File:Plot of various initial mass functions.svg

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Original file ‎(SVG file, nominally 370 × 355 pixels, file size: 73 KB)

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English: Plot of various initial mass functions (IMF). (The vertical axis is actually not ξ(m)Δm, but a scaled version of ξ(m). For m greater than 1 solar mass, it is (m/solar mass)^-2.35.)
Date
Source Own work
Author JohannesBuchner
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Generating Python Code[edit]

import matplotlib.pyplot as plt
import numpy
from numpy import exp, log10 as log

def salpeter55(m):
	alpha = 2.35
	return m**-alpha

def millerscalo79(m):
	return numpy.where(m > 1, salpeter55(m), salpeter55(1))

def chabrier03individual(m):
	k = 0.158 * exp(-(-log(0.08))**2/(2 * 0.69**2))
	return numpy.where(m <= 1,\
	        0.158*(1./m) * exp(-(log(m)-log(0.08))**2/(2 * 0.69**2)),\
	        k*m**-2.3)

def chabrier03system(m):
	k = 0.086 * exp(-(-log(0.22))**2/(2 * 0.57**2))
	return numpy.where(m <= 1,\
	        0.086*(1./m) * exp(-(log(m)-log(0.22))**2/(2 * 0.57**2)),\
	        k*m**-2.3)

def kroupa01(m):
	return numpy.where(m<0.08, m**-0.3, numpy.where(m < 0.5, 0.08**-0.3 * (m/0.08)**-1.3, 0.08**-0.3 * (0.5/0.08)**-1.3 * (m/0.5)**-2.3))

plt.figure(figsize=(4,4))
m = numpy.logspace(-2, 2, 400)

for label, imf in zip('Salpeter55 MillerScalo79 Kroupa01 Chabrier03individual Chabrier03system'.split(),\
        [salpeter55, millerscalo79, kroupa01, chabrier03individual, chabrier03system]):
	plt.plot(m, imf(m)/imf(1), label=label)

plt.gca().set_yscale('log')
plt.gca().set_xscale('log')
plt.xlim(1e-2, 100)
plt.ylim(1e-3, 1e3)
plt.legend(loc='best', prop=dict(size=8))
plt.xlabel('Mass [Solar mass]')
plt.ylabel(r'Mass Function $\xi(m)\Delta m$')
plt.savefig('imf.pdf', bbox_inches='tight')
plt.savefig('imf.svg', bbox_inches='tight')
plt.savefig('imf.png', bbox_inches='tight')

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current19:14, 4 November 2015Thumbnail for version as of 19:14, 4 November 2015370 × 355 (73 KB)JohannesBuchner (talk | contribs)Cross-wiki upload from en.wikipedia.org

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