Using APOGEE Stellar Abundances

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 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, P, K, V, Cr, Mn, Fe, Co, Ni, Cu, Ge, Rb), the uncalibrated (ASPCAP FERRE-produced) abundances are determined relative to hydrogen (i.e., [X/H]). 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 (FELEM ARRAY [SAS]; FELEM_* [CAS]): We provide the initial, uncalibrated abundances for all stars, 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. 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, P, K, V, Cr, Mn, Fe, Co, Ni, Cu, Ge, Rb).  The CAS column names accurately relay this information. The uncertainties as returned from the fitting program for the stellar parameters are given in the FPARAM_COV matrix and for individual [X/H] or [X/M] 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 (X_H, X_M arrays, and X_FE named tags [SAS]; Elem_FE [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 parameters are stored in the X_M and X_H arrays of the summary files, and are also copied into explicitly named tags (X_FE). The X_H and X_M arrays 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 and X_H, respectively. In the named tag uncertainties (X_FE_ERR), the X_M uncertainties (which are usually smaller) are adopted.

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 ([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. (note that this differs from DR12, where abundances in named tags were provided relative to H).

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.  The ELEM_VALUE tags specifies whether [X/M] or [X/H] is given.

Regardless of how you get 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 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.).

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

• Abundance analysis is particularly challenging at lower temperatures (Teff < 4000 K). In DR13 we have included spectral libraries computed using a set of MARCS stellar atmospheres; these extend results below the 3500 K limit imposed by our Kurucz model atmosphere grid. However, the derived stellar parameters do not show a smooth transition between in the two grids. Even in the overlap region (3500 < Teff < 4000 K), there are some systematic differences between the results from the two grids. At cooler effective temperatures (Teff < 3500K) , there is some distinct clumping in stellar parameter space. These highlight the challenges of working at these temperatures. There are several known issues:
  • the Kurucz models are for plane-parallel atmospheres while the MARCS models at low surface gravity are spherical models, so this could lead to systematic differences
  • for the MARCS grid, there were many non-converged atmospheric structures. To allow ASPCAP to work, these “holes” were filled with “nearby” adjacent models. Given the coarseness of the MARCS grid and the use of cubic interpolation within the grids, many of the stars fall in regions of parameter space that are affected by these “filled” models, which could introduce significant systematics, and could be related to the apparent clumping of results in effective temperature

  The situation is further complicated because we have few stars against which we can calibrate our results; our calibration clusters do not include stars with Teff < ~3750. For DR13, 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. Below this temperature, we provide only uncalibrated results from the MARCS grid; these should be used with extreme caution!

• 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. If the ASPCAP pipeline errors reported in the FELEM_ERR array or tag are large, this can indicate that abundances are poorly measured because a true minimum is not found for weak lines. The ASPCAP pipeline determines an abundance for all elements, regardless of whether an upper limit is more appropriate. Therefore judgement should be applied about the appropriate parameter space to study abundances. 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.
• Since the 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.

Caveats regarding certain element abundance determinations are listed below:

• We have determined that the ASPCAP abundances of titanium (Ti) do not show the expected trend with metallicity found in previous literature studies (see Holtzman et al. 2015); see also Hawkins et al. 2016. Since the reason(s) for these departures are still not well understood, users are cautioned about the titanium abundances.
• Measurement of Co, Ge, and Rb in clusters show very significant trends with effective temperature. We have derived temperature-dependent calibration relations and applied them to derived calibrated abundances, but results for these have a large potential for systematic error.
• Measurements of Y and Nd are derived from weak, blended lines. The current methodology does a poor job with these and results from 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 future work is needed to extract these, and the current tags are just placeholders.

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 errors (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 in all cluster members (apart from C and N, which have mixing effects in giants).  We have chosen to employ only clusters with metallicity greater than [M/H] > -1, which restricts the sample to mostly 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:

log σ = A + B (Teff -4500)/1000. + C [M/H] + D (S/N -100)/100.

where σ is the scatter among cluster stars relative the the mean derived abundance.
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 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); given the larger uncertainties and the potential for real abundance spread in metal poor clusters, this is calculated across six relatively metal-rich cluster (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 alpha abundance parameters, the coefficients and uncertainties are as follows:

Element	A	B	C	D	σ(4500,[M/H]=0,S/N=100)	“Global” uncertainty
C 1	-3.243	0.608	-0.757	-0.257	0.039
CI 1	-2.804	0.403	-0.743	-0.319	0.061
N 1	-2.671	0.373	-0.407	-0.192	0.069
O	-3.410	1.471	-0.778	-0.182	0.033	0.045
Na	-2.389	0.140	-0.926	-0.323	0.092	0.059
Mg	-3.980	0.284	-0.949	-0.115	0.019	0.029
Al	-2.616	-0.192	-0.628	-0.399	0.073	0.072
Si	-3.464	0.548	-0.482	-0.212	0.031	0.040
P	-1.988	0.384	-0.568	-0.369	0.137	0.120
S	-2.199	-0.030	-0.402	-0.295	0.111	0.122
K	-3.098	0.208	-0.583	-0.496	0.045	0.048
Ca	-3.520	0.153	-0.895	-0.405	0.030	0.032
Ti	-3.108	0.295	-0.741	-0.185	0.045	0.057
TiII	-2.192	0.328	-0.538	-0.267	0.112	0.116
V	-2.447	1.030	-1.096	-0.519	0.087	0.089
Cr	-3.191	0.290	-0.775	-0.455	0.041	0.048
Mn	-3.523	0.235	-0.614	-0.488	0.029	0.049
Fe	-5.316	0.202	-0.874	0.019	0.005	0.053
Co	-2.062	1.064	-0.656	-0.523	0.127	0.095
Ni	-4.067	0.442	-0.816	-0.395	0.017	0.015
Cu	-2.140	-0.096	-0.559	-0.426	0.118	0.083
Ge	-1.893	0.258	-0.665	-0.395	0.151	0.107
Rb	-2.325	0.466	-1.117	-0.360	0.098	0.082
M	-3.730	0.232	-0.524	0.013	0.024	0.052
alpha	-4.219	0.053	-0.794	-0.127	0.015	0.017
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.

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 scatter observed within clusters; we independently estimate uncertainties in [X/H] and [X/M]. In general, the scatter in [X/M] appears to be smaller for most elements than the scatter in [X/H].