Low luminosity Type II supernovae -- IV. SN 2020cxd and SN 2021aai, at the edges of the sub-luminous supernovae class

Photometric and spectroscopic data for two Low Luminosity Type IIP Supernovae (LL SNe IIP) are presented. SN 2020cxd reaches a peak absolute magnitude $M_{r}$ = -13.90 $\pm$ 0.05 mag two days after explosion, subsequently settling on a plateau for $\sim$120 days. Through the luminosity of the late light curve tail, we infer a synthesized $^{56}$Ni mass of (1.8$\pm$0.5) $\times$ 10$^{-3}$ M$_{\odot}$. During the early evolutionary phases, optical spectra show a blue continuum ($T$ $>$ 8000 K) with broad Balmer lines displaying a P Cygni profile, while at later phases Ca II, Fe II, Sc II and Ba II lines dominate the spectra. Hydrodynamical modelling of the observables yields $R$ $\simeq$ 575 $R_{\odot}$ for the progenitor star, with $M_{ej}$ = 7.5 M$_{\odot}$ and $E$ $\simeq$ 0.097 foe emitted during the explosion. This low-energy event originating from a low-mass progenitor star is compatible with both the explosion of a red supergiant (RSG) star and with an Electron Capture Supernova arising from a super asymptotic giant branch star. SN 2021aai reaches a maximum luminosity of $M_{r}$ = -16.4 mag (correcting for $A_{V}$=1.9 mag), and displays a remarkably long plateau ($\sim$140 days). The estimated $^{56}$Ni mass is (1.4$\pm$0.5) $\times$ 10$^{-2}$ M$_{\odot}$. The expansion velocities are compatible with those of other LL SNe IIP (few 10$^{3}$ km s$^{-1}$). The physical parameters obtained through hydrodynamical modelling are $R$ $\simeq$ 575 R$_{\odot}$, $M_{ej}$ = 15.5 M$_{\odot}$ and $E$ = 0.4 foe. SN 2021aai is therefore interpreted as the explosion of a RSG, with properties that bridge the class of LL SNe IIP with standard SN IIP events.