SN 2020kyg and the rates of faint Iax Supernovae from ATLAS

We present multi-wavelength follow-up observations of the ATLAS discovered faint Iax supernova SN 2020kyg that peaked at an absolute magnitude of $M_g \approx -14.9 \pm 0.2$, making it another member of the faint Iax supernova population. The bolometric light curve requires only $\approx 7 \times 10^{-3}$ M$_{\odot}$ of radioactive $^{56}$Ni, with an ejected mass of $M_{\rm ej} \sim 0.4$ M$_{\odot}$ and a low kinetic energy of $E \approx 0.05 \pm 0.02 \times 10^{51}$ erg. We construct a homogeneous volume-limited sample of 902 transients observed by ATLAS within 100 Mpc during a 3.5 year span. Using this sample, we constrain the rates of faint Iax ($M_r \gtrsim -16$) events within 60 Mpc at $12^{+14}_{-8}\%$ of the SN Ia rate. The overall Iax rate, at $15^{+17}_{-9}\%$ of the Ia rate, is dominated by the low-luminosity events, with luminous SNe Iax ($M_r \lesssim -17.5$) like 2002cx and 2005hk accounting for only $0.9^{+1.1}_{-0.5}\%$ of the Ia rate (a 2$σ$ upper limit of approximately 3\%). We favour the hybrid CONe WD + He star progenitor channel involving a failed deflagration of a near Chandrasekhar mass white dwarf, expected to leave a bound remnant and a surviving secondary companion, as a candidate explanation for faint Iax explosions. This scenario requires short delay times, consistent with the observed environments of SNe Iax. Furthermore, binary population synthesis calculations have suggested rates of $1-18\%$ of the SN Ia rate for this channel, consistent with our rate estimates.