Result of a simulation in which the parameterization for the a-parameter as given by Eqs. (36) through (38) is used throughout the infall phase. Left: evolution of the total mass present in each of the molecular cloud, star and disk as a function of time. In this scenario, mass can’t accrete onto the star from the disk rapidly enough, so the disk keeps growing in mass until it even exceeds the mass present in the star. Even at the end of the simulation after 5 Myr, the star has only gained roughly 0.5 M_⊙ of mass. Right: resulting value of the Toomre Q as a function of radius in the disk, shown for several intermediate time steps. As the disk grows in mass, Q drops below the safe value of 2 (indicated by the horizontal dashed line) everywhere except in the innermost part of the disk. This means that the self-gravity of gas in the disk can no longer be ignored, and the disk becomes susceptible to the gravitational instability.