Study of anisotropic quark stars with interacting quark matter in f(R,T) gravity

We explore the structural properties of quark stars (QSs) in a modified gravity theory known as $f(R,T)$ gravity, which introduces a coupling between matter and spacetime geometry, through a basic linear functional form $f(R,T)=R+2\beta T$. Our study focuses on QSs made of interacting quark matter (IQM) as an equation of state. We first derive the modified Tolman-Oppenheimer-Volkoff (TOV) equations for anisotropic matter in a spherically symmetric context and solve them numerically to obtain the structural properties of QSs. Stability is analyzed through static stability analysis, critical adiabatic indices, and sound speed profiles. Using astrophysical constraints from the “black widow” pulsar PSR J0952-0607 and the GW190814 event, we calibrate our model parameters. Our results indicate that with higher $\overline{\lambda }$, both the maximum mass and radius of QSs increase, achieving a maximum mass of over $2M_{\odot }$, peaking at $3.15M_{\odot }$ for a radius of $14.90\text{km}$ at $\overline{\lambda }=0.9$. The maximum compactness also rises to $M/R=0.313$ while adhering to the Buchdahl limit. Additionally, varying β in the range $[-0.2,0.2]$ with fixed parameters shows that lower β values enhance the maximum mass of QSs, reaching $2.65M_{\odot }$ at $\beta =-0.2$, with the compactness remaining around $M/R\approx 0.3$. Furthermore, changes in μ from $[-1.0,1.0]$ significantly affect maximum mass; at $\mu =1.0$, the mass peaks at $3.15M_{\odot }$ and decrease to $2.68M_{\odot }$ at $\mu =0$. The compactness increases with μ, indicating that anisotropic pressure influences the $M-R$ relations. In summary, our findings reveal that the parameters $\overline{\lambda }$, β, and μ play crucial roles in shaping the physical properties of QSs in the $f(R,T)$ gravity framework, consistent with astrophysical observations from pulsars and gravitational wave events.