[Paper Review] Constraining bosonic asymmetric dark matter with neutron star mass-radius measurements

Nathan Rutherford, G. Raaijmakers+2 more|arXiv (Cornell University)|Aug 5, 2022

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper uses Bayesian inference to constrain bosonic asymmetric dark matter (ADM) in neutron stars via mass-radius measurements from X-ray telescopes. It finds that current uncertainties in the baryonic equation of state prevent firm ADM constraints, but high ADM particle mass and low self-interaction strength are disfavored due to the observed $1\,\mathrm{M}_{\odot}$ minimum neutron star mass, while the ADM mass-fraction remains measurable.

ABSTRACT

Neutron stars can accumulate asymmetric dark matter (ADM) in their interiors, which affects the neutron star's measurable properties and makes compact objects prime targets to search for ADM. In this work, we use Bayesian inference to explore potential neutron star mass-radius measurements, from current and future x-ray telescopes, to constrain the bosonic ADM parameters for the case where bosonic ADM has accumulated in the neutron star interior. We find that the current uncertainties in the baryonic equation of state do not allow for constraints on the ADM parameter space to be made. However, we also find that ADM cannot be excluded and the inclusion of bosonic ADM in neutron star cores relaxes the constraints on the baryonic equation of state space. If the baryonic equation of state were more tightly constrained independent of ADM, we find that statements about the ADM parameter space could be made. In particular, we find that the high bosonic ADM particle mass ($m_χ$) and low effective self-interaction strength ($g_χ/m_ϕ)$ regime is disfavored due to the observationally and theoretically motivated constraint that neutron stars must have at least a mass of $1 \, \mathrm{M_\odot}$. However, within the remaining parameter space, $m_χ$ and $g_χ/m_ϕ$ are individually unconstrained. On the other hand, the ADM mass-fraction, i.e., the fraction of ADM mass inside the neutron star, can be constrained by such neutron star measurements.

Motivation & Objective

• To investigate whether current and future X-ray telescope mass-radius measurements can constrain bosonic asymmetric dark matter (ADM) in neutron stars.
• To assess the impact of ADM on neutron star structure, particularly through changes in mass and radius.
• To determine the extent to which ADM parameters—particle mass $m_\chi$, self-interaction strength $g_\chi/m_\phi$, and mass-fraction—can be constrained by neutron star observations.
• To explore how ADM affects the baryonic equation of state (EoS) and whether ADM inclusion relaxes EoS constraints.

Proposed method

• Uses Bayesian inference to analyze potential mass-radius measurements from current and future X-ray telescopes.
• Models bosonic ADM as a scalar field with a self-interaction term and a coupling to a vector field, assuming mean-field approximation.
• Applies the stress-energy tensor formalism to derive the ADM equation of state, with energy density $\epsilon_\chi = m_\chi c^2 n_\chi + \frac{1}{2} \frac{g_\chi^2}{m_\phi^2} \frac{\hbar^3}{c} n_\chi^2$ and pressure $p_\chi = \frac{1}{2} \frac{g_\chi^2}{m_\phi^2} \frac{\hbar^3}{c} n_\chi^2$.
• Assumes flat spacetime and spherically symmetric, stationary scalar field solutions with $\chi(r,t) = (A e^{ikr} + B e^{-ikr}) e^{-i\omega t}$, setting $k=0$ for ground state.
• Derives the relation $\phi_0 = \frac{g_\chi}{m_\phi^2} n_\chi$ from the field equations, linking the scalar field to ADM number density.
• Compares neutron star models with and without ADM cores to compute percent changes in mass and radius, using a $2.3\,\mathrm{M}_\odot$ baryonic star as baseline.

Experimental results

Research questions

• RQ1 Can current and future X-ray mass-radius measurements constrain the parameter space of bosonic asymmetric dark matter in neutron stars?
• RQ2 How does the presence of ADM affect the mass and radius of neutron stars, and can these changes be detected?
• RQ3 Which regions of the ADM parameter space—specifically $m_\chi$ and $g_\chi/m_\phi$—are disfavored by the requirement that neutron stars must have at least $1\,\mathrm{M}_\odot$ mass?
• RQ4 To what extent does ADM inclusion relax constraints on the baryonic equation of state?
• RQ5 Can the ADM mass-fraction inside neutron stars be constrained by mass-radius measurements?

Key findings

• Current uncertainties in the baryonic equation of state prevent meaningful constraints on the bosonic ADM parameter space.
• The high $m_\chi$ and low $g_\chi/m_\phi$ regime is disfavored due to the requirement that neutron stars must have at least $1\,\mathrm{M}_\odot$ mass.
• Within the remaining parameter space, $m_\chi$ and $g_\chi/m_\phi$ are individually unconstrained by current data.
• The inclusion of bosonic ADM in neutron star cores relaxes constraints on the baryonic equation of state space.
• The ADM mass-fraction—defined as the fraction of ADM mass inside the neutron star—can be constrained by future mass-radius measurements.
• For a $2.3\,\mathrm{M}_\odot$ baryonic neutron star with a $7\%$ ADM mass-fraction, the radius decreases by $6\%$ and the gravitational mass by $9\%$ due to the ADM core.