Using APOGEE Stellar Abundances

As described in the ASPCAP documentation, the various elemental abundances are determined by varying different library dimensions: for the element C, the [C/M] ratio is varied; for the element N, the [N/M] ratio is varied; and for the α-elements (O, Mg, Si, S, Ca, Ti), the [α/M] ratio is varied. So, the uncalibrated (ASPCAP 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, K, V, Mn, Fe, Ni), the uncalibrated (ASPCAP FERRE-produced) abundances are determined relative to hydrogen (i.e., [X/H]).

UNCALIBRATED PARAMETERS (FELEM ARRAY [SAS]; FPARAM_Elem_* [CAS]): We provide the initial, uncalibrated abundances for all stars. 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., FPARAM_C_M, FPARAM_N_M, FPARAM_O_M, FPARAM_NA_H, etc. As mentioned above, uncalibrated values are reported relative to the overall metallicity for some elements (C, N, O, Mg, Si, S, Ca, Ti), whereas the other uncalibrated values are reported relative to hydrogen (for Na, Al, K, V, Mn, Fe, Ni).  The CAS column names accurately relay this information.

CALIBRATED PARAMETERS (ELEM ARRAY [SAS]; Elem_H [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. Calibrated abundances are provided for the giants only (a subset of the total APOGEE stellar sample).  Calibrated parameters are stored in the ELEM array of the summary files, and are also copied into explicitly named tags. In the CAS, they are stored in individual columns. Note that all of the quantities for the calibrated, named tags are converted to be abundances relative to hydrogen ([X/H]). Consequently, for the elements that were determined relative to metals, the [M/H] ratios were added to convert these values to [X/H]. Thus, the calibrated elemental abundances are listed as, C_H, N_H, O_H, NA_H, MG_H, AL_H, etc.

For the FELEM and ELEM arrays, the elements are listed by increasing atomic number, as given in HDU3 of the allStar FITS table in the ELEM_SYMBOL tag.  The dimension used in the fit, i.e. reflecting [X/M] or [X/H], is specified in the ELEM_VALUE tag.

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 for the specific elemental abundances that are being used. ELEMFLAG currently flags two possible issues with individual elemental abundances.  First, 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. Second, 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.

The reliability of the ASPCAP individual element abundances does vary. As expected, the most robust abundance derivations rely upon larger numbers of (high-quality) transitions. Abundances inferred from molecular species (C, N and O) are anticipated to have large associated errors (as they are highly sensitive to effective temperature, surface gravity, molecular equilibrium, etc.).

We have determined that the ASPCAP abundances of titanium (Ti) do not show the expected trend with metallicity as has been found in previous literature studies (see Holtzman et al. 2015). Since the reason(s) for these departures are still not well understood, users are cautioned about the titanium abundances.

In certain regions of atmospheric parameter space, the reliability of ASPCAP abundances is suspect. We have reasons to doubt the abundance results for the coolest stars in the APOGEE sample (Teff < 3800 K). At warm temperatures (Teff > 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 and should be discarded. ASPCAP provides error bars that assist user understanding regarding the detectability of features. 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.

The ASPCAP 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 errors (e.g., LSF-matching).

To determine the uncertainties, we then rely upon the abundance derivations in both open and globular cluster stars with the underlying assumption that for individual element abundances, the derived values should be uniform in all cluster members (C and N being the exceptions).  We have chosen to employ only clusters with metallicity greater than [M/H] > -1, which consequently restricts the sample to mostly open clusters. In the selected cluster stellar 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:

log σ = A + B (Teff -4500) + C [M/H] + D (S/N -100)

Note that in the above relation, the fit to the log (of the σ quantity) 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 of APOGEE abundances at a single temperature. Across a broader temperature range, discernible abundance trends as a function temperature arise within the clusters. Small internal calibrations have been consequently made to the element abundances as described on the ASPCAP page . The scatter around the calibrations for each element yields a “global” uncertainty quantity (displayed in the table below).  For the set of 15 elements as well as the overall metallicity and relative alpha abundance parameters, the coefficients and uncertainties are as follows:

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, so scatter will not reflect the measurement uncertainty.
Element	A	B	C	D	σ(4500,[M/H]=0,S/N=100)	“Global” uncertainty
C1	-3.350	0.769	-0.919	-0.066	0.035
Al	-2.764	0.471	-0.868	-0.162	0.063	0.067
Ca	-3.226	0.284	-0.879	-0.429	0.040	0.059
Fe	-3.357	0.098	-0.303	-0.071	0.035	0.053
K	-2.770	0.216	-0.667	-0.275	0.063	0.065
Mg	-3.537	0.263	-0.825	-0.297	0.029	0.053
Mn	-3.031	0.639	-0.661	-0.326	0.048	0.061
Na	-2.352	-0.002	-0.915	-0.263	0.095	0.064
Ni	-3.153	0.135	-0.493	-0.185	0.043	0.060
N1	-2.704	0.291	-0.591	-0.078	0.067
O	-3.649	0.670	-0.614	-0.093	0.026	0.050
Si	-3.150	0.383	-0.224	-0.105	0.043	0.077
S	-3.037	0.507	-0.625	-0.299	0.048	0.063
Ti	-3.186	0.657	-0.819	-0.068	0.041	0.072
V	-1.608	0.900	-0.400	-0.418	0.200	0.088
[M/H]	-3.603	0.109	-0.433	0.039	0.027	0.049
[α/M]	-4.360	0.060	-0.848	-0.096	0.013	0.048

Further details may be found in Holtzman et al. (2015).

Another issue is the determination of uncertainty for relative abundance ratios. As mentioned above, the ASPCAP abundances are presented in [X/H]. In the calculation of the relative [X/Y] abundance ratio and its associated uncertainty (where [X/Y] = [X/H] – [Y/H]), it is not necessarily appropriate to add the ([X/H], [Y/H]) uncertainties in quadrature. While it would be correct to do so in the case of random, uncorrelated errors, it is possible that the abundance derivations for two individual elements could be correlated (e.g., if both had [similar] dependence upon the uncertainties in the underlying stellar parameters). We do not offer any prescription here for as how to best deal with correlated errors, but users should be aware of this issue.