Effects of dark boson mediated feeble interaction between dark matter (DM) and quark matter on f-mode oscillation of DM admixed quark stars

Abstract We investigate the behavior of the prominent non-radial fundamental f -mode oscillations of dark matter (DM) admixed strange quark stars (DMSQSs), by adopting an equation of state (EoS) developed in Ref. Sen and Guha (Mon Not R Astron Soc 517:518, 2022. https://doi.org/10.1093/mnras/stac2675 ), which considers the possible presence of feebly interacting DM in strange quark stars (SQSs) for the first time. Within the model, feeble interaction between fermionic DM $$\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> and strange quark matter (SQM) is invoked via a vector new physics mediator $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> with coupling strength $$y_{\xi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>y</mml:mi> <mml:mi>ξ</mml:mi> </mml:msub> </mml:math> . The pure SQM is described by the vector MIT Bag model. By varying different EoS parameters, the structural properties viz. the mass, radius and tidal deformability ( $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> ) of the DMSQSs are studied with respect to various astrophysical constraints. We study in detail the f -mode spectra within the Cowling approximation by obtaining the frequencies as a function of mass, compactness and $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> of the star. To the best of our knowledge, this study represents the first analysis of non-radial f -mode oscillations of DMSQSs. Our investigation indicates that the presence of DM and its interaction with SQM has great impact on the f -modes. We show that the f -mode frequencies are larger for DMSQSs, which are largely populated with massive DM fermions, compared to the SQSs. Further, we obtain a linear empirical relation between the f -modes and the average density of the star. We also find that the mass-scaled angular frequency varies universally with compactness and $$\ln {\Lambda }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>ln</mml:mo> <mml:mi>Λ</mml:mi> </mml:mrow> </mml:math> for DMSQSs. Further, our studies indicate that the inclusion of DM in compact stars reduces the deviation of f -mode frequency from general relativistic to Cowling approximation.