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

Abstract

We use Monte Carlo simulations of the Cal�n/Tololo photographic supernovasurvey to show that a simple model of the survey's selection effectsaccounts for the observed distributions of recession velocity, apparentmagnitude, angular offset, and projected radial distance betweenthe supernova and the host galaxy nucleus for this sample of TypeIa supernovae (SNe Ia). The model includes biases due to the flux-limitednature of the survey, the different light-curve morphologies displayedby different SNe Ia, and the difficulty of finding events projectednear the central regions of the host galaxies. From these simulationswe estimate the bias in the zero point and slope of the absolutemagnitude-decline rate relation used in SNe Ia distance measurements.For an assumed intrinsic scatter of 0.15 mag about this relation,these selection effects decrease the zero point by 0.04 mag. Theslope of the relation is not significantly biased. We conclude thatdespite selection effects in the survey, the shape and zero pointof the relation determined from the Cal�n/Tololo sample are quitereliable. We estimate the degree of incompleteness of the surveyas a function of decline rate and estimate a corrected luminosityfunction for SNe Ia in which the frequency of SNe appears to increasewith decline rate (the fainter SNe are more common). Finally, wecompute the integrated detection efficiency of the survey in orderto infer the rate of SNe Ia from the 31 events found. For a valueof H_0=65 km s^-1 Mpc^-1 we obtain a SN Ia rate of 0.21^+0.30_-0.13SNu. This is in good agreement with the value 0.16+/-0.05 SNe recentlydetermined by Capellaro et al.