Internal Consistency of Each Parameter in SSPP
There are about 43,000 stars that have more than one spectroscopic observation with the SDSS spectrographs. From these, we select ~9000 stars where 1) both spectra have S/N ≥ 10, 2) the difference in S/N between the two spectra is <10, 3) SSPP flags are set to ‘nnnnn’ for both spectra, 4) the correlation coefficients between the model and observed spectra are larger than zero, 5) there are no bad pixels in flux, and 6) valid stellar parameters are available for both spectra. Comparison of the parameter estimates for these duplicate observations provides an excellent basis for an estimate of the internal uncertainties of the SSPP. We look at the residual distribution between two measurements of each parameter from two different observations as a function of signal-to-noise ratio (S/N) in four different regions of g-r and two metallicity ranges (metal-poor for [Fe/H] < -1.5 and metal-rich for [Fe/H] > -1.5).
Three figures below show the residual distribution of the effective temperature, surface gravity, and metallicity. Each panel in each figure lists the color and metallicity ranges and the Gaussian mean (μ) and scatter (σ) is calculated for the stars in each color and metallicity bin. In this analysis, when we compute the Gaussian sigma, we do not attempt to clip the outliers as we already imposed various restrictions on each object to obtain parameters as reliable as possible. The dashed line indicates the Gaussian sigma listed in each panel, while the red-dashed line denotes one Gaussian sigma as computed for bins of 200 stars ordered in S/N. Each bin overlaps by 100 stars with the neighboring bins.
Inspection of each figure tells that internal error of Teff is ~50 K for a typical G-type dwarf or redder stars in the color range of 0.4 < g-r < 1.3 with S/N = 30. This error increases to ~80 K for stars with -0.3 < g-r < 0.2, [Fe/H] < -1.5, and S/N < 15. Similarly for the surface gravity and metallicity, the middle and right figures indicate that we can achieve the internal errors of log g and [Fe/H] to ~0.12 dex and ~0.10 dex, respectively, for a typical G-type dwarf or redder stars in the color range of 0.4 < g-r < 1.3 with S/N = 30. These errors increase to ~0.30 dex for log g and 0.25 dex for [Fe/H] for stars with -0.3 < g-r < 0.2, [Fe/H] < -2.0, and S/N < 15.
