Monte Carlo simulations of type Ia supernova observations in supernova surveys

We have performed Monte Carlo simulations of Type Ia supernova (SN Ia) surveys to quantify their efficiency in discovering peculiar overluminous and underluminous SNe Ia. We determined how the type of survey (magnitude-limited, distance-limited, or a hybrid) and its characteristics (observation frequency and detection limit) affect the discovery of peculiar SNe Ia. We find that there are strong biases against the discovery of peculiar SNe Ia introduced by at least four observational effects : the Malmquist bias, the age of the SN Ia at the time of its discovery, the shape of its light curve, and its degree of extinction. Surveys with low observation frequency (less than once per 10 days) tend to discover SNe Ia that are too old for observers to easily recognize their peculiarity. Subluminous SNe Ia are underrepresented in magnitude-limited surveys because they can only be found within a small volume and they remain above the detection limit for less time. Conversely, overluminous SNe Ia are more easily found in magnitude-limited surveys, although their likely association with dusty regions reduces the volume in which they can be discovered. The unbiased rate of peculiar SNe Ia can be recovered only in distance-limited surveys with high observation frequencies and with detection limits that are fainter than the peak magnitude of a subluminous SN Ia in the farthest potential host.