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A few Type Ia supernovae (SNe Ia) have been suggested to be an explosion of a super‐Chandrasekhar‐mass white dwarf (WD) in order to account for their large luminosities, requiring a large amount of  56 Ni. However, the candidate overluminous SNe Ia 2003fg, 2006gz and (moderately overluminous) SN 1991T have very different observational features: the characteristic time‐scale and velocity are very different. We examine if and how the diversity can be explained, by one‐dimensional  spherical  radiation transport calculations covering a wide range of model parameters (e.g. WD mass). The observations of SN 2006gz are naturally explained by the super‐Chandrasekhar‐mass model. SN 1991T represents a marginal case, which may either be a Chandrasekhar or a super‐Chandrasekhar‐mass WD explosion. In contrast, the low velocity and short time‐scale seen in SN 2003fg indicate that the ejecta mass is smaller than the Chandrasekhar mass, which is in apparent contradiction to the large luminosity. We suggest that the problem is solved if the progenitor WD, and thus the SN explosion, is aspherical. This may reflect a rapid rotation of the progenitor star, likely a consequence of the super‐Chandrasekhar‐mass WD progenitor. The observed differences between SNe 2003fg and 2006gz may be attributed to different viewing orientations.

Observational characteristics and possible asphericity of overluminous Type Ia supernovae