Thermodynamic Consistent Description of Compact Stars of Two Interacting Fluids: The Case of Neutron Stars with Higgs Portal Dark Matter

Abstract

We consider a thermodynamically consistent approach for the computation of the masses, radii, and tidal deformabilities of compact stars consisting of two interacting fluids with separately conserved quantum numbers. We apply this interacting fluid approach to the case of compact stars of neutron star matter with the Higgs portal fermionic dark matter model for the first time in a thermodynamically consistent manner. The patterns for the mass-radius curves and the tidal deformability depend on the dark matter particle mass and are different from former studies. Compared to ordinary neutron star properties, we obtain smaller masses and radii for dark matter particle masses similar to the nucleon mass and, hence, smaller tidal deformabilities as a result of the softening of the equation of state due to the presence of dark matter. For dark matter particle masses below the nucleon mass and sizable chemical potentials with respect to the dark matter particle mass, there will be a dark halo instead of dark core. Our investigation provides the basis for studying mergers of compact stars where the two fluids of neutron star matter and dark matter are coupled kinetically to each other and are described by one combined energy-momentum tensor of the two interacting fluids but are chemically different with two separately conserved number currents.

Figures (6)

• Figure 1: Energy (left panels) and pressure (right panels) densities versus nucleon and DM chemical potentials i.e. $\mu_{\rm N}$ and $\mu_{\chi}$ . Each row corresponds to a specific DM particle mass $M_{\chi}=100~$MeV (first row), $M_{\chi}=500~$MeV (second row), $M_{\chi}=1000~$MeV (third row) and $M_{\chi}=5000~$MeV (fourth row). We normalize the DM and nucleon chemical potentials with respect to the nucleon mass.
• Figure 2: Speed of sound versus nucleon and DM chemical potentials i.e. $\mu_{\rm N}$ and $\mu_{\chi}$ . Each row is for a specific DM particle mass, that is, $M_{\chi}=100~$MeV (top left), $M_{\chi}=500~$MeV (top right), $M_{\chi}=1000~$MeV (bottom left) and $M_{\chi}=5000~$MeV (bottom right). We normalize the DM and nucleon chemical potentials with respect to the nucleon mass.
• Figure 3: A comparison of the radial dependence of various neutron star quantities i.e. DM and nucleon chemical potentials, total mass of a neutron star, DM number density and nucleon number density for different DM particle masses. We choose $M_{\chi}=100$ MeV (left panels) and $M_{\chi}=500$ MeV (right panels). The blue parts of the curves indicate the DM and nucleonic matter mixed region and red regions show pure nucleonic matter region. The central chemical potentials we considered here are $\mu_{\rm N}= M_{\rm N}+1.8$ and $\mu_{\rm DM}= M_{\chi}+0.1$ (in nucleon mass units).
• Figure 4: A comparison of the radial dependence of various neutron star quantities i.e. DM and nucleon chemical potentials, total mass of a neutron star, DM number density and nucleonic number density for different DM particle masses. We choose $M_{\chi}=1000$ MeV (left panels) and $M_{\chi}=5000$ MeV (right panels). The blue parts of the curves indicate DM and nucleonic matter mixed region and red parts show pure nucleonic matter region. The central chemical potentials we considered here are $\mu_{\rm N}= M_{\rm N}+1.8$ and $\mu_{\rm DM}= M_{\chi}+0.1$ (in nucleon mass units).
• Figure 5: Mass-radius relation for DM-admixed neutron stars. From the top left panel to the bottom right one, we consider for DM particle mass $M_{\chi}=100~$MeV, $M_{\chi}=500~$MeV, $M_{\chi}=1000$ MeV and $M_{\chi}=5000~$MeV. The different colored lines display the mass-radius relation for various DM chemical potentials at the center (in terms of $M_{\chi}$). Whereas the solid curves are the mass-radius relations for the total mass versus the total radius, the green dashed curves are examples of the total mass versus the radius of DM.