InitialMassFunctions.jl

Stellar initial mass functions describe the distribution of initial masses that stars are born with. This package aims to implement and provide interfaces for working with initial mass functions, including but not limited to evaluating and sampling from published distributions. See the linked documentation above for more details.

Published IMFs we include are

Salpeter1955(mmin::Real=0.4, mmax::Real=Inf)
Chabrier2001BPL(mmin::Real=0.08, mmax::Real=Inf)
Chabrier2001LogNormal(mmin::Real=0.08, mmax::Real=Inf)
Chabrier2003(mmin::Real=0.08, mmax::Real=Inf)
Chabrier2003System(mmin::Real=0.08, mmax::Real=Inf)
Kroupa2001(mmin::Real=0.08, mmax::Real=Inf)

These all return subtypes of Distributions.ContinuousUnivariateDistribution and have many of the typical methods from Distributions.jl defined for them. These include

• pdf, logpdf
• cdf, ccdf
• quantile(d, x::Real), quantile(d,x::AbstractArray), quantile!(y::AbstractArray, d, x::AbstractArray)
• rand
• minimum, maximum, extrema
• mean, median, var, skewness, kurtosis (some of the higher moments don't work for mmax=Inf with instances of BrokenPowerLaw)

Note that var, skewness, and kurtosis are not currently defined for instances of LogNormalBPL, such as those returned by the Chabrier2003 function.

Many other functions that work on Distributions.ContinuousUnivariateDistribution will also work transparently on these AbstractIMF instances.

Continuous broken-power-law distributions (such as those used in Chabrier 2001 and Kroupa 2001) are provided through a new BrokenPowerLaw type. The lognormal distribution for masses m<1.0 with a power law extension for higher masses as given in Chabrier 2003 is provided by a new LogNormalBPL type. Simpler models (e.g., Salpeter1955 and Chabrier2001LogNormal) are implemented using built-in distributions from Distributions.jl in concert with their truncated function.

Efficient samplers are implemented for the new types BrokenPowerLaw and LogNormalBPL such that batched calls (e.g., rand(Chabrier2003(),1000)) are more efficient than single calls (e.g., d=Chabrier2003(); [rand(d) for i in 1:1000]). These samplers can be created explicitly by calling Distributions.sampler(d), with d being a BrokenPowerLaw or LogNormalBPL instance.

InitialMassFunctions.jl follows Julia's recommended versioning strategy, where breaking changes prior to version 1.0 will result in a bump of the minor version (e.g., 0.1.x |> 0.2.0) whereas feature additions and bug patches will increment the patch version (0.1.0 |> 0.1.1).