Towards Rate Estimation for Transient Surveys I: Assessing Transient Detectability and Volume Sensitivity for iPTF

The last couple of decades have seen an emergence of transient detection facilities in various avenues of time domain astronomy which has provided us with a rich dataset of transients. The rates of these transients have implications in star formation, progenitor models, evolution channels and cosmology measurements. The crucial component of any rate calculation is the detectability and space-time volume sensitivity of a survey to a particular transient type as a function of many intrinsic and extrinsic parameters. Fully sampling that multi-dimensional parameter space is challenging. Instead, we present a scheme to assess the detectability of transients using supervised machine learning. The data product is a classifier that determines the detection likelihood of sources resulting from an image subtraction pipeline associated with time domain survey telescopes, taking into consideration the intrinsic properties of the transients and the observing conditions. We apply our method to assess the space-time volume sensitivity of type Ia supernovae (SNe~Ia) in the intermediate Palomar Transient Factory (iPTF) and obtain the result,$\langle VT\rangle_{\mathrm{Ia}}=2.93\pm 0.21\times 10^{-2}\mathrm{Gpc^{3}yr}$. With rate estimates in the literature, this volume sensitivity gives a count of $680-1160$ SNe~Ia detectable by iPTF which is consistent with the archival data. With a view toward wider applicability of this technique we do a preliminary computation for long-duration type IIp supernovae (SNe~IIp) and find $\langle VT\rangle_{\mathrm{IIp}}=7.80\pm0.76\times10^{-4}\mathrm{Gpc^{3}yr}$. This classifier can be used for computationally fast space-time volume sensitivity calculation of any generic transient type using their lightcurve properties. Hence, it can be used as a tool to facilitate calculation of transient rates in a range of time-domain surveys, given suitable training sets.