Characterising the secondary maximum in the r-band for Type Ia Supernovae: Diagnostic for the ejecta mass

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 $\sim$ 2 weeks after maximum light, i.e. the second maximum. We characterise the second maximum by its timing ($t_{r_2}$) and the integrated flux ($\overline{\mathcal{F}}_{r_2}$). We find that the \bump\, correlates with the `colour-stretch' parameter s$_{BV}$, which can be used as a proxy for $^{56}$Ni mass and the $\overline{\mathcal{F}}_{r_2}$, correlates with the transparency timescale, t$_0$, which traces the total ejected mass. Using the $\overline{\mathcal{F}}_{r_2}$, for a sample of 199 SNe from the Palomar Transient Factory and intermediate Palomar Transient Factory, we evaluate a distribution on t$_0$ for an untargeted sample of SNe~Ia. Comparing this distribution to the predictions of t$_0$ ranges from models we find that the largest overlap in t$_0$ values between models and observations is for the sub-Chandrasekhar double detonation models. We also compare our relations between t$_0$ and $\overline{\mathcal{F}}_{r_2}$, with that from 1-D explosion models of \citet{GK18} and confirm that the $\overline{\mathcal{F}}_{r_2}$, can be used as a robust diagnostic of the total ejecta mass.