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One of the major challenges for theoretical modeling of Type Ia supernovaexplosions is to explain the diversity of these events and the empiricallyestablished correlation between their peak luminosity and light curve shape. Inthe framework of the so-called Chandrasekhar mass models, the progenitor'scarbon-to-oxygen ratio has been suggested to be a principal source of peakluminosity variations due to a variation in the production of radioactive$^{56}$Ni during the explosion. The underlying idea is that an enhanced carbonmass fraction should result in a more vigorous explosion since here the energyrelease from nuclear reactions is increased. It was suspected that this wouldproduce a higher amount of $^{56}$Ni in the ejecta. In this letter we describea mechanism resulting from an interplay between nucleosynthesis and turbulentflame evolution which counteracts such an effect. Based on three-dimensionalsimulations we argue that it is nearly balanced and only minor differences inthe amount of synthesized $^{56}$Ni with varying carbon mass fraction in theprogenitor can be expected. Therefore this progenitor parameter is unlikely toaccount for the observed variations in Type Ia supernova luminosity. We discusspossible effects on the calibration of cosmological measurements.Comment: 5 pages, 4 figures, resolution of Figs. 1 and 2 is reduced, submitted  to A&A Letter

The case against the progenitor's carbon-to-oxygen ratio as a source of peak luminosity variations in type Ia supernovae