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 originate only from a neutron star. That’s because the all-important separation between a pulsar’s rotation axis and its magnetic poles requires a surface, which black holes lack. The 0.42 s pulsations in the ULX NGC 7793 P13 (“P13” for short) were discovered by Felix Fürst of Caltech and his colleagues in observations made with NASA’s NuSTAR orbiter (depicted here). Accounting for a neutron star’s super-Eddington luminosity is not necessarily a challenge. If the neutron star’s magnetic field is strong enough, infalling material can be funneled onto its magnetic poles while radiation escapes sideways. The trouble is, in P13’s case the field strength implied by the luminosity is so high that the magnetic funnel must be narrow. But a narrow funnel would yield sharply peaked pulses; P13’s are sinusoidal. Just how the two sources, and possibly others, evade the Eddington limit remains a mystery. (F. Fürst et al., Astrophys. J. 831, L14, 2016.)