Initial Mass Function

• Parameterized by power low slope, $dN/dM \propto M^{-\alpha}$, although clear that a single power law doesn't fit over entier range of masses (Scalo 1998)

• Complications
  • stochastic effects at low SF rates, small systems (e.g. Kroupa 2001)

  • unresolved binaries

  • dynamical and primordial mass segregation in clusters

• Techniques
  • Local determinations from star counts, corrections for kinematics, binaries, etc.

  • IMF determinations from clusters: coeval, but potential for dynamical effects

  • IMF determinations from field stars
    • Observations of faint stars, which are almost unevolved, give the low-mass IMF independent of history of star formation rate, if we assume IMF constant in time. Currently feasible for Milky Way neighbors.

    • For higher masses, interplay of IMF with star formation history, so degree to which IMF can be disentangled depends on confidence in derived star formation histories. Derive IMF/SFR from distribution along (and perpendicular) to main sequence; the more distant the object, only the more massive stars can be probed.

• Results
  • Summary ``$\alpha$-plot'' from Kroupa 2002
    

  • Qualitative overview: Amazing degree of similarity, over wide range of metallicity, density, etc.: Galactic Bulge (Zocali et al 2000, Holtzman et al. 1998), LMC (Holtzman et al. 1997, Draco (Grillmair et al. 1998), Ursa Minor (Wyse et al. 2002), globular clusters (Paresce & de Marchi et al. 2000), all consistent with solar neighborhood (Kroupa et al.). This is not a single-slope Salpeter power law!

  • Possible exceptions
    • Clusters: Arches (Figer et al 1999, but see Stolte et al 2002), M82F (Smith & Gallagher 2001), NGC 3603 (Eisenhauer et al 1998), R136 (Sirianni et al 2000), all suggest flatter IMFs, but note no evidence for any lower mass cutoff.
      

      Change in relative number of stars above and below 2$M_\odot$ impossible to observe directly in any old population!

    • Field: LMC field: Massey (1999) observes steep slope of near $-4$; issues with escape of massive stars from associations, SF history?

• Is the IMF different in extreme star formation events?Need to probe the IMF of a field population with high SF rate.

• Is there variation in the binary fraction in different populations? (chemical relevance via type Ia SN...)

• Implications of IMF/binary variations could be significant for chemical evolution, M/L, SFHs