Two Stellar Mass Functions Combined into One by the Random Sampling Model of the IMF

The turnover in the stellar initial mass function (IMF) at low mass suggests the presence of two independent mass functions that combine in different ways above and below a characteristic mass given by the thermal Jeans mass in the cloud. In the random sampling model introduced earlier, the Salpeter IMF at intermediate to high mass follows primarily from the hierarchical structure of interstellar clouds, which is sampled by various star formation processes and converted into stars at the local dynamical rate. This power law part is independent of the details of star formation inside each clump and therefore has a universal character. The flat part of the IMF at low mass is proposed here to result from a second, unrelated, physical process that determines only the probability distribution function for final star mass inside a clump of a given mass, and is independent of both this clump mass and the overall cloud structure. Both processes operate for all potentially unstable clumps in a cloud, regardless of mass, but only the first shows up above the thermal Jeans mass, and only the second shows up below this mass. Analytical and stochastic models of the IMF that are based on the uniform application of these two functions for all masses reproduce the observations well.Comment: 4 pages, 2 figures, MNRAS pink pages in press 199

Formation of stars and clusters over cosmological time

The concept that stars form in the modern era began some 60 years ago with the key observation of expanding OB associations. Now we see that these associations are an intermediate scale in a cascade of hierarchical structures that begins on the ambient Jeans length close to a kiloparsec in size and continues down to the interiors of clusters, perhaps even to binary and multiple stellar systems. The origin of this structure lies with the dynamical nature of cloud and star formation, driven by supersonic turbulence and interstellar gravity. Dynamical star formation is relatively fast compared to the timescale for cosmic accretion, and then the star formation rate keeps up with the accretion rate, leading to a sequence of near-equilibrium states during galaxy formation and evolution. Dynamical star formation also helps to explain the formation of bound clusters, which require a local efficiency that exceeds the average by more than an order of magnitude. Efficiency increases with density in a hierarchically structured gas. Cluster formation should vary with environment as the relative degree of cloud self-binding varies, and this depends on the ratio of the interstellar velocity dispersion to the galaxy rotation speed. As this ratio increases, galaxies become more clumpy, thicker, and have more tightly bound star-forming regions. The formation of old globular clusters is understood in this context, with the metal-rich and metal-poor globulars forming in high-mass and low-mass galaxies, respectively, because of the galactic mass-metallicity relation. Metal-rich globulars remain in the disks and bulge regions where they formed, while metal-poor globulars get captured as parts of satellite galaxies and end up in today's spiral galaxy halos. Blue globulars in the disk could have formed very early when the whole Milky Way had a low mass.Comment: 14 pages, 1 figure, in conference "Lessons from the Local Group," ed. K. Freeman et al., Springer, 201