Selection effects, biases, and constraints in the Calan/Tololo supernova survey

We use Monte Carlo simulations of the Calan/Tololo photographic supernova s urvey to show that a simple model of the survey's selection effects account s for the observed distributions of recession velocity, apparent magnitude, angular offset, and projected radial distance between the supernova and th e host galaxy nucleus for this sample of Type Ia supernovae (SNe Ia). The m odel includes biases due to the flux-limited nature of the survey, the diff erent light-curve morphologies displayed by different SNe Ia, and the diffi culty of finding events projected near the central regions of the host gala xies. From these simulations we estimate the bias in the zero point and slo pe of the absolute magnitude-decline rate relation used in SNe Ia distance measurements. For an assumed intrinsic scatter of 0.15 mag about this relat ion, these selection effects decrease the zero point by 0.04 mag. The slope of the relation is not significantly biased. We conclude that despite sele ction effects in the survey, the shape and zero point of the relation deter mined from the Calan/Tololo sample are quite reliable. We estimate the degr ee of incompleteness of the survey as a function of decline rate and estima te a corrected luminosity function for SNe Ia in which the frequency of SNe appears to increase with decline rate (the fainter SNe are more common). F inally, we compute the integrated detection efficiency of the survey in ord er to infer the rate of SNe Ia from the 31 events found. For a value of H-0 = 65 km s(-1) Mpc(-1) we obtain a SN Ia rate of 0.21(-0.13)(+0.30) SNu. Th is is in good agreement with the value 0.16 +/- 0.05 SNe recently determine d by Capellaro et al.