Exploring physical properties of anisotropy dependent self-gravitating massive compact stars in \(f(\mathbb {Q})\) gravity

In this paper, we present anisotropy-dependent well behaved non-singular solutions for static and spherically symmetric self-gravitating compact objects in the framework of \(f(\mathbb {Q})\) gravity assuming the linear form of \(f(\mathbb {Q})=-\beta _1\, \mathbb {Q} - \beta _2\), where \(\beta _1\) and \(\beta _2\) are coupling constants. In particular, we have considered a physical form of metric potential along with the anisotropy factor dependent on the coupling constant K. The field equations are solved to obtain the three different classes of solutions for different ranges of anisotropy parameter K as \(0\le K <1\), \(K=1\), and \(K>1\). The physical behavior of the solution for all cases is analyzed and explored by inspecting physical features, various stability criteria, energy conditions, mass function, etc. successfully with a graphical presentation. In addition, the present model justifies the existence of observed compact objects with masses in the range [2.08 \(M_{\odot }\), 2.83 \(M_{\odot }\)], with the upper value located in the mass gap regime as observed in gravitational wave events such as GW190814 and GW200210. The mass–radius and moment of inertia (MI) relation for all three cases are examined in connection with the observational constraints of the massive stars, which are related to the lower mass gap region. The range of predicted radius of the massive stars involved in GW190814 and GW200210 subject to the three cases are found to be as [11.12 km, 15.72 km] and [11.08 km, 15.55 km] respectively. In connection to mass-gap region, GW190814 (Abbott et al. in ApJ 896:L44, 2020) and GW200210 (Abbott et al. in Phys. Rev. X 13(4):041039, 2023) can possess higher moment of inertia, \(I = 6.56 \times 10^{45}\) g-\(\hbox {cm}^{2}\) and \(I = 7.98 \times 10^{45}\) g-\(\hbox {cm}^{2}\) respectively for \(\beta _1=1.2\) and \(K=1\).