Selection Effects, Biases, and Constraints in the CalÁn/Tololo Supernova Survey

We use Monte Carlo simulations of the Calan/Tololo photographic supernovasurvey to show that a simple model of the survey's selection effects accountsfor the observed distributions of recession velocity, apparent magnitude,angular offset, and projected radial distance between the supernova and thehost galaxy nucleus for this sample of Type Ia supernovae (SNe Ia). The modelincludes biases due to the flux-limited nature of the survey, the differentlight curve morphologies displayed by different SNe Ia, and the difficulty offinding events projected near the central regions of the host galaxies. Fromthese simulations we estimate the bias in the zero-point and slope of theabsolute magnitude-decline rate relation used in SNe Ia distance measurements.For an assumed intrinsic scatter of 0.15 mag about this relation, theseselection effects decrease the zero-point by 0.04 mag. The slope of therelation is not significantly biased. We conclude that despite selectioneffects in the survey, the shape and zero-point of the relation determined fromthe Calan/Tololo sample are quite reliable. We estimate the degree ofincompleteness of the survey as a function of decline rate and estimate acorrected luminosity function for SNe Ia in which the frequency of SNe appearsto increase with decline rate (the fainter SNe are more common). Finally, wecompute the integrated detection efficiency of the survey in order to infer therate of SNe Ia from the 31 events found. For a value of Ho=65 km/sec/Mpc weobtain a SN Ia rate of 0.21(+0.30)(-0.13) SNu. This is in good agreement withthe value 0.16+/-0.05 SNu recently determined by Capellaro et al. (1997).Comment: 36 pages, 19 figures as extra files, to appear in the A