ARA Collaboration, N. Alden, S. Ali, P. Allison, J. J. Beatty, D. Z. Besson, A. Bishop, P. Chen, Y. C. Chen, Y. -C. Chen, S. Chiche, B. A. Clark, A. Connolly, K. Couberly, L. Cremonesi, A. Cummings, P. Dasgupta, R. Debolt, S. de Kockere, K. D. de Vries, C. Deaconu, M. A. DuVernois, J. Flaherty, E. Friedman, R. Gaior, P. Giri, J. Hanson, N. Harty, K. D. Hoffman, M. -H. Huang, K. Hughes, A. Ishihara, A. Karle, J. L. Kelley, K. -C. Kim, M. -C. Kim, I. Kravchenko, R. Krebs, C. Y. Kuo, U. A. Latif, C. H. Liu, T. C. Liu, W. Luszczak, A. Machtay, M. S. Muzio, J. Nam, R. J. Nichol, A. Novikov, A. Nozdrina, E. Oberla, C. W. Pai, Y. Pan, C. Pfendner, N. Punsuebsay, J. Roth, A. Salcedo-Gomez, D. Seckel, M. F. H. Seikh, Y. -S. Shiao, J. Stethem, S. C. Su, S. Toscano, J. Torres, J. Touart, N. van Eijndhoven, A. Vieregg, M. Vilarino Fostier, M. -Z. Wang, S. -H. Wang, P. Windischhofer, S. A. Wissel, C. Xie, S. Yoshida, R. Young

The Askaryan Radio Array (ARA) is an ultra-high energy (UHE) neutrino observatory designed to detect the impulsive radio waves produced by relativistic particle cascades in the Antarctic glacial ice. Using a significantly enhanced simulation pipeline, which adds data-driven detector simulations and fully incorporates secondary particle production, we calculate the trigger-level acceptance of the entire array. We compare the resulting trigger-level sensitivity to constraints on the UHE neutrino flux from other detectors. Given its exposure from 2013 to 2023, we find that ARA achieves a world-leading sensitivity above about $10^{19}$ eV, depending on the details of the event selection used in a search. Moreover, we find that up to 13 neutrinos are predicted to have been observed in this period at trigger-level, assuming the most optimistic neutrino flux models. We show that observations of secondary particles account for up to 30\% of the total acceptance starting at $10^{19}$ eV, and we explore the potential signatures and implications of both multi-pulse (from direct and refracted pulses and/or from secondary particle interactions) and multi-station events. Finally, we comment on the implications of this study for the design of next-generation UHE neutrino experiments, in particular IceCube-Gen2 Radio.