The lighthouse in the Crab Nebula blinks thirty times per second. It's a pulsar — a dead star that, as it spins, shoots out narrow beams of light, and Earth sweeps through them like a ship crossing a lighthouse beam. This lighthouse has two beams: the main pulse and the interpulse. Astronomers accumulated 78.8 thousand seconds of observations — more than two million individual X-ray flashes — and set out to count how often photons (light particles) arrive in each beam.

It turned out that the interpulse behaves like a fair coin: the number of photons in each flash follows the Skellam distribution. This distribution describes the difference between two random processes, like counting rain in two buckets when water is poured out of one and into the other. In other words, in the interpulse, light comes and goes, and these two streams are independent. The main pulse is more complex: sometimes it produces flashes with an anomalously large number of photons. But if you add up many flashes in a row, these outliers average out, and the main pulse also starts to follow the Skellam distribution. This means the excess brightness does not accumulate from one rotation to the next.

The astronomers also checked whether the pulsar remembers its previous flash. It turns out it doesn't: there is no statistically significant correlation between successive pulses. Even giant radio bursts, which sometimes appear in the main pulse phase, do not explain the excess brightness. This means the emission mechanisms of the two beams are different. Perhaps the main pulse originates in a more turbulent region of the pulsar's magnetosphere, where plasma occasionally breaks into instability, like a boiling pot that occasionally splashes out drops.

Such statistical precision matters not only for pulsars. The Skellam distribution is rarely testable against real data with such accuracy. Now astrophysicists have a benchmark: if another source shows deviations from Skellam, it means an additional process is hidden in its emission. And for the Crab pulsar, this provides quantitative constraints on models: any theory must explain why the main pulse has rare super-bright flashes while the interpulse does not.