Protostellar disks are the product of angular momentum conservation during
the protostellar collapse. Understanding their formation is crucial because
they are the birthplace of planets and because their formation is tightly
related to star formation. Unfortunately, the initial properties of Class 0
disks and their evolution are still poorly constrained observationally and
theoretically. We aim to better understand the mechanisms that set the
statistics of disk properties as well as to study their formation in massive
protostellar clumps. We also want to provide the community with synthetic disk
populations to better interpret young disk observations. We use the ramses code
to model star and disk formation in massive protostellar clumps with MHD
including the effect of ambipolar diffusion and RT including the stellar
radiative feedback. Those simulations, resolved up to the astronomical unit
scale, allow to investigate the formation of disk populations. Magnetic fields
play a crucial role in disk formation. A weaker initial field leads to larger
and massive disks and weakens the stellar radiative feedback by increasing
fragmentation. We find that ambipolar diffusion impacts disk and star formation
and leads to very different disk magnetic properties. The stellar radiative
feedback also have a strong influence, increasing the temperature and reducing
fragmentation. Comparing our disk populations with observations reveals that
our models with a mass-to-flux ratio of 10 seems to better reproduce observed
disk sizes. This also sheds light on a tension between models and observations
for the disk masses. The clump properties and physical modeling impact disk
populations significantly. The tension between observations and models for disk
mass estimates is critical to solve with synthetic observations in future
years, in particular for our comprehension of planet formation.Comment: 20 pages, 15 figures, accepted for publication in Astronomy &
Astrophysic