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We have been searching for surviving companions of progenitors of GalacticType-Ia supernovae, in particular SN 1572 and SN 1006. These companion starsare expected to show peculiarities: (i) to be probably more luminous than theSun, (ii) to have high radial velocity and proper motion, (iii) to be possiblyenriched in metals from the SNIa ejecta, and (iv) to be located at the distanceof the SNIa remnant. We have been characterizing possible candidate stars usinghigh-resolution spectroscopic data taken at 10m-Keck and 8.2m-VLT facilities.We have identified a very promising candidate companion (Tycho G) for SN 1572,but we have not found any candidate companion for SN 1006, suggesting that SNevent occurred in 1006 could have been the result of the merging of two whitedwarfs. Adding these results to the evidence from the other direct searches,the clear minority of cases (20\% or less) seem to disfavour thesingle-degenerate channel or that preferentially the single-degenerateescenario would involve main-sequence companions less massive than the Sun.Therefore, it appears to be very important to continue investigating these andother Galactic Type-Ia SNe such as the Johannes Kepler SN 1604.

Origin of Galactic Type-Ia supernovae: SN 1572 and SN 1006