I-Love-Q Relations of Fermion-Boson Stars

Abstract

We investigate the properties of fermion-boson stars (FBSs), which can be viewed as neutron stars with a bosonic dark matter (DM) admixture. A challenge in studying the impact of DM on neutron stars is the absence of a universally accepted nuclear-matter equation of state (EOS), making it difficult to distinguish between the effects of DM and various EOS models. To address this issue, we extend the study of the I-Love-Q universal relations of neutron stars to FBSs with a nonrotating bosonic component by solving the Einstein-Klein-Gordon system. We study how DM parameters, such as the boson particle mass and self-interaction strength, would affect the structure of FBSs and explore the parameter space that leads to deviations from the I-Love-Q relations. The properties of FBSs and the level of deviations in general depend sensitively on the DM parameters. For boson particle mass within the range of $\mathcal{O}(10^{-10} \ \mathrm{eV})$, where the Compton wavelength is comparable to the Schwarzschild radius of a $1 M_\odot$ star, the deviation is up to about 5% level if the star contains a few percent of DM admixture. The deviation increases significantly with a higher amount of DM. We also find that the universal relations are still valid to within a 1% deviation level for boson particle mass $m_b \geq 26.8\times10^{-10} \ \mathrm{eV}$. This effectively sets an upper bound on the boson particle mass, beyond which it becomes not feasible to probe the properties of FBSs by investigating the I-Love-Q relation violations.

Figures (8)

• Figure 1: Stability curve (black) of FBSs with $m_b=2.68\times10^{-10}\,\mathrm{eV}$ and $\Lambda=0$. The contours and colorbar represent the total mass of the FBS corresponding to different central densities $\rho_c$ and $\sigma_c$. The stable configurations are located in the lower left region bounded by the stability curve.
• Figure 2: Mass-radius relation of FBSs with $m_b=2.68\times10^{-10}\,\mathrm{eV}$ and $\Lambda=0$. The colorbar represents the DM mass fraction of the FBSs. Configurations with the same $\rho_c$ are connected by thin gray lines.
• Figure 3: Top panels: I-Love (left) and Q-Love (right) relations for FBSs with $m_b=2.68\times10^{-10}\,\mathrm{eV}$ and $\Lambda=0$. Bottom panels: The fractional errors between the FBS data and the corresponding fitting curves (black solid lines in the top panels) for NSs found in Ref. yagi2017approximate. Note that the fitting curves are insensitive to NS EOS models to within $1\%$ in the range $\bar{I}<30$, $\bar{Q}<20$ and $\bar{\lambda}_{\rm tidal}<10^4$, which is bounded by the red dashed lines in the top panels. Different FBSs with the same $\rho_c$ are connected by thin gray lines, while the colorbar represents the DM mass fraction of each FBS.
• Figure 4: Three sequences of FBSs with $m_b=2.68\times10^{-10}\,\mathrm{eV}$, $\Lambda=0$ and $\rho_c=\{2.03,0.89,0.35\}\times10^{15}\,\mathrm{g/cm}^3$ (from left to right column). Top row: The fractional errors between the FBS data and the Q-Love relation for NSs, with horizontal dashed lines indicating the 1% EOS-insensitive level as in Fig. \ref{['fig:ILoveQ']}. The color of each data point represents the DM fraction of the star, as defined by the colorbar. Middle row: Trends of the fermionic NM mass $M_{\rm NM}$ (green data points) and bosonic DM mass $M_{\rm DM}$ (red data points), with arrows indicating the direction of increasing $\sigma_c$. Bottom row: Trends of the fermionic NM and bosonic DM radii. The quantities in all panels are plotted against the dimensionless tidal deformability ${\bar{\lambda}}_{\rm tidal}$, but the panels in different columns do not have the same range of ${\bar{\lambda}}_{\rm tidal}$.
• Figure 5: Similar to Fig. \ref{['fig:structure']}, but for four sequences of FBSs with $m_b=2.68\times10^{-10}\,\mathrm{eV}$, $\rho_c=1.65\times10^{15}\,\mathrm{g/cm}^3$ and $\Lambda=\{-10,0,10,100\}$ (from left to right). The value of $\rho_c$ is chosen to produce FBSs within the astrophysically relevant range where $\bar{\lambda}_{\rm tidal} \lesssim \mathcal{O}(10^2)$. Note that the colorbar ranges from 0.0 to 0.3, unlike in Fig. \ref{['fig:structure']} where it ranges from 0.0 to 1.0.