Optimization of Survey Strategies for Detecting Slow Radio Transients

We investigate the optimal tradeoff between sensitivity and field of view in surveys for slow radio transients using the event detection rate as the survey metric. We investigate (i) a survey in which the events are distributed homogeneously throughout a volume centred on the Earth, (ii) a survey in which the events are homogeneously distributed, but are only detectable beyond a certain minimum distance, and (iii) a survey in which all the events occur at an identical distance, as is appropriate for a targetted survey of a particular field which subtends N_point telescope pointings. For a survey of fixed duration, T_obs, we determine the optimal tradeoff between number of telescope pointings, N, and integration time per field. We consider a population in which the event luminosity distribution follows a power law with index -\alpha, and t_slew is the slewing time between fields or, for a drift scan, the time taken for the telescope drift by one beamwidth. Several orders of magnitude improvement in detection rate is possible by optimization of the survey parameters. The optimal value of N for case (i) is N_max ~ T_obs/4 t_slew, while for case (iii) we find N_max = (L_max/L_0)^2 [ (3 -\alpha)/2 ]^{2/(\alpha-1)}, where L_max is the maximum luminosity of a transient event and L_0 is the minimum luminosity event detectable in an integration of duration T_obs. For a telescope field of view, \Omega, and a minimum detectable flux density, S_0, the detection rate scales as N \Omega S_0^{-3/2} for homogeneously distributed events, while for targetted events (iii) it scales as N \Omega S_0^{1-\alpha}. The quantity \Omega S_0^{-2} is often used as the metric of telescope performance in the SKA transients literature, but only under special circumstances is it the metric that optimizes the event detection rate. [abstract abbreviated]