kappacorotation: Compute the co-rotational kinetic energy fraction

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Compute the co-rotational kinetic energy fraction

Description

Computes the co-rotational kinetic energy fraction, \kappa_\mathrm{co}, of a particle distribution. This quantity is defined as the fraction of the total kinetic energy invested in ordered co-rotation about the total angular momentum axis. It is commonly used as a measure of the rotational support of galaxies in particle-based simulations.

Usage

kappacorotation(m, x, v, x0 = NULL, v0 = NULL)

Arguments

m	n-vector of particle masses.
x	n\times3 matrix of particle positions.
v	n\times3 matrix of particle velocities.
x0	Optional length-3 vector specifying the origin. If NULL (default), the centre of mass is used.
v0	Optional length-3 vector specifying the reference velocity. If NULL (default), the centre-of-mass velocity is used.

Details

The rotation axis is taken to be the direction of the total angular momentum of the particle distribution after subtracting the centre-of-mass position and velocity. Only particles with positive angular momentum about this axis contribute to the co-rotational kinetic energy.

Value

A scalar in the range [0,1] giving the fraction of the total kinetic energy contained in co-rotating azimuthal motion,

\kappa_\mathrm{co} = \frac{\sum_{j_z>0} m\,v_\phi^2} {\sum m\,|\mathbf{v}|^2},

where j_z is the specific angular momentum about the total angular momentum axis and v_\phi=j_z/R is the azimuthal velocity. The common factor of 1/2 in the kinetic energies cancels.

If m is NULL, NA is returned.

See Also

angularmomentum #'

Examples

m <- rep(1, 100)
x <- matrix(rnorm(300), ncol = 3)
v <- matrix(rnorm(300), ncol = 3)
kappacorotation(m, x, v)

cooltools documentation built on Sept. 11, 2026, 5:06 p.m.