SN 2019muj -- a well-observed Type Iax supernova that bridges the luminosity gap of the class

We present early-time ($t < +50$ days) observations of SN 2019muj (= ASASSN-19tr), one of the best-observed members of the peculiar SN Iax class. Ultraviolet and optical photometric and optical and near-infrared spectroscopic follow-up started from $\sim$5 days before maximum light ($t_{max}(B)$ on $58707.8$ MJD) and covers the photospheric phase. The early observations allow us to estimate the physical properties of the ejecta and characterize the possible divergence from a uniform chemical abundance structure. The estimated bolometric light curve peaks at 1.05 $\times$ 10$^{42}$ erg s$^{-1}$ and indicates that only 0.031 $M_\odot$ of $^{56}$Ni was produced, making SN 2019muj a moderate luminosity object in the Iax class with peak absolute magnitude of $M_{V}$ = -16.4 mag. The estimated date of explosion is $t_0 = 58698.2$ MJD and implies a short rise time of $t_{rise}$ = 9.6 days in $B$-band. We fit of the spectroscopic data by synthetic spectra, calculated via the radiative transfer code TARDIS. Adopting the partially stratified abundance template based on brighter SNe Iax provides a good match with SN 2019muj. However, without earlier spectra, the need for stratification cannot be stated in most of the elements, except carbon, which is allowed to appear in the outer layers only. SN 2019muj provides a unique opportunity to link extremely low-luminosity SNe Iax to well-studied, brighter SNe Iax.