APOGEE stellar parameters and abundances

Introduction

A primary goal of the APOGEE survey is to get chemical abundances of multiple elements for the survey sample. To determine chemical abundances from lines of different elements, the stellar atmospheric parameters -- effective temperature, surface gravity, overall metallicity, and microturbulence -- must be known. The APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP) implements a two-step process: first to determine the stellar parameters from a fit to the entire APOGEE spectrum, and then to use these parameters to fit various small regions of the spectrum dominated by spectral features associated with one particular element to derive individual abundances.

The wavelength region covered by the APOGEE spectra includes lines of many elements, but molecular features, in particular, from CN, CO, and OH can be very prominent, especially in cooler stars that comprise the bulk of the survey sample. A global fit needs to include the possibility of variations in elemental abundance ratios that involve elements that contribute to these species. For this reason, the stellar parameters portion of the ASPCAP pipeline allows for variations in seven parameters: effective temperature, surface gravity, microturbulence, overall metal abundance [M/H] , and relative α-element (which includes O) [α /M], carbon [C/M], and nitrogen [N/M] abundances. The abundance of each individual element X heavier than helium, is defined as

[X/H] = log₁₀ (n_X/n_H) - log₁₀(n_X/n_H)_☉

where n_X and n_H are respectively the number of nuclei of element X and hydrogen, per unit volume in the stellar photosphere. We define [M/H] as an overall scaling of metal abundances with a solar abundance ratio pattern, and [X/M] as the deviation of element X from the solar abundance pattern:

[X/M] = [X/H] - [M/H].

The α elements are defined as O, Ne, Mg, Si, S, Ca, and Ti. For the current release, the raw ASPCAP metallicities have been calibrated to objects with known [Fe/H]; see more details about the implications in the section on calibration below.

In DR10, we provide the best fitting values of these seven parameters. DR10 does not include abundances of other elements; the derivation of these is currently being developed and they will be included in subsequent data releases.

On this page, we describe the basic operation of ASPCAP. More operational details are available in Garcia-Perez et al. (2013), and discussions of the accuracy and precision of the results can be found in Garcia-Perez et al. (2013) and Meszaros et al (2013).

For a discussion of the quality of the derived parameters, and important things to know about using them, all users of ASPCAP results should read Using APOGEE stellar parameters.

APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP)

ASPCAP Components

Large grids of synthetic spectra are computed for the APOGEE wavelength region, using a custom linelist derived for this portion of the spectrum. The grids cover the full expected range of the seven parameters mentioned above: T_eff, log g, vmicro, [metals/H], [α/M], [C/M], and [N/M]. The synthetic spectra are "pseudo-continuum normalized" using a fitting procedure so that they can be compared with observed spectra that are normalized in the same way (because the true continuum level is hard to determine from the observed spectra).
Combined APOGEE spectra are pseudo-continuum normalized to remove variations of spectral shape arising from interstellar reddenning, errors in relative fluxing, and atmospheric absorption. This normalization is done the same way as for the synthetic spectra, so that they can be directly compared.
An independent code (FERRE -- see Allende Prieto et al. 2006) searches for the best matching synthetic spectrum for each star via a χ² minimization technique, allowing for interpolation in the synthetic spectra grid.
From the results of the different synthetic grids, the best-fit synthetic spectrum is identified for each object, and the best-fitting results for all of the stars are compiled. Using results from the derived parameters for objects of known parameters, some calibration relations have been derived, and these relations are applied to the derived parameters. In addition, this stage sets a series of data quality flags for the stellar parameter results.

Stellar Spectral Libraries (pre-computed)

Grids of normalized stellar synthetic spectra are computed with the spectral synthesis code ASSεT (Koesterke 2009), using model atmospheres from Castelli and Kurucz (2003), and a linelist for the APOGEE wavelength region tuned to match the spectrum of the Sun (see Shetrone et al.). The model atmospheres are calculated using scaled-solar abundances from Grevesse and Sauval (1998), while the synthetic spectra adopt scaled-solar abundances by Asplund et al. 2005 and variations in [α/M], [C/M], and [N/M] not considered in the calculations of atmospheric structures; as a result, the synthetic spectra are not fully self-consistent. Future work will include the use of consistent ATLAS9 and MARCS model atmospheres calculated by Meszaros et al. 2012 (see this site for ATLAS and this one for MARCS models).

The synthetic spectra are smoothed to a nominal spectral resolution of R=22500 (using an assumed Gaussian profile) and sampled on a logarithmic wavelength scale (~10⁴ frequencies) that matches the sampling of the combined APOGEE spectra. While the actual APOGEE spectra have some variations of LSF depending on wavelength and on the fiber in which they were observed, initial tests suggest that the assumption of a constant LSF does not change the derived parameters by much, although future work may consider this in more detail.

Ideally we would store the entire grid of stellar spectra in memory to allow for efficient computation comparison of our observed normalized data to the spectrum match each grid point. However, the multi-dimensional synthetic spectrum library is too large to store simultaneously in the memory of a typical computer. For this reason, the flux arrays are compressed using Principal Component Analysis, and the full parameter space is split into several different grids that cover different temperature regimes; we refer to these grids by their approximate spectral classes: A, F, G, and K.

In general, seven parameters are required to adequately describe the spectra: effective temperature, surface gravity, microturbulence, metal abundance (all elements heavier than He), α element (O, Ne, Mg, Si, S, Ca, and Ti) relative abundance, carbon relative abundance, and nitrogen relative abundance. However, for hotter stars, there are far fewer spectral features, and for these, the grids only cover ranges in effective temperature, surface gravity, and metal abundance. While microturbulence can be considered a free parameter, we have adopted a fixed relation that sets microturbulence as a function of surface gravity: ξ_t=2.24-0.3*log g, which was derived from a run of a subset of data that fit microturbulence as a free parameter. Fixing microturbulence in this way decreases the time needed to do the fittings and enhances precision in the remaining parameters.

The following table summarizes the synthetic grids:

Libraries
Class	Dimensions	`T`_eff	log `g`	[M/H]	[C/M]	[N/M]	[α/M]
K	6	3500 to 5000	0 to 5	-2.5 to 0.5	-1 to 1	-1 to 1	-1 to 1
G	6	4750 to 6500	1 to 5	-2.5 to 0.5	-1 to 1	-1 to 1	-1 to 1
F	3	6000 to 10000	2 to 5	-2.5 to 0.5
A	3	8000 to 15000	3 to 5	-2.5 to 0.0

ASPCAP Pre-processing (IDL wrapper)

The comparison of observations with the library requires the pre-processing of the combined APOGEE spectra, which is carried out by an IDL wrapper, and consists of masking out bad pixels and normalizing the spectra.

Since FERRE minimizes χ², realistic estimates of flux uncertainties are critical, and any bad data must be masked. Pixels flagged as bad (saturated, cosmic ray, etc) in the data-reduction process and pixels around the sky emission lines are ignored for continuum normalization, and in the χ² minimization. To account for small systematic errors in spectral calibration, we set a minimum error of 0.5 percent for all pixels.
To normalize the spectra, the spectral regions covered by each of the three chips used in the APOGEE spectrograph are considered separately. In each region, a sigma-clipping algorithm is used to fit a polynomial to the upper envelope of the spectrum. In order to allow a meaningful comparison to the library of synthetic spectra, an identical normalization is performed on the library, using the same spectral regions with the same sigma-clipping and polynomial form. We emphasize that this normalization is not a normalization to the true continuum, because, especially for metal-rich stars, the upper envelope of the data may still not be at the true continuum level. Thus, we do not calculate abundances from eduivalent widths from these "pseudo-continuum" normalized spectra, but rather comparing to models that have had the same normalization procedure applied.

Determination of stellar parameters (FERRE)

Stellar parameters and the relative abundances of C, N and α-elements are determined by the FORTRAN90 code FERRE, which compares the observations with the grid of pre-computed synthetic spectra. The code uses a χ² criterion as the merit function, and searches for the best matching synthetic spectrum using the Nelder-Mead algorithm (Nelder and Mead 1965). The search is run 12 times starting from different locations: the center of the grid for [C/M], [N/M] and [α/M], and at two different places symmetrically located from the grid center for [M/H] and log g, and at three for T_eff. Interpolation within the grid of synthetic spectra is accomplished using cubic Bezier interpolation. The code returns the best matching spectrum, the parameters associated with that spectrum (stellar parameters and [C/M], [N/M] and [α/M] abundance ratios), the covariance matrix of these parameters, and the χ² value for the best-matching spectrum.

ASPCAP post-processing (IDL wrapper)

Once FERRE has delivered results for the different temperature grids, the IDL wrapper chooses the result that produces the lowest χ². These results (pseudo continuum, normalized observed spectra, flux errors, stellar parameters and [C/M], [N/M], [α/M] values, covariance matrix, χ² values) along with other relevant information (e.g. 2MASS photometry, reddening, radial velocities, signal-to-noise ratios etc.) are compiled.

Output data files

ASPCAP is generally run separate for each APOGEE field (i.e. location in the sky). The ASPCAP output for all stars in the field is stored in a single aspcapField file. Results for each individual star are stored in aspcapStar files. See the links for a full description of the data in these files, but briefly, these files are binary FITS tables that contain three separate tables: the first contains the information about the star and the derived stellar parameters, the second contains the observed and best-matching synthetic spectra, and the third contains library and wavelength information.

External Calibration and Final Error Estimates of the Parameters

In addition to the raw FERRE output parameters, we also provide a calibrated set of parameters. The calibrations have been derived from observation and analysis of spectra from stars in stellar clusters that span a range of stellar parameters. These observations allow us to quantify systematic deviations of the raw FERRE output from reference literature values. Presumably, these systematics arise because of issues in the analysis: inaccaccuracies in the atomic/molecular line data, inadequacies of the stellar models, line formation, etc.

The ASPCAP metallicities have been calibrated to metallicities from optical spectral analysis of stars in clusters. Since most optical metallicity values track iron abundances ([Fe/H]), the ASPCAP metallicity indicator [M/H] can generally be interpreted as [Fe/H] after the calibration has been applied, and the abundances relative to metallicity ([alpha/M], [C/M], and [N/M]) can be interpreted as relative to Fe. However, we maintain the M notation to underline that they are the result of the fit of lines by many elements other than Fe. In the next data release we intend to publish individual elemental abundances, including [Fe/H] (which would allow non-zero values of [Fe/M]), based on fits to specific absorption lines in the APOGEE spectral region, making it possible to establish the detailed abundance patterns of the sample stars beyond the current set of elements.

The data used to derive the calibration relations and the derivation of the relations themselves are described in Meszaros et al. (2013). The calibrations are summarized here:

Temperatures have been calibrated to photometric temperatures using the González Hernández and Bonifacio (2009) IRFM scale.
- Teff = Teff_ASPCAP - 0.3968 *Teff_ASPCAP + 1938.3 (4600 < Teff < 5500);
  Teff = Teff_ASPCAP + 113 (Teff < 4600)
Metallicity results have been calibrated using a sample of well studied clusters covering a wide range of metallicities (M/H]=-2.35–+0.47) against their overall published spectroscopic metallicities.
- [M/H] = [M/H]_ASPCAP + 0.06199([M/H]_ASPCAP)² - 1.125×10^-4T_eff + 4.734×10^-5T_eff[M/H]_ASPCAP + 0.544
Corrections for the surface gravities were estimated from the same set of clusters and using stellar isochrones assuming the ASPCAP T_effs and the literature metallicity overall values, as well as from a reference sample of stars with asteroseismic surface gravities from observations by the Kepler mission. Based on these, we have used the following calibration relations:
- log g = log g (ASPCAP) + 0.1222 ([M/H]_ASPCAP) - 0.2396
Internal parameter error estimates are delivered by FERRE as derived from the χ² curvature. These internal errors are generally quite small. We provide a set of guiding external errors estimated from the scatter observed in well-studied Galactic stellar clusters covering the bulk of the parameter range in APOGEE (Meszaros et al., 2013):
- σ(Teff) = 83.8 - 39.8*[M/H]
- σ(log g) = 0.2 dex
- σ([M/H]) = 0.0548 - 0.0361 [M/H]
- σ([α/M]) = 0.1