the metallicity gradient and its evolution over eight different age bins. Both studies explore the potential effects of radial migration in open clusters, which is possible due to the availability of high quality kinematic data from the ESA Gaia mission (Gaia Collaboration et al. 2016). The results from the ESA Gaia mission have also significantly improved the ability to refine cluster membership, which is utilized in many studies (e.g., Cantat-Gaudin et al. 2018Castro-Ginard et al. 2021;Kounkel et al. 2020;Monteiro & Dias 2019;Dias et al. 2021).
Galactic abundance gradients are important observable constraints to models of Milky Way chemical evolution, but limitations to these constraints arise from (1) the use of inhomogenous or small datasets, (2) systematic offsets in the abundance results when combining data sets, and (3) uncertainties in cluster ages and distances adopted in the different studies. For example, Donor et al. (2018) found a 40% variation in the gradient slopes when using different distance catalogs but the same set of abundance results. Complications like these have led to a range of values for the metallicity gradients derived from open cluster samples -between roughly −0.05±0.011 dex/kpc (Reddy et al. 2016;Casamiquela et al. 2019) and −0.1 ± 0.02 dex/kpc (Jacobson et al. 2016).
Even more recent studies have been able to break down the iron gradient into individual elements to further investigate the processes which enrich the Milky Way, for instance, OCCAM-IV, Spina et al. (2021Spina et al. ( , 2022, and Sales-Silva et al. (2022), all do so with large open cluster samples.
In this paper, we present the complete OCCAM sample, which is based on the APOGEE results given in the SDSS-IV Data Release 17 (DR17) (Blanton et al. 2017;Abdurro'uf et al. 2022), the most recent and final release of data products from Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2; Majewski et al. 2017, Holtzman et al., in prep). We analyze Galactic gradient trends in metallicity ([Fe/H]), α elements (O, Mg, Si, S, Ca, Ti), iron-peak elements (V, Cr, Mn, Co, Ni), and other elements (Na, Al, K, Ce) represented in the APOGEE DR17 database, and explore the evolution of these gradients as a function of age. We also calculate the trends with Galactocentric guiding center radius (R guide ) to investigate the potential biases that may affect the analysis by using the current cluster locations. Finally, we discuss this sample in comparison to other recent literature studies of open clusters.  (Table 1). Stars from Gaia EDR3 within twice the cluster radius, as defined in , are included; stars identified as PM members and inside the cluster radius are blue. Non-member stars are shown as a Hess diagram in grey. The OCCAM pipeline-identified APOGEE members from DR16 (Donor et al. 2020) are shown in purple. New DR17 OCCAM pipeline-identified APOGEE member stars are shown as orange stars.

DATA
To minimize the systemic offsets inherent to blending multiple data sources, we create a uniform sample for our abundance gradient analyses by pulling the majority of our data from only two sources: SDSS/APOGEE and Gaia. To supplement the SDSS/APOGEE data and provide astrometric and photometric parameters for our analysis we use data from 3, 720, 692 Gaia Early Data Release 3 (EDR3 Gaia Collaboration et al. 2021) stars and radial velocities for 38, 667 Gaia stars (Seabroke et al. 2021). We check the offset between Gaia EDR3 RVs and APOGEE DR17 RVs and find the median offset to be roughly −0.14 km/s with a standard deviation of approximately 2.80 km/s.

SDSS/APOGEE DR17
The chemical abundances and radial velocities for the open cluster stars in our sample are from the APOGEE SDSS-IV values in DR17 (Blanton et al. 2017;Abdurro'uf et al. 2022). As previously mentioned, this final data release derives data from the completed collection of high resolution, near-infrared spectra taken with the APOGEE spectrographs (Wilson et al. 2019) for over 650,000 stars as part of the APOGEE and APOGEE-2 surveys. The SDSS/APOGEE data were taken using two telescopes: the Sloan Foundation telescope at the Apache Point Observatory (New Mexico, APO Gunn et al. 2006) in the Northern Hemisphere and Du Pont telescope at the Las Campanas Observatory (Chile, LCO Bowen & Vaughan 1973) in the Southern Hemisphere. Observations for APOGEE-2N were concluded in November 2020, while those for APOGEE-2S were concluded in January 2021.
Targeting for the APOGEE survey, including details from this program, are described in Frinchaboy et al. (2010), Zasowski et al. (2013), Zasowski et al. (2017), Beaton et al. (2021), and Santana et al. (2021). APOGEE data are reduced using the APOGEE data reduction pipeline (Nidever et al. 2015) and the ASPCAP data analysis pipeline (García Pérez et al. 2016). The latter produces the detailed abundances of chemical elements (Holtzman et al. , 2018Jönsson et al. 2020, Holtzman et al., in prep) that are central to the present study.

Pipeline Changes in APOGEE DR17
Some significant changes were made to the APOGEE pipeline for DR17. New synthetic spectral libraries were created using the Synspec code (Hubeny & Lanz 2017;Hubeny et al. 2021) that now allows for the Non-LTE analysis of the elements Na, Mg, K, and Ca using the computations in Osorio et al. (2020). The APOGEE line list used for DR17 is Smith et al. (2021), which updates from Shetrone et al. (2015). While schematic description of the DR17 pipeline is given in Abdurro'uf et al. (2022), further specifics about updates to the APOGEE pipeline will be discussed in Holtzman et al. (in prep).

METHODS
To identify cluster member stars, we employ the analysis described in Donor et al. (2018Donor et al. ( , 2020, which uses the celestial coordinates (RA/Dec), proper motion (PM), radial velocity (RV), and metallicity of stellar candidates to sift likely cluster members from nonmembers. All stars designated as cluster members must have RV, PM, and [Fe/H] values within 3σ of the cluster mean. For a more thorough discussion of the probability values, see §4.1. As in OCCAM-IV, we also use visual quality checks of both the color magnitude diagrams (CMDs) and Kiel diagrams (T ef f vs log(g)) for the APOGEE stars in each cluster to distinguish between high quality clusters (with quality flag 1 and 2 1 ) and potentially unreliable clusters (with quality flag 0). This procedure is discussed in more detail in OCCAM-IV. As an example of both the CMDs used and the difference between APOGEE DR16 and DR17, we show five example clusters, (all with a quality flag of 1 or 2), in Figure 1. As can be seen, the addition of APOGEE DR17 not only expands the number of stars that are identified to be likely cluster members in previously known clusters, but it also allows new clusters to be added to our sample.
3.1. Methodology Changes from Donor et al. (2020) The present analysis adopts several changes in methodology from that employed in Donor et al. (2020). In addition to using the latest stellar parameters and abundances from the greatly expanded APOGEE DR17 sample, we also use the latest data from the Gaia Collaboration et al. (2016), EDR3, to take advantage of the extended baseline and expanded astrometric catalog. Additionally, we use the open cluster parameters from , which exclusively uses Gaia DR2 to compile a catalog that provides uniform measurements of age and distance (among other parameters) for roughly 2,000 open clusters. This includes all the open clusters used here for analysis of the Galactic chemical gradients.
Another change in methodology applied to our analysis is the addition of the guiding center radius, R guide , which is now used along with galactocentric radius, R GC , to compute the Galactic abundance gradients. Methods for the calculation of R guide are further discussed in §3.2. 2 Finally, because more Ce II lines were used in DR17 to determine the abundance of Ce in ASPCAP, the cerium 1 The quality flag of 2 denotes a cluster used in the calibration sample from Donor et al. (2018). 2 For two clusters (FSR 0542 and NGC 2232) that were not initially recovered using the OCCAM-IV pipeline, we implemented a parallax cut for stars greater than twice the reported distance to the cluster (Cantat-Gaudin et al. 2020) and those less than half the distance to the cluster.
abundance measurements have significantly improved over those in DR16; as a result, we are able to report more precise Galactic trends in cerium here.

Computing Guiding Center Radii R guide
For each cluster in the sample, we compute its guidingcenter radius R guide using the circular velocity rotation curve from the best-fitting Milky Way model described in Price-Whelan et al. (2021). The guiding center radius of a given general, eccentric orbit is the radius of a circular orbit with the same angular momentum as the generic orbit. We compute the approximate guiding center radii for the OCCAM clusters by first transforming their heliocentric position and velocity data (sky position, distance, proper motions, and radial velocity) into Galactocentric Cartesian coordinates, assuming solar parameters: for the Sun-Galactic center distance we adopt R = 8.275 kpc (Gravity Collaboration et al. 2021), a solar height above the Galactic midplane of z = 20.8 pc (Bennett & Bovy 2019), and a solar velocity with respect to the Galactic center v = (8.42, 250.2, 7.90) km s −1 (Drimmel & Poggio 2018;Gravity Collaboration et al. 2018;Reid & Brunthaler 2004). We then compute the z-component of the angular momentum vector L z for each cluster in the Galactocentric frame and estimate the guiding center radii as R guide = L z /v c (R), where R is the present-day cylindrical radius of each cluster and v c (r) is the circular velocity curve evaluated at the radius of each cluster.
The use of the guiding center radius of a cluster, rather than its present galactocentric radius, has the advantage of correcting for orbital blurring effects in the metallicity gradients (e.g., Netopil et al. 2021, Zhang et al. 2021, Spina et al. 2021. To illustrate and explore the differences between R guide and R GC , we calculate R guide , and discuss both radii in §5 and §6.

Membership Comparison to Cantat-Gaudin et al. (2018)
Cantat-Gaudin et al. (2018) performed a fundamentally different membership analysis than presented here and previously by OCCAM (Donor et al. 2018(Donor et al. , 2020. Whereas our analysis relies on kernel convolution and Gaussian fitting to define a rigid boundary for what constitutes "the cluster", Cantat-Gaudin et al. (2018) performed a clustering search in the 5 dimensional Gaia phase space (RA, dec, proper motion, and parallax [ ]), requiring no fitting or boundary setting. Besides the difference in methodology, the absence of a constraint on parallax in our method, and inclusion of RV and [Fe/H], are noteworthy.
In order to compare the results from the two methods, we divide stars into three categories: common (stars We create a statistic that accentuates differences between these three samples in RV, transverse velocity (V T , calculated using the cluster distance measured by Cantat-Gaudin et al. 2020), and parallax ( ). To compute this statistic, we first measure the mean cluster value for stars in the common sample (x common ). We then compute the average deviation of the OCCAM only and the CG only samples (x single sample ) fromx common , shown in Eq. 1.
In Figure 2, we plot a histogram of RV, V T , and with (1) the 1-σ standard deviation of the common sample within each cluster in gray, (2) σ mod for OCCAM only in orange, and (3) σ mod for CG only in purple. There are 92 clusters in our sample where the results of our membership analysis differ from Cantat-Gaudin et al. (2018); we omit the remaining clusters from this analysis as it is designed to show differences. To show relevant detail we artificially cut off each histogram at 30; in all 3 panels the lowest bin is populated beyond what is shown. Since the common sample is more restrictive than either individual sample it is not surprising that we measure a small standard deviation for the common sample of stars in most clusters. We note the scale difference between the RV and V T histograms: the first 5 bins in the V T plot span 0-2.5 km/s, which is the size of the first bin in the RV plot.
For the common sample, 67 of 92 clusters for which we measure RV dispersion have measured dispersions below 1 km/s, and in V T we find 71 of 92 clusters showing a dispersion below 1 km/s, in good agreement with typical cluster dispersions (e.g., Cantat-Gaudin & Anders 2020) and despite not explicitly removing binary stars. For the majority of the OCCAM only clusters show low dispersions, comparable to the common sample and CG only sample, with 83 of 92 clusters having dispersions < 0.25 mas, despite the fact we have not used in our selection. For the remaining nine clusters, five are in our low quality sample. Of the four in our high quality sample two are very nearby, Melotte 22 (The Pleiades) and Ruprecht 147, so some dispersion in is expected. The remaining two clusters, FSR 0496 and NGC 7789, each have one star with negative reported, significantly affecting the measured dispersion. This analysis shows that despite different selection criteria, the reliability of our sample is comparable to Cantat-Gaudin et al. (2018), where we can compare directly. We find inconsistencies in in our sample, which is not surprising since is not accounted for in our analysis. Similarly, we show there is significant RV variation in the Cantat-Gaudin et al. (2018) sample since RV was not accounted for in that analysis. A union of the two samples is straightforward to create using the VAC discussed in §4.1. Combining the 5 dimensional Gaia phase space with RV and [Fe/H] would produce a purer sample, but in the present work we have chosen to continue Square points are "high quality" clusters, triangles are the lower quality clusters, and crosses denote clusters which were in the "high quality" sample of OCCAM-IV but are now in the "low quality" sample.
using the OCCAM IV membership selection pipeline for consistency.

THE OCCAM DR17 SAMPLE
Our final sample consists of 150 open clusters with 2061 member stars, out of ∼ 26, 700 stars in the vicinity of a known open cluster considered in this analysis. The final sample of clusters is shown in Figure 3. After a visual CMD inspection (described further in OCCAM-IV), we designate 94 clusters as "high quality". All clusters analyzed are presented in Table 1 and Table  2. Where Table 1 includes bulk cluster parameters derived or adopted for this study, and Table 2 includes bulk cluster abundances, which are averaged over the stellar members.
For all Galactic abundance analysis in this study, we choose to use only clusters flagged as high quality and that have distances available from Cantat-Gaudin et al. (2020). Additionally, we also cut out two clusters with an age less than 50 Myrs (NGC 7058 and Teutsch 1), due to previous studies suggesting the young star pipeline results from APOGEE may be unreliable (e.g., Kounkel et al. 2018). This results in a sample of 85 clusters.

Data Access -SDSS Value Added Catalog
The VAC consists of two FITS tables. The first, occam cluster-DR17.fits, is a combination of Ta-ble 1 and Table 2, providing bulk cluster parameters derived here, PM from Gaia, as well as RVs and average abundances for 16 reliable chemical species available in APOGEE DR17.
The second table, occam member-DR17.fits, contains all of the APOGEE stars considered in this analysis (all of the stars that fall within two radii of the cluster center given by ; 2 × Radius CG ) and reports the membership probabilities determined by the OCCAM pipelines (for [Fe/H], RV, and PM) as well as the membership probability from Cantat-Gaudin et al. (2020) for convenience. These four probabilities reported reflect how far a given stellar parameter is from the fit cluster mean, where a reported probability of > 0.01 is within 3σ of the cluster mean. In practice these fit distributions are fairly tight (see Donor et al. 2018 for a figure set showing distributions for [Fe/H], PM and RV for 19 clusters), therefore a star falling within 3σ 3 of the cluster mean in all 3 parameter spaces is likely to be a cluster member.
We also note that within the VAC, R GC was calculated with an R of 8 kpc, whereas for this work, we recalculated R GC with a solar radius of 8.275 kpc to be consistent with Gravity Collaboration et al. (2021). Table 3 shows all columns available in the occam member table. The catalog is available from sdss.org. 4 5. RESULTS

The Galactic Metallicity Gradient
With the large, uniform sample of open cluster data from APOGEE DR17, we are well positioned to more reliably characterize and report Galactic abundance gradients for 16 chemical species. Figure 4 shows [Fe/H] versus both R guide (top panel) and R GC (bottom panel) for our final sample of 85 open clusters. In both cases we use a two-function gradient, where the gradient is described with two linear functions and where the intersection point of the two lines is also allowed to be a free parameter. We use the fitting procedures described in OCCAM-IV, which uses a maximum likelihood method to fit the data, and the emcee python package (Foreman-Mackey et al. 2013) to estimate the fit errors. We assume a 5% error on the distance to each cluster, as (Cantat-Gaudin et al. 2020) did not include Table 1. OCCAM DR17 "High Quality" Sample -Basic Parameters   a Taken directly from APOGEE DR17.
b From Gaia EDR3.
c Negative values indicate the star is outside the adopted cluster radius, while '2' indicates the star failed our PM membership analysis, but is a member in Cantat-Gaudin et al. (2020).
distance errors, and these are taken into account in the fitting procedure. We denote the gradient with radius less than the intersection point (hereafter known as the "knee") as the inner gradient and the gradient with radius greater than the knee as the outer gradient. We find an inner gradient of −0.074 ± 0.002 dex/kpc for R guide , and a nearly identical inner gradient of −0.073 ± 0.002 for R GC . Meanwhile, the outer gradients for the two cases are: d[Fe/H]/R guide = −0.023 ± 0.003 dex/kpc and d[Fe/H]/R GC = −0.032 ± 0.002 dex/kpc, with the knee located at 12.2 ± 0.12 kpc and 11.5 ± 0.09 kpc, respectively. For completeness, we also fit the open cluster data from Figure 4 with a single linear function, which is recorded in Table 4, along with the two-function fit and the number of clusters used to calculate both fits (N ).

Galactic Trends for Other Elements
The Galactic abundance ratio trends for six αelements (O, Mg, Si, S, Ca, and Ti) over iron versus R guide are shown in Figure 5, these slopes are also reported in Table 5, along with the slopes calculated with R GC . We find positive slopes for all studied [α/Fe] abundances but note a significant scatter among the [S/Fe] values and the large uncertainty in the cluster [Ti/Fe] values. There are no significant differences between the best fit slopes calculated using either R guide or R GC .    While not explicitly discussed in text we report the gradient cut at 14kpc in order to easily compare to previous work.

Iron-Peak Elements -V, Cr, Mn, Co, Ni
In Figure 6, we investigate the Galactic trends versus R guide of the iron-peak element ratios included in DR17 (V, Cr, Mn, Co, and Ni). 5 The gradients for iron-peak elements over iron all show negative, shallow trends (Table 5) with vanadium having the steepest gradient value of all at −0.012 ± 0.008 dex/kpc, although this is still relatively flat. The cluster values for [V/Fe] also have the largest scatter of the iron-peak elements, however, [Co/Fe] also has three significant outliers: the clusters

Odd-Z Elements -Na, Al, K
The abundance gradients with respect to R guide for the three "odd-z" elements: Na, Al, and K are plotted in Figure 7, and recorded in Table 5 for both R guide and R GC . We report similar positive trends for Al and K, but a steep negative gradient for Na. The single onestar outlier for [Na/Fe] corresponds to the open cluster NGC 136.

The Neutron Capture Element Ce
With the availability of reliable abundances for the sprocess element Ce, obtained automatically by the AS-PCAP pipeline in DR17, we are now able to investigate the abundance gradient of Ce with 69 open clusters in our sample. In Figure 8, we fit [Ce/Fe] abundance versus R guide and find a positive gradient of 0.024 ± 0.006 dex/kpc. In Table 5, we also report the slope with respect to R GC and find a value of 0.022 ± 0.006 dex/kpc.

Iron
One of the important questions in chemical evolution models is how the Galactic metallicity gradients have evolved over time. Fortunately, the size of our sample lends itself to investigating this question. The open cluster sample studied here can be split into four age bins, divided at 400 Myrs, 800 Myrs, and 2 Gyrs, identical to the bins chosen in OCCAM-IV, although in this study we use the open cluster ages derived in .
In Figure 9, we plot R guide and R GC versus metallicity for each age bin, showing only clusters with both R GC and R guide < 16 kpc. The gradients shown in the figure, however, are calculated with all clusters located 5 As discussed in Abdurro'uf et al. (2022) and Holtzman et al. (in prep), the APOGEE DR17 pipeline analysis did not yield sufficiently reliable abundance measurements for the element copper. The [X/Fe] versus R guide trend for the αelements. As before the color bar indicates number of member stars, saturating at five, and light blue circles represent clusters with high uncertainty in that element.
within that region (thus the number of clusters changes between the R GC and R guide fits). This gives a sample of 73 clusters for the R guide plots and a sample of 76 clusters for the R GC . Two sets of symbols are used in Figure 9: colored triangles denote guiding center radii while galactocentric radii are marked with gray Xs; horizontal bars connect the two radii values for the same cluster. The slope of the gradient calculated with respect to R guide is shown as a solid line, and the slope calculated with R GC is represented as a dashed line. The slopes calculated for each age bin and the number of clusters used for each fit are recorded in Table 4.
As can be seen in Figure 9, the gradients calculated with R GC appear to remain relatively constant between the four age bins, with the first and the fourth bins showing relatively shallow slopes and the two middle bins having identical slopes. The gradients calculated with R guide seem to show a more constant transition from young to old clusters up until the final age bin, wherein the slope becomes significantly shallower. Additionally, we can see in the last two panels of Figure 9 (i.e,. the two older age bins), that on average the difference between a cluster's R GC and R guide is larger than in the first two age bins (i.e., the younger two age bins). This suggests that as the clusters have had more time to be affected by interactions in the Galaxy, e.g asymmetric drift, their orbits have become more elliptical. Plus, a potential survivor bias in the older cluster samples and/or possible radial migration of clusters could have affected the gradients.

[X/Fe]
To understand the evolution in the radial gradients of elements other than iron, we split the cluster sample into the same four age bins as in §6.4.1 and fit each gradient as in Figure 9. Fit parameters for all elements measured both with R guide and with R GC are reported in Table 5. In Figure 10, we also show the slopes (d[X/Fe]/dR guide ) for all four age bins and each of the 16 elements (where, for iron, we show the abundance ratio [Fe/H]); this figure is comparable to Figure 14 in OCCAM-IV. We note that, as explained in §6.4.1, all clusters used in the fit have a radius (R guide or R GC ) less than 16 kpc.
We find no convincing trends through the four age bins in α elements. While there could be a slight trend in [Mg/Fe], with oldest clusters perhaps showing a steeper slope than younger clusters, the changes between samples are roughly as significant as the uncertainties.
Both In the odd-Z elements, the gradient for [Na/Fe] seems to have an increasingly negative trend in R guide as clusters get younger, though within the sizeable uncertainty the trend may be less significant. Finally for cerium, the uncertainties in the DR17 measurements are still too large to measure a significant trend over time.

Comparison to OCCAM-IV sample
Between this sample and OCCAM-IV, 111 clusters can be found in both samples, 42 new clusters were added to this sample, and 17 clusters were not recovered, including two "high quality" clusters: Berkeley 44 and NGC 2355. With updated Gaia EDR3 data, the 2D Gaussian fit to the kernel convolution in proper motion space was narrower by enough that the APOGEE star now fell further than 3σ from the distribution. For Berkeley 44, the star that was included in OCCAM-IV is now slightly outside of the 2D Gaussian fit to the Gaia EDR3 proper motions. It is also not reported as a member in CG18. For NGC 2355, the star that was included in OCCAM-IV is considered a member in CG18 with a membership probability of 70%, but using updated EDR3 proper motions, the 2D Gaussian fit was more narrow and thus this star was rejected by our pipeline.
Additionally, there were three "high-quality" clusters in OCCAM-IV which were demoted to being flagged as "potentially unreliable" in this sample (SAI 16,BH 211,and Basel 11b). BH 211 failed the visual quality check, and both Basel 11b and SAI 16 had only two potential members with conflicting [Fe/H] values. However, there are seven clusters (Berkeley 91, FSR 0496, King 8, NGC 136, NGC 2202, Saurer 1, and Teutsch 10) which were previously marked "0" or "potentially unreliable" that are now included in the "high quality" sample due to the addition of new data.
For designated "high quality" clusters in common between this sample and Donor et al. (2020), a total of 66 clusters, Figure 11 shows the change in [Fe/H] between APOGEE DR16 and DR17. The median change, measured to be -0.020, is well within the measured scatter of 0.033, although this scatter seems to be due mostly to the lowest metallicity clusters ([Fe/H] −0.4). A visual inspection of the plot suggests that closer to Solar [Fe/H] there may be a real, albeit slight offset from DR16. However, this small offset is easily explainable by the significant changes to the APOGEE pipeline. The single outlier in Figure 11 with a ∆[Fe/H]= 0.18 is NGC 752. Figure 12 shows the change in OCCAM measured cluster abundances for 14 elements from APOGEE DR16 to DR17, plotted as a function of their reported DR17 abundance. These differences are due to pipeline and membership changes. Copper and phosphorus are not included because of unsuccessful measurements in DR17 (Abdurro'uf et al. 2022, Holtzman et. al, in prep). Cerium is also not included in Figure 12 because the values reported in DR16 were not considered particularly reliable (Jönsson et al. 2020). The measured median offset is within the measured scatter for all 14 abundances investigated. It is worth commenting on the particularly large scatter, and potential trend, for vanadium and sodium. Vanadium is considered less reliable in both DR16 and DR17; sodium is considered reliable in DR17 but less so in DR16 (Jönsson et al. 2020). Spina et al. (2021) use data from GALAH+, APOGEE DR16, and Gaia to compile a list of 226 open clusters, 134 of which have high-quality spectroscopic data for up to 21 elements. Of these clusters 85 are in common with our sample. We compare our sample to the GALAH sample, much like Figure 11, and measure a median offset, (∆ dex, DR17-GALAH) of −0.018±0.046, with two major outliers: King 2 at +0.18 and Berkeley 18 at +0.25, which both only have one member in the GALAH catalog.

Comparison to other surveys
In a recent APOGEE study, Sales-Silva et al. (2022) investigated the abundance gradient for the s-process element, Ce, with a detailed abundance analysis of several # of clusters Figure 10. The slopes of each elemental gradient in four age bins (as in Figure 9), for R guide . Point size increases with age, and the color indicates the number of clusters included in the gradient measurement. Given the possible uncertainties with cerium, we present the DR17 OCCAM results here, but suggest further work is needed to settle this discrepancy.

Comparison of Galactic Abundance Trends
In order to evaluate our reported gradients, we compare them against previous studies in this section. For our metallicity gradient comparisons, we use our full sample of open clusters. However, for the individual abundance gradient comparisons in §6.3.2-6.3.5, we use gradients with a cut in radius at 14 kpc (Table 5), as the other studies do not have significant clusters beyond 14 kpc.

Galactic Metallicity Gradient
Our derived metallicity trend -namely an inner gradient of −0.073 ± 0.002 dex/kpc, outer gradient of −0.032 ± 0.002 dex/kpc, and break at 11.5 kpc for R GC -shows a very similar inner gradient to that reported in OCCAM-IV (theirs being −0.068 ± 0.004 dex/kpc). However, our measured outer gradient is significantly steeper than the OCCAM-IV value of −0.009 ± 0.011 dex/kpc, and the knee measured here is farther inwards than theirs (13.9kpc). These discrepancies are most likely due to poor coverage of clusters at R GC > 14 kpcs in the OCCAM-IV sample, as noted in that study.
The Netopil et al. (2021) study finds an overall linear gradient of −0.058±0.004 dex/kpc, which is only slightly steeper than our measured single linear slope of −0.056± 0.001 dex/kpc. They also measure an inner disk (R GC < 12 kpc) gradient of −0.058 ± 0.005 dex/kpc which is significantly shallower than our reported values.
Similarly, Spina et al. (2021)  = −0.073± 0.008 dex/kpc, for clusters between roughly 6 ≤ R ≤ 14 kpc. Both of these slopes are consistent with the present inner gradients of −0.073 ± 0.002 dex/kpc and −0.074 ± 0.002 dex/kpc respectively, however with the additional clusters beyond ∼ 14 kpc in this sample, we find a much shallower linear gradient in both R GC and R guide .

α−Elements -O, Mg, Si, S, Ca, Ti
Our results for the α−elements are largely in agreement with those of OCCAM-IV, with an exception for the gradient in [Ca/Fe] which, in the DR17 sample is significantly flatter (0.007 ± 0.002 dex/kpc) than was reported with the DR16 sample (0.012 ± 0.001 dex/kpc). Our gradients for silicon and titanium (d[Si/Fe]/dR GC = +0.001 ± 0.001 dex/kpc and d[Ti/Fe]/dR GC = 0.003 ± 0.003 dex/kpc) are also slightly steeper than those reported in OCCAM-IV (d[Si/Fe]/dR GC = −0.001 ± 0.001 dex/kpc and d[Ti/Fe]/dR GC = 0.000 ± 0.002 dex/kpc), but they are nearly the same within the measured uncertainties. Spina et al. (2021) Spina et al. (2021), steep gradients in α elements are not commonly reported. Indeed, gradients measured for other α elements (Mg, Si, Ca, and Ti) by Spina et al. (2021) are nearly flat. This also stands in some contrast to the present work as we consistently measure mildly positive gradients in the same elements. This general trend of mildly positive gradients in α elements is consistent with OCCAM-IV, and previous literature (e.g., Carrera & Pancino 2011;Yong et al. 2012;Reddy et al. 2016) as discussed in OCCAM-IV.

Iron-Peak Elements -V, Cr, Mn, Co, Ni
The gradients we reported in Table 5 for nickel, cobalt, manganese, and vanadium are in good agreement with those in OCCAM-IV. However, the gradient for [Cr/Fe] measured here (−0.002±0.005 dex/kpc) does deviates slightly from that measured in OCCAM-IV (0.010±0.004 dex/kpc). This seems to be due to minute changes in abundances, particularly in those clusters at radii less than ∼ 7 kpc, which affects the gradient and accounts for the discrepancy.
The  Figure 8, and reported in Table 5 Figure 13. The age slopes measured if the age bins used in (Netopil et al. 2021) are adopted.  Netopil et al. (2016) and Netopil et al. (2021). The latter used this sample to investigate radial migration in open clusters and also measure the age-metallicity gradient with eight overlapping age bins. These age bins span from the youngest clusters (age < 0.4 Gyrs) to clusters with age ≥ 5.2 Gyrs.

Shown in
To better compare our results to that of Netopil et al. (2021), we divided our sample into their age bins (Fig.  13); however, to populate the oldest age bin with more than 10 clusters, we modified the oldest age bin from the Netopil et al. limits 3.0 ≥ age ≥ 5.2 Gyrs to instead include all clusters with age ≥ 3.0 Gyr.
Comparing to Table 6 in Netopil et al. (2021), the gradients we measure in Figure 13 are in good agreement for nearly every age bin, with measurements in 6 of the 8 samples agreeing well within the reported uncertainties. However, in the first age bin, the discrepancy between the two gradients is ∼ 0.004 dex/kpc; and for the final age bin the discrepancy is ∼ 0.008 dex/kpc. We note that the final age bin is largely affected by two relatively metal poor clusters at R guide 12 kpc, NGC 2243 and Trumpler 5.
Finally, we compare our [Fe/H] evolution results to the thin-disk chemical evolution model of (Chiappini 2009) and the chemo-dynamical simulation of (Minchev et al. 2013, 2014 Figure 14), using the same age bins as Figure 9. In the youngest three age bins we notice good agreement for both R GC and R guide trends. The third age bin also shows decent agreement, though there may be a slight offset between the R guide cluster sample and the model results. In the final age bin, both the R GC and R guide cluster sample have a noticeable offset from the models. This could potentially suggest either a real effect that would require a change to the models or that the older open clusters are possibly a biased sample due to which clusters survive to older ages and/or that these old clusters may have undergone migration and migrated outward during their lifetimes (whereas clusters that moved inward in the Milky Way are more likely to be disrupted).

[X/Fe]
The evolution of abundance gradients for elements besides iron were explored in §5.2. A similar analysis in OCCAM-IV indicated no convincing trends in α elements with time. As in OCCAM-IV, it could be argued that there is a slight trend for [Mg/Fe], with older clusters perhaps showing generally steeper slopes than the younger clusters, but also as in OCCAM-IV the changes between samples are roughly as significant as the uncertainties.
There is very little evolution found for [Cr/Fe] and [Ni/Fe], which is consistent with the OCCAM-IV results. As is the case here, OCCAM-IV found significant uncertainty in the [Cr/Fe] measurements, but the [Ni/Fe] gradients were fairly well determined. OCCAM-IV found a significant trend for [Mn/Fe] with the gradient becoming more negative for younger cluster pop- Figure 14. The open cluster sample from this study (red dots) overlaid on the models of (Chiappini 2009) (the blue line) and (Minchev et al. 2013(Minchev et al. , 2014 (blue dots). The plots are split into the same age bins used in Figure 9.
ulations. With the new DR17 data, this trend is no longer present; indeed the new APOGEE results seem to indicate that the younger samples have less negative gradients.
Finally, while we do seem to see an increasingly negative trend in d[Na/Fe]/dR guide as clusters get younger, the uncertainties in the gradients are large. This is roughly consistent with the slopes calculated in OCCAM-IV, though they found a flatter trend with a significantly steeper slope in the oldest age bin that we do not see here.

CONCLUSIONS
We present the final APOGEE-2 DR17 OCCAM sample, which consists of 150 open clusters, and 94 that we designate as "high quality". To gain insights into the chemical enrichment history of the Milky Way, we use the high quality sample to measure Galactic abundance gradients in 16 chemical elements and investigate their evolution over four age bins. With clusters spanning roughly 6.0 to 18 kpc, we measure a two-function Galactic radial metallicity trend, with −0.073 ± 0.002 dex/kpc for the inner slope, −0.032 ± 0.002 dex/kpc for the outer slope, and a knee located at 11.5 kpc. In order to account for blurring effects in the clusters orbits, we also calculate the guiding center radii, R guide , of each cluster. By using R guide as the independent variable, we find an inner slope of −0.074 ± 0.002 dex/kpc, an outer slope of −0.023 ± 0.003 dex/kpc, and a knee at 12.2 kpc.
The Galactic radial gradients for the 15 elements measured in this survey are in good agreement with other recent studies (e.g., Reddy et al. 2016;Casamiquela et al. 2019;Donor et al. 2020;Spina et al. 2021). In this work, we find significant (3σ or greater) trends in 9 of the 15 elements, including four of the α−elements (O, Mg, S, Ca), all of the odd-Z elements (Na, Al, K), and cerium. We don't find significant gradients in the iron-peak elements, except manganese.
We explore the variation in the trends for all elements throughout time, by splitting the open cluster sample into four age bin. We find no significant evolution compared with solar ratios, besides two elements (V and Na) which have large uncertainty in their measurements. This lack of age variation in the gradients points to well-mixed enrichment through the age range covered (10 Myr -9 Gyr), which implies that chemical tagging distinct age populations may be difficult with these elements, but could be improved with the inclusion of C and N (e.g., Casali et al. 2019;Spoo et al. 2022) for distinct stellar evolutionary phases.
We compare this DR17-based sample to OCCAM-IV and the GALAH sample from Spina et al. (2021) and find no significant differences between the abundances in either case. Additionally, we compare against the cerium abundances derived in Sales-Silva et al. (2022) and find an abundance correlated offset for sub-solar cerium abundances between the BACCHUS analyses and the DR17 ASPCAP-derived values.
We find general agreement in the first three age-bins when we compare to the chemo-dynamical models of Chiappini (2009) and Minchev et al. (2013Minchev et al. ( , 2014, however in the final age bin we do find an offset between the cluster sample and the models. This could be explained by either an offset in the models or, possibly, by a potential survivor bias in the older open cluster sample. Also, we note that APOGEE DR17 is able to measure Galactic trends for many of the CHNOPS elements, e.g., C,N,O, and S, which are important in the astrobiological study of the Galactic habitable zone. In this work, we present the gradients for oxygen and sulfur. The gradients for carbon and nitrogen are not presented here due to stellar evolutionary effects that change stellar surface chemistry due to the dredge up; however, these elements and their correlations with age are explored in Spoo et al. (2022).
We would like to greatly thank Friedrich Anders for helping with the creation of figures used for comparison to the Chiappini model.