We study the relationship between the mid-infrared and sub-mm variability of deeply embedded protostars using the multi-epoch data from the Wide Infrared Survey Explorer ( WISE /NEOWISE ) and the ongoing James Clerk Maxwell Telescope ( JCMT ) transient survey .
Our search for signs of stochastic ( random ) and/or secular ( roughly monotonic in time ) variability in a sample of 59 young stellar objects ( YSOs ) revealed that 35 are variable in at least one of the two surveys .
This variability is dominated by secular changes .
Of those objects with secular variability , 14 objects ( 22 \% of the sample ) show correlated secular variability over mid-IR and sub-mm wavelengths .
Variable accretion is the likely mechanism responsible for this type of variability .
Fluxes of YSOs that vary in both wavelengths follow a relation of \log _ { 10 } F _ { 4.6 } ( t ) = \eta \log _ { 10 } F _ { 850 } ( t ) between the mid-IR and sub-mm , with \eta = 5.53 \pm 0.29 .
This relationship arises from the fact that sub-mm fluxes respond to the dust temperature in the larger envelope whereas the mid-IR emissivity is more directly proportional to the accretion luminosity .
The exact scaling relation , however , depends on the structure of the envelope , the importance of viscous heating in the disc , and dust opacity laws .