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XRF 100316D/SN 2010bh: clue to the diverse origin of nearby supernova-associated GRBs

X-ray Flash (XRF) 100316D, a nearby super-long under-luminous burst with a peak energy E_p \sim 20 keV, was detected by Swift and was found to be associated with an energetic supernova SN 2010bh. Both the spectral and the temporal behavior of this burst are rather similar to that of XRF 060218, except that the latter was associated with a "less energetic" SN 2006aj and had a prominent soft thermal emission component in the spectrum. We analyze the spectral and temporal properties of this burst, and interpret the prompt gamma-ray emission and the early X-ray plateau emission as synchrotron emission from a dissipating Poynting-flux-dominated outflow, probably powered by a magnetar with a spin period of $P \sim 10$ ms and the polar cap magnetic field $B_{\rm p} \sim 3\times 10^{15}$ G. The energetic supernova SN 2010bh associated with this burst is, however, difficult to interpret within the slow magnetar model, which implies that the nascent magnetar may spin much faster with an initial rotation period $\sim 1$ ms, and thus suggests a delay between the core collapse and the emergence of the relativistic magnetar wind from the star. The diverse behaviors of low-luminosity GRBs and their associated SNe may be understood within a unified picture that invokes different initial powers of the central engine and different delay times between the core collapse and the emergence of the relativistic jet from the star.