A new model for dark matter fluid sphere

TL;DR

This paper proposes a new spherically symmetric dark matter fluid model with an inner isotropic core and an outer anisotropic shell, providing physically consistent solutions that are analyzed using a compact star example.

Contribution

It introduces a novel dark matter sphere model with a specific density profile and linear equation of state, ensuring stability and physical acceptability.

Findings

Solutions are well-behaved and physically acceptable.

Model satisfies TOV, causality, and stability conditions.

Applied to a real compact star, demonstrating practical relevance.

Abstract

We develop a new model for a spherically symmetric dark matter fluid sphere containing two regions: {\bf (i)} Isotropic inner region with constant density and {\bf (ii)} Anisotropic outer region. We solve the system of field equation by assuming a particular density profile along with a linear equation of state. The obtained solutions are well-behaved and physically acceptable which represent equilibrium and stable matter configuration by satisfying the TOV equation and causality condition, condition on adiabatic index, Harrison-Zeldovich-Novikov criterion, respectively. We consider the compact star EXO 1785-248 (Mass $M=1.3~M_{\odot}$ and radius $R = 8.8 ~km.$) to analyze our solutions by graphical demonstrations.