We present the discovery and extensive early-time observations of the Type Ic supernova (SN) PTF12gzk. Our finely sampled light curves show a rise of 0.8mag within 2.5hr. Power-law fits [f(t)sim(t-t_0)^n] to these data constrain the explosion date to within one day. We cannot rule out the expected quadratic fireball model, but higher values of n are possible as well for larger areas in the fit parameter space. Our bolometric light curve and a dense spectral sequence are used to estimate the physical parameters of the exploding star and of the explosion. We show that the photometric evolution of PTF12gzk is slower than that of most SNe Ic, and its high ejecta velocities (~30,000km/s four days after explosion) are closer to the observed velocities of broad-lined SNe Ic associated with gamma-ray bursts (GRBs) than to the observed velocities in normal Type Ic SNe. The high velocities are sustained through the SN early evolution, and are similar to those of GRB-SNe when the SN reach peak magnitude. By comparison with the spectroscopically similar SN 2004aw, we suggest that the observed properties of PTF12gzk indicate an initial progenitor mass of 25-35 solar mass and a large (5-10E51 erg) kinetic energy, close to the regime of GRB-SN properties. The host-galaxy characteristics are consistent with GRB-SN hosts, and not with normal SN Ic hosts as well, yet this SN does not show the broad lines over extended periods of time that are typical of broad-line Type Ic SNe.
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