Note on the use of stellar IMFs in cosmology

The stellar initial mass function (IMF) is used for computing stellar masses and colors of galaxies in cosmology.

List of some IMFs used in cosmology: Salpeter '55 eq. 5; Miller & Scalo '79 table 7; Kennicutt '83 section V; Scalo '86 table; Kroupa, Tout & Gilmore '93 eq. 13; Kroupa '01 eq. 2; Baldry & Glazebrook '03 abstract; Chabrier '03 table 1.

Stellar initial mass function (IMF) comparisons This figure compares the IMFs by ploting mass fraction per dex versus mass, i.e., normalized so that the integral under each curve is unity. They are assumed to be valid from 0.1 to 120 solar masses.


  • The Kennicutt, Kroupa01, BG03 and Chabrier IMFs are the best bet for reasonable mass-to-light ratios and galaxy colors (solid lines). The BG03 analysis favoured a slope shallower than Salpeter at the high-mass end based on constraints from local luminosity densities and cosmic star-formation history; IMFs with high-mass slopes steeper than Kennicutt's were ruled out as a universal IMF.
  • The Salpeter IMF has too many low mass stars (dotted line). It was never measured down to 0.1 solar masses by Salpeter.
  • The MS79, Scalo and KTG93 IMFs have too few high mass stars (dashed lines). They were based on galactic disk measurements which cannot be used to accurately infer the high-mass end because of the complicated SFH of the galaxy. Measured IMFs within star clusters generally give a shallower IMF close to the Salpeter value. Elmegreen '06 finds that galaxy-averaged IMFs are not in general steeper than this.

    List of population synthesis codes: BaSTI; GALAXEV (BC03); Maraston '05; PEGASE; Starburst99.

    For consistency, stellar mass should include normal stars (main sequence + giant branch) and evolved degenerate stars (white dwarfs + neutron stars + stellar-mass black holes) as this is the material that is not in the ISM or IGM. For example, there are three lines to combine in PEGASE. Depending on the IMF and population age, evolved stars can add 30% to the mass due to normal stars. Another definition of stellar mass that is sometimes used is the integral of the SFR; this can be twice the stellar mass defined above.

    Ivan Baldry, written 2006 August 14th; updated 2008 April 20.