Charged spherical solution in torsion and matter coupling gravity and influence of torsion parameter and electric charge on compact stars in lower mass gap

In this study, we explore a new exact solution for a charged spherical model as well as the astrophysical implications of the torsion parameter χ1 and electric charge Q on compact stars in lower mass gaps in the $f(\mathcal {T})$ gravity framework. Commencing with the field equations that describe anisotropic matter distributions, we select a well-behaved ansatz for the radial component of the metric function, along with an appropriate formulation for the electric field. The resulting model undergoes rigorous testing to ensure its qualification as a physically viable compact object within the $f(\mathcal {T})$ gravity background. We extensively investigate two factors: χ1 and Q, carefully analyzing their impacts on the mass, radius, and stability of the star. Our analyses demonstrate that our models exhibit well-behaved behavior, free from singularities, and can successfully explain the existence of a wide range of observed compact objects. These objects have masses ranging from $0.85^{+0.15}_{-0.15}$ to 2.67 M⊙, with the upper value falling within the mass gap regime observed in gravitational events like GW190814. A notable finding of this study has two aspects: we observe significant effects on the maximum mass (Mmax) and the corresponding radii of these objects. Increasing values of χ1 lead to higher Mmax (approximately $2.64^{+0.13}_{-0.14}$) and smaller radii (approximately $10.40^{+0.16}_{-0.60}$), suggesting the possibility of the existence of massive neutron stars (NSs) within the system. Conversely, increasing values of Q result in a decrease in Mmax (approximately $1.70^{+0.05}_{-0.03}$) and larger radii (approximately $13.71^{+0.19}_{-0.20}$). Furthermore, an intriguing observation arises from comparing the results: for all values of χ1, non-rotating stars possess higher masses compared to slow-rotating stars, while this trend is reversed when adjusting Q.