Barcelona talk on Supernovae rate

Supernovae rate at z=0.4

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This memo is a written version of the talk on Supernovae rate at z=0.4 presented at the Barcelona meeting on June 29th, 1995.


In planning (and proposing) high-redshift supernova searches, it has been necessary up till now to predict supernova rates and discovery rates by assuming nearby rates. The supernovae discovered in our high-redshift supernova search yield a first measurement of supernova rate at redshifts of order z=0.4. We report on our measurement of the search detection efficiencies as a function of supernova apparent magnitude, image depth, host galaxy magnitude and proximity, supernova phase and observing intervals, and other factors. We use these efficiencies, together with estimates of the number of galaxies in our images at a given redshift and magnitude, to estimate supernova rates. We compare these high-redshift rates to nearby rates.

Title Page

Description of data used in this analysis

Method for calculation of rate

Model for galaxy Evolution

This plot shows the model of Lilly et al, which gives galaxy counts as a function of magnitude and redshift. This model is used to determine the number of galaxies (as a function of redshift) to which the survey is sensitive.

Check of Galaxy model counts vs Data

This page describes a check of the galaxy counts produced by the Lilly et al evolution model against our data. A plot showing the comparison is here

Contribution from Clusters

Surveillance Time

The Surveillance time (sometimes called Control time ) is different in Nearby and Distant searches. Instead of observing one or a few galaxies many times, we observe, in a distant search, a very large number of galaxies during 2 observation periods. During the first observation we obtain the references images and the new (or search) images are obtained during the second run. The Surveillance time, DT, is therefore the effective time during wich we would have detected a supernova of a given magnitude (exploding in a galaxy with a given magnitude) with two observations separated by a given period dt.

A very naive estimate of DT is given by the time during which the supernova lightcurve is above a given threshold corresponding to the "limiting" magnitude of the observations. In our case, this gives a DT overestimated by more than a factor 2, for the following reasons :

The Surveillance Time is therefore equal to the weighted sum of days during wich the SN can be detected where the weights are given by the corresponding detection efficiency.

Detection efficiency

The Detection efficiency is a very complicated function of many parameters. The exact shape as a function of the SN magnitude depends on the quality of the subtracted images (seeing, transmission) together with the detailled technique (convolution, cuts) used to extract the signal (SNe candidates) from the background (cosmics, asteroids, bad subtractions, etc..). In addition, there is a slight dependence on the host galaxy magnitude. It is therefore very difficult, if not impossible, to calculate it without using a Monte-Carlo simulation technique.

Efficiency determination

The Detection efficiency was calculated using a (semi) Monte-Carlo method. A fake image was created for every field by adding fake supernovae to real images. A search was ran on these images using the exact same software used for the supernovae search. This technique allows us to measure detection efficiencies vs supernovae magnitude individually for every field.

Search For Supernovae

Number of SNe per degree^2 per year

Expected number of Supernovae

The expected number of supernovae as a function of z together with the overall detection efficiency (mixed line) and the luminosity weighted number of galaxies (dashed line) are shown in this figure. We expected to find Supernovae most probably Between z=0.3 and z=0.4. Below z=0.2 and above z=0.5, discoveries were very unlikely. This is consistent with the discovery of the three candidates respectively at z=0.358, z=0.375 and z=0.420.

Observed Supernovae rate

The observed Supernovae rate at z=0.4 was obtained by fitting the observed distribution to the expected one. Because of the small number of events found, a maximum likelihood fit using Poisson statistics was done.

Preliminary Distant Supernovae rate

Isobel Hook ( Reynald Pain ( July 20, 1995