How to design your next generation Laser Guide Star Facility: Assessing Sodium photon return availability for the GLAO Laser Guide Star Facility in ULTIMATE-Subaru

The Ground Layer Adaptive Optics (GLAO) system is a pivotal component of ULTIMATE, the next-generation instrumentation program for the Subaru Telescope. This collaborative effort led by the Subaru Telescope and the National Astronomical Observatory of Japan, involves Tohoku University, Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), and the Australian National University (ANU). ANU is spearheading the design of the Laser Guide Star Facility (LGSF) and Wavefront Sensor work packages. The GLAO LGSF comprises two Sodium guidestar lasers, each of them splits into two beams, creating an asterism of four artificial stars in the Hawaiian skies. Organized into beam transfer optics, beam diagnostics, and beam projection subsystems, the GLAO LGSF is responsible for conditioning, splitting, and steering laser beams, optimizing their launch configuration over a 20 arcmin on-sky patrol field. We have investigated the expected photon return availability from the GLAO Laser Guide Star Facility (LGSF) on Maunakea, building upon previous studies conducted by our ESO colleagues in Paranal. This analysis incorporates statistics on sodium content and atmospheric parameters, including sodium abundance derived from LIDAR measurements near Sao Paulo, Brazil, semi-empirical models of sodium monthly variation tailored to Maunakea, and measurements of sodium column abundance from our ESO colleagues. In challenging scenarios, including large zenith angles, low sodium abundance, northern telescope pointing, and poor seeing conditions, the return flux may significantly decrease, potentially rendering it insufficient for certain observing cases. We present the impact of sodium photon return availability on ULTIMATE-Subaru science cases, along with variables to consider when designing the next-generation Laser Guide Star Facilities.