The quick and precise localization of GRBs by the Swift telescope allows the early evolution of the afterglow light curve to be captured by ground-based telescopes. With GROND measurements we can investigate the optical/near-infrared light curve of the afterglow of gamma-ray burst 080413B in the context of late rebrightening. Multi-wavelength follow-up observations were performed on the afterglow of GRB 080413B. X-ray emission was detected by the X-ray telescope onboard the Swift satellite and obtained from the public archive. Optical and near-infrared photometry was performed with the seven-channel imager GROND mounted at the MPG/ESO 2.2 m telescope and additionally with the REM telescope, both in La Silla, Chile. The light curve model was constructed using the obtained broad-band data. The broad-band light curve of the afterglow of GRB 080413B is well fitted with an on-axis two-component jet model. The narrow ultra-relativistic jet is responsible for the initial decay, while the rise of the moderately relativistic wider jet near its deceleration time is the cause of the rebrightening of the light curve. The later evolution of the optical/NIR light curve is then dominated by the wide component, the signature of which is almost negligible in the X-ray wavelengths. These components have opening angles of theta(narrow) ~1.7 degrees and theta(wide) ~9 degrees, and Lorentz factors of Gamma(narrow) >188 and Gamma(wide) ~18.5. We calculated the beaming-corrected energy release to be 7.9 x 10^48 erg.
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