Design of a Void Tomography Survey Configuration Optimised for Underdensity Statistics

This is a design study, simulated and not measured, for a spectroscopic survey configuration optimised for void statistics rather than for galaxy clustering generally. Three configurations are compared on a common footing: a wide-shallow survey of 14,000 square degrees, a reference survey of 8,000 square degrees at intermediate tracer density, and a deep-narrow survey of 3,000 square degrees at high tracer density. The reference configuration covers an effective volume of 24.8 cubic gigaparsecs per h to redshift one, finds voids down to a minimum reliable radius of 23.7 megaparsecs per h, and yields about 7.67e+05 voids above that radius. On the figure of merit defined in the paper, which rewards yield and penalises minimum radius, the best configuration is the reference design, with a figure of merit of 450 and a void yield of 7.67e+05. The wide-shallow configuration, despite the largest area, reaches a figure of merit of only 340, because its tracer density leaves the high-value void population unresolved. The design lesson is that void science rewards area only after tracer density passes the threshold at which the voids of interest are resolved; below that threshold area is wasted, and above it additional depth buys little, because the marginal value of smaller voids saturates. SIMULATED, NOT MEASURED.