When two neutron stars circle each other, they don't remain rigid spheres. The partner's gravity stretches each star, creating tidal bulges — much like the Moon raises ocean tides on Earth. But unlike water, here it's superdense matter that deforms: a teaspoon of this stuff weighs billions of tons.
The authors have for the first time built a complete relativistic picture of such a dynamic tide. They accounted not only for the star's instantaneous response but also for how the deformation depends on orbital frequency — to second order. The calculations revealed an unexpected 'running' contribution. This effect grows logarithmically and doesn't reduce to simple excitation of the star's eigenmodes. The material's response seems to depend on the rate of loading, not just its magnitude.
For gravitational waves, this means the following. Although dynamic corrections formally enter the signal's phase only at the eighth post-Newtonian order, their contribution at the late inspiral stage is no longer small. Fisher matrix calculations show that third-generation detectors like the Einstein Telescope will be able to measure dynamic Love numbers for different masses and equations of state of neutron stars. If these effects are ignored, conclusions about static Love numbers and hence about nuclear matter properties could be skewed.
The tidal dance of neutron stars turns out to be more intricate than we thought. But it's precisely this complexity that offers a new key to what the universe's densest objects are made of.
The Love numbers are named after the English mathematician Augustus Love, who studied Earth's tidal deformation in the early 20th century — long before neutron stars were discovered.
In Robert Forward's novel 'Dragon's Egg', life is depicted on the surface of a neutron star, where tidal forces are so strong that a mountain a centimeter high is considered enormous.