Astronomy & Celestial Mechanics
the sky, computed
Concept

Effective spin — where it appears

The single combination of two black holes' spins that a merger's gravitational waves measure best: their components along the orbit's axis, weighted by mass. It is well measured while the individual spins and their tilts usually are not.

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

Also named here as spin precession — the same set of essays touches all of them, so they are one junction rather than several.

Two assembly histories, and the sign that separates them. The distribution of effective spin produced by two ways of making a black-hole binary, from 40,000 draws each. A pair that evolved together as two stars keeps its spins near the orbital axis — drawn here aligned to within 25 degrees — and cannot produce a negative projection at all: 0.0 per cent of its mergers fall below zero, and its mean is 0.45. A pair assembled by chance encounters in a dense cluster has no memory of any plane, so its tilts are isotropic, its distribution is symmetric, and exactly half of its mergers have an effective spin below zero. The sign of one number distinguishes two histories — and it does so without any of the individual spins being measured, which is the only reason the question is answerable at all from a catalogue in which every event's spins are individually uncertain. The third curve is a mixture with 50 per cent of its mergers drawn isotropically: its mean is 0.22 and 25 per cent of it lies below zero, which is the shape an observed distribution with a small positive mean and a real negative tail requires. Neither channel alone produces it.

A spin that is measured as an angular momentum

Every other method of measuring a black hole's spin reads it from what the hole does to matter. A merging pair's waveform reads it from the orbit instead — and what it recovers is one mass-weighted projection onto the orbital axis, which is a number that two non-rotating holes and two extremal ones can share.

gravitation · Black hole spin Precession cycles grow as the inverse of the lowest frequency heard. The number of times the orbital plane precesses between a detector's lowest frequency and the last stable orbit, against that lowest frequency, both on logarithmic scales, for pairs of 36 + 29 solar masses, 10 + 8 solar masses, 8 + 1.4 solar masses with spins tilted into the orbital plane. The count grows as the inverse of the lowest frequency — the slopes are −1.07, −1.02, −1.01. Above 20 Hz, the limit of the ground-based detectors that have heard every merger so far, the heaviest pair precesses 0.9 times, the middle 4.4 and the lightest 6.2. Above 5 Hz the counts are 4.9, 18.7, 25.5; above 1 Hz, 26, 95, 129.

Precessions bought one hertz at a time

A merging pair of black holes whose spins are tilted makes its orbital plane wobble, and the wobble is the only part of the signal that separates one hole's spin from the other's. How many wobbles a detector records is a simple formula: two plus three halves of the mass ratio, divided by the total mass and by the lowest frequency the detector can hear. The detectors that have heard every merger so far stop at twenty hertz, where a typical heavy pair wobbles less than once.

gravitation · Black hole spin

Named alongside it

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

Black hole spinInnermost stable circular orbitSpin precessionAngular momentumChirp massDegeneracyGravitational wavesHierarchical mergerKerr metricOrbital hang upSelection effectSpin orbit coupling

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