Deciphering the explosion mechanism of Type-Ia SNe using their remnants I: general properties and a case study on Tycho's SNR

Type-Ia supernovae (SNe), or runaway thermonuclear explosions of white dwarfs (WDs), play a critical role in the chemical evolution of galaxies, and are important cosmological distance indicators due to their 'standardizable' lightcurves. Growing evidence, however, suggests greater diversity in their observed lightcurves (and spectra) than thought previously. This is usually attributed to a variety of WD explosion mechanisms and progenitor system properties, but a direct link between the explosion mechanisms and Type-Ia SN observables remains elusive. Here we present a novel approach to identify explosion mechanisms of Type-Ia SNe, by analyzing the sizes of small-scale turbulent substructures of different elements in their extended ejecta, i.e., in Supernova Remnants (SNRs). Our three-dimensional hydrodynamical models show that substructures in an SNR dominated by iron-group elements may have a typical size different from substructures dominated by intermediate mass elements (e.g., Si, S) in the same SNR. This size difference is governed by the explosion mechanism. Applying this approach to Tycho's SNR, we find that its observed structure is most consistent with an SNR model in our suite that originated from a sub-Chandrasekhar mass WD via the double-detonation mechanism. Extending this method to other well-characterized SNRs can let us connect the inferred explosion mechanism to the associated historical SNe, which often have spectra reconstructed through light echo observations.