Relativistic wormhole surrounded by dark matter halos in symmetric teleparallel gravity

In this article we study the wormhole geometry in the galactic halo region under modified f(Q)$f(\mathcal {Q})$ gravity, especially symmetric teleparallel gravity, where the nonmetricity scalar Q$\mathcal {Q}$ drives the gravitational interaction. The wormhole solutions for the assumed form f(Q)=alpha Q+beta$f(\mathcal {Q})=\alpha \mathcal {Q}+ \beta$ have been presented, where alpha and beta are the model parameters. The assumption of f(Q)$f(\mathcal {Q})$ is based on the fact that its behavior should change with assumed parametric values of alpha as well as beta within specific physical bounds. Two such models are presented based on the physically motivated shape function and energy conditions. We have elaborately shown, via mathematical calculations and graphical plots, the following features in our model: (i) energy conditions, especially NEC, which is very instructive in connection to energy violation in modified gravity theory, (ii) the wormhole solutions in the regime of Navarro-Frenk-White (NFW) density profiles for the galactic halo regions, (iii) treatment with particles moving in closed orbits around the wormholes which exhibit epicyclic frequencies, and (iv) the red-blue shifts of the light coming from the wormhole throat in the vicinity of the dark matter halos. All the results and behaviors are satisfactory as well as interesting.