Abstract

Our understanding of Population III star formation is still in its infancy. They are formed in dark matter minihaloes of 10(5)-10(6) M-circle dot at z = 20-30. Recent high-resolution cosmological simulations show that a protostellar disc forms as a consequence of gravitational collapse and fragments into multiple clumps. However, it is not entirely clear if these clumps will be able to survive to form multiple stars as simulations are unable to follow the disc evolution for longer times. In this study, we employ a simple analytical model to derive the properties of marginally stable steady-state discs. Our results show that the stability of the disc depends on the critical value of the viscous parameter alpha. For alpha(crit) = 1, the disc is stable for an accretion rate of <= 10(-3) M-circle dot yr(-1) and becomes unstable at radii about >= 100 au in the presence of an accretion rate of 10(-2) M-circle dot yr(-1). For 0.06 < alpha(crit) < 1, the disc can be unstable for both accretion rates. The comparison of the migration and the Kelvin-Helmholtz time-scales shows that clumps are expected to migrate inwards before reaching the main sequence. Furthermore, in the presence of a massive central star, the clumps within the central 1 au will be tidally disrupted. We also find that UV feedback from the central star is unable to disrupt the disc, and that photoevaporation becomes important only once the accretion rate has dropped to 2 x 10(-4) M-circle dot yr(-1). As a result, the central star may reach a mass of 100 M-circle dot or even higher.