IMF: Chabrier and Kroupa Initial Mass Functions (IMFs)

In asgr/ProSpect: Professional Spectral Analysis Package

Chabrier and Kroupa Initial Mass Functions (IMFs)

Description

Simple interface to differential forms of the Chabrier and Kroupa IMFs. This is useful when checking the fraction of mass returned for different IMFs etc.

Usage

IMF_Chabrier(mass, alpha = 2.3, a = 0.08, b = 0.69, masslow = 0.01, massmax = 150,
  massform = 1, massmult = FALSE, rel.tol = .Machine$double.eps^0.25)

IMF_Kroupa(mass, alpha1 = 0.3, alpha2 = 1.3, alpha3 = 2.3, masslow = 0.01, mass1 = 0.08,
  mass2 = 0.5, massmax = 150, massform = 1, massmult = FALSE,
  rel.tol = .Machine$double.eps^0.25)

IMF_Salpeter(mass, alpha = 2.35, masslow = 0.1, massmax = 150, massform = 1,
  massmult = FALSE, rel.tol = .Machine$double.eps^0.25)

binlims(input, log = FALSE)

Arguments

mass	Numeric vector or data.frame/list; the target stellar mass to be evaluated (Msol). If a numeric vector then it will be the value of the IMF at the mass specfied. If a data.frame/list it must have components mass$lo and mass$hi (same length), and the output is the IMF integral between these mass limits (either numeric integral if massmult = FALSE, or mass integral if massmult = TRUE).
input	Numeric vector; the mid-point of the targets bins (in log or linear space depending on the log arguments).
alpha	Numeric scalar; the high mass slope (mass > 1 Msol) of the Chabrier IMF.
a	Numeric scalar; controls the gradient of the low mass slope close to mass = 1 Msol for the Chabrier IMF (lower is steeper).
b	Numeric scalar; controls the curvature of the low mass slope for the Chabrier IMF (lower is more curved).
masslow	Numeric scalar; the extreme low mass limit (Msol), where mass < masslow = 0. massform is then the mass formed between masslow and massmax. The lower default mass limit of Salpeter (0.1 Msol) is deliberate since the lack of low mass turn over would make it far too bottom (low mass star) heavy otherwise.
massmax	Numeric scalar; the max mass limit (Msol), where mass > massmax = 0. massform is then the mass formed between masslow and massmax.
alpha1	Numeric scalar; the low mass slope (masslow < mass < mass1) of the Kroupa IMF.
alpha2	Numeric scalar; the mid mass slope (mass1 < mass < mass2) of the Kroupa IMF.
alpha3	Numeric scalar; the high mass slope (mass2 < mass < massmax) of the Kroupa IMF.
mass1	Numeric scalar; the low mass limit (Msol), see alpha1.
mass2	Numeric scalar; the mid mass limit (Msol), see alpha2.
massform	Numeric scalar; the mass formed between masslow and massmax, i.e. what the IMF should integrate to (Msol). Since the default is 1, this means the IMF returned is a true PDF and can be used as such.
massmult	Should the returns value be dN/dM (FALSE) or M.dN/dM (TRUE)? dN/dM is useful when evaluating the number of stars formed within limits, whilst M.dN/dM is used for evaluating the mass of stars formed within limits.
rel.tol	Numeric scaler; relative accuracy requested. See integrate.
log	Logical; should the bins be evenly split in log or linear space?

Details

Mostly useful for exploring the fraction of mass in different stellar mass ranges when determining feedback etc. See Examples.

Value

For the IMF functions, if massmult = FALSE then the return is dN/dM for the specified mass, if massmult = TRUE then the return is M.dN/dM.

For binlims the output is a list with elements 'lo' and 'hi'. This can be uses as an input for the IMF functions for the mass arguments.

Author(s)

Aaron Robotham

References

Chabrier, 2003, PASP, 115, 763
Kroupa, 2001, MNRAS, 322, 231

Examples

curve(IMF_Salpeter, 0.01, 150, log='xy', xlab='Star Mass / Msol', ylab='dN/dM (1 Msol)')
curve(IMF_Kroupa, 0.01, 150, add=TRUE, col='red')
curve(IMF_Chabrier, 0.01, 150, add=TRUE, col='blue')
legend('topright', legend=c('Salpeter', 'Kroupa', 'Chabrier'),
  col=c('black', 'red', 'blue'), lty=1)

#Check the fraction of mass that will go SNII (around 20%) and rapidly enrich:

integrate(IMF_Chabrier, lower=10, upper=150, massmult=TRUE)$value

#If we form a cloud with 10^6 Msol, how many stars more massive than Msol will be formed?

integrate(IMF_Chabrier, lower=1, upper=150, massform=1e6, massmult=FALSE)$value

#And how much mass will there be in these stars?:

integrate(IMF_Chabrier, lower=1, upper=150, massform=1e6, massmult=TRUE)$value

#How many stars in total?

integrate(IMF_Chabrier, lower=0.01, upper=150, massform=1e6, massmult=FALSE)$value

#So numerically 6% of the stars will be more massive than Msol, but more than half the
#mass will be in these stars! This shows why rare processes in a massive stars can matter
#so much.

asgr/ProSpect documentation built on Feb. 21, 2025, 1:43 a.m.