Illuminating dark matter admixed in neutron stars with simultaneous mass-radius constraints

TL;DR

This work evaluates how simultaneous mass–radius measurements of massive neutron stars, notably PSRJ0740+6620, constrain dark matter that may be admixed in neutron stars. By employing a fermionic dark matter model that interacts only through gravity alongside a constrained nuclear matter EOS (PEOS) and solving the two-fluid TOV equations, the authors show that joint M–R data reduce the uncertainty in the central DM energy density by over 50% compared to using the observables separately. The analysis finds that the DM fraction is generally small, with f_D < 2% from the maximum-mass constraint and potentially as low as ~0.3% when mass and radius are measured simultaneously, while the DM interaction parameters C_DS and C_DV remain unconstrained. The results highlight a degeneracy between nuclear and dark matter EOSs and underscore the need for additional observables to tighten constraints on DM properties in dark matter admixed neutron stars (DANS).

Abstract

We investigate how simultaneous mass and radius measurements of massive neutron stars (NSs) can help constrain properties of dark matter (DM) possibly admixed in them. Within a fermionic DM model that interacts only through gravitation, along with a well-constrained nuclear matter equation of state, we show that the simultaneous mass and radius measurement of PSRJ0740+6620 reduces the uncertainty of DM central energy density by more than 50\% compared to the results obtained from using the two observables independently, while other DM parameters remain unconstrained. Additionally, we find that the DM fraction $f_D$ should be smaller than 2\% when constrained by the observed NS maximum mass alone, and it could be even smaller than 0.3\% with the simultaneous measurement of mass and radius, supporting the conclusion that only a small amount of DM exists in DM admixed neutron stars (DANS).

Figures (5)

• Figure 1: The effects of dark matter mass $m_D$ (left panel), $C_{DV}$ (middle panel), and $C_{DS}$ (right panel on the EOS of dark matter. The black dashed line, labeled as PEOS, is the neutron star EOS mentioned in Section \ref{['2.1']} and is given for comparison.
• Figure 2: The constant surfaces of $M_{\rm max}=2.08$ M$_\odot$ (blue surfaces) and $R_{2.08}=12.2$ km (pink surfaces) in the 3D parameter space of $C_{DS}-C_{DV}-\varepsilon_D^c/\varepsilon_N^c$ for $m_D=500$, 1000, 1500, and 2000 MeV, respectively. The red arrows indicate the directions that satisfy the corresponding observation, while the black arrow points to the surface of $R_{2.08}=12.2$ km.
• Figure 3: The projection of $C_{DS}=C_{DV}$ to the $C_{DS}\sim\varepsilon_D^c/\varepsilon_N^c$ or $C_{DV}\sim\varepsilon_D^c/\varepsilon_N^c$ plane with $m_D$ = 500 (red lines), 1000 (blue lines), 1500 (green lines), and 2000 (orange lines) MeV for the surfaces of $M_{\rm max}=2.08$ M$_\odot$ (solid lines) and $R_{2.08}=12.2$ km (dashed lines).
• Figure 4: The profile of energy density as functions of distance $r$ for $M_{\rm max}=2.08$ M$_\odot$ and $R_{2.08}=12.2$ km and $C_{DS}=C_{DV}$ = 0, 10, 20 GeV$^{-1}$, respectively. The red and green lines correspond to the profiles of nuclear matter, while the blue and orange lines correspond to the profile of dark matter.
• Figure 5: The profile of dark matter fraction $f_D$ (left title, red and blue lines) and total mass $M_t$ (right title, green and orange lines) as functions of distance $r$ for $M_{\rm max}=2.08$ M$_\odot$ and $R_{2.08}=12.2$ km and $C_{DS}=C_{DV}$ = 0, 10, 20 GeV$^{-1}$, respectively.