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 < days) joined with published GCN data indicate a steepening decay, approaching F(v) proportional to t(-0.6) at early times (t << day) and at late times. The break at days is the earliest reported jet break among all GRB afterglows. During our first night, we obtained 39 exposures spanning 2.15 hr 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 days, the decay slows considerably, and the light curve remains approximately flat at mag t similar to 4 R similar to 24 for a month before decaying by another magnitude to reach mag 2 months after the burst. This "bump" is R similar to 25 well fit by a k-corrected light curve of supernova SN 1998bw, but only if stretched by a factor of 1.38 in time. In comparison with the other GRB-related SN bumps, GRB 041006 stakes out new parameter space for GRBs/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.