Tile or Stare? Cadence and Sky-monitoring Observing Strategies That Maximize the Number of Discovered Transients

To maximize the number of transients discovered on the sky, shouldsky-monitoring projects stare at one location or continually jump from locationto location, tiling the sky? If tiling is preferred, what cadence maximizes thediscovery rate? As sky monitoring is a growing part of astronomical observing,utilized to find such phenomena as supernovae, microlensing, and planettransits, well thought out answers to these questions are increasinglyimportant. Answers are sky, source, and telescope dependent and should includeinformation about the source luminosity distribution near the observationlimit, the duration of variability, the nature of the dominant noise, and themagnitude of down and slew times. Usually, a critical slope of the effectivecumulative transient apparent luminosity distribution (Log N - Log S) at thelimiting magnitude will define when "tile" or "stare" is superior. Forshallower slopes, when "tile" is superior, optimal cadences and pointingalgorithms are discussed. For transients discovered on a single exposure ortime-contiguous series of exposures, when down and slew times are small and thecharacter of the noise is unchanged, the most productive cadence for isotropicpower-law luminosity distributions is the duration of the transient -- fastercadences waste time re-discovering known transients, while slower cadencesneglect transients occurring in other fields. A "cadence creep" strategy mightfind an optimal discovery cadence experimentally when one is not uniquelypredetermined theoretically. Guest investigator programs might diversifypreviously dedicated sky monitoring telescopes by implementing bandpasses andcadences chosen to optimize the discovery of different types of transients.Example analyses are given for SuperMACHO, LSST, and GLAST.Comment: 28 pages, 4 figures. Accepted to Astronomical Journal. Mission specific correspondence welcome (to nemiroff@mtu.edu