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.
ABSTRACT
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.
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.
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
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 data presented here were obtained during a attempt to measure q0 by
conducting a search for SNe on the rise (before their maximum light) using a
subtraction technique.
A search
for a positive signal is done on the subtracted images. The signal
on the new image must therefore be bigger than on the
reference image reducing DT by approximatively a factor 2.
- In addition, the detection efficiency depends strongly on the magnitude
of the supernova at the detection time, on the host galaxy magnitude, the
images quality and the search technique (see below).
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
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.
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.
Isobel Hook (imh@panisse.lbl.gov) Reynald Pain (rgpain@lbl.gov) July 20, 1995