Gravitational Lensing of Distant Supernovae in Cold Dark Matter Universes

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Abstract
Ongoing searches for supernovae (SNe) at cosmological distances have recently started to provide large numbers of events with measured redshifts and apparent brightnesses. Compared to quasars or galaxies, Type Ia SNe represent a population of sources with well-known intrinsic properties and could be used to detect gravitational lensing even in the absence of multiple or highly distorted images. We investigate the lensing effect of background SNe due to mass condensations in three popular cold dark matter cosmologies (ΛCDM, OCDM, and SCDM) and compute lensing frequencies, rates of SN explosions, and distributions of arrival-time differences and image separations. If dark halos approximate singular isothermal spheres on galaxy scales and Navarro-Frenk-White profiles on group/cluster scales, and are distributed in mass according to the Press-Schechter theory, then about one of every 12 SNe at z ~ 1 will be magnified by Δm ≥ 0.1 mag (SCDM). The detection rate of SNe Ia with magnification Δm ≥ 0.3 is estimated to be of the order of a few events yr-1 deg-2 at maximum B light and IAB ≤ 25, 100 times smaller than the total rate expected at these magnitude levels. In the field, events magnified by more than 0.75 mag are 7 times less frequent; about one-fifth of them give rise to observable multiple images. While the time delay between the images is shorter than 3 days in ~25% of the cases (shorter than 30 days in 50%) (SCDM), a serious bias against the detection of small-separation events in ground-based surveys is caused by the luminosity of the foreground lensing galaxy. Because of the flat K-correction and wide luminosity function, Type II SNe dominate the number counts at IAB > 25 and have the largest fraction of lensed objects. The optimal survey sensitivity for Type Ia SNe magnified by Δm ≥ 0.75 mag is IAB ≈ 23. Magnification bias increases their incidence by a factor of 50 in samples with IAB ≤ 22, dropping to a factor of 3.5 at 24 mag. At faint magnitudes, the enhancement is larger for SNe II.

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