Rederivation of STIS Secondary Echelle Mode Traces

The STIS echelle gratings can be used with a variety of different central wavelength settings. "Secondary" wavelength settings, designed to cover select absorption or emission lines, have not been calibrated as precisely as their primary mode counterparts. In particular, secondary echelle mode traces (and subsequent extraction regions) have been previously defined using straight line fits to each spectral order. In this work, we define a new general method for defining echelle traces that utilizes Gaussian process regression and accounts for the detailed curvature of each order across the detector. Across a variety of echelle grating and central wavelength settings, we find that this method can improve flux throughput by $\sim4\%$ especially near wavelengths located close to the edge of the detector. We have used this method to provide new traces and update reference files for 9 different echelle modes for both pre- and post-Servicing Mission 4 (SM4; in 2009) observations.