saprEMo: a simplified algorithm for predicting detections of electromagnetic transients in surveys

The multi-wavelength detection of GW170817 has inaugurated multi-messenger astronomy. The next step consists in interpreting observations coming from population of gravitational wave sources. We introduce saprEMo, a tool aimed at predicting the number of electromagnetic signals characterised by a specific light curve and spectrum, expected in a particular sky survey. By looking at past surveys, saprEMo allows us to constrain models of electromagnetic emission or event rates. Applying saprEMo to proposed astronomical missions/observing campaigns provides a perspective on their scientific impact and tests the effect of adopting different observational strategies. For our first case study, we adopt a model of spindown-powered X-ray emission predicted for a binary neutron star merger producing a long-lived neutron star. We apply saprEMo on data collected by XMM-Newton and Chandra and during $10^4$ s of observations with the mission concept THESEUS. We demonstrate that our emission model and binary neutron star merger rate imply the presence of some signals in the XMM-Newton catalogs. We also show that the new class of X-ray transients found by Bauer et al. in the Chandra Deep Field-South is marginally consistent with the expected rate. Finally, by studying the mission concept THESEUS, we demonstrate the substantial impact of a much larger field of view in searches of X-ray transients.