Massive star formation by accretion I. Disc accretion

Context. Massive stars likely form by accretion and the evolutionary track of an accreting forming star corresponds to what is called the birthline in the Hertzsprung-Russell (HR) diagram. The shape of this birthline is quite sensitive to the evolution of the entropy in the accreting star. Aims. We first study the reasons why some birthlines published in past years present different behaviours for a given accretion rate. We then revisit the question of the accretion rate, which allows us to understand the distribution of the observed pre-main-sequence (pre-MS) stars in the HR diagram. Finally, we identify the conditions needed to obtain a large inflation of the star along its pre-MS evolution that may push the birthline towards the Hayashi line in the upper part of the HR diagram. Methods. We present new pre-MS models including accretion at various rates and for different initial structures of the accreting core. We compare them with previously published equivalent models. From the observed upper envelope of pre-MS stars in the HR diagram, we deduce the accretion law that best matches the accretion history of most of the intermediate-mass stars. Results. In the numerical computation of the time derivative of the entropy, some treatment leads to an artificial loss of entropy and thus reduces the inflation that the accreting star undergoes along the birthline. In the case of cold disc accretion, the existence of a significant swelling during the accretion phase, which leads to radii >= 100 R-circle dot and brings the star back to the red part of the HR diagram, depends sensitively on the initial conditions. For an accretion rate of 10(-3) M-circle dot yr(-1), only models starting from a core with a significant radiative region evolve back to the red part of the HR diagram. We also obtain that, in order to reproduce the observed upper envelope of pre-MS stars in the HR diagram with an accretion law deduced from the observed mass outflows in ultra-compact HII regions, the fraction of the mass that is accreted onto the star should represent a decreasing fraction of the mass outflows when the mass of the accreting object increases. In other words, the accretion efficiency (mass effectively accreted onto the star with respect to the total in falling matter) decreases when the mass of the star increases.