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Data reduction was performed with the public MOSFIRE data reduction pipeline (DRP; version 2015A), in which flat fielding, wavelength calibration, sky subtraction, and rectification were performed to create two-dimensional (2D) spectra with a spectral resolution of 1.09 Å pixel$^{-1}$ and a spatial resolution of 018 pixel$^{-1}$. Upon monitoring the centroid of the slit star in each raw frame, we identified a $\sim$1 pixel hr$^{-1}$ drift along the slit, which was also noted by several other studies [e.g., @kriek15; @oesch15]. We thus split the data on each night into $\sim$1 hr chunks and reduced them seperately, to prevent loss of signal due to this drift.

Following this, analysis was done using our custom software. From the 2D spectrum created by the pipeline, we combined the data from the four nights by generating final inverse-variance-weighted stacks for each object, following @gawiser06. Spatial offsets between data chunks due to the drift were accounted for when combining data based on the centroids of the slit star. We extracted one-dimensional (1D) spectra at the expected position of each source with a width of 13 (about a 1.8$\times$ the median Gaussian FWHM), using an optimal extraction algorithm described in @horne86. This extraction scheme is similar 