An increase in the number of studied Type Ia supernovae (SNe Ia) has demonstrated that this class of explosions has a greater diversity in its observables than was previously assumed. The reasons (e.g. the explosion mechanism, progenitor system) for such a diversity remain unknown. Here, we analyse a sample of r-band light curves of SNe Ia, focusing on their behaviour ~2-4 weeks after maximum light, i.e. the second maximum. We characterize the second maximum by its timing (t_r2_) and the integrated flux (F_r2_). We find that tr2 correlates with the 'colour-stretch' parameter sBV , which can be used as a proxy for ^56^Ni mass, and F_r2_ correlates with the transparency time-scale, t0. Using F_r2_ for a sample of 199 SNe from the Palomar Transient Factory and intermediate Palomar Transient Factory, we evaluate a distribution on t0 for a sample of SNe Ia found in an 'untargeted' survey. Comparing this distribution to the predictions of t0 ranges from models we find that the largest overlap in t0 values between models and observations is for the sub-Chandrasekhar double detonation models. We also compare our relations between t0 and F_r2_ with that from the 1D explosion models of Goldstein & Kasen (2018ApJ...852L..33G) and confirm that F_r2_ can be used as a diagnostic of the total ejecta mass.

Cone search capability for table J/MNRAS/485/2343/tablea1 (The parameters for the CfA SNe in the r-band)

Cone search capability for table J/MNRAS/485/2343/tablea2 (The parameters for the CSP-I SNe in the r-band)

Cone search capability for table J/MNRAS/485/2343/tablea3 (The parameters for the CfA SNe in the i-band)

Cone search capability for table J/MNRAS/485/2343/tablea5 (t0 values from the CSP-I SNe with sufficient multi-band data)