We propose an “ extended Schmidt law ” with explicit dependence of the star formation efficiency ( SFE=SFR/ M _ { gas } ) on the stellar mass surface density ( \Sigma _ { star } ) .
This relation has a power-law index of 0.48 \pm 0.04 and an 1- \sigma observed scatter on the SFE of 0.4 dex , which holds over 5 orders of magnitude in the stellar density for individual global galaxies including various types especially the low-surface-brightness ( LSB ) galaxies that deviate significantly from the Kennicutt-Schmidt law .
When applying it to regions at sub-kpc resolution of a sample of 12 spiral galaxies , the extended Schmidt law not only holds for LSB regions but also shows significantly smaller scatters both within and across galaxies compared to the Kennicutt-Schmidt law .
We argue that this new relation points to the role of existing stars in regulating the SFE , thus encoding better the star formation physics .
Comparison with physical models of star formation recipes shows that the extended Schmidt law can be reproduced by some models including gas free-fall in a stellar-gravitational potential and pressure-supported star formation .
By implementing this new law into the analytic model of gas accretion in \Lambda CDM , we show that it can re-produce the observed main sequence of star-forming galaxies ( a relation between the SFR and stellar mass ) from z =0 up to z =2 .