  The radiation mechanism of the prompt emission of gamma-ray bursts (GRBs)
remains an open question. Although their spectra are usually well fitted with
the empirical Band function, which is widely believed to be fully non-thermal
and interpreted as an optically thin synchrotron emission, accumulating
evidence shows that a thermal component actually exists. In this paper, a
multi-color blackbody (mBB) model is proposed for the time-integrated spectrum
of GRB 081221 by assuming a power-law distribution of the thermal luminosities
with temperature, which manifests photospheric emissions from a different
radius and/or angle. The effects of the minimum temperature $kT_{\min }$, the
maximum temperature $kT_{\max }$ and the power law index $m$ of the luminosity
distribution of an mBB are discussed. The fitting to the time-integrated
spectrum during the bright phase (from 20s to 30s since the trigger) of GRB
081221 by the mBB model yields $kT_{\min }$ = $4.4\pm 0.3$ keV, $kT_{\max }$ =
57.0 $_{-1.4}^{+1.6}$ keV, and $m=-0.46_{-0.06}^{+0.05}$. When the time bin is
small enough, the time-resolved spectra of GRB 081221 are well fitted with a
series of single-temperature blackbodies. Our results imply the prompt emission
of GRB 081221 is dominated by the photosphere emission and its time-integrated
spectrum is a superposition of pure blackbody components at different times,
indicating that some empirical Band spectra may be interpreted as mBB if the
temperature is widely distributed.

High Energy Astrophysical Phenomena