The Dark Matter Redemption Arc for Neutron Star Equations of State

Title: Dark matter effects on neutron star properties

Authors: John Ellis, Gert Hütsi, Kristjan Kannike, Luca Marzola, Martti Raidal, Ville Vaskonen

First Author’s Institution: National Institute for Chemical Physics and Biophysics (NICPB), Rävala puiestee 10, Tallinn 10143, Estonia

Status: Published in Physical Review D [open access]

It’s tough to predict how matter behaves when you cram one-and-a-half times the mass of the Sun into a sphere the size of Manhattan. While such extreme densities are far beyond what we can replicate on Earth, the universe offers its own cosmic laboratories: neutron stars. These ultra-dense objects are fascinating to astrophysicists studying how they form and evolve, and to nuclear physicists trying to figure out what happens inside them. Nuclear physicists use the equation of state, a relationship between pressure and density, to describe the structure and properties of neutron stars. Many equations of state have been proposed, based on different assumptions about the particles and forces inside neutron stars. But how do we determine which one is correct?

Researchers compare the predictions of each model to real neutron star observations, ruling out those that don’t match the data. However, the plot thickens when dark matter enters the picture. Detectable only through its gravitational effects on ordinary matter, dark matter could be drawn into neutron stars by their extreme gravity. It may accumulate in their cores, like the filling of a jelly donut, or form a surrounding halo. This paper explores how dark matter might alter neutron star properties, and could even bring some previously excluded equations of state back into the running.

Modeling neutron stars with dark matter

Beyond a certain maximum mass, neutron stars can no longer sustain their own structure. Equations of state predict this maximum neutron star mass, which must be greater than the heaviest neutron star we’ve observed—a record held by pulsar PSR J0348+0432 at 1.97 times the mass of the Sun. This study considers eleven equations of state consistent with this mass limit. It also incorporates limits from the gravitational wave event GW170817, which suggest the maximum neutron star mass is likely capped at 2.33 times the mass of the Sun.

So, how does dark matter factor in? The authors assume that dark matter consists of special particles called self-interacting bosons. These particles repel each other but can cluster into the same quantum state, forming a Bose-Einstein condensate with a known equation of state. They combine this with the eleven neutron star equations of state, assuming these two types of matter interact only through gravity. The results depend on the strength of dark matter’s self-interaction. At low self-interaction strengths, dark matter forms a core, while at higher strengths, it forms a halo. The authors focus on the core scenario to explore how dark matter affects neutron star properties.

Dark matter makes neutron stars smaller

The authors find that a dark matter core generally lowers the maximum mass of a neutron star, as shown in Figure 1. This would make some equations of state more compatible with the upper limit from GW170817. It may also rule out some equations that previously satisfied the lower limit from PSR J0348+043.

Curves with neutron star mass as a function of its radius predicted by different equations of state with and without dark matter.
Figure 1: Neutron star mass-radius relationship for different equations of state. Each color corresponds to an equation of state, with their names listed in the legend. Solid curves show the original mass-radius relationship, while dashed curves show the changes when dark matter makes up 5% of the star’s total mass. The horizontal dashed lines mark the upper and lower limits on the maximum mass. Figure 1 in the paper.

Dark matter makes neutron stars stiffer

Besides their maximum mass, another important property of neutron stars is whether they are squishy or stiff. A quantity called tidal deformability measures how much they can stretch or change shape when pulled by another object’s gravity. A star with greater tidal deformability will change shape more, while one with less will stay mostly the same shape. GW170817 and its electromagnetic signals helped set an upper limit and suggested a possible lower limit on the tidal deformability of neutron stars.

In this study, the authors found that as the amount of dark matter in the neutron star’s core increases, the star becomes stiffer, as shown in Figure 2. As a result, equations of state that previously predicted very high tidal deformabilities might still be compatible with the observed limits if we include dark matter. Additionally, confirming the lower limit would rule out large dark matter cores. If dark matter cores do exist in neutron stars, they would have to make up a small fraction of the star’s total mass.

Curves showing tidal deformability decreasing smoothly as a function of dark matter fraction.
Figure 2: Tidal deformability of a neutron star with 1.4 times the mass of the Sun as dark matter is added to its core. The x-axis shows the dark matter fraction of the star, and the y-axis represents the tidal deformability (Λ). The horizontal dashed lines mark the observational limits. As the dark matter amount increases, the tidal deformability decreases, falling in and out of these bounds. Figure 3 in the paper.

Conclusions

This paper shows that dark matter could make it harder to interpret measurements of neutron stars, especially if different stars have different amounts of dark matter. Since dark matter cores reduce the maximum mass and the tidal deformability predicted by a neutron star’s equation of state, some models previously ruled out by observations might still be viable. Meanwhile, those once considered safely within constraints may no longer hold up.

Scientists worldwide are working to improve our observatories and models and prepare for new measurements. Each new neutron star observation could change how we understand dark matter, gravitational physics, and the behavior of matter in extreme conditions. So stay tuned—the next big discovery could be just around the corner!

Astrobite edited by Sandy Chiu and Katherine Lee.

Featured image credit: NOIRLab/NSF/AURA/J. da Silva/Spaceengine

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