Stellar Parameters and Abundances: ASPCAP
One main objective of the APOGEE survey is to extract the chemical abundances of several elements for the entire stellar sample. This is achieved by comparing APOGEE observations to a large library of synthetic spectra and determining the best matching synthetic spectrum, allowing for interpolation within the library. To determine the elemental abundances, the stellar atmospheric parameters -- effective temperature, surface gravity, overall metallicity, microturbulent and macroturbulent velocities, and rotation -- must be known. The APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP) employs a two-step process to extract abundances: first, determination of the atmospheric parameters by fitting the entire APOGEE spectrum, and second, use of these parameters to fit limited regions of the spectrum dominated by spectral features associated with a particular element in order to derive the individual element abundance ([X/H] or [X/M], see below).
The wavelength region covered by the APOGEE spectra includes a vast number of atomic transitions 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 have a significant effect in the equation of state (e.g. through CO formation or contributing free electrons) or the opacity. For this reason, the stellar parameters portion of the ASPCAP pipeline has the potential to allow for variations in nine parameters: effective temperature, surface gravity, microturbulence, macroturbulence, rotation, overall metal abundance [M/H] , relative α-element abundance [α /M] (defined as O, Mg, Si, S, Ca, and Ti changing with solar proportions in lockstep), carbon [C/M], and nitrogen [N/M] abundances. For giant stars, this is simplified by deriving relations for macroturbulence as a function of metallicity; for dwarf stars, this is simplified by the assumption that solar abundance ratios for carbon and nitrogen are sufficient for the global stellar parameter fits (carbon and nitrogren abundances are still derived separately during the abundance determinations).
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. For a discussion of the quality of the individual elemental abundances, and important things to know about using them, all users of ASPCAP results should read Using APOGEE chemical abundances.
For additional information on ASPCAP, consult Garcia-Perez et al. (2015).
The APOGEE abundance scale
The abundance of each individual element X heavier than helium, is defined as
where nX and nH 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 the metal abundance pattern in the Sun, and therefore [X/M] different from zero involves deviation of the abundance of element X from the solar abundance pattern:
Once the stellar parameters have been determined, abundances for individual elements are derived individually, by fitting the spectrum in limited spectral windows that contain features of the desired element (see the section on abundances below).
Some caveats apply. The abundances are NOT truly differential to the Sun. Solar abundances are adopted from Asplund et al. (2005), and used for computing model atmospheres (see Mészáros et al. 2012) and synthetic spectral grids. The line list used for spectral synthesis includes, in addition to laboratory and theoretical transition probabilities and damping constants, modifications to match the solar spectrum and that of the red giant Arcturus. Please consult Shetrone et al. (2015) for further details.
APOGEE DR14 also includes a spectrum of the Sun observed through reflected light on the asteroid Vesta, and also a spectrum of Arcturus observed using the NMSU 1m telescope in conjunction with the APOGEE instrument. These allow some independent checks of the abundance scale.
In DR14, we provide the best fitting values of the global stellar parameters as well as individual elemental abundances for C, N, O, Na, Mg, Al, Si, P, S, K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, and Rb. The raw measurements from the fits to the spectral grid are internally calibrated (small temperature-dependent corrections), predominantly using observations of stellar clusters. In DR14, the abundances are calibrated by forcing the mean abundance of stars near the solar circle that have overall metal abundance near the solar abundance to be the solar abundance. For more details, see the section on calibration below.
APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP)
Following is a brief overview of ASPCAP. For more details, see the sections below.
- 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 eight parameters mentioned above: Teff, log g, vmicro, vmacro/vsini, [M/H], [α/M], [C/M], and [N/M].
- 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 (the true continuum level is hard to determine from the observed spectra).
- An independent code (FERRE -- see Allende Prieto et al. 2006) searches for the best matching synthetic spectrum for each star via 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 the best-fit parameters, small windows around features of specific individual elements are fit to derive the elemental abundances.
- Internal calibration relations are applied that make small temperature-dependent corrections to the abundances; these were derived by looking at abundances as a function of temperature within (mostly metal-rich, open) clusters, under the assumptions that these clusters have homogeneous abundances. Using results from the derived parameters for objects of known parameters, some external calibration relations have been derived, and these relations are applied to some of the derived parameters. In addition, this stage sets a series of data quality flags for the stellar parameter and abundances results.
This procedure works only as well as the synthetic spectra match the observed data, and to the degree that the observed data contain parameter and abundance information. At cooler temperatures (T<4000K) the model spectra do not match as well, so parameters and abundances there are currently less certain. At warmer temperatures (T>5500 K), spectral features of some elements become very weak, so their measurement is significantly less certain.
Stellar Spectral Libraries
Grids of normalized stellar synthetic spectra are computed with the spectral synthesis code
Turbospectrum ( Alvarez and Plez 1998; Plez 2012), using ATLAS9 (or MARCS) model atmospheres described by Mészáros et al. 2012 (see also Zamora et al 2015), and a line list for the APOGEE wavelength region compiled from the literature and tuned to match the spectrum of the Sun (see Shetrone et al. 2015). The model atmospheres and the synthetic spectra adopt solar abundances by Asplund et al. 2005, but with varying metallicities, carbon, and α-element abundances. Variations in nitrogen abundances are also considered, but only at the synthesis stage (not in the model atmospheres). A comparison between spectra computed with ATLAS9 model atmospheres and the ASSET ( Koesterke 2009) spectral synthesis code with MARCS models and Turbospectrum has been made by Zamora et al. 2015).
Ideally we would store the entire grid of stellar spectra in memory to allow for efficient computation comparison between observed and interpolated model spectra. 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 different grids that cover different temperature regimes. For DR14 we use five grids: a GK giant grid which covers 3500-6000 K with giant-like CNO isotopic ratios, a GK dwarf grid which covers 3500-6000 K with solar isotope ratios, the F grid which covers 5500-8000 K with solar isotope ratios, an M giant grid which covers 2500-4000 K with giant isotope ratios, and an M dwarf grid that covers 2500-4000K with solar isotope ratios. Note that the GK and F grids are based on ATLAS9 model atmospheres, while the cooler M grids are based on MARCS atmospheres.
To determine the final grid, a coarse run is performed with the F, GK giant, and M giant grids is done, fixing the abundance ratios C/Fe and N/Fe to solar values, and the results are used to decide what grid(s) for a full run. If more than one grid is used, then the grid that produces the best fit is adopted; however, in the range 3500<Teff<4000 K, we force the use of the GK grid over the M grid, so that results are uniform over this temperature range.
In general, many parameters may be required to adequately describe the spectra, but for warm stars (Teff>6000 K) there is not sufficient information in the APOGEE spectra to independently determine all of those parameters. In addition there are instances in which full fits including all of the relevant parameters is computationally expensive and therefore some compromises are made.
For the giant grids in DR13, we did not have microturbulent velocity as a separate dimension and instead derived a fixed relation between microtubulence and surface gravity. In DR14, we return to a 7D approach and derive microturbulent velocity independently (as was done in DR12). We still adopt a fixed relation for macroturbulent velocity. The adopted relation for macroturbulent velocity for giants is:
This relation was derived from a calibration subsample of APOGEE spectra. We use this subsample to first derive a microturbulence relation. We then do another 7D run on this calibration subsample with microtublence fixed by the previously-derived relation, but macroturbulence floating as the 7th dimension. We derive the macroturbulence relation from this run where it is used in the final 7D run to determine the final stellar parameters.
For the dwarf grids, the relative carbon and nitrogen abundances are fixed to solar values, i.e., [C/M]=[N/M]=0, for the parameter determination, and microturbulent velocity and rotation are retained as independent dimensions. This results in a 6D grid.
The synthetic spectra are smoothed using a line spread function (LSF) measured from APOGEE sky spectra. However, the LSF varies with wavelength and location in the frame. In DR13, we made a first effort to account for this by creating four different library versions for different groups of mean fiber number for each star (stars are observed with different fibers in different visits); (note that DR12 used a single average LSF). After smoothing, the library spectra are interpolated onto the same wavelength scale as the combined APOGEE spectra, and pseudocontinuum normalized. We use this same approach in DR14.
The following table summarizes the synthetic grids:
|Class||Dimensions||Teff||log g||log vmicro||log vmacro||log vrot||[M/H]||[C/M]||[N/M]||[α/M]|
|GK giant||7||3500 to 6000||0 to 5||-0.301 to 0.903||f([M/H])||0.||-2.5 to 0.5||-1 to 1||-1 to 1||-1 to 1|
|step: 250||step: 0.5||step: 0.301||...||...||step: 0.5||step: 0.25||step: 0.5||step: 0.25|
|GK dwarf||6||3500 to 6000||0 to 5||-0.301 to 0.903||0.||0.176 to 1.982||-2.5 to 0.5||-1 to 1||-1 to 1||-1 to 1|
|step: 250||step: 0.5||step: 0.301||...||step: 0.301||step: 0.25||step: 0.25||step: 0.5||step: 0.25|
|M giant||7||2500 to 4000||-0.5 to 5||-0.301 to 0.903||f([M/H])||...||-2.5 to 0.5||-1 to 1||-1 to 1||-1 to 1|
|step: 100||step: 0.5||step: 0.301||...||...||step: 0.5||step: 0.5||step: 0.5||step: 0.5|
|M dwarf||6||2500 to 4000||-0.5 to 5||-0.301 to 0.903||0.||0.176 to 1.982||-2.5 to 0.5||-1 to 1||-1 to 1||-1 to 1|
|step: 100||step: 0.5||step: 0.301||...||step: 0.301||step: 0.5||step: 0.5||step: 0.5||step: 0.5|
|F||6||5500 to 8000||1 to 5||-0.301 to 0.903||0.||0.176 to 1.982||-2.5 to 0.5||-1 to 1||-1 to 1||-1 to 1|
|step:250||step: 0.5||step: 0.301||...||step: 0.301||step: 0.25||step: 0.25||step: 0.5||step: 0.25|
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.
- In DR13 and prior data releases, a polynomial fit with an asymmetric iterative rejection scheme was used to do the normalization, in an effort for the normalization continuum to more closely approximate the true continuum, i.e. by rejecting absorption lines in the continuum fit. However, the asymmetric rejection causes the derived continuum to be a function of S/N, especially at lower S/N, because pixels with larger statistical fluctuations are rejected in the fit. This is apparent, e.g., in metal-poor stars that have weaker absorption features, in which statistical fluctuations in the continuum in lower S/N spectra may be rejected. To remove this bias, DR14 adopts a continuum normalization that is just a straight 4th order polynomial fit to the spectrum, with no iterative rejection. To avoid contamination of the fit from bad pixels, e.g., those with imperfect sky subtraction, pixels marked as bad or in the vicinity of sky lines in the observed spectra are masked in the fit. It is not possible to use the same masks for the model as for the observed since sky features appear at different rest wavelengths in stars with different radial velocities, so no pixels are masked in the fits to the model spectra: however, since the fit is low order, applying masks to the model spectra have very little effect.
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 Teff. 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.
The abundance derivation takes place after the atmospheric parameters (Teff, log g, vmicro, [M/H], [α/M], [C/M], and [N/M]) have been simultaneously determined from the APOGEE spectra. A second call to the optimization program (FERRE) is performed for the abundance determination. For these fits, the same library of synthetic spectra is used, but with two main changes:
- Abundances of individual α elements (O, Mg, Si, S, Ca, and Ti) are derived by varying the [α/M] dimension of the grid, the abundance of carbon and nitrogen by varying the [C/M] and [N/M] dimensions (in the giant grids; in the dwarf grids C and N are derived using the [M/H] dimension), and the abundances of all other elements by varying the [M/H] dimension. All other atmospheric parameters are held at the values previous determined. NOTE: for the dwarf grids, the C and N abundances are not valid with this approach; since most of the information for C and N come from molecules, varying C and N with [M/H] is incorrect; this was only recognized after the data release files were frozen; users should not use C and N abundances for stars fit with the dwarf grids!
- The weights for the chi-square calculations are now changed so that we only consider spectral features that are primarily sensitive to the element we are interested in. The assumption here is that, within the defined windows (see below), the abundance of the desired element dominates over variations from other elements contained in the same grid dimension.
Therefore, we are not really changing the element of interest only, but the element of interest and others: all α elements as a block when fitting an α element, or all metals when changing a non-α element. This approach works well when the abundance we derive is not very different from the group it belongs to (either just the α elements, or all metals).
Transitions used (weight determination)
Deriving the relevant weights for each element is basically equivalent to deciding which transitions and which parts of the line profiles are to be used for each element.
This is accomplished by using first a algorithm that evaluates the derivatives of the model fluxes with respect to each elemental abundance for a star like Arcturus (Teff=4300 K, logg=1.7, [Fe/H]=-0.5). Frequencies (wavelengths) at which the amplitude of the derivative for the element of interest is large are given a high weight, with a negative contribution when the module of the derivatives are large for any other element in the same element family. Weights are adjusted with a multiplicative factor that takes into account how well the model spectrum for Arcturus reproduces an actual observation of this star. A second multiplicative factor takes into account how well APOGEE spectra are reproduced by the model fluxes, using the median residuals at each frequency based on fitting the entire APOGEE sample.
The number of transitions/features used for each element varies from element to element: there are 45 for C (C I, but mainly CO and CN), 77 for N (CN), 50 for O (OH), 2 for Na (Na I), 4 for Mg (Mg I), 2 for Al (Al I), 10 for Si (Si I), 3 for S (S I), 5 for P, 1 for K (K I), 3 for Ca (Ca I), 9 for TiI (1 for Ti II), 2 for V (V I), 7 for Cr, 4 for Mn (Mn I), 61 for Fe (Fe I), 4 for Co, 7 for Ni (Ni I), and 1 for Rb. However, these numbers do not reflect the number of transitions in a window, the different strengths of the features, and the degree to which they are blended with other features. The attached pdf file shows the fittings for the observations of Arcturus in the Hinkle et al. (1995) atlas (smoothed with a Gaussian profile to R~22,500) and this one is the equivalent for the APOGEE observation of the same star from thee APO 1m telescope (with 4 Fe I transitions illustrated in the figure).
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.
Calibration and Final Error Estimates of the Parameters
In addition to the raw FERRE output parameters, we also provide a calibrated set of parameters. Temperatures and surface gravities are calibrated relative to independent measurements of these quantities in a calibration subset. Abundances are internally calibrated to provide homogeneous results within clusters and are externally calibrated to force solar metallicity stars in the solar circle to have solar abundances on average.
The abundance parameters ([M/H] and [α/M]), as well as all of the individual element abundances are internally calibrated based on observations of stellar clusters with [Fe/H]>-1. Under the assumption that such clusters have internally homogeneous abundances, we find small systematic variations of abundance with temperature, and use these to derive internal calibration relations of the form:
(although not all terms are used for all elements) to provide internally calibrated abundances. We obtain separate calibration relations for giants and for dwarfs. The derived calibration relations are shown in the figures above. For giants, we do not do any calibration for carbon and nitrogen, since these are known to have varying abundances due to mixing along the giant branch.
For giants, the calibration sample is restricted in effective temperature range from around 3800K to 5250K; for sample stars outside this range, we apply the correction at the edge of the range (i.e., we don't extrapolate the relation), and set a bit (CALRANGE_WARN) in the abundance flags.
Note that results for Nd and Y suggest that no useful information on these elements is being extracted, so we do not present any calibrated abundances for these.
The adopted external calibrations are summarized here:
- Accuracy of the ASPCAP effective temperatures have been judged by comparing to temperatures obtained from photometric temperatures (e.g., González Hernández and Bonifacio (2009) IRFM scale) for a low-reddening sample of giants. In general, it appears that the ASPCAP temperatures are relatively close to those expected from the colors for the bulk of the sample, which is near solar metallicity. In DR13, we noticed a metallicity-dependent offset between ASPCAP temperatures and temperatures obtained from photometry. Similar metallicity-dependent offsets are observed in DR14, so we apply a metallicity-dependent temperature correction for dwarfs and giants separately, shown below:
- Corrections for the surface gravities were estimated from a set of stars observed in the Kepler field, for which asteroseismic analysis yields highly accurate surface gravities. There is an apparent offset in the derived calibration from red giant (RGB) and red clump (RC) stars that is currently not well-understood. Since we now have a large sample of stars with asteroseismic surface gravity measurements, we apply separate calibrations for RGB and RC stars. For RGB stars, we use
log g = log gASPCAP - ( 0.528018 - 0.127300 log g + 0.183278 [M/H])
while for RC stars, we uselog g = log gASPCAP - ( -0.642968 + 0.346114 log g + 0.0146857 [M/H])
We attempt to distinguish between RGB and RC stars on the basis of the raw ASPCAP stellar parameters. For every star, we compute the temperature difference between the derived temperature and a fiducial metallicity-dependent ridgeline derived by Bovy et al. (2014):Tridge = 4444.14+ 554.311 (log g-2.5) - 307.962 [M/H]
To first order, stars with T>Tridge are more likely to be RC stars, while stars cooler than Tridge are more likely to be RGB stars. However, we have found there is additional discrimination power based on the C/N ratio. We adopt the criterion for RGB stars to be:[C/N] < -0.08 - 0.5 [M/H] - 0.0039 (T - Tridge)
- The parameter-level [M/H] has an external calibration based on observations of mean abundances in stellar clusters: for [M/H]>-0.5, there is a small correction of 0.027 dex, for [M/H]<-1.0 there is a constant offset of -0.108 dex, with a linear ramp between these values for -1 <[M/H]<-0.5
- The parameter-level [α/M] and the individual elemental abundances have been externally calibrated by separately determining the mean abundances ([X/M]) of stars with near-solar metallicity (-0.1<[M/H]<0.1) dwarfs and giants in a restricted range of Galactic longitude (70<l<110), in an effort to restrict stars to those near the Solar circle. Since previous studies have shown that stars in the solar neighborhood typically have solar abundance ratios at solar metallicity, we apply an offset to the individual [X/M] abundances to force this to be true for the APOGEE measurements.
- Empirical parameter uncertainties have been estimated based on scatter observed within clusters as a function of temperature and S/N. Abundance uncertainties have been estimated based on scatter observed within clusters. See the Using Stellar Parameters and the abundance uncertainty section of the Using Abundances page for additional details.
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, the aspcapField 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; aspcapStar files are FITS image files with the spectrum, the uncertainty, and the best fitting synthetic spectrum for the star.