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Α in figure 6 which indicates that dealing with those

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αin 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 sortedsources with well-sampled SED (requiring all five bands) and com-pared theLMIRderived from real measurements or inferred fromα. The good 1-to-1 correlation shown in Fig.7indicates that themissing-band bias ofLMIRcan be mitigated by inferring the missingband flux fromα. Since the J, H, and Ks bands contribute little tothe integration of fluxes, requiring 5 bands (all 4 IRAC + MIPS 24orFORCAST31) could promise a relatively accurate calculation ofLMIR. Note that in order to consistently use Eq.1, we are interpolat-ing the MIPS 24μm photometry when we haveFORCAST31μmdata 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 ofLMIR.3.2.3 Sample SelectionThe calculation of protostar luminosities largely relies on the calcu-lation of SED slopes. In order to guarantee an accurate estimation ofα, all 4 IRAC bands plus the MIPS 24 band (orFORCAST31 bandas a substitution) are required in our ’clean’ protostar sample forPLF calculation. By requiring the photometry in 5 bands and thatMNRAS000, 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 atotal of 981 protostars (953 from SESNA and 28 fromFORCAST).We will refer to this protostar sample as Sample I afterwards. SinceIRAC Channel 1 or 2 alone with MIPS 24 band could guarantee afairly good estimation ofα, we develop a more inclusive protostarsample by requiring only 2 bands, which will be referred as Sam-ple II. The sample size is increased to 1212 protostars (1180 fromSESNA and 32 fromFORCAST).When neither MIPS 24μm norFORCAST31μm data are avail-able, the MIPS 24 90% completeness flux,FORCAST31μm fluxlimit and WISE 22μm flux are used for SED fitting, providing de-cent upper limits ofα(see Section3.3for details). Considering thedouble-beam contamination, theFORCASTCycle 5 data had biguncertainties in source positions and photometry, thus were not usedfor deriving upper limits. In this way, we are missing less than 10upper limits derived fromFORCASTdata, while limits from otherapproaches are still available. Focusing on all protostars in theFOR-CASTfield of view of valid observations without MIPS 24μm orMNRAS000, 000–000 (2021)
8Figure 6.The differences ofLMIRderived from real measurements or power-law interpolation. The sample includes all the SESNA protostars with one ormore missing IRAC bands.

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Term
Fall
Professor
NoProfessor
Tags
Test, Luminosity function, Spitzer Space Telescope, Lyman Spitzer

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