Depth of Ultra High Energy Cosmic Ray Induced Air Shower Maxima Measured by the Telescope Array Black Rock and Long Ridge FADC Fluorescence Detectors and Surface Array in Hybrid Mode

The Telescope Array observatory utilizes fluorescence detectors and surface detectors to observe air showers produced by ultra high energy cosmic rays in the Earth's atmosphere. Cosmic ray events observed in this way are termed hybrid data. The depth of air shower maximum is related to the mass of the primary particle that generates the shower. This paper reports on shower maxima data collected over 8.5 years using the Black Rock Mesa and Long Ridge fluorescence detectors in conjunction with the array of surface detectors. We compare the means and standard deviations of the observed $X_{\mathrm{max}}$ distributions with Monte Carlo $X_{\mathrm{max}}$ distributions of unmixed protons, helium, nitrogen, and iron, all generated using the QGSJet~II-04 hadronic model. We also perform an unbinned maximum likelihood test of the observed data, which is subjected to variable systematic shifting of the data $X_{\mathrm{max}}$ distributions to allow us to test the full distributions, and compare them to the Monte Carlo to see which elements are not compatible with the observed data. For all energy bins, QGSJet~II-04 protons are found to be compatible with Telescope Array hybrid data at the 95% confidence level after some systematic $X_{\mathrm{max}}$ shifting of the data. Three other QGSJet~II-04 elements are found to be compatible using the same test procedure in an energy range limited to the highest energies where data statistics are sparse.