The stellar birthrate

Several parametrizations, besides the simple one of a constant ip(t), are used in the literature for the SFR  

The tracers of star formation The main tracers of star formation in galaxies are  

All of these formulations for the SFR need the assumption of an IMF and viceversa, the derivation of the IMF needs the assumption of a star formation history, as described in the next section. The local SFR, derived under the assumption of a particular IMF, suitable for the solar neighbourhood, gives the following range of values  

The IMF is a probability distribution function and is normally approximated by a power law, namely  

The IMF is derived locally from the present day mass function (PDMF) which in turn is obtained by counting the Main Sequence stars per interval of magnitude. Then the star counts are transformed into number of stars per pc2 and then a mass-luminosity relation is adopted to pass from the luminosity to the mass. 

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The birthrate function- Stars form and die continuously in galaxies, therefore a recipe for star formation is necessary. We define the stellar birthrate function as the number of stars formed in the time interval dt and in the mass range dm as ... 

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