Testing the Homogeneity of Type Ia Supernovae in the Near-Infrared for Accurate Distance Estimations

Type Ia Supernovae (SNe Ia) have been extensively used as standardisable candles in the optical for several decades. However, SNe Ia have shown to be more homogeneous in the near-infrared (NIR), where the effect of dust extinction is also attenuated. In this work, we explore the possibility of using a low number of NIR observations for accurate distance estimations, given the homogeneity at these wavelengths. We found that one epoch in $J$ and/or $H$ band, plus good $gr$-band coverage, gives an accurate estimation of peak magnitudes in $J$ ($J_{max}$) and $H$ ($H_{max}$) bands. The use of a single NIR epoch only introduces an additional scatter of $\sim0.05$ mag for epochs around the time of $B$-band peak magnitude ($T_{max}$). We also tested the effect of optical cadence and signal-to-noise ratio (S/N) in the estimation of $T_{max}$ and its uncertainty propagation to the NIR peak magnitudes. Both cadence and S/N have a similar contribution, where we constrained the introduced scatter of each to $<0.02$ mag in $J_{max}$ and $<0.01$ in $H_{max}$. However, these effects are expected to be negligible, provided the data quality is comparable to that obtained for observations of nearby SNe ($z\lesssim0.1$). The effect of S/N in the NIR was tested as well. For SNe Ia at $0.08<z\lesssim0.1$, NIR observations with better S/N than that found in the CSP sample is necessary to constrain the introduced scatter to a minimum ($\lesssim0.05$ mag). These results provide confidence for our FLOWS project that aims in using SNe Ia with public ZTF optical light curves and few NIR epochs to map out the peculiar velocity field of the local Universe. This will allow us to determine the distribution of dark matter in our own supercluster, Laniakea, and test the standard cosmological model by measuring the growth rate of structures, parameterised by $fD$, and the Hubble-Lema\^itre constant, $H_0$.