Constraining Type Ia Supernovae Progenitor Parameters via Light Curves

I study thermonuclear explosions of White Dwarf (WD) stars, or so-called Type Ia supernovae (SNe Ia). A WD is the final stage of stellar evolution of a star with an initial mass of less than 8 Solar masses, and the thermonuclear explosion occurs either when the WD is in a close binary system where mass overflows from a companion star in a red-giant or asymptotic-branch giant phase, or when two WDs merge. SNe Ia are as bright as their entire host galaxy, which allows their use as long-range cosmic beacons. Although their maximum brightness may vary by a factor of 20, an empirical correlation between their primary parameters of light curve (LC) shape and their intrinsic brightness allows us to account for the majority of this dispersion, with a residual uncertainty of roughly 20%. This calibration has led to their use as standardizable candles, which led to the discovery of the dark energy. Higher precision is needed to determine the nature of the dark energy, however, and to accomplish this we turn to secondary parameters of LC variation. I have devised a general scheme and developed a code to analyze large sets of LC data for these secondary parameter variations which is based on a combination of theoretical model template fitting and Principal Component Analysis. Novel methods for finding statistical trends in sparsely-sampled and non-coincidental light curve data are explored and utilized. In practice, data sets for different supernovae are inhomogeneous in time, time coverage and accuracy, but I have developed a method to remap these inhomogeneous data sets of large numbers of individual objects to a homogeneous data set centered in time and magnitude space from which we can obtain the external, primary, and secondary LC parameters of individual objects. The set of external parameters of a given SN include the time of its maximum light in various bands, its distance modulus, the extinction along the light path, and redshift corrections (K-corrections) due to cosmic expansion. I investigate the intrinsic primary parameter variation of SNe Ia via template fitting, and then probe the secondary LC variations using monochromatic differential analysis in the (UBV) bands. We use photometry from 25 SNe Ia which were recently and precisely observed by the Carnegie Supernova Project to analyze the presence of theoretical model-based differential LC signatures of Main-Sequence mass variation of the progenitor stars when they formed, central density variation of the WD at the time of the explosion, and metallicity Z variation the in the progenitors. The light curves in the V band are found to provide the highest accuracy in determining the distance modulus, K-corrections, extinction, main-sequence mass and central density of the WD progenitor, and also the V-band LCs are insensitive to metallicity. Moreover, the V-band appears to be the band which is most stable for differential creation due to the stability of the differentials with respect to uncertainties in the SNe pairs' primary parameters. The B-band's larger K-correction uncertainties and dependence on progenitor metallicity and primary parameter uncertainties discourages its use in secondary parameter differential analysis. As with B, the U-band also suffers large uncertainties in extinction and K-corrections, but this band is a good indicator of metallicity, because the effects of metallicity variation on differential LCs are larger by an order of magnitude than the Main-Sequence mass and central density effects combined. Our sample includes three SN1991T-like objects, but we find no evidence of secondary parameter variation among them, and conclude that this class of object may be identified by its primary LC parameter as well as its lack of secondary parameter features. Accounting for these secondary parameters reduces the residuals in the fiducial LC fits from 0.2 magnitude to approximately 0.02 magnitude, a requirement for high-precision cosmology based on SNe Ia. I also reconstruct the distributions of Main-Sequence mass, central density, and metallicity for the progenitors of the 25 SNe in our sample. I find that most SNe in our sample originate from stars close to the upper limit of the range of possible Main-Sequence masses, indicating that most SNe Ia explode relatively soon after the progenitor star's formation. However, the reconstructed progenitor mass distribution displays a long tail down to lower-mass objects of about 1.5 Solar masses. The central density secondary parameter distribution is much flatter, and shows SNe originate from WD progenitors of a wide range of central densities, from as low as 1.5E9 grams per cubic centimeter, and up to the limit of accretion-induced collapse, suggesting that some potential SNe Ia progenitors become neutron stars instead. Although our sample size is small, all SN1991bg-like objects in it come from progenitors with low reconstructed central density and metallicity secondary parameters. Because SN1991bg-like objects are only found in local samples and not in high-redshift searches, our findings suggest that these progenitor systems are formed at high redshifts but exhibit long delay times before the explosion.