Gravitational Lensing Magnification and Time Delay Statistics for Distant Supernovae

Abstract

Strong gravitational lensing of distant supernovae (SNe), particularly Type Ia's, has some exploitable properties not available when other sorts of cosmologically distant sources are lensed. One such property is that the ``standard candle'' nature of the SN at peak brightness allows a direct determination of the lensing magnification factor for each well observed image. Another is that the duration of an SN event is of the same order as the differential time delays between the various lens images. The comparable time scales of the photometric event and the time delay invite a variety of applications, including high precision measurements of the delay and the targeting of especially interesting phases of the explosion for intensive observation when they appear in trailing images. As an initial exploration of these possibilities we present calculations of SN lensing statistics in a ``concordance cosmology''. We emphasize magnification and time delay effects. Plausible SN surveys, such as the proposed SNAP space mission, would discover several to some tens of strongly lensed SNe Ia per year, and at least a few of these will be at redshifts well beyond those that would be accessible via unlensed events. The total number of such anomalously high redshift SNe Ia will be a useful test of high redshift star formation models. SN surveys of finite duration will, of course, miss the appearance of some images; we quantify this selection bias. Finally, we investigate how well the appearance of trailing images can be predicted based on various amounts of available information on the lensing event. Knowledge of the magnification factor for the leading image makes it possible to predict the appearance of a trailing image relatively accurately if the lens redshift is also known. (Abridged)