In this paper, we present and analyse optical photometry and spectra of the extremely luminous and slowly evolving Type Ia supernova (SN Ia) 2009dc, and offer evidence that it is a super-Chandrasekhar mass (SC) SN Ia and thus had a SC white dwarf (WD) progenitor. Optical spectra of SN 2007if, a similar object, are also shown. SN 2009dc had one of the most slowly evolving light curves ever observed for a SN Ia, with a rise time of ~23 days and Delta m_15(B) = 0.72 mag. We calculate a lower limit to the peak bolometric luminosity of ~2.4e43 erg/s, though the actual value is likely almost 40% larger. Optical spectra of SN 2009dc and SN 2007if obtained near maximum brightness exhibit strong C II features (indicative of a significant amount of unburned material), and the post-maximum spectra are dominated by iron-group elements. All of our spectra of SN 2009dc and SN 2007if also show low expansion velocities. However, we see no strong evidence in SN 2009dc for a velocity plateau near maximum light like the one seen in SN 2007if (Scalzo et al. 2010). The high luminosity and low expansion velocities of SN 2009dc lead us to derive a possible WD progenitor mass of more than 2 M_Sun and a Ni-56 mass of about 1.4-1.7 M_Sun. We propose that the host galaxy of SN 2009dc underwent a gravitational interaction with a neighboring galaxy in the relatively recent past. This may have led to a sudden burst of star formation which could have produced the SC WD progenitor of SN 2009dc and likely turned the neighboring galaxy into a post-starburst galaxy. No published model seems to match the extreme values observed in SN 2009dc, but simulations do show that such massive progenitors can exist (likely as a result of the merger of two WDs) and can possibly explode as SC SNe Ia.
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