Constraining mass–radius limit of gravitationally decoupled binary compact star mergers PSR J0952-0607 and GW200210 generated by dual matter density profiles

Abstract In this article, we present exact solutions to Einstein’s field equations through a process known as minimally gravitational decoupling (MGD). Our study posits strange quark matter (SQM) as the initial seed source and introduces pseudo-Isothermal (PI) dark matter (DM) as the new source. We derive the metric potentials, deformation functions, and physical quantities of gravitating compact objects, thoroughly analyzing the MGD effect on these quantities. By applying Herrera’s cracking concept and the adiabatic condition, we demonstrate that the anisotropic stellar system we studied, influenced by two interconnected sources, achieves stable equilibrium. Focusing on models related to the mass gap identified in the GW200210 event $$(2.83^{+0.47}_{-0.42})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>83</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.42</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.47</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and the “black widow” pulsar PSR J0952-0607 $$(2.35_{-0.17}^{+0.17})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>35</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.17</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.17</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , the fastest known spinning neutron star in the Milky Way, we constrain the mass–radius relationship and moment of inertia values under the MGD effects within the framework of general relativity (GR). Our findings indicate that the maximum allowable mass tends to increase in the lower mass gap region as the MGD effect parameter $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> and the central DM density $$\sigma _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> rise. Conversely, this maximum mass decreases with an increase in the bag constant $${\mathcal {B}}_g,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> which correlates with the surface density of SQM in our model. Interestingly, when the stellar structure undergoes deformation due to MGD, it responds differently to the density profiles of DM and SQM. Specifically, as $${\mathcal {B}}g$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mi>g</mml:mi> </mml:mrow> </mml:math> increases, SQM tends to inhibit the formation of supermassive compact stars (CSs) governed by MGD and PI-DM. Notably, supermassive CSs can exceed 2 $$M{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:math> for values of $${\mathcal {B}}_g \le 62.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>62.5</mml:mn> </mml:mrow> </mml:math> $$\text {MeV}\,\text {fm}^{-3}.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>MeV</mml:mtext> <mml:mspace/> <mml:msup> <mml:mtext>fm</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> Finally, we conclude that a maximum mass of approximately 3 $$M_{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> in the mass gap region can be attained by incorporating DM and adjusting the MGD effects within the stellar structure under GR. The elevated moment of inertia values suggests a stiffer equation of state (EOS) for the current anisotropic system.