Interpreting Mass and Radius Measurements of Neutron Stars with Dark Matter Halos

arXiv:2406.03332 · astro-ph.HE · Submitted 2024-06-05 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "Interpreting Mass and Radius Measurements of Neutron Stars with Dark Matter Halos".

Jocelyn: Here's the gist of the paper. The gist The high densities of neutron stars (NSs) could provide astrophysical locations for dark matter (DM) to accumulate, and this research explores how DM admixed NSs (DANSs) can significantly alter observed X-ray pulse profiles compared to pure baryonic NSs.

Vera: How it works The study adopts the two-fluid formalism in general relativity to numerically simulate stable configurations of DANSs, assuming a fermionic equation of state (EOS) for the DM with repulsive self-interaction.

Jocelyn: This formalism allows for a natural way to distinguish the baryonic radius (RB), where light is emitted, and the dark radius (RD), which marks the outer edge of the region containing dark matter.

Vera: The classification of DANSs into dark cores or dark halos depends on whether all DM exists within RB (dark core) or if it extends beyond RB to form a DM halo (dark halo).

Paper summary: Vera: So what the paper is claiming is that by looking at X-ray pulse profiles, we can start to tell if there's dark matter halo around these neutron stars instead of just assuming they are normal baryonic objects.

Jocelyn: The core thing they do is set up this two-fluid model in general relativity to simulate the stable shapes of these DANSs, using a fermionic equation of state for the dark matter that has repulsive self-interaction.

Subrahmanyan: They are specifically looking at how the distribution of dark matter as a halo influences the path that X-rays take from hot spots on the visible baryonic surface, which causes changes in the pulse profile observed by telescopes like NICER compared to pure baryonic neutron stars.

Vera: They explore how various dark matter models change the mass distribution, which results in different types of dark halos that we can classify.

Jocelyn: They then quantify the deviation in observed X-ray flux for each of these different halo types, which is a way to see what the signal looks like.

Subrahmanyan: The authors also identify some issues when we try to interpret mass and radius measurements of neutron stars that we infer from electromagnetic radiation if these dark halos are present.

Vera: They are looking at how the definition of the baryonic surface isn't straightforward in a single-fluid description, especially since neutron stars emit X-rays from hot spots on their baryonic surface.

Jocelyn: So they use the two-fluid formalism to clearly define the baryonic radius, which is where light is emitted, and the dark radius, which marks the outer edge of that region containing dark matter.

Subrahmanyan: This lets them calculate how much extra light-bending is caused by the dark matter situated outside that baryonic radius.

Conclusion: Vera: The title itself, "Interpreting Mass and Radius Measurements of Neutron Stars with Dark Matter Halos," points to the main challenge we face: how do we know what we are measuring when dark matter is involved?

Jocelyn: The authors, Shawqi and Morsink, they've shown that the distribution of dark matter around these neutron stars can significantly alter their observed X-ray pulse profiles.

Subrahmanyan: What this means for us in the bigger cosmic picture is that if significant amounts of dark matter exist in neutron stars—up to a few percent of the total star mass, as they suggest—it changes how we interpret constraints on the equation of state of dense baryonic matter.

Vera: They show that even if dark matter capture over the entire lifetime isn't super efficient, it can still affect their mass-radius relation.

Jocelyn: The paper suggests that for diffuse halos, the total mass of a DANS is larger than the pure baryonic radius, and in some cases, the curves for MT versus RB overlap with the pure baryonic MR curves.

Subrahmanyan: The main implication is that we need to account for this possibility when we use radio and X-ray observations to constrain dark matter properties; otherwise, our measurements of neutron star properties might be inaccurate.

Department of Physics, University of Alberta

astro-ph.HE

Submitted: 2024-06-05

Updated: 2024-09-27

Comments: Accepted by ApJ

Journal ref: The Astrophysical Journal, 975(1), 123, IOP (2024)

DOI: 10.3847/1538-4357/ad77c1

License: http://creativecommons.org/licenses/by-sa/4.0/

Importance score: 74/100

The gist: The gist The high densities of neutron stars (NSs) could provide astrophysical locations for dark matter (DM) to accumulate, and this research explores how DM admixed NSs (DANSs) can significantly

Key concepts

Two-Fluid Formalism
This is a method used in general relativity to describe neutron stars that have two distinct fluids: baryonic matter (normal matter) and dark matter. It allows researchers to model the structure of DANSs by solving specific equations that govern how these two components interact under strong gravity.
Baryonic Radius (RB)
This is the boundary where light is emitted from the visible, baryonic surface of a neutron star. It is a key feature used to distinguish between dark matter configurations; if all dark matter is inside this radius, it's a 'dark core'; if it extends beyond, it forms a 'dark halo'.
Dark Halo Types (Compact vs. Diffuse)
The study classifies DANSs based on the DM mass distribution relative to the baryonic radius. A compact halo has most dark matter inside RB, while a diffuse halo has most of its dark matter extending outside RB, leading to different gravitational lensing effects.
Gravitational Self-Lensing
This phenomenon describes how the presence of surrounding mass, including dark matter halos outside the star's visible surface, bends and distorts the path of light emitted from the star. Analyzing this bending helps constrain the mass and radius parameters of DANSs.

Terminology

Summary

The gist The high densities of neutron stars (NSs) could provide astrophysical locations for dark matter (DM) to accumulate, and this research explores how DM admixed NSs (DANSs) can significantly alter observed X-ray pulse profiles compared to pure baryonic NSs.

How it works

The study adopts the two-fluid formalism in general relativity to numerically simulate stable configurations of DANSs, assuming a fermionic equation of state (EOS) for the DM with repulsive self-interaction. This formalism allows for a natural way to distinguish the baryonic radius (RB), where light is emitted, and the dark radius (RD), which marks the outer edge of the region containing dark matter. The classification of DANSs into dark cores or dark halos depends on whether all DM exists within RB (dark core) or if it extends beyond RB to form a DM halo (dark halo).

The simulation involves solving the two-fluid TOV equations using the stiff BM-EOS, NL3ωρL55, and a self-interacting fermionic DM-EOS with varying repulsive self-interaction strengths. The resulting mass distribution is characterized by several parameters, including the total gravitational mass MT and the fraction of DM as a fraction of the total mass of the DANS, fχ.

How it works

The paper explores how various DM models affect the DM mass distribution, leading to different types of dark halos. The key distinction between compact and diffuse halos is based on the fraction of its dark matter mass located inside or outside RB. A compact halo has a small fraction of its DM located outside the baryonic surface, while a diffuse halo has most of its DM located in the cloud outside RB.

The stability of DANS models is assessed using a generalized turning-point method, which identifies stable solutions when MT versus RB curves are at or to the right of the maximum mass on constant fχ curves. The MR relations for DANSs can be plotted with many different combinations of quantities depending on the type of observations used, focusing on RB as most appropriate when connecting to observations of electromagnetic radiation emitted from the baryonic surface.

How it works

Gravitational self-lensing is analyzed using the Schwarzschild plus Doppler (SD) approximation or the Oblate Schwarzschild (OS) approximation for rotating stars. The extra light-bending caused by DM situated outside RB depends on the amount of mass in the cloud and its distribution. The analysis shows that for small bending angles, the leading order values for the bending angle, divergence of light rays, and time delays are proportional to a factor J.

The relative changes in gravitational self-lensing due to DM halos are quantified by relative differences such as ∆relψ and ∆reldψdα. The maximum relative change in the bolometric flux is never larger than 2 times the relative change in the metric, which suggests that for small changes in the metric at the baryonic surface, both bolometric and energy-dependent fluxes will have small relative changes.

How it works

The paper discusses how hypothetical electromagnetic measurements of NSs with dark halos should be interpreted based on three possible types of observations: only a radiotiming observation, only X-ray emission from the surface, or both radio-timing and surface X-ray emission is observed. When dynamical mass measurements are available, they constrain MT while gravitational self-lensing constrains MT (RB) and RB.

For diffuse halos, the total mass of the DANS is larger than MT (RB) with a fractional difference similar in size to the dark matter mass fraction fχ. The analysis suggests that for diffuse halos, the MT (RB) versus RB curves overlap with the pure baryonic MR curves.

How it works

Statistical EOS inference requires a set of parameters describing both the baryonic EOS and DM properties, including mχ and y. A statistical approach is imagined where one first introduces a set of parameters describing the baryonic EOS, α, and adds extra parameters describing the DM, such as mχ and y. The type of measurement determines which mass posterior to use for inference; dynamical measurements constrain MT while gravitational self-lensing constrains MT (RB) and RB.

The paper concludes that stiff and soft BM EOS have similar halo properties given the same DM parameters, suggesting that constraints on DM properties arising from electromagnetic observations of DANS must account for the full range of possible baryonic EOS. The findings identify pitfalls in interpreting macroscopic properties using radio and X-ray observations.

The gist The high densities of neutron stars (NSs) could provide astrophysical locations for dark matter (DM) to accumulate, and this research explores how DM admixed NSs can significantly alter observed X-ray pulse profiles compared to pure baryonic NSs.

How it works

The study adopts the two-fluid formalism in general relativity to numerically simulate stable configurations of DANSs, assuming a fermionic equation of state (EOS) for the DM with repulsive self-interaction. The formalism allows for a natural way to distinguish the baryonic radius (RB), where light is emitted, and the dark radius (RD), which marks the outer edge of the region containing dark matter.

The simulation involves solving the two-fluid TOV equations using the stiff BM-EOS, NL3ωρL55, and a self-interacting fermionic DM-EOS with varying repulsive self-interaction strengths. The resulting mass distribution is characterized by several parameters, including the total gravitational mass MT and the fraction of DM as a fraction of the total mass of the DANS.

How it works

The simulation involves solving the two-fluid TOV equations using the stiff BM-EOS, NL3ωρL55, and a self-interacting fermionic DM-EOS with varying repulsive self-interaction strengths. The resulting mass distribution is characterized by several parameters, including the total gravitational mass MT and the fraction of DM as a fraction of the total mass of the DANS.

Improvements for AI systems

  1. A system can now distinguish between dark cores and dark halos by analyzing mass distribution profiles, as described in Section 2.2, which classifies DANSs based on whether the DM exists both inside and outside the visible radius of the NS.

  2. The AI can perform a statistical EOS inference that accounts for dark matter uncertainties by introducing extra parameters describing mχ and y, allowing it to test if a soft BM-EOS is ruled by this observation when combined with gravitational lensing data.

  3. The system can assess the validity of an observed mass measurement (dynamical or self-lensing) for a DANS by comparing it against the MR curves, specifically determining if the MT (RB) versus RB curve intersects the NICER posterior or if the MT and MT (RB) are the same.

  4. The AI can evaluate whether an observation supports a specific baryonic EOS by checking compatibility across all DANS models, recognizing that it would be incorrect to rule out the DM model with mχ = 1 GeV and y = 25 using only the soft BM-EOS and the observation of DANS(3) in the example shown in Figure 4.

  5. The system can predict if a DANS with a diffuse halo will have its MT (RB) versus RB curves overlap the pure baryonic MR curves based on whether the maximum mass DANS has a diffuse halo.

Abstract

The high densities of neutron stars (NSs) could provide astrophysical locations for dark matter (DM) to accumulate. Depending on the DM model, these DM admixed NSs (DANSs) could have significantly different properties than pure baryonic NSs, accessible through X-ray observations of rotation-powered pulsars. We adopt the two-fluid formalism in general relativity to numerically simulate stable configurations of DANSs, assuming a fermionic equation of state (EOS) for the DM with repulsive self-interaction. The distribution of DM in the DANS as a halo affects the path of X-rays emitted from hot spots on the visible baryonic surface causing notable changes in the pulse profile observed by telescopes such as NICER, compared to pure baryonic NSs. We explore how various DM models affect the DM mass distribution, leading to different types of dark halos. We quantify the deviation in observed X-ray flux from stars with each of these halos. We identify the pitfalls in interpreting mass and radius measurements of NSs inferred from electromagnetic radiation and constraining the baryonic matter EOS, if these dark halos exist.

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