(i.e. linear) SFR indicators [see, e.g @2003ApJ...586..794B]. The FIR emission does not only depends on star formation but also on the dust opacity. The dust mass and spatial distribution (e.g. clumpiness) are important factors. The non-thermal radio emission is even more complicated. It depends on many different factors, such as supernova rate, magnetic field and cosmic ray escaping. Only the supernova rate is directly linked with SFR, with a fixed initial mass function[^1]. The non-linearity of both FIR-SFR and radio-SFR relations, combined with the fact that FIR and radio correlate linearly very well, leads to an intriguing “conspiracy” [@2003ApJ...586..794B], which is not yet well understood. The physics behind FRC is still an interesting field to investigate.

Numerous theoretical models have been proposed to explain this correlation. Almost all the models use recent star formation as the basis, yet they differ on details of how to “convert” star formation rate to FIR and radio luminosities, while keeping a constant FIR-to-radio flux ratio. One way is to assume that both far-UV (FUV) star light and cosmic ray energy are fully converted to FIR and radio emission . However, the assumption is over-simplified. Only the most dense regions are expected to be “optically 