Context: Research on supernovae (SNe) over the past decade has confirmed that there is a distinct class of events which are much more luminous (by $sim2$ mag) than canonical core-collapse SNe (CCSNe). These events with visual peak magnitudes $lesssim-21$ are called superluminous SNe (SLSNe). Aims: There are a few intermediate events which have luminosities between these two classes. Here we study one such object, SN 2012aa. Methods: The optical photometric and spectroscopic follow-up observations of the event were conducted over a time span of about 120 days. Results: With V_abs at peak ~-20 mag, the SN is an intermediate-luminosity transient between regular SNe Ibc and SLSNe. It also exhibits an unusual secondary bump after the maximum in its light curve. We interpret this as a manifestation of SN-shock interaction with the CSM. If we would assume a $^{56}$Ni-powered ejecta, the bolometric light curve requires roughly 1.3 M_sun of $^{56}$Ni and an ejected mass of ~14 M_sun. This would also imply a high kinetic energy of the explosion, ~5.4$times10^{51}$ ergs. On the other hand, the unusually broad light curve along with the secondary peak indicate the possibility of interaction with CSM. The third alternative is the presence of a central engine releasing spin energy that eventually powers the light curve over a long time. The host of the SN is a star-forming Sa/Sb/Sbc galaxy. Conclusions: Although the spectral properties and velocity evolution of SN 2012aa are comparable to those of normal SNe Ibc, its broad light curve along with a large peak luminosity distinguish it from canonical CCSNe, suggesting the event to be an intermediate-luminosity transient between CCSNe and SLSNe at least in terms of peak luminosity. We argue that SN 2012aa belongs to a subclass where CSM interaction plays a significant role in powering the SN, at least during the initial stages of evolution.
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