  Photospheric (thermal) emission is inherent to the gamma-ray burst (GRB)
"fireball" model. We show here, that inclusion of this component in the
analysis of the GRB prompt emission phase naturally explains some of the prompt
GRB spectra seen by the Fermi satellite over its entire energy band. The
sub-MeV peak is explained as multi-color black body emission, and the high
energy tail, extending up to the GeV band, results from roughly similar
contributions of synchrotron emission, synchrotron self Compton(SSC) and
Comptonization of the thermal photons by energetic electrons originating after
dissipation of the kinetic energy above the photosphere. We show how this
analysis method results in a complete, self consistent picture of the physical
conditions at both emission sites of the thermal and non-thermal radiation. We
study the connection between the thermal and non-thermal parts of the spectrum,
and show how the values of the free model parameters are deduced from the data.
We demonstrate our analysis method on GRB090902B: We deduce a Lorentz factor in
the range 920 <= \eta <= 1070, photospheric radius r_{ph} ~ 7.2 - 8.4 * 10^{11}
cm and dissipation radius r_\gamma >= 3.5 - 4.1 * 10^{15} cm. By comparison to
afterglow data, we deduce that a large fraction, epsilon_d ~85% - 95% of the
kinetic energy is dissipated, and that large fraction, ~equipartition of this
energy is carried by the electrons and the magnetic field. This high value of
epsilon_d questions the "internal shock" scenario as the main energy
dissipation mechanism for this GRB.
