Decision Tree to Calculate Atmospheric Parameters - SSPP

Introduction

The SSPP uses multiple methods in order to obtain estimates of the atmospheric parameters for each star over a very wide range in parameter space. Each technique has limitations as to its ability to estimate each parameter, arising from, e.g., the coverage of the grids of synthetic spectra, the methods used for spectral matching, and their sensitivity to the S/N of the spectrum, the range in parameter space over which the particular calibration used for a given method extends, etc.. Hence, it is necessary to specify a prescription for the inclusion or exclusion of a given technique for the estimation of a given atmospheric parameter. At present, this is accomplished by the assignment of a null (0, meaning the parameter estimate is dropped), unity (1, meaning the parameter estimate is accepted), or 2 (in case for [Fe/H]) value to an indicator variable associated with each parameter estimated by a given technique, according to the g-r and S/N criteria listed in the table. Among the parameters, it is recommended to use the adopted T_eff, log g, and [Fe/H] calculated by these decision trees. These are named "TEFF_ADOP", "LOGG_ADOP", and "FEH_ADOP", respectively, in the data model.

Effective Temperature

There are six primary temperature estimates determined by the SSPP, and an auxiliary set of five empirically and theoretically determined estimates. Note that a few of the primary techniques extend to temperatures below 4500 K and above 7500 K, although the accuracy obtained by these are lower than in the interval T_eff = 4500 - 7500 K. Thus, for stars with temperatures outside of this interval, we also include the auxiliary temperature estimates (in fact, just those that lie within 3 sigma of the mean of the full auxiliary set) in assembling the final average estimate of T_eff). Averages are taken using the robust biweight procedure (See Beers, Flynn, & Gebhardt 1990, and references therein). In cases where the color flag 'C' is raised, we ignore all temperatures that rely on the reported g-r color, and only consider those based on spectroscopy alone (e.g., the spectral matching techniques and Balmer-line based temperature). A robust average of the accepted temperature estimates (those with indicator variables equal to 1) is taken for the final adopted temperature. An internal robust estimate of the scatter around this value is also obtained.

Surface Gravity

There are ten methods used to estimate surface gravity by the SSPP. Application of the limits on g-r and S/N eliminates a number of these estimates, and the biweight average of the accepted log g estimates (those with indicator variables equal to 1) is taken for the final adopted surface gravity. An internal robust estimate of the scatter around this value is also calculated.

Metallicity

There are 12 estimates of [Fe/H] in the SSPP. We adopt the validity ranges of S/N and g-r listed in the table in Lee et al. (2008a) to assign 1 or 0 as an indicator variable for each method. We then proceed as follows.

First, we generate a synthetic spectrum for each estimate of [Fe/H] that has an indicator variable of 1 (using the adopted T_eff and log g) by interpolating within the pre-existing grid of synthetic spectra from the NGS1 approach. Next, we calculate a correlation coefficient (CC) and the mean of the absolute residuals (MAR) between the observed and the generated synthetic spectrum in two different wavelength regions: 3850 - 4250 Å and 4500 - 5500 Å, where the Ca II K and H lines, as well as numerous metallic lines, are present, yielding two values of CC and MAR for each metallicity estimator. We then select between the two values by choosing the one with CC closest to unity, and with MAR closest to zero. This applies for all estimates of [Fe/H] from the individual methods. At the end of this process, we have N values of the CC and MAR (maximum of N=12) for the N estimates of [Fe/H] with indicator variables of 1.

There are thus two arrays with N elements: one from the CC and the other one from the MAR values. We then sort the CC array in descending order, and select the metallicity estimate corresponding to the first and second element of the sorted array. The same procedure is carried out for the MAR array, after sorting in ascending order. The reason for implementing calculations involving the MARs is that, although we may have a correlation coefficient close to unity between the observed and the synthetic spectrum, from time to time there are large residuals between the two spectra, indicating a poor match. Thus, the computations involving the MAR provide additional security that the methods are producing reasonable abundance estimates at this stage.

At this point we have two metallicity estimates with the highest CCs, and two metallicity estimates with the lowest MARs. We then take an average of the four metallicities, and use this average to select from among the full set of metallicity estimates with an indicator variable of 1 and within +/-0.5 dex of the average. We carry along the CCs and MARs for the selected metallicity estimates for further processing. In the next step we obtain an average μ_CC (μ_MAR) and standard deviation σ_CC (σ_MAR) of the CCs (MARs) for the surviving metallicity estimates from the previous step. As a final step to reject likely outliers, we select from the surviving metallicity estimates the ones with the CC greater than (μ_CC - σ_CC) and the MAR less than (μ_MAR + σ_MAR). The metallicity estimators that remain after this step are assigned indicator variables of 2. This procedure effectively ignores metallicity estimates that produce poor matches with the synthetic spectra. The final adopted value of [Fe/H] is computed by taking a biweight average of the remaining values of [Fe/H] (those with indicator variables of 2).