Rotating Neutron Stars with Dark Matter Halos

Abstract

If dark matter (DM) exists in halos around rotating neutron stars (NSs), it will be essential to understand the effects of rotation on the distribution of DM and baryonic matter (BM) in the stars to interpret observations. In this work, we construct rapidly rotating dark matter admixed neutron stars (DANS) with DM halos using the two-fluid approximation, where the BM and DM interact only through gravity. Our goal is to describe rapidly rotating millisecond-period DANS spun up by the accretion of BM from a zero angular momentum state. We extend the Rapidly Rotating Neutron Star (RNS) code to compute axisymmetric configurations in which the BM rotates rigidly while the DM remains torque-free and differentially rotates through the frame-dragging of spacetime. For the first time, we examine in detail local and global definitions of mass in general relativity for two-fluid systems, showing how their differences affect the interpretation of baryonic and dark component masses. We compute energy density and frame-dragging frequency profiles for DANS with three different characteristic DM halos. We demonstrate that rapid BM rotation reduces DM halo sizes if central energy densities are kept constant between non-rotating and rotating models. We also construct sequences of DANS to create mass and radius curves and compare rotating and non-rotating cases. Finally, we quantify deviations in the spacetime metric outside the baryonic surfaces of these sequences of stars caused by the DM halos. We hypothesize that the size of this quantity could indicate whether a DM halo will significantly impact X-ray pulse profile modeling. These results provide a framework for assessing the observational consequences of DM halos around rapidly rotating NSs.

Figures (7)

• Figure 1: Fractional differences in $R_{B}$ (upper) and $R_{D}$ (lower), calculated in spherical symmetry using the RNS code and by solving the two-fluid TOV equations. The differences arise from numerical resolution errors associated with the two-fluid RNS code. The dashed vertical line represents the $M_{T, \textrm{TOV}} = 1.4 M_{\odot}$ stars shown in Table \ref{['tab:densityDANS']} and Figures \ref{['fig:density']} and \ref{['fig:omega']}.
• Figure 2: Fractional differences in five different mass definitions calculated in spherical symmetry using the RNS code and by solving the two-fluid TOV equations. The differences in $M_{T}$ arise from numerical resolution and errors associated with the two different methods of calculation. Differences in $M_{B}$, $M_{D}$, $M_{D} \left( R_{B} \right)$ and $M_{T} \left( R_{B} \right)$ arise from the difference in the definitions of global and local (TOV) masses. Dashed vertical line represents the $M_{T, \textrm{TOV}} = 1.4 M_{\odot}$ stars shown in Table \ref{['tab:densityDANS']} and Figures \ref{['fig:density']} and \ref{['fig:omega']}.
• Figure 3: Energy density distributions as a function of radial distance from the centre for DANS in Table \ref{['tab:densityDANS']}. Top: Baryonic (dash-dot) and dark halo (solid) energy densities of $M_{T} = 1.4 M_{\odot}$ DANS models with $f_{\chi, \textrm{TOV}} = 0.05$ and $\bar{r}_{B \textrm{ratio}} = 1$. Center: Equatorial energy densities of rotating ($\bar{r}_{B \textrm{ratio}} = 0.9$) DANS models with the same central energy densities as the models in the top plots. Bottom: Polar energy densities of rotating ($\bar{r}_{B \textrm{ratio}} = 0.9$) DANS models with the same central energy densities.
• Figure 4: Equatorial frame-dragging frequency as a function of radial distance from the centre for the rotating DANS in Table \ref{['tab:densityDANS']} with $\bar{r}_{B \textrm{ratio}} = 0.9$. Coloured circles and stars represent the baryonic and dark surfaces of the stars, respectively.
• Figure 5: Various properties [$R_{Be}$ (top left), $R_{De}$ (top right), $M_{B, \textrm{g}}$ (centre left), $M_{D, \textrm{g}}$ (centre right), $M_{T, \textrm{g}}$ (bottom left), and $M_{T, \textrm{g}} \left( R_{B} \right)$ (bottom right)] for sequences of DANS as functions of $\epsilon_{Dc}/\epsilon_{Bc}$. Solid curves correspond to non-rotating DANS, and dotted curves are rotating DANS with the same central densities as the non-rotating models. All non-rotating models have $f_{\chi, \textrm{TOV}} = 0.05$.