Description Usage Arguments Details Value Author(s) References Examples
Compute an Ncomponent powerlaw 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 â€˜initialâ€™ 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 powerlaw 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 powerlaw 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, 1278 http://adsabs.harvard.edu/abs/1986FCPh...11....1S
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  # 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)

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