Measuring Dwarf Galaxy Intrinsic Abundance Scatter with Mid-resolution Spectroscopic Surveys: Calibrating APOGEE Abundance Errors

The first generations of stars left their chemical fingerprints on metal-poor stars in the Milky Way and its surrounding dwarf galaxies. While instantaneous and homogeneous enrichment implies that groups of conatal stars should have the same element abundances, small amplitudes of abundance scatter are seen at fixed [Fe/H]. Measurements of intrinsic abundance scatter have been made with small high-resolution spectroscopic data sets where measurement uncertainty is small compared to this scatter. In this work, we present a method to use mid-resolution survey data, which have larger errors, to make this measurement. Using APOGEE Data Release 17, we calculate the intrinsic scatter of Al, O, Mg, Si, Ti, Ni, and Mn relative to Fe for 333 metal-poor stars across six classical dwarf galaxies around the Milky Way, and 1604 stars across 19 globular clusters (GCs). We calibrate the reported abundance errors in bins of signal-to-noise ratio and [Fe/H] using a high-fidelity halo data set. Applying these calibrated errors to the APOGEE data, we find small amplitudes of average intrinsic abundance scatter in dwarf galaxies ranging from 0.03 to 0.09 dex, with a median value of 0.047 dex. For the GCs, we find intrinsic scatters ranging from 0.01 to 0.11 dex, with particularly high scatter for Al and O. Our measurements of intrinsic abundance scatter place important upper bounds, which are limited by our calibration, on the intrinsic scatter in these systems, as well as constraints on their underlying star formation history and mixing that we can look to simulations to interpret.