It takes the stellar pair J05+50 nearly two months to complete one orbit around their common center. From Earth, it appears as a faint point in the constellation Hercules — 4625 parsecs away. Photometry of the binary star only captures a steady flicker of brightness, like the pulse of a giant heart. This is how this rare stellar ballet was revealed: two red giants — Suns swollen to enormous sizes in the late stage of stellar evolution — perform a duet, intertwining their fates closely.

The gravitational Roche lobe is an invisible boundary beyond which a star's matter is no longer held by its own gravity. The smaller partner has overflowed it: the red giant, whose mass is only one-eighth that of its neighbor, slowly streams onto the more massive star. The LAMOST spectrographs caught the trail of this flow — in the hydrogen H-alpha line, a blue shift appeared, as if gas moving away from us is rushing toward the receiver. Likely, a thin accretion disk is already forming around the primary star — a whirlwind of material spun up by rotation.

To build a detailed portrait of the system, scientists employed an arsenal of methods. Medium-resolution spectroscopy from the Chinese LAMOST telescope over 41 nights disentangled each star's contribution and yielded their velocities, temperatures, and even metallicity — slightly below solar. Photometry from ZTF and the infrared WISE produced a perfect sine wave of brightness: no hint of eclipses, only ellipsoidal distortion from mutual gravity. And the PHOEBE code, like a choreographer, calculated the orbit using all these data. Numerical simulation in MESA rewound history: the system began as a close pair with a period of just 2.24 days, then mass exchange widened the orbit to the current 60 days. They also had to account for a subtle effect: leakage of rotational energy via gravitational radiation, described by the formulas of Landau and Lifshitz.

Such choreography is doomed to a finale. The mass transfer slows the orbital motion — and in 13 thousand years, a common envelope will engulf both stars. They will merge into a single star, but for now, J05+50 remains the first and only example of a pair of red giants in an active mass-exchange phase. For the theory of stellar evolution, it is a living illustration of a key stage preceding the birth of white dwarfs and sources of gravitational waves. Such systems are the missing link that will calibrate merger models, which the space interferometer LISA will begin detecting in a few years.

Two red giants dance in the void. Their waltz lasts 60 days, but each orbit brings disaster closer. And when the orbit shrinks to the limit, the stellar ballet will end with a final chord — a flash that will be known only 15 thousand years later.