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Type Ia SNe along redshift: the R(Si II) ratio and the expansion velocities in intermediate z supernovae

We study intermediate--z SNe Ia using the empirical physical diagrams which enable to learn about those SNe explosions. This information can be very useful to reduce systematic uncertainties of the Hubble diagram of SNe Ia up to high z. The study of the expansion velocities and the measurement of the ratio $\mathcal{R}$(\SiII) allow to subtype those SNe Ia as done for nearby samples. The evolution of this ratio as seen in the diagram $\mathcal{R}$(\SiII)--(t) together with $\mathcal{R}$(\SiII)$_{max}$ versus (B-V)$_{0}$ indicate consistency of the properties at intermediate z compared with local SNe. At intermediate--z, the expansion velocities of Ca II and Si II are similar to the nearby counterparts. This is found in a sample of 6 SNe Ia in the range 0.033$\leq z \leq$0.329 discovered within the {\it International Time Programme} (ITP) of {\it Cosmology and Physics with SNe Ia} during the spring of 2002. Those supernovae were identified using the 4.2m William Herschel Telescope. Two SNe Ia at intermediate z were of the cool FAINT type, one being a SN1986G--like object highly reddened. The $\mathcal{R}$(\SiII) ratio as well as subclassification of the SNe Ia beyond templates help to place SNe Ia in their sequence of brightness and to distinguish between reddened and intrinsically red supernovae. This test can be done with very high z SNe Ia and it will help to reduce systematic uncertainties due to extinction by dust. It should allow to map the high-z sample into the nearby one.