  Surveys of protoplanetary disks in star-forming regions of similar age
revealed significant variations in average disk mass between some regions. For
instance, disks in the Orion Nebular Cluster (ONC) and Corona Australis (CrA)
are on average smaller than disks observed in Lupus, Taurus, Chamaeleon I or
Ophiuchus. In contrast to previous models that study truncation of disks at a
late stage of their evolution, we investigate whether disks may already be born
with systematically smaller disk sizes in more massive star-forming regions as
a consequence of enhanced ionization rates. Assuming various cosmic-ray
ionization rates, we compute the resistivities for ambipolar diffusion and
Ohmic dissipation with a chemical network, and perform 2D non-ideal
magnetohydrodynamical protostellar collapse simulations. A higher ionization
rate leads to stronger magnetic braking, and hence to the formation of smaller
disks. Accounting for recent findings that protostars act as forges of cosmic
rays and considering only mild attenuation during the collapse phase, we show
that a high average cosmic-ray ionization rate in star-forming regions like the
ONC or CrA can explain the detection of smaller disks in these regions. Our
results show that on average a higher ionization rate leads to the formation of
smaller disks. Therefore, smaller disks in regions of similar age can be the
consequence of different levels of ionization, and may not exclusively be
caused by disk truncation via external photoevaporation. We strongly encourage
observations that allow measuring the cosmic-ray ionization degrees in
different star-forming regions to test our hypothesis.
