How accurate are current $^{56}$Ni mass estimates in Type Ia Supernovae?

The diversity of type Ia supernovae (SNe Ia) has become increasingly apparent with the rapid growth in observational data. Understanding the explosion mechanism of SNe Ia is crucial for their cosmological calibration and for advancing our knowledge of stellar physics. The estimation of $^{56}$Ni mass produced in these events is key to elucidating their explosion mechanism. This study compares two methods of $^{56}$Ni mass estimation. We first examine the relationship between peak luminosity and the second maximum in near-infrared (NIR) bands using observations of 18 nearby SNe Ia. Based on this relationship, we estimate the Ni mass for a set of nine well-observed SNe Ia using the Arnett rule. Additionally, we estimate the $^{56}$Ni mass using bolometric light curves of these SNe through energy conservation arguments. A comparison of these two estimation methods using Student's t-test reveals no statistically significant differences between the estimates. This finding suggests that both methods provide robust estimates of Ni mass in SNe Ia.