The increase in the number of Type Ia supernovae (SNe,Ia) has demonstrated that the population shows larger diversity than has been assumed in the past. The reasons (e.g. parent population, explosion mechanism) for this diversity remain largely unknown. We have investigated a sample of SNe,Ia near-infrared light curves and have correlated the phase of the second maximum with the bolometric peak luminosity. The peak bolometric luminosity is related to the time of the second maximum (relative to the {it B} light curve maximum) as follows : $L_{max}(10^{43} erg s^{-1}) = (0.039 pm 0.004) times t_2(J)(days) + (0.013 pm 0.106)$. $^{56}$Ni masses can be derived from the peak luminosity based on Arnetts rule, which states that the luminosity at maximum is equal to instantaneous energy generated by the nickel decay. We check this assumption against recent radiative-transfer calculations of Chandrasekhar-mass delayed detonation models and find this assumption is valid to within 10% in recent radiative-transfer calculations of Chandrasekhar-mass delayed detonation models. The $L_{max}$ vs. $t_2$ relation is applied to a sample of 40 additional SNe,Ia with significant reddening ($E(B-V) >$ 0.1 mag) and a reddening-free bolometric luminosity function of SNe~Ia is established. The method is tested with the $^{56}$Ni mass measurement from the direct observation of $gamma-$rays in the heavily absorbed SN 2014J and found to be fully consistent. Super-Chandrasekhar-mass explosions, in particular SN,2007if, do not follow the relations between peak luminosity and second IR maximum. This may point to an additional energy source contributing at maximum light. The luminosity function of SNe,Ia is constructed and is shown to be asymmetric with a tail of low-luminosity objects and a rather sharp high-luminosity cutoff, although it might be influenced by selection effects.
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