Influence of density-dependent bag function $B(n)$ on strange stars for non-zero strange quark mass ($m_s\mathrm{\ne }0$) in $f(R,T)$ gravity consistent with observational validation

In this work, a new class of solution of the Einstein field equation for an isotropic strange star using the modified Mak-Harko type density profile along with the equation of state as proposed in the MIT bag model and considering finite mass of the strange quark ($m_s$) is presented in the framework of $f(R,T)$ gravity with $f(R,T)=R+2\zeta T$, where, $\zeta$ is the coupling parameter. To incorporate the quark matter hypothesis with a physically viable stellar framework, a baryon number density ($n$) dependent bag function $B(n)$ is analysed, using exponential type parametrisation. The energy per baryon ($E_B$) has been investigated to restrict $B(n)$ and corresponding $n$ within a stable window, specifically satisfying the condition $E_B\le 930.4MeV$, which corresponds to the binding energy of $\text{isotope}[56]Fe$. We note a lower limit of $n$ below which $E_B>930.4MeV$ as $E_B$ increases with the decrease of $n$. This value, however, depends on $m_s$. Additionally, $n$ has a maximum value of $0.36f{m}^{-3}$ irrespective of $m_s$ depending on the range of bag function. All the essential characteristics are satisfactorily fulfilled within the stellar interior for the selected set of parameter space. In this model, the maximum mass and radius are found by solving the TOV equations numerically which yields $M=2.03M_{\odot }$ with a radius of $11.49km$ for $m_s=0MeV$ and $n=0.36f{m}^{-3}$ and $\zeta =-0.1$. It is also noted that the maximum mass and the corresponding radius are the function of $m_s$, $\zeta$ and $n$. The proposed model has been shown to comply with the required energy conditions and satisfies the criterion for dynamical stability, thereby confirming its physical plausibility as a physically consistent stellar model within the parameter space used.