Observationally , a massive disk galaxy can harbor a bulge component that is comparably inactive as a quiescent galaxy ( QG ) .
It has been speculated that the quenched component contained in star-forming galaxies ( SFGs ) is the reason why the star formation main sequence ( MS ) has a shallow slope at high masses .
In this paper , we present a toy model to quantify the quenched mass portion of SFGs ( f _ { Q } ) at fixed stellar mass ( M _ { \ast } ) and to reconcile the MS slopes both in the low and the high mass regimes .
In this model , each SFG is composed by a star-forming plus a quenched component .
The mass of the star-forming component ( M _ { SF } ) correlates with the star formation rate ( SFR ) following a relation SFR \propto M _ { SF } ^ { \alpha _ { SF } } , where \alpha _ { SF } \sim 1.0 .
The quenched component contributes to the stellar mass but does not to the SFR .
It is thus possible to quantify f _ { Q } based on the departure of the observed MS slope \alpha from \alpha _ { SF } .
Adopting the redshift-dependent MS slope reported by \citet Whitaker 2014 , we explore the evolution of the f _ { Q } - M _ { \ast } relations over z = [ 0.5 , 2.5 ] .
We find that Milky-Way-like SFGs ( with M _ { \ast } \approx 10 ^ { 10.7 } M _ { \sun } ) typically have a f _ { Q } = 30 \% - 40 \% at z \sim 2.25 , whereas this value rapidly rises up to 70 \% - 80 \% at z \sim 0.75 .
The origin of an \alpha \sim 1.0 MS slope seen in the low mass regime is also discussed .
We argue for a scenario in which the majority of low mass SFGs stay in a ‘ ‘ steady-stage '' star formation phase .
In this phase , the SFR is mainly regulated by stellar feedback and not significantly influenced by the quenching mechanisms , thus keeping roughly constant over cosmic time .
This scenario successfully produces an \alpha \sim 1.0 MS slope , as well as the observed MS evolution from z = 2.5 to z = 0 at low masses .