Malmquist Bias

Fault of time, the complete study of the effects of bias of Malmquist was not carried out in a systematic way for all the supernovæ. We present here the study which was made in the case of 2001gn discovered to the CFHT.

Figure 10.26 shows, for an effectiveness of detection close to the effectiveness noted at the time of this research campaign (reproduced in top of the figure), bias to the measure for 2 value of cut in signal on noise. The first with $5 \sigma$ represents the value used at the time of research; for a supernova with a redshift of 1.1, bias lower than 0.01 magnitude, and thus lower than the percent. For the closer supernovæ, this bias will be even weaker. The second value with $10 \sigma$ corresponds to the cut which was applied in fact at the time of the spectroscopic identification taking into account the limits of the Keck instrument. In this case, for a supernova with a shift of $1.1$, bias is approximately 0.04 magnitude i.e. 4%. For supenovæ with redshifts lower than 1 bias is negligible.

The bias of Malmquit is thus negligible for our supernovæ with a shift towards the red lower than 1 and limited to 4% for our most remote supernova.

Figure 10.26: Estimate of the Malmquist bias for the observations of spring 2001 with the CFHT. In top, the operating characteristic of detection at the time of research by considering a cut in signal on noise of 5. In the medium, the Malmquist bias according to the redshift for a cut in signal on noise of 5. In bottom, the same curve for a cut in signal on noise of 10 correspondent to the cut in fact due to the limitations of the instruments of spectroscopic identification.