Revealing the dust grain size in the inner envelope of the Class I
  protostar Per-emb-50
  A good constraint of when the growth of dust grains from sub-micrometer to
millimeter sizes occurs, is crucial for planet formation models. This provides
the first step towards the production of pebbles and planetesimals in
protoplanetary disks. Currently, it is well established that Class II objects
have large dust grains. However, it is not clear when in the star formation
process this grain growth occurs. We use multi-wavelength millimeter
observations of a Class I protostar to obtain the spectral index of the
observed flux densities $\alpha_\mathrm{mm}$ of the unresolved disk and the
surrounding envelope. Our goal is to compare our observational results with
visibility modeling at both wavelengths simultaneously. We present data from
NOEMA at 2.7 mm and SMA at 1.3 mm of the Class I protostar, Per-emb-50. We
model the dust emission with a variety of parametric and radiative transfer
models to deduce the grain size from the observed emission spectral index. We
find a spectral index in the envelope of Per-emb-50 of $\alpha_{\rm
env}$=$3.3\pm0.3$, similar to the typical ISM values. The radiative transfer
modeling of the source confirms this value of $\alpha_{\rm env}$ with the
presence of dust with a $a_\mathrm{max}$$\leq$100 $\mu$m. Additionally, we
explore the backwarming effect, where we find that the envelope structure
affects the millimeter emission of the disk. Our results reveal grains with a
maximum size no larger than $100$ $\mu$m in the inner envelope of the Class I
protostar Per-emb-50, providing an interesting case to test the universality of
millimeter grain growth expected in these sources.
