Two stars circle each other, gradually drawing closer. Their dance loses energy, and that energy escapes into space — in the form of gravitational waves, and sometimes other fields. A group of physicists led by Stephen Hawking (though he is not an author of this work, his name is familiar to many) asked: exactly how much rotation does each particle of such radiation carry away?
It turns out the accounting is very strict. Each graviton, a quantum of gravitational waves, carries away a portion of rotation equal to about two Planck constants (the fundamental unit of quantum rotation). Particles of scalar and vector radiation (waves of a different sort, simpler than gravitational ones) carry away exactly one such portion. It's like a mail carrier who always delivers letters in bundles of two or one, and never otherwise. Remarkably, this rule works not only for elongated elliptical orbits but also for open hyperbolic orbits, where the stars fly apart forever.
The scientists also showed that all emitted energy and rotation can be computed simply by tracking how the orbital frequency and eccentricity change. But there's a catch: it's impossible to separate how much of a particle's rotation is its own (spin) versus its orbital motion around the center of mass. This is like trying to tell whether a spinning top is rotating on its own or just running in circles — from the outside, you can't distinguish.
The rotation carried away by a gravitational wave from a typical pair of neutron stars is comparable to the angular momentum of Earth as it moves around the Sun — only it is emitted in a fraction of a second.
In Carl Sagan's novel "Contact," aliens use gravitational waves for communication — perhaps they can modulate exactly those portions of rotation discussed in this article.