Bose-Einstein Condensate Dark Matter in the Core of Neutron Stars: Implications for Gravitational-wave Observations

Abstract

We investigate neutron stars admixed with dark matter (DM) in the form of a finite-temperature Bos-Einstein condensate (BEC) within a general relativistic two-fluid framework in which the nuclear and dark components interact only gravitationally. Using realistic nuclear matter equations of state (EOS), APR4, MPA1, and SLy, we construct equilibrium configurations and compute mas-radius relations, tidal Love numbers, and dimensionless tidal deformabilities. We quantify how the presence of a BEC dark component modifies the mas-$Λ$ relation relevant for gravitational wave observations, finding that increasing the DM mass fraction generically reduces the maximum mass, radius, and tidal deformability of neutron stars. By comparing theoretical mass-$Λ$ curves with EOS-insensitive posteriors from GW170817, we evaluate, in a conditional sense, the dark matter fractions that would align a given nuclear EOS with the observed tidal constraints; for example, under the assumption that APR4 describes nuclear matter and that the GW170817 components were dark-matter admixed neutron stars, our study favors dark matter fractions of order a few percent, whereas stiffer EOSs require larger fractions to achieve comparable agreement. This interpretation assumes that inspiral waveforms are adequately characterized by tidal deformability and should therefore be regarded as structural rather than a direct detection of dark matter. We also examine finite-temperature effects in the BEC sector and find that, for moderate dark matter fractions, temperature has a negligible impact on the stability and tidal properties of admixed configurations. Our results demonstrate how even modest DM admixtures can influence neutron star structure and tidal observables, highlighting the importance of considering non-standard matter components in multimessenger constraints on dense matter.

Figures (5)

• Figure 1: Pressure–density relations for the finite-temperature BEC dark matter EOS (shown for $T_{11}=10^{11}\,$K) compared with the nuclear matter EOSs APR4, MPA1, and SLy.
• Figure 2: Mass-radius relation for pure BEC stars at different temperatures (0-$4 \times 10^{11}$K) and NSs described by APR4, MPA1, and SLy EOSs. The shaded bands represent observational constraints: grey, red, and pink correspond to mass measurements from PSR J0740+6620, PSR J0348+0432, and PSR J1614$-$2230, respectively. The orange contour denotes the 90% credible region of GW170817 from GW observations.
• Figure 3: Dimensionless tidal deformability $\Lambda(M)$ as a function of mass for pure BEC stars and neutron stars described by the EOSs: APR4, MPA1, and SLy.
• Figure 4: Mass-radius relations (first column), variation of the dimensionless tidal deformability $\Lambda$ (middle column), and the distribution of probabilities $p(f_{\rm DM})$ (equation \ref{['eq:p_f']}) of a dark matter fraction $f_{\rm DM}$ being present in the NSs observed in the GW170817 event (third column) for the EOSs APR4, MPA1, and SLy. The constraint patches from pulsar observations and the GW event are the same as in Fig. \ref{['MRFinal']}, but posteriors for the two stars in GW170817 are plotted in different colors in this plot, and the same color choice is maintained in plotting $p(f_{\rm DM})$ on the third column. In the first two columns, the DM fraction is varied from 0 to 30% for APR4 and SLy, and up to 40% for MPA1, with intermediate curves shown in 1% increments. $M$-$R$ and $M$-$\Lambda$ curves with the highest dark matter and half that value are highlighted for reference. Each curve on the $M$-$R$ plots corresponds to a $p(f_{\rm DM})$ value on the third column, and the distribution is estimated by a Gaussian fit, for which the median values are reported for both stars.
• Figure 5: Effects of finite temperature on DANS with fixed $f_{\rm DM}=5\%$. $T_{11}=10^{11}$ K.