Properties of SN Ia progenitors from light curves and spectra

With recent advances in theory and observations, direct connections emerge between the progenitors of Type Ia Supernovae (SNe Ia) and the observed light curves and spectra. A direct link is important for our understanding of the supernovae physics, the diversity of SNe Ia and the use of SNe Ia for high-precision cosmology because the details of the explosion depends sensitively on the initial conditions and the explosion scenario(s) realized in nature. Do SNe Ia originate from SD- or DD systems, and do they lead to M_Ch mass explosions or dynamical mergers? Does the statistical distribtion of SNe Ia depend on their environment which can be expected to change with redshift? In this contribution, we will exam from the theoretical point of view the tell-tails for this connection, their consistency with the observations, and future directions. In a first section, we present the physics of the explosion, light curves and spectral formation in a nutshell to help understanding the connection. For details of the progenitor evolution and explosion physics, we refer to reviews and the other contributions in this issue. Each of the topical sections starts with a brief general review followed by a more detailed discussion of specific results. Because the youth of the field, some bias is unavoidable towards results obtained within our collaborations (and FSU). The imprint of the metallicity, progenitor stars and properties such as the central density of the exploding WD are presented. IR spectroscopy, polarimetry and imaging of SNR remnants are discussed as a tool to test for the WD properties, magnetic fields and asymmetries. We discuss different classes of Type Ia supernovae, and their environment. Possible correlations between the spectroscopic and light curve properties of SN Ia are discussed. Finally, the overall emerging picture and future developments are discussed.