Stellar masses the IMF

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One of the main goals for a theory of star formation (Bonnell et al. 2006c) is to understand the origin of the stellar IMF. In order to construct a theory for the IMF, we need to explain first the origin of the characteristic stellar mass near 0.3Mq and then the decreasing frequency (a power-law distribution) of stars of higher and lower masses. The best explanation to date for the characteristic mass is that it derives from the thermal Jeans mass at the point of fragmentation. It needs to be the thermal Jeans mass because this is the only support mechanism which cannot be fully removed and can therefore be expected to provide a near-universal characteristic mass.

The Jeans mass at the point of fragmentation is most probably set by the thermal physics of the line and dust cooling which counteracts the compressional heating. Larson (2005) has recently re-emphasised that, at low densities, atomic and molecular line cooling results in an effective polytropic y < 1 (y ~ 0.75), whereas at higher densities, where dust cooling dominates, the effective polytopic y is Y ~ 1-1. This transition from a slight cooling to a slow heating regime with compression is likely to set the Jeans mass for fragmentation at ~ 0.5M0, corresponding to the characteristic stellar mass (Jappsen et al. 2005). In such a case, the characteristic stellar mass is relatively insensitive to the initial conditions for star formation and thus likely to produce a robust and-near universal IMF. For example, such an equation of state naturally produces a realistic IMF when an isothermal equation

Figure 39.3. A schematic diagram of the physics of accretion in a stellar cluster. The gravitational potentials of the individual stars form a larger-scale potential that funnels gas down to the cluster core. The stars located there are therefore able to accrete more gas and become higher-mass stars. The gas reservoir can be replenished by infall into the large-scale cluster potential.

Figure 39.3. A schematic diagram of the physics of accretion in a stellar cluster. The gravitational potentials of the individual stars form a larger-scale potential that funnels gas down to the cluster core. The stars located there are therefore able to accrete more gas and become higher-mass stars. The gas reservoir can be replenished by infall into the large-scale cluster potential.

of state produces an IMF that depends on the exact Jeans mass under the initial conditions (Bonnell et al. 2006a). The broad peak can be understood as being due to the dispersion in gas densities and temperature at the point where fragmentation occurs. Lower-mass stars are most probably formed through the gravitational fragmentation of a collapsing region such that the increased gas density allows the production of lower-mass fragments. For them to maintain their low-mass status it is required that they be ejected from their natal environment, or at least accelerated by stellar interactions such that their accretion rates drop to close to zero (Bate et al. 2002a).

Higher-mass stars are probably due to continued accretion in a group or cluster environment. This competitive accretion (see Figure 39.3) naturally produces higher-mass stars in the centre of clusters due to the action of the larger-scale gravitational potential funnelling mass down to the centre (Bonnell et al. 2001a, 2004). This produces a Salpeter-like IMF (Bonnell etal. 2001b) for higher-mass stars due primarily to the increasing gravitational attraction of more-massive stars coupled with the increased gas density due to the cluster potential; see the right-hand panel of Figure 39.4 and Bonnell & Bate (2006). Continued accretion and dynamical interactions can also explain the existence of closer binary stars, and the dependence of properties of binaries on stellar masses (Bate et al. 2002b; Bonnell & Bate 2005).

Turbulence has also been invoked to produce a stellar IMF directly from the distribution of clump masses (Padoan & Nordlund 2002). The main difficulties with this possibility are that it relies on a very problematic one-to-one mapping of clump to stellar masses and that it should produce an inverse mass segregation whereby the massive stars are the least likely to form in dense stellar regions (Bonnell et al. 2006c).

s is isotherm-

Larson

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1 10 Mass

Figure 39.4. The mass functions for the two simulations starting with a Jeans mass of MJeans = 5M0 are shown at t = 1.55teff. The isothermal simulation (left panel) produces an unrealistically flat IMF extending to high masses whereas the Larson (2005)-type barotropic equation of state (right panel) produces a realistic IMF with a characteristic knee at «M0. This barotropic equation of state effectively reproduces the low-Jeans-mass results from more-general initial conditions. From Bonnell et al. 2006a).

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