Using APOGEE Stellar Abundances

ASPCAP results should not be used blindly. They are provided with the general caveats that affect abundances determined spectroscopically under the standard assumptions. The ability to measure abundances in any given star depends on the temperature and the metallicity, so the accuracy and precision of the abundances vary across stellar parameter space. Users are encouraged to thoroughly examine both the detectability and quality of the spectral features employed in the derivation of the desired elemental abundances.

Users should be particularly aware of the calibrations that have been applied to raw spectroscopic abundances, as described on the ASPCAP page (additional description provided in Holtzman et al. [2018]). In particular, note that internal temperature-dependent corrections have been applied and that an external zero-point shift has been made to force the mean abundance ratios of near-solar metallicity stars near the solar Galactocentric radius to be zero.

As described in the ASPCAP documentation, the various elemental abundances are determined by varying different library dimensions. For stars fit with the giant grids, the [C/M] ratio is varied for carbon; the [N/M] ratio is varied for nitrogen; and the [α/M] ratio is varied for the α-elements (O, Mg, Si, S, Ca, Ti); the [M/H] ratio is varied for all other elements (Na, Al, P, K, V, Cr, Mn, Fe, Co, Ni, Cu, Ge, Rb, Y^†, Nd). For the dwarf grids, there are no [C/M] or [N/M] dimensions^‡, so for stars fit with these grids the carbon and nitrogen abundances are fit by varying the [M/H] grids to give abundances relative to H.

Uncalibrated Parameters

The uncalibrated parameters are in the FELEM array in the SAS and in the FELEM_* parameters in the CAS.

We provide the initial, uncalibrated abundances for all of the stars in the catalog as they are output from the fitting program. In the summary data files, these uncalibrated parameters are stored in an array called FELEM, while in the CAS, the uncalibrated abundances are stored in separately named columns, e.g., FELEM_C_M, FELEM_N_M, FELEM_O_M, FELEM_NA_H, etc. The uncalibrated (FERRE-produced) abundances for C, N, O, Mg, Si, S, Ca, Ti are determined relative to the overall solar-scaled metallicity (i.e., [X/M]), while for the other elements (Na, Al, P, K, V, Cr, Mn, Fe, Co, Ni, Cu, Ge, Rb, Y^†, Nd) the uncalibrated (ASPCAP FERRE-produced) abundances are determined relative to hydrogen (i.e., [X/H]). The CAS column names accurately relay this information. The covariances as returned from the fitting program for the stellar parameters are given in the FPARAM_COV matrix and the uncertainties (from diagonal of the covariance matrix) for [X/H] or [X/M] are given in in the FELEM_ERR array in the summary data file. In the CAS, these values are reported in the aspcapStarCovar table for the parameters, and in columns FELEM_*_ERR for the abundances. As discussed below, however, these formal uncertainties are likely to significantly underestimate the true uncertainties.

Calibrated Parameters

The calibrated parameters are stored in the X_H, X_M arrays, and X_FE named tags in the SAS and in the Elem_FE in the CAS.

As described in the ASPCAP pages, internal calibration relations have been applied to all of the ASPCAP individual element abundances except C and N. The X_H and X_M arrays (SAS) are provided for convenience and directly related to each other via M_H; X_M = X_H - M_H. However, empirical uncertainties in these quantities (X_M_ERR and X_H_ERR) are determined from the scatter observed in clusters in X_M. These are also transferred to the named tag uncertainties (X_FE_ERR).

In the CAS, the abundances are stored in individual columns. Note that all of the quantities for the calibrated, named tags are converted to be abundances relative to iron (or [X/Fe]). Consequently, for the elements that were determined relative to metals, the [M/H] ratios were first added to convert these values to [X/H] before subtracting [Fe/H]. Thus, the calibrated elemental abundances are listed as, C_FE, N_FE, O_FE, NA_FE, MG_FE, AL_FE, etc.

For the FELEM X_M, and X_H arrays, the elements are listed by increasing atomic number, as given in HDU3 of the allStar FITS table in the ELEM_SYMBOL tag.  For the FELEM array, the ELEM_VALUE tags specify whether the raw [X/M] or [X/H] is given.

Regardless of how you obtain the parameters, it is important to pay attention to how the data have been flagged, because not all of the values are reliable. This is particularly true for uncalibrated values. For information on the flags, see the bitmask section below.

Before employing the abundances, users should check the values of the ASPCAPFLAG bitmask to confirm that there were no issues in the determination of the stellar parameters (e.g., by making sure that the STAR_BAD bit is not set). In addition, users need to check the value of the ELEMFLAG bitmask (also called PARAMFLAG) for the specific elemental abundances that are being used. If the derived abundance is near a grid edge, then the GRIDEDGE_BAD (within 1/8 grid spacing to the grid edge) or the GRIDEDGE_WARN (within 1/2 grid spacing to the grid edge) bit is set. If the temperature of the star is outside the range used to determine the internal calibration relation, then the calibration value at the closest end of the range is used, and the CALRANGE_WARN bit is set. If the elemental abundance from the window differs significantly from the parameter abundance (relevant for C, N, and the α-elements), then the PARAM_MISMATCH_BAD bit is set. If FERRE failed to deliver a value for the abundance, then the FERRE_BAD bit is set.

The reliability of the ASPCAP individual chemical abundances does vary. As expected, the most robust abundance derivations rely upon larger numbers of (high-quality) transitions. For a more in-depth assessment of ASPCAP abundances, see Jönsson et al. (2018), where a comparison to abundances independently determined from optical spectra is presented. In short, this paper find that for most of the elements -- C, Na, Mg, Al, Si, S, Ca, Cr, Mn, Ni -- the ASPCAP analysis has systematic differences to the comparisons samples of less than 0.05 dex (median), and random differences of less than 0.15 dex (standard deviation). However, the abundances of some elements -- N, O, K, Ti I, V, Co -- show strong correlations with some stellar parameters when comparing to reference studies. Note also that some abundances -- P, Cu, Ge, Rb, Y^† (Yb, see below) -- are not evaluated in this paper.

In certain regions of atmospheric parameter space, the reliability of ASPCAP abundances is suspect:

• Abundance analysis is particularly challenging at lower temperatures (T_eff < 4000 K). Currently, our calibration cluster sample does not include stars with T_eff < ~3750 K. Here we give calibrated results from the Kurucz grid down to 3500 K, where the calibration is extended slightly beyond the region over which the calibration relations are derived; these should be used with extreme caution!
• At warm temperatures (T_eff > 5250 K) or low metallicities ([Fe/H] < -1), the number of measurable spectral features is dramatically reduced and caution must be exercised. For example, CN lines in warm, low-metallicity stars are not detected and, consequently, the inferred nitrogen abundances for these stars are incorrect.
• The ASPCAP pipeline determines an abundance for all elements, regardless of whether an upper limit is more appropriate. Therefore, judgment should be applied regarding appropriate parameter spaces to use for specific scientific investigations. We also note also the presence of systematic effects due to simplifications in the modeling and line transfer (e.g. if atmospheric temperature inhomogeneities change significantly the strength of the predicted CO lines), which have not been properly characterized at this stage.
• Because stellar parameters are determined using global [M/H] and [α/M] as dimensions, if stars have non-solar variations within these elemental abundance groups, the stellar parameters can inferred incorrectly. This is a known problem for second-generation globular cluster stars, which can have significant variations in oxygen abundance; this can lead the ASPCAP methodology to infer an incorrect effective temperature, especially for cooler stars where OH is a strong function of effective temperature, and this, in turn, can lead to systematic errors in other parameters and abundances.

Except what has already been stated above, more caveats regarding certain element abundance determinations are given below:

• For dwarf stars, calibrated abundances are not provided for Na, Ti II, and Co.
• For dwarf stars, the reported abundances for C and N^‡ C and N are not reliable.
• Measurements of Cu, Ge, Rb, Y^† (Yb, see below), and Nd are derived from weak, blended lines. The current methodology does a poor job with these and the results from star clusters demonstrate that there is probably little real information being extracted. No calibrated results are presented and even the uncalibrated results are not reliable. Additional work is needed to extract these and the current tags are placeholders only.
• The measurements for Y^† were determined from a Yb line, and are not valid (for either element!).

The ASPCAP internal calculation of the abundance uncertainties is based upon the quality of the synthetic spectral fits.  Ideally, the ASPCAP uncertainty estimates would well approximate the true uncertainties in the derived stellar parameters. However, the pipeline-reported errors seem to substantially underestimate the true error associated with the derived parameters as they do not account for systematic uncertainties (e.g., LSF-matching).

To get a better estimate of the uncertainties, we use the abundance derivations in both open and globular cluster stars with the underlying assumption that for individual element abundances are uniform for all cluster members (apart from C and N, which have mixing effects in giants). The full details of this procedure are described in Holtzman et al. [2018]).  We have chosen to use only those clusters with metallicity greater than [M/H] > -1, which restricts the sample primarily to open clusters. In the selected cluster sample, we measure the element abundance scatter in bins of temperature, metallicity, and signal-to-noise (S/N). For each individual element, we fit these values with a simple functional form:

where σ is the scatter among cluster stars relative to the mean derived abundance for the same stars.
Note that in the above relation, the fit to log σ ensures that the derived relation will always yield a positive uncertainty. The values for the coefficients (A, B, C, D) associated with each element are given in the table below.

These calculated uncertainties represent the internal scatter for APOGEE abundances at a single temperature. Across a broader temperature range, discernible abundance trends as a function of temperature arise for stars within the clusters. In consequence, small internal calibrations have been been made to the element abundances as described on the ASPCAP page . The scatter around the calibrations for each element yields a "global" measure of the uncertainty (displayed in the table below); given the larger uncertainties and the potential for real abundance spread in metal poor clusters, the "global" measurement is calculated across six relatively metal-rich clusters (NGC 2420, M67, NGC 188, NGC 7789, NGC 6819, and NGC 6791).  For each of the elements as well as the overall metallicity and relative α abundance parameters, the coefficients and uncertainties for each element are as follows:

Element	A	B	C	D	σ(4500,[M/H]=0,S/N=100)	"Global" uncertainty
C	-3.488	9.42E-04	-1.93E-03	-0.685	0.030
CI	-3.010	4.24E-04	-2.82E-03	-0.567	0.049
N	-3.138	8.24E-04	-1.20E-03	-0.632	0.043
O	-3.454	8.48E-04	-3.15E-03	-0.649	0.031	0.039
Na	-2.413	4.62E-04	-2.84E-03	-0.188	0.089	0.132
Mg	-3.826	-7.13E-05	-2.50E-03	-0.693	0.021	0.039
Al	-2.974	6.91E-04	-2.00E-03	-0.345	0.051	0.081
Si	-3.643	3.17E-04	-1.60E-03	-0.473	0.026	0.037
P	-2.233	3.10E-04	-2.59E-03	-0.149	0.10	0.13
S	-2.704	1.12E-04	-3.68E-03	-0.453	0.066	0.062
K	-2.966	2.52E-04	-5.55E-03	-0.467	0.051	0.061
Ca	-3.510	2.02E-04	-5.21E-03	-0.634	0.029	0.038
Ti	-3.243	5.48E-04	-2.68E-03	-0.508	0.039	0.064
Ti II	-2.386	4.63E-04	-1.49E-03	-0.188	0.092	0.147
V	-2.626	6.87E-04	-2.50E-03	-0.381	0.072	0.117
Cr	-3.100	4.30E-04	-4.13E-03	-0.626	0.045	0.071
Mn	-3.424	3.30E-04	-4.60E-03	-0.582	0.032	0.054
Fe	-4.757	-1.80E-04	-8.32E-04	-0.443	0.009	0.047
Co	-2.469	7.21E-04	-4.16E-03	-0.065	0.084	0.141
Ni	-3.779	2.84E-04	-5.71E-03	-0.659	0.022	0.024
M	-3.667	5.80E-04	3.98E-04	-0.568	0.025	0.035
α	-4.284	2.10E-05	-1.45E-03	-0.793	0.013	0.014
1Note that no "global" uncertainties are given for carbon and nitrogen, because the abundances of these elements are expected to vary within clusters across a broad temperature range. As a result, the scatter will not reflect the measurement uncertainty for C and N as it does for other species.

Another issue is the determination of uncertainty for relative abundance ratios. As mentioned above, the ASPCAP abundances are presented in both [X/H] and [X/Fe]. We present empirical uncertainty estimates based on the scatter observed within cluster member stars; we estimate uncertainties in [X/M] and adopt this for the empirical uncertainties in elemental abundances.
Note that the values derived in this way for [Fe/H] are underestimates because the measurement of [M/H] is determined to a large extent from Fe features, so the scatter in [Fe/M], from which the [Fe/H] uncertainty is taken, is artificially low.