Some red giants (huge, old stars) change brightness very slowly: one cycle can last more than a year. Astronomers have long been puzzled about why. One idea: an invisible companion orbits nearby, periodically blocking part of the light. Another: the star itself pulsates, like a heart, but very leisurely: its outer layers alternately contract and expand.

In the new study, they took observational data for 249 such stars. For each, they identified the primary rhythm of brightness variation and its "overtone"—a faster secondary oscillation. It turned out that the phase shift between them reveals whether we are seeing an eclipse by a companion or the star's own pulsation. For most stars, the phase indicated a companion. But for a small group, roughly one in fifty, the pattern matched pulsation, and a very specific kind: the star oscillates as a whole, alternately swelling on one side and then the other.

This type of pulsation had been predicted theoretically, but no reliable examples were known. Now they have been found. This means that stable oscillations, akin to slow breathing, can arise inside red giants. They allow us to peer into the star's depths, which direct observations cannot reach.