Concept

Orbital frequency — where it appears

The rate at which a body goes round its orbit, in radians or cycles per unit time. Its dependence on radius sets how orbits shear past one another, and where it is the same for every orbit, as inside a uniform core, that shearing vanishes.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

$A slow shock still heats the cluster. The energy a Plummer star cluster gains from a compressive tidal pulse, as a fraction of what the same impulse delivered instantaneously would give, against the pulse's duration times the orbital frequency at the half-mass radius. The points come from integrating 1200 stars through the pulse one by one. The lines are prescriptions applied to the same stars: an oscillator's exponential suppression and a power law, each applied star by star at the star's own orbital frequency, and the shortcut of one power-law factor for the whole cluster, evaluated at the half-mass radius. At the longest pulse drawn the cluster keeps 0.28 of the impulsive energy; the star-by-star rules give 0.24 and 0.36, bracketing it, and the half-mass shortcut gives 0.017, 17 times too little. The total is set by the outermost stars, which carry most of the impulsive energy and are always slower than the shock.$

A slow shock heats the halo and robs the core

The textbook treatment of a slow tidal shock multiplies the instantaneous answer by a suppression factor that falls steeply as the shock lengthens. Integrated star by star through shocks of intermediate length, a cluster behaves differently. Its total heating falls slowly, because the outer stars are always slower than any shock and carry most of the energy, and its core does not merely escape the heating: on balance its stars lose energy, which no factor that multiplies a positive number can describe.

gravitation · Impulse approximation

A cluster sinking by Chandrasekhar's formula alone. The orbital radius of a 2.0 × 10⁵ solar-mass globular cluster released on a circular orbit at 1 kpc in the two Fornax halo models, decaying under Chandrasekhar's dynamical friction with a velocity dispersion of 11.7 km/s and a Coulomb logarithm of 3. In the cusp it reaches the centre in 6.7 billion years. In the core the formula gives no arrival within 12 billion years, crossing into the core at 2.8. The formula already slows the cluster inside the core, because the circular speed there drops below the stars' velocity dispersion and few stars move slower than the cluster; but it still lets the cluster creep inward without limit. N-body experiments of clusters sinking into cored haloes find something stronger: the decay stops altogether near the core, which the local formula cannot produce at any setting of its logarithm.

A drag that stops where every orbit keeps time

Chandrasekhar's formula reads the density and the velocities where a sinking body is, and nothing about the orbits those stars are on. Inside a constant-density core every orbit has the same frequency, the differential motion that drags a body inward disappears, and the sinking stops — which is why the five globular clusters of the Fornax dwarf galaxy are still where they are.

gravitation · Dynamical friction

Named alongside it

The objects these essays reach for when they reach for this one.

Globular cluster Adiabatic invariant The core–cusp problem Coulomb logarithm Dark matter halo Dwarf spheroidal Dynamical friction Energy diffusion Galactic disc Impulse approximation Linear response Plummer sphere

All concepts