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. This tradeoff bears implications for the design of surveys conducted with upcoming widefield radio interferometers, such as the ASKAP VAST survey and the MeerKAT TRAPUM survey. 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 Npoint telescope pointings. For a survey of fixed duration, Tobs, 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 − α, and tslew 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 Nmax ~ Tobs/4tslew, while for case (iii) we find Nmax = (Lmax/L0)2[(3 − α)/2]2/(α − 1), where Lmax is the maximum luminosity of a transient event and L0 is the minimum luminosity event detectable in an integration of duration Tobs. (The instance Nmax > Npoint in (iii) implies re-observation of fields over the survey area, except when the duration of transient events exceeds that between re-observations of the same field, where Nmax = Npoint applies instead.) We consider the balance in survey optimization between telescope field of view, Ω, and sensitivity, characterised by the minimum detectable flux density, S0. For homogeneously distributed events (i), the detection rate scales as NΩS−3/20, while for targetted events (iii) it scales as NΩS1 − α0. However, if the targetted survey is optimised for N the event detection rate scales instead as ΩS−20. This analysis bears implications for the assessment of telescope designs: the quantity ΩS−20 is often used as the metric of telescope performance in the SKA transients literature, but only under special circumstances is it the metric that optimises the event detection rate.