tree.entropy: Tree entropy of halo or galaxy mergers

In obreschkow/mergertrees: Handle astrophysicsal merger trees

Description

Computes the tree entropy and generalized entropy of a merger of n>=0 masses, accounting also for smooth accretion. See Obreschkow et al. 2020 (arxiv.org/abs/1911.11959) for the astrophysical context and mathematical definitions.

Usage

tree.entropy(
  m = c(1, 1),
  s = m * 0,
  mfinal = sum(m),
  alpha = 1/log(2) + 1,
  beta = 3/4,
  gamma = 1/3,
  generalized = FALSE
)

Arguments

m	vector of masses of the merging haloes (normalization is irrelevant)
s	vector of tree entropies of the merging haloes
mfinal	final mass
alpha	free parameter specifying the relative importance of different orders of mergers
beta	free parameter specifying the importance of the most destructive mergers
gamma	free parameter specifying the importance of smooth accretion
generalized	logical flag, if set to TRUE the function returns the generalized entropy rather than the tree entropy

Author(s)

Danail Obreschkow

See Also

https://arxiv.org/abs/1911.11959

Examples

## check major merger
txt = 'Tree entropy of an equal-mass binary merger with zero input entropy'
cat(sprintf('%s = %.5f = beta\n',txt,tree.entropy()))

## check smooth accretion
txt = 'Tree entropy of a maximum-entropy halo that doubles its mass by smooth accretion'
cat(sprintf('%s = %.5f = (1/2)^gamma\n',txt,tree.entropy(1,1,2)))

## check nearly smooth collapse
txt = 'Tree entropy of a halo grown from an instantaneous merger of 1e6 haloes of random entropies'
cat(sprintf('%s = %.5f ~ 0\n',txt,tree.entropy(rep(1,1e6),runif(1e6))))

obreschkow/mergertrees documentation built on June 25, 2021, 6:40 p.m.