  It is established that both radiative transfer and magnetic field have a
strong impact on the collapse and the fragmentation of prestellar dense cores,
but no consistent calculation exists yet at such scales. We present original
AMR calculations including magnetic field (in the ideal MHD limit) and
radiative transfer, within the Flux Limited Diffusion approximation, of the
collapse of a 1 solar mass dense core. We compare the results with calculations
performed with a barotropic EOS. We show that radiative transfer has an
important impact on the collapse and the fragmentation, through the cooling or
heating of the gas, and is complementary of the magnetic field. A larger field
yields a stronger magnetic braking, increasing the accretion rate and thus the
effect of the radiative feedback. Even for a strongly magnetized core, where
the dynamics of the collapse is dominated by the magnetic field, radiative
transfer is crucial to determine the temperature and optical depth
distributions, two potentially accessible observational diagnostics. A
barotropic EOS cannot account for realistic fragmentation. The diffusivity of
the numerical scheme, however, is found to strongly affect the output of the
collapse, leading eventually to spurious fragmentation. Both radiative transfer
and magnetic field must be included in numerical calculations of star formation
to obtain realistic collapse configurations and observable signatures.
Nevertheless, the numerical resolution and the robustness of the solver are of
prime importance to obtain reliable results. When using an accurate solver, the
fragmentation is found to always remain inhibited by the magnetic field, at
least in the ideal MHD limit, even when radiative transfer is included.
