Formation of massive stars by growing accretion rate

We perform calculations of pre-main sequence evolution of stars from 1 to $85 M_{\odot}$ with growing accretion rates $\dot{M}$. The values of $\dot{M}$ are taken equal to a constant fraction $\tilde{f}$ of the rates of the mass outflows observed by Churchwell (\cite{church}) and Henning (\cite{henning2000}). The evolution of the various stellar parameters is given, as well as the evolution of the disc luminosity; electronic tables are provided as a supplement to the articles. Typically, the duration of the accretion phase of massive stars is $\simeq 3 \cdot 10^5$yr. and there is less than 10% difference in the time necessary to form a 8 or $80 M_{\odot}$ star. If in a young cluster all the proto-stellar cores start to accrete at the same time, we then have a relation $M(t)$ between the masses of the new stars and the time $t$ of their appearance. Since we also know the distribution of stellar masses at the end of star formation (IMF), we can derive the star formation history $N(t)$. Interestingly enough, the current IMF implies two peaks of star formation: low mass stars form first and high mass star form later.