By the time infalling material nears a black hole’s event horizon or a neutron star’s surface, it flows so vigorously that it glows in the x-ray spectrum. The x rays exert outward radiation pressure on the infalling material. At a critical value—the Eddington limit—the radiation and gravitational pressures balance, and further infall no longer boosts the luminosity. In the 1980s astronomers discovered, in the Milky Way and nearby galaxies, point-like x-ray sources whose luminosities exceed the Eddington limit for neutron stars by at least an order of magnitude. Dubbed ultraluminous x-ray sources (ULXs), the sources were presumed to harbor black holes of masses around 10M—that is, three times as large as the maximum possible neutron star mass (here, M is the mass of the Sun). The first neutron-star ULX was discovered in 2014. Now a second ULX has been found whose x-ray emission, being coherently pulsed, can...

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