Anisotropic compact stars: Constraining model parameters to account for physical features of tidal Love numbers

Highlights: • Investigation of a compact star with anisotropic stresses. • We assume a linear equation of state to solve the Einstein field equations. • Love numbers are calculated from the presented model. • We have compared the results with the observed compact stars. • Solutions provide a physical viability of the proposed approach. In this paper, we develop a new class of models for a compact star with anisotropic stresses inside the matter distribution. By assuming a linear equation of state for the anisotropic matter composition of the star we solve the Einstein field equations. In our approach, for the interior solutions we use a particular form of the an satz for the metric function $g_{rr}$. The exterior solution is assumed as the Schwarzschild metric and is joined with the interior metric obtained across the boundary of the star. These matching of the metrices along with the condition of the vanishing radial pressure at the boundary lead us to determine the model parameters. The physical acceptability of the solutions has verified by making use of the current estimated data available from the pulsar $4U1608-52$. Thereafter, assuming anisotropy due to tidal effects we calculate the Love numbers from our model and compare the results with the observed compact stars, viz. $KS1731-260$, $4U1608-52$, $4U1724-207$, $4U1820-30$, $SAXJ1748.9-2021$ and $EXO1745-268$. The overall situation confirms physical viability of the proposed approach, which can shed new light on the interior of the compact relativistic objects.