  Using high-quality, broad-band afterglow data for GRB 091127, we investigate
the validity of the synchrotron fireball model for gamma-ray bursts, and infer
physical parameters of the ultra-relativistic outflow. We used multi-wavelength
follow-up observations obtained with GROND and the XRT onboard the Swift
satellite. The resulting afterglow light curve is of excellent accuracy, and
the spectral energy distribution is well-sampled over 5 decades in energy.
These data present one of the most comprehensive observing campaigns for a
single GRB afterglow and allow us to test several proposed emission models and
outflow characteristics in unprecedented detail. Both the multi-color light
curve and the broad-band SED of the afterglow of GRB 091127 show evidence of a
cooling break moving from high to lower energies. The early light curve is well
described by a broken power-law, where the initial decay in the optical/NIR
wavelength range is considerably flatter than at X-rays. Detailed fitting of
the time-resolved SED shows that the break is very smooth with a sharpness
index of 2.2 +- 0.2, and evolves towards lower frequencies as a power-law with
index -1.23 +- 0.06. These are the first accurate and contemporaneous
measurements of both the sharpness of the spectral break and its time
evolution. The measured evolution of the cooling break (nu_c propto t^-1.2) is
not consistent with the predictions of the standard model, wherein nu_c propto
t^-0.5 is expected. A possible explanation for the observed behavior is a time
dependence of the microphysical parameters, in particular the fraction of the
total energy in the magnetic field epsilon_B. This conclusion provides further
evidence that the standard fireball model is too simplistic, and time-dependent
micro-physical parameters may be required to model the growing number of
well-sampled afterglow light curves.
