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

A reddening-free method to estimate the $^{56}$Ni mass of Type Ia supernovae