The Open Cluster Chemical Abundances and Mapping Survey:
VI. Galactic Chemical Gradient Analysis from 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., 2015, 2018; Jönsson et al., 2020, Holtzman et al., in prep) that are central to the present study.

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 Cantat-Gaudin et al. (2020), 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. ²²2For 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.

Finally, because more Ce II lines were used in DR17 to determine the abundance of Ce in ASPCAP, the cerium abundance measurements have significantly improved over those in DR16; as a result, we are able to report more precise Galactic trends in cerium here.

For each cluster in the sample, we compute its guiding-center 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 $R_{\odot}=8.275~\textrm{kpc}$ (Gravity Collaboration et al., 2021), a solar height above the Galactic midplane of $z_{\odot}=20.8~\textrm{pc}$ (Bennett & Bovy, 2019), and a solar velocity with respect to the Galactic center $\boldsymbol{v}_{\odot}=(8.42,250.2,7.90)~\textrm{km}~\textrm{s}^{-1}$ (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.

Cantat-Gaudin et al. (2018) performed a fundamentally different membership analysis than presented here and previously by OCCAM (Donor et al., 2018, 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 [$\varpi$]), 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 considered cluster members in both the OCCAM and the CG samples), OCCAM only (stars that are included in the present sample but not in Cantat-Gaudin et al. 2018), and CG only (stars rejected from the present sample but included in Cantat-Gaudin et al. 2018). 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 ($\varpi$). To compute this statistic, we first measure the mean cluster value for stars in the common sample ($\bar{x}_{common}$). We then compute the average deviation of the OCCAM only and the CG only samples ($x_{single\textrm{ }sample}$) from $\bar{x}_{common}$, shown in Eq. 1.

In Figure 2, we plot a histogram of RV, $V_{T}$, and $\varpi$ with (1) the $1\mbox{-}\sigma$ standard deviation of the common sample within each cluster in gray, (2) $\sigma_{mod}$ for OCCAM only in orange, and (3) $\sigma_{mod}$ 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 $\varpi$ 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 $\varpi$ 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 $\varpi$ is expected. The remaining two clusters, FSR 0496 and NGC 7789, each have one star with negative $\varpi$ 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 $\varpi$ in our sample, which is not surprising since $\varpi$ 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 using the OCCAM IV membership selection pipeline for consistency.

The VAC consists of two FITS tables. The first, occam_cluster-DR17.fits, is a combination of Table 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 Cantat-Gaudin et al. (2020); $2\times Radius_{CG}$) 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 $3\sigma$ 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 $3\sigma$³³3In practice we adopt a threshold of 0.01 for all membership probabilities; see Donor et al. (2018, 2020) for further discussion. 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 $R_{\odot}$ 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.⁴⁴4The full url is https://www.sdss.org/dr17/data_access/value-added-catalogs/?vac_id=open-cluster-chemical-abundances-and-mapping-catalog

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 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 $-0.074\pm 0.002$ dex/kpc for $R_{guide}$, and a nearly identical inner gradient of $-0.073\pm 0.002$ for $R_{GC}$. Meanwhile, the outer gradients for the two cases are: d[Fe/H]/$R_{guide}$ $=-0.023\pm 0.003$ dex/kpc and d[Fe/H]/$R_{GC}=-0.032\pm 0.002$ dex/kpc, with the knee located at $12.2\pm 0.12$ kpc and $11.5\pm 0.09$ 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 ($N$).

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 $3\sigma$ 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] $\lesssim-0.4$). 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 $\Delta$[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, ($\Delta$ dex, DR17-GALAH) of $-0.018\pm 0.046$, 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.

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 Ce II lines from Cunha et al. (2017). They use 218 stellar members of 42 open clusters from the OCCAM-IV sample. In a manner identical to the comparisons above for the OCCAM-IV and GALAH surveys, we compare the [Ce/Fe] abundances for all clusters in common between this sample and the one reported in Sales-Silva et al. (2022). We find not only a systematic shift, but also a sub-solar offset for the cerium abundances between the two samples, both between the open clusters and individual stellar abundances. This shift may be due to BACCHUS, as used by Sales-Silva et al. (2022), not properly excluding CNO blending from targeted lines. We additionally compared to the high-resolution optical follow-up analysis of APOGEE stars in clusters from O’Connell (2017) and O’Connell et al., in prep, which gives similar results to (Sales-Silva et al., 2022). Given the possible uncertainties with cerium, we present the DR17 OCCAM results here, but suggest further work is needed to settle this discrepancy.

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.