We present a model that unifies the cosmic star formation rate ( CSFR ) , obtained through the hierarchical structure formation scenario , with the ( Galactic ) local star formation rate ( SFR ) .
It is possible to use the SFR to generate a CSFR mapping through the density probability distribution functions ( PDFs ) commonly used to study the role of turbulence in the star-forming regions of the Galaxy .
We obtain a consistent mapping from redshift z \sim 20 up to the present ( z = 0 ) .
Our results show that the turbulence exhibits a dual character , providing high values for the star formation efficiency ( \langle \varepsilon \rangle \sim 0.32 ) in the redshift interval z \sim 3.5 - 20 and reducing its value to \langle \varepsilon \rangle = 0.021 at z = 0 .
The value of the Mach number ( \mathcal { M } _ { crit } ) , from which \langle \varepsilon \rangle rapidly decreases , is dependent on both the polytropic index ( \Gamma ) and the minimum density contrast of the gas .
We also derive Larson ’ s first law associated with the velocity dispersion ( \langle V _ { rms } \rangle ) in the local star formation regions .
Our model shows good agreement with Larson ’ s law in the \sim 10 - 50 { pc } range , providing typical temperatures T _ { 0 } \sim 10 - 80 { K } for the gas associated with star formation .
As a consequence , dark matter halos of great mass could contain a number of halos of much smaller mass , and be able to form structures similar to globular clusters .
Thus , Larson ’ s law emerges as a result of the very formation of large-scale structures , which in turn would allow the formation of galactic systems , including our Galaxy .