imf: Compute an N-component power-law logarithmic stellar initial...
In astrolibR: Astronomy Users Library

Description Usage Arguments Details Value Author(s) References Examples

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

1	imf(mass, expon, mass_range)

`mass`	mass in units of solar masses, scalar or vector
`expon`	power law exponent, usually negative, scalar or vector
`mass_range`	vector containing the mass upper and lower limits of the IMF and masses where the IMF exponent changes, in solar masses. The number of values in mass_range should be one more than in expon and should be monotonically increasing.

The mass spectrum f(m) gives the number of stars per unit mass interval is related to psi(m) by m*f(m) = psi(m). The ‘initial’ mass function (IMF) refers to the mass spectrum before stellar evolution has reduced the number of higer mass stars. ' For background, see Scalo (1986).

The imf function 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. That is, the normalization condition is that the integral of psi(m) between the upper and lower mass limit is unity. The IMF is then calculated for the supplied masses.

The number of values in expon equals the number of different power-law components in the IMF. A Saltpeter (1955) IMF has a scalar value of expon = -1.35.

psi

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

Written W. Landsman 1989

R adaptation by Arnab Chakraborty June 2013

Salpeter, E. D., 1955, The luminosity function and stellar evolution, Astrophys. J. 121, 161 http://adsabs.harvard.edu/abs/1955ApJ...121..161S

Scalo, J., 1986, The stellar initial mass function, Fund. of Cosmic Physics, 11, 1-278 http://adsabs.harvard.edu/abs/1986FCPh...11....1S

# Calculate 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.

imf(3, -1.35, c(0.1, 110) ) / 3

# Lequeux et al. (1981) 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)

m = seq(0.01,0.1,length=110)  # construct a mass vector
expon = c(-0.6, -1.7)         # exponent vector
mass_range = c(0.007, 1.8, 110)    # mass range
plot (log10(m), log10(imf(m, expon, mass_range) / m), pch=20)