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To measure the supernova (SN) rates at intermediate redshift we performed the Southern inTermediate Redshift ESO Supernova Search (STRESS). Unlike most of the current high redshift SN searches, this survey was specifically designed to estimate the ra te for both type Ia and core collapse (CC) SNe. We counted the SNe discovered in a selected galaxy sample measuring SN rate per unit blue band luminosity. Our analysis is based on a sample of ~43000 galaxies and on 25 spectroscopically confirmed SNe plus 64 selected SN candidates. Our approach is aimed at obtaining a direct comparison of the high redshift and local rates and at investigating the dependence of the rates on specific galaxy properties, most notably their colour. The type Ia SN rate, at mean redshift z=0.3, amounts to 0.22^{+0.10+0.16}_{-0.08 -0.14} h_{70}^2 SNu, while the CC SN rate, at z=0.21, is 0.82^{+0.31 +0.30}_{-0.24 -0.26} h_{70}^2 SNu. The quoted errors are the statistical and systematic uncertainties. With respect to local value, the CC SN rate at z=0.2 is higher by a factor of ~2 already at redshift, whereas the type Ia SN rate remains almost constant. This implies that a significant fraction of SN Ia progenitors has a lifetime longer than 2-3 Gyr. We also measured the SN rates in the red and blue galaxies and found that the SN Ia rate seems to be constant in galaxies of different colour, whereas the CC SN rate seems to peak in blue galaxies, as in the local Universe. SN rates per unit volume were found to be consistent with other measurements showing a steeper evolution with redshift for CC SNe with respect to SNe Ia. Finally we have exploited the link between star formation (SF) and SN rates to predict the evolutionary behaviour of the SN rates and compare it with the path indicated by observations.
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