The maximum mass of dark matter existing in compact stars based on the self-interacting fermionic model

TL;DR

This paper investigates the maximum amount of dark matter that can exist in compact stars using a self-interacting fermionic model, deriving universal relationships that connect dark matter properties with star characteristics.

Contribution

It introduces a universal formula for the maximum dark matter mass in neutron stars based on particle mass and interaction strength, independent of nuclear matter equations of state.

Findings

Derived a universal relationship for maximum dark matter mass in stars.

Found a linear relation between dark matter radius and maximum mass.

Demonstrated independence of results from nuclear matter equations of state.

Abstract

By assuming that only gravitation acts between dark matter (DM) and normal matter (NM), we studied DM admixed neutron stars (DANSs) using the two-fluid TOV equations. The NM and DM of compact stars are simulated by the relativistic mean field (RMF) theory and non-self-annihilating self-interacting fermionic model, respectively. The effects of the particle mass of fermionic DM $m_f$ and the interaction strength parameter $y$ on the properties of DANSs are investigated in detail. $m_f$ and $y$ are considered as the free parameters due to the lack of information about the particle nature of DM so far. For a DANS, we suggest a simple universal relationship $M_D^{\max}=(0.267 y +0.627-3.21\frac{M_N}{\M_{\odot}})( \frac{1\GeV}{{m_f}})^2 \M_{\odot}$ for $y>100$, where $M_D^{\max}$ is the maximum mass of DM existing in DANSs and $M_N$ is the mass of the neutron star without DM. For free fermion DM model ($y$=0), the relationship becomes $ M_D^{\max}=(0.627-0.027\frac{M_N^2}{\M_{\odot}^2}) ( \frac{1\GeV}{{m_f}})^2 \M_{\odot}$. The radius of DM $R_D$ shows a linear relationship with $M_D^{\max}$ in DANSs, namely $R_D=(7.02 \frac{M_D^{\max}}{ \M_{\odot}}+1.36)$~km. These conclusions are independent of the different NM EOSs from RMF theory. Such a kind of universal relationship connecting the nature of DM particle and mass of stars might shed light on the constraining the nature of the DM by indirect method.