Formation of massive stars by growing accretion rate

We perform calculations of pre-main sequence evolution of stars from 1 to 85 M. with growing accretion rates (M) over dot. The values of (M) over dot are taken equal to a constant fraction (f) over tilde of the rates of the mass outflows observed by Churchwell (1998) and Henning (2000). 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 similar or equal to 3 x 10(5) yr and there is less than 10% difference in the time necessary to form a 8 or 80 M. 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 ata 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.