Deep Photometry of GRB 041006 Afterglow: Hypernova Bump at Redshift z=0.716

We present deep optical photometry of the afterglow of gamma-ray burst (GRB) 041006 and its associated hypernova obtained over 65 days after detection (55 R-band epochs on 10 different nights). Our early data (t<4 days) joined with published GCN data indicates a steepening decay, approaching F_nu ~t^{-0.6} at early times (<<1 day) and F_nu ~t^{-1.3} at late times. The break at t_b=0.16+-0.04 days is the earliest reported jet break among all GRB afterglows. During our first night, we obtained 39 exposures spanning 2.15 hours from 0.62 to 0.71 days after the burst that reveal a smooth afterglow, with an rms deviation of 0.024 mag from the local power-law fit, consistent with photometric errors. After t~4 days, the decay slows considerably, and the light curve remains approximately flat at R~24 mag for a month before decaying by another magnitude to reach R~25 mag two months after the burst. This ``bump'' is well-fitted by a k-corrected light curve of SN1998bw, but only if stretched by a factor of 1.38 in time. In comparison with the other GRB-related SNe bumps, GRB 041006 stakes out new parameter space for GRB/SNe, with a very bright and significantly stretched late-time SN light curve. Within a small sample of fairly well observed GRB/SN bumps, we see a hint of a possible correlation between their peak luminosity and their ``stretch factor'', broadly similar to the well-studied Phillips relation for the type Ia supernovae.