Can neutron stars contain dark matter inside of them?

Cosmological studies have found that over 80% of matter in the Universe is not made out of protons and neutrons, but by an unknown kind of matter. For lack of a better word, we call this matter dark matter. Although we do not know exactly what dark matter is, we do know at least three things: it is everywhere, it interacts gravitationally, and all other interactions with matter are negligible.

Neutron stars are some of the densest objects in the universe. A tablespoon of neutron star matter weighs as much as Mt Everest. Could some of the dark matter be hiding within these giants? This possibility has become more pressing with the recent discovery of neutron stars that are more massive than previously thought possible. Understanding these so-called dark-matter admixed neutron stars, or DMANSs, could contribute significantly to both our understanding of the internal composition of neutron stars—which remains a deep mystery—and to our understanding of dark matter. In our recent paper “Radial mode stability of two-fluid neutron stars,” we asked the fundamental question of whether such DMANSs are possible.

Stability is a necessary property for the astrophysical viability of DMANSs. From the simple observation that neutron stars live for billions of years, we know they must be stable. Therefore, if DMANSs were unstable, we would know that the neutron stars we see cannot contain dark matter. Criteria to determine whether a given internal configuration of a DMANS is stable have been developed. Such criteria assume that stable DMANS are possible. Surprisingly, prior to our work, there have been no studies on whether a stable DMANS can exist.

To study the possibility of stable DMANS, we employed one of the most powerful tools in any physicist’s toolkit: perturbation theory. In essence, we looked at what happens to a DMANS when it is subject to a very small change. A small change can be, for example, a small piece of debris falling into the star. After all, a DMANS could not exist for billions of years if a small piece of debris causes it to explode. Our work consisted of rigorously proving two theorems: first that DMANSs can be stable, and second that the existing stability criteria do indeed determine stability for an experimentally observed DMANS.

To prove that a DMANS could be stable, we studied its radial modes of oscillation—the fundamental ways the star can react to small perturbations. Our proof had three stages. First, we showed that only two types of modes exist: purely oscillatory modes, which are stable, and unstable modes. Second, we showed that these modes are complete, meaning that any radial perturbation of the star can be described by an underlying combination of these modes. Mode completeness is an often-underappreciated characteristic of stability. Without it, unstable non-mode solutions could exist, even if all mode solutions are stable. Finally, we proved the existence of a fundamental mode: a mode that, if stable, then immediately implies that all other modes must be stable, too. The existence of a fundamental mode is crucial because, in the case that it does not exist, there must be unstable modes and the DMANS will be unstable.

By proving these results, we showed that DMANSs can be stable and provided needed support for the already-in-use criteria used to determine whether an observed DMANS is stable. We were also able to extend most of our results to multiple different dark sectors, with the exception of our result on the fundamental mode.

Although our work rigorously proved the results, there are a couple of limitations to its applicability. The first is that we assumed that dark matter does not interact at all with normal matter outside of gravity. This is consistent with observations, but different models of dark matter can lead to interactions being more significant. Secondly, our proof for the existence of a fundamental mode fails when there are first-order phase transitions deep inside the star, the existence of which is an active area of research. Our work provides needed support to the research of DMANSs, which can help answer fundamental questions concerning dark matter and neutron stars.