  Frequency-dependent/hybrid approaches for stellar irradiation are of primary
importance in numerical simulations of massive star formation. We seek to
compare outflow and accretion mechanisms in star formation simulations. We
investigate the accuracy of a hybrid radiative transfer method using the gray
M1 closure relation for proto-stellar irradiation and gray flux-limited
diffusion (FLD) for photons emitted everywhere else. We have coupled the FLD
module of the adaptive-mesh refinement code Ramses with Ramses-RT, which is
based on the M1 closure relation. Our hybrid (M1+FLD) method takes an average
opacity at the stellar temperature for the M1 module, instead of the local
environmental radiation field. We have tested this approach in radiative
transfer tests of disks irradiated by a star for three levels of optical
thickness and compared the temperature structure with RADMC-3D and MCFOST. We
applied it to a radiation-hydrodynamical simulation of massive star formation.
Our tests validate our hybrid approach for determining the temperature
structure of an irradiated disk in the optically-thin and moderately
optically-thick regimes and the most optically-thick test shows the limitation
of our approach. The optically-thick setups highlight the ability of the hybrid
method to partially capture the self-shielding in the disk while the FLD
cannot. The radiative acceleration is 100 times greater with the hybrid method.
It consistently leads to about +50% more extended and wider-angle radiative
outflows in the massive star formation simulation. We obtain a $17.6 M_\odot$
at $t{\simeq}0.7 \tau_\mathrm{ff}$, while the accretion phase is ongoing.
Finally, despite the use of refinement to resolve the radiative cavities, no
Rayleigh-Taylor instability appears in our simulations, and we justify their
absence by physical arguments based on the entropy gradient. (abridged)
