Tile or Stare? Maximizing Transient Discovery Rates for Sky Monitors Such as SuperMACHO, LSST, and GLAST

To maximize the number of transients discovered on the sky, should sky-monitoring projects stare at one location or continually jump from location to location, tiling the sky? If tiling is preferred, what cadence maximizes the discovery rate? As sky monitoring is a growing part of astronomical observing, well thought out answers to these questions are increasingly important. Answers are shown to be source, sky, and telescope dependent, and should include information about the transient luminosity function near the observation limit, the duration of variability, the duration of down and slew times, and the nature of the dominant noise. Typically, sky monitors should stare at a single region of the sky only until the apparent source/transient brightness distribution slope falls more shallow than a given power law that is a function of the above parameters, or risk losing more numerous sources/transients occurring in neighboring fields. Example cases are discussed including SuperMACHO, LSST and GLAST.