Α in figure 6 which indicates that dealing with those

α in Figure. 6 ,
which indicates that dealing with those missing IRAC bands is im-
portant, especially for protostars with lower SED slopes.
To further test the validity of this interpolation method, we sorted
sources with well-sampled SED (requiring all five bands) and com-
pared the L
MIR
derived from real measurements or inferred from
α . The good 1-to-1 correlation shown in Fig. 7 indicates that the
missing-band bias of L
MIR
can be mitigated by inferring the missing
band flux from α . Since the J, H, and Ks bands contribute little to
the integration of fluxes, requiring 5 bands (all 4 IRAC + MIPS 24
or FORCAST 31) could promise a relatively accurate calculation of
L
MIR
. Note that in order to consistently use Eq. 1 , we are interpolat-
ing the MIPS 24 μ m photometry when we have FORCAST 31 μ m
data instead. As for our more inclusive sample that requires 2 bands,
all the missing bands are interpolated and added into the integration,
which results in an acceptable estimation of L
MIR
.
3.2.3 Sample Selection
The calculation of protostar luminosities largely relies on the calcu-
lation of SED slopes. In order to guarantee an accurate estimation of
α , all 4 IRAC bands plus the MIPS 24 band (or FORCAST 31 band
as a substitution) are required in our ’clean’ protostar sample for
PLF calculation. By requiring the photometry in 5 bands and that
MNRAS 000 , 000–000 (2021)

7
࠵?
!"#$
࠵?
!"#$
࠵?
".&,("
࠵?
).*,("
࠵?
!"#$
࠵?
!"#$
࠵?
&.+,("
࠵?
+.,,("
Figure 5. correlations of SED slopes derived from two bands (MIPS 24 + one of the IRAC bands) and all five bands (MIPS 24 + IRAC 4 bands). Protostars
(class 0 and I) are plotted in black while class II sources are plotted in green. The red dashed line shows the 1-to-1 relation.
the magnitude uncertainty of each band less than 0.2, we obtain a
total of 981 protostars (953 from SESNA and 28 from FORCAST ).
We will refer to this protostar sample as Sample I afterwards. Since
IRAC Channel 1 or 2 alone with MIPS 24 band could guarantee a
fairly good estimation of α , we develop a more inclusive protostar
sample by requiring only 2 bands, which will be referred as Sam-
ple II. The sample size is increased to 1212 protostars (1180 from
SESNA and 32 from FORCAST ).
When neither MIPS 24 μ m nor FORCAST 31 μ m data are avail-
able, the MIPS 24 90% completeness flux, FORCAST 31 μ m flux
limit and WISE 22 μ m flux are used for SED fitting, providing de-
cent upper limits of α (see Section 3.3 for details). Considering the
double-beam contamination, the FORCAST Cycle 5 data had big
uncertainties in source positions and photometry, thus were not used
for deriving upper limits. In this way, we are missing less than 10
upper limits derived from FORCAST data, while limits from other
approaches are still available. Focusing on all protostars in the FOR-
CAST field of view of valid observations without MIPS 24 μ m or
MNRAS 000 , 000–000 (2021)

8
Figure 6. The differences of L
MIR
derived from real measurements or power-
law interpolation. The sample includes all the SESNA protostars with one or
more missing IRAC bands.