## Accretion and the formation of massive stars

The model for the IMF discussed above provides a framework in which to understand the formation of massive stars. In this scenario, the massive stars form due to competitive accretion onto the core of the cluster in which the massive star is forming. Numerical simulations have indicated that the vast majority of the mass which comprises the massive stars comes from large distances and is accreted onto

0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 Mass (M0) Mass (M0)

Figure 39.5. A comparison between two calculations with identical initial conditions except for the Jeans mass, which is M0 in the left panel and 0.3M0 in the right panel. The lower Jeans mass could correspond to an increase in the metallicity by a factor of 25. From Bate & Bonnell (2005).

0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 Mass (M0) Mass (M0)

Figure 39.5. A comparison between two calculations with identical initial conditions except for the Jeans mass, which is M0 in the left panel and 0.3M0 in the right panel. The lower Jeans mass could correspond to an increase in the metallicity by a factor of 25. From Bate & Bonnell (2005).

the star after a stellar cluster has formed (Figure 39.6) (Bonnell et al. 2004). The initial fragment mass which forms the star is of low mass, as is typical for the mean stellar mass. The infalling gas then has to pass through the cluster in order for it to be accreted by the central massive star. It should be noted that these simulations neglect the effect of radiation pressure from the massive stars, or equivalently assume that accretion through a disc (Yorke & Sonnhalter 2002) occurs.

An alternative model (McKee & Tan 2003) envisages that massive-star formation is just a scaled-up version of low-mass-star formation whereby an individual massive clump collapses to form a single massive star. The potential problem with this scenario is that massive stars are formed in dense stellar clusters where stars are closely packed together. There is at present no known physical mechanism to produce the necessary initial conditions for a clump that will not be susceptible to fragmentation (Dobbs et al. 2005) long before reaching the state of collapsing to form a single star.

In competitive accretion, the infalling gas is accompanied by newly formed stars such that the formation of a massive star is a necessary byproduct of the formation of a stellar cluster. This produces a strong correlation between the number of stars, or the total mass in a cluster, and the mass of the most-massive star therein (Figure

39.7). This correlation follows Mmax a Mst'ars, where Mstars is the total mass in the cluster stars. This can be understood in the following way. Given an effective initial efficiency of fragmentation, for every star that falls into the cluster a certain amount of gas also enters the cluster. This gas joins the common reservoir from which the most-massive star takes the largest share in this competitive environment. Thus, the mass of the most-massive star increases as the cluster grows in numbers of stars. We therefore have a prediction from this model that there should exist a strong

Figure 39.6. The mass that forms the most-massive (30M0) star is plotted at three different times during the formation of a stellar cluster. Note that the gas is very distributed when star formation is initiated (left) and when the cluster is growing through the infall of newly formed stars and gas (middle and right). The vast majority of the final mass is due to competitive accretion in a clustered environment (Bonnell et al. 2004).

K 10

K 10

Figure 39.7. The total mass in stars is plotted against the mass of the most-massive star in the system. The hypothesis of competitive accretion predicts that, as the total mass grows, the mass of the most-massive star also increases as Mmax a M^ (Bonnell et al. 2004).

Mmax (MJ

Figure 39.7. The total mass in stars is plotted against the mass of the most-massive star in the system. The hypothesis of competitive accretion predicts that, as the total mass grows, the mass of the most-massive star also increases as Mmax a M^ (Bonnell et al. 2004).

Mmax (MJ

correlation between the mass of the most-massive star and the number of stars (or the total mass) in the cluster (Figure 39.7) (Bonnell et al. 2004).