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IMF

IMF

Name


      IMF

Purpose


      Compute an N-component power-law logarithmic initial mass function

Explantion


      The function is normalized so that the total mass distribution
      equals one solar mass.

Calling Sequence


      psi = IMF( mass, expon, mass_range )

Inputs


      mass - mass in units of solar masses (scalar or vector)
              Converted to floating point if necessary
      expon - power law exponent, usually negative, scalar or vector
              The number of values in expon equals the number of different
              power-law components in the IMF
              A Saltpeter IMF has a scalar value of expon = -1.35
      mass_range - vector containing the mass upper and lower limits of the
              IMF and masses where the IMF exponent changes. The number
              of values in mass_range should be one more than in expon.
              The values in mass_range should be monotonically increasing.

Outputs


      psi - mass function, number of stars per unit logarithmic mass interval
              evaluated for supplied masses

Notes


      The mass spectrum f(m) giving the number of stars per unit mass
      interval is related to psi(m) by m*f(m) = psi(m). The normalization
      condition is that the integral of psi(m) between the upper and lower
      mass limit is unity.

Example


      (1) Print the number of stars per unit mass interval at 3 Msun
              for a Salpeter (expon = -1.35) IMF, with a mass range from
              0.1 MSun to 110 Msun.
              IDL> print, imf(3, -1.35, [0.1, 110] ) / 3
      (2) Lequex et al. (1981, A & A 103, 305) describes an IMF with an
              exponent of -0.6 between 0.007 Msun and 1.8 Msun, and an
              exponent of -1.7 between 1.8 Msun and 110 Msun. Plot
              the mass spectrum f(m)
              IDL> m = [0.01,0.1,indgen(110) + 1 ] ;Make a mass vector
              IDL> expon = [-0.6, -1.7] ;Exponent Vector
              IDL> mass_range = [ 0.007, 1.8, 110] ;Mass range
              IDL> plot,/xlog,/ylog, m, imf(m, expon, mass_range ) / m

Method


      IMF first calculates the constants to multiply the power-law
      components such that the IMF is continuous at the intermediate masses,
      and that the total mass integral is one solar mass. The IMF is then
      calculated for the supplied masses. Also see Scalo (1986, Fund. of
      Cosmic Physics, 11, 1)

Procedures Called


      None

Revision History


      Written W. Landsman August, 1989
      Set masses LE mass_u rather than LT mass_u August, 1992
      Major rewrite to accept arbitrary power-law components April 1993
      Convert EXPON to float if necessary W. Landsman March 1996
      Remove call to DATATYPE, V5.3 version W. Landsman August 2000



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