# Line Index Measurement in SSPP

The SSPP measures line indices of 82 atomic and molecular absorption lines. Line-index calculations are performed in two modes; one uses a global continuum fit over the entire wavelength range (3850 – 9000 Å), while the other obtains local continuum estimates around the line bands of interest. The choice between which mode is used depends on the line depth and width of the feature under consideration. Local continua are employed for the determinations of stellar atmospheric parameters based on techniques that depend on individual line indices. Other techniques, such as the neural network, spectral matching, and auto-correlation methods, require wider wavelength ranges to be considered; for these the global continuum (or their own internal continuum routine) is used. We make use of the errors in the fluxes reported by the SDSS spectroscopic reduction pipeline to measure the uncertainty in the line indices. Details of the procedures used to obtain the continuum fits and line index measures (and their errors) are discussed below.

## Continuum Fit Techniques

### Global Continuum Fit

Determination of the appropriate continuum for a given spectrum is a delicate task, even more so when it must be automated and obtained for stars having wide ranges of effective temperatures, as is the case for the present application. To obtain a global continuum fit, the SSPP first divides the wavelength range into two pieces: blue (3850 – 5800 Å) and red (5800 – 9000 Å). After removing the strong Balmer lines present in most spectra, the blue side is iteratively fit to a ninth-order polynomial, rejecting points that are more than 3 sigma above the fitted function. The same procedure is applied to the red side, but using a fourth-order polynomial. Then, the two fitted pseudo-continua are spliced together, and the joined continuum is again fitted to a ninth-order polynomial. This is the final global pseudo-continuum used to calculate line indices.

The reason for dividing a spectrum into two regions is to avoid the continuum being placed at too high a level around the Ca II Triplet, because of the poor sky-line subtraction in this region in some cases. Because fitting the entire range of a spectrum requires a high-order polynomial, the continuum on the red side of a spectrum will be artificially boosted due to the presence of any poorly subtracted sky lines or noise spikes. Use of a lower order polynomial fit to the red side avoids this potential problem.

### Local Continuum Fit

To compute a local continuum over the line band of interest, we first calculate a 5 sigma-clipped average of the observed fluxes over the (blue and red) sidebands corresponding to each feature, as listed in the line index datamodel. Using these two points, a linear interpolation is carried out over the region between the end point of the blue sideband and the starting point of the red sideband. This linearly interpolated flux is then connected piecewise with the fluxes of the red and blue sidebands, and a robust line fit is performed over the entire region of the blue sideband + line band + red sideband to derive the final local continuum estimate.

## Measurement of Line Indices

Line indices (or equivalent widths) are calculated by integrating a continuum-normalized flux over the specified wavelength regions of each line band. Two different measurements of line indices, obtained from the two different continuum methods described above, are reported, even though the line-index based methods for stellar parameter estimates only make use of the local continuum-based indices. In order to avoid spurious values for the derived indices, if a given index measurement is greater than 100 Å, or is negative, we set the reported value to -9.999. Thus, the value should be between 0.0 and 100 Å. No parameter estimates based on that particular line index are used.

Note that, unlike the case for most of the features in the line index datamodel, the line indices listed as TiO5, TiO8, CaH1, CaH2, and CaH3 are calculated following the prescription given by the “Hammer” program (Covey et al. 2007), UVCN and BLCN by Smith & Norris (1982), and FeI_4 and FeI_5 by Friel (1987). The line index for Ca I at 4227 Å, and the Mg Ib and MgH features around 5170 Å, are computed by following Morrison et al. (2003), so that they could be used to estimate log *g*.