In this case the burst was unusually long, said Joshua Bloom, an associate professor of astronomy at Berkeley and the first author of one of the studies.

The burst also came from the center of a galaxy four billion light years away. Most galaxies are thought to have black holes at their center, a clue that tipped off Dr. Bloom and his colleagues.

“Astronomers are not so different from real estate agents — location, location, location,” he said. “This picture had emerged for me and I saw that this was a black hole swallowing up a star.”