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IMF

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)

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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