SN 2012ij: A Low-luminosity Type Ia Supernova and Evidence for a Continuous Distribution from a 91bg-like Explosion to Normal Ones*

In this paper, we present photometric and spectroscopic observations of a subluminous type Ia supernova (SN Ia) 2012ij, which has an absolute $B$-band peak magnitude $M_{B,\rm{max}}$ = $-$17.95 $\pm$ 0.15 mag. The light curve exhibits fast post-peak decline with $\Delta m_{15}(B)$ 1.86 0.05 All the $R$ $I$/$i$-band curves show weak secondary peak/shoulder feature at about 3 weeks after peak, like some transitional subclass SNe Ia, could result from incomplete merger near-infrared (NIR) double peaks. spectra are characterized by Ti~{\sc ii} strong Si~{\sc $\lambda$5972 absorption features that usually seen in low-luminosity objects SN 1999by. NIR spectrum before maximum reveals carbon features, implying existence unburned materials. We compare observed properties 2012ij those predicted sub-Chandrasekhar-mass Chandrasekhar-mass delayed-detonation models, find both optical spectral can be explained to extent these two models. By comparing $I$ $i$ bands, suggest is object linking normal typical 91bg-like ones. From published sample $Carnegie~Supernova~Project~II$ (CSP-II), estimate fraction 2012ij-like not lower than $\sim$ 2%.