At the center of many galaxies lurks a black hole, wrapped in an invisible cloud — the halo of dark matter. This is not just a featureless mass: its density changes from the edge to the center, and the degree of this "compression" is called compactness. It is precisely the compactness of the halo that can awaken a new property in the black hole — spontaneous scalarization.
The scalar field is like the temperature in a room: at every point in space it has a single value. In a normal situation, around a black hole this field is constant and imperceptible. But add a dense dark matter halo, and the field suddenly "wakes up," forming a complex pattern. A whole spectrum of possible configurations emerges, like a string that can vibrate at different harmonics.
The physical mechanism resembles tuning a musical instrument. The dark matter halo sets the "pitch," and the scalar field responds only at strictly selected frequencies. Each such state is a separate "note," and together they form a discrete spectrum dictated by a single number — the compactness of the halo. The denser the cloud, the higher the "sound."
Thus, dark matter ceases to be just gravitational glue and becomes a conductor that controls the behavior of fields around black holes. Perhaps someday, by observing the radiation from such systems, we will be able to hear this cosmic music and, from its notes, reconstruct the properties of the invisible halo.
Halo compactness is roughly the same as the ratio of mass to size. For a typical dark matter halo hundreds of thousands of light-years across, compactness can be on the order of one millionth — about like a mountain the weight of Everest fitting into a thimble.
In Peter Watts's novel Blindsight, alien life forms use gravitational fields for quantum computing — here, nature itself "quantizes" the field around a black hole.