Does the external radiation causes significantly different SED?
The external radiation field might be the most important heating source for grains far from the central source (> 3000-4000 au), but do the grains heated by the ISRF contribute significantly to the envelope emission?
Effect of the background interstellar radiation field on the SED
We included a uniform external radiation field to account for the heating from outside of the envelope. The protostar only heats the inner ~1000 au. If the external radiation is neglected then at few 1000 au from the central source the dust temperature might drop significantly below 10 K.
Once the external irradiation is included in both the thermal and raytracing RT, we see strong background contribution in the SED. This is not seen typically in observations.
We investigated whether our model is correct by computing the SED without the background source (I_0 = 0) and with the background source, but correcting for the background by measuring the background flux in a ring around the model mask. The results are shown below. The two cases match up well, thus we might choose either of them (i.e. removing the background as post-processing or excluding it from the raytracing RT all together).