It's thought that about 85% of all matter in the universe is dark matter. We can't see this mysterious substance, but we think it exists because we can measure its gravitational effects on ordinary matter. One theory is that dark matter could be made up of axions, hypothetical subatomic particles that have yet to be detected. Last month, a team of physicists said that axions should gather in dense clouds around neutron stars. If this is correct, then dark matter must also be inside the neutron stars. It must change the physical properties of the neutron matter under the pressure in the core of neutron stars. The volume content of the dark matter must affect the overall structure of the neutron stars, since it is unlikely to interact with the ordinary neutrons via the electroweak or strong forces. If so, the small amounts of dark matter must cause the neutron stars to collapse immediately. But these stars are relatively stable, with similar diameters and no tendency to collapse without an influx of ordinary, visible matter from nearby companions. White dwarf stars are similarly stable. Is there a physical explanation for this observable stable behaviour in a world full of heavy dark matter with no repulsive or interactive properties?