Particle motion and QPOs around Euler-Heisenberg black hole immersed in cold dark matter halo

We explore the motion of particles in the vicinity of an Euler-Heisenberg black hole immersed in a cold dark matter halo, focusing on how the black hole parameters influence particle dynamics. This black hole solution is characterized by five parameters, namely, the black hole mass M, the feature radius R, the parameter ρ describing the density of the cold dark matter halo, the quantum electrodynamics parameter α, and the black hole charge Q. We confine ourselves to an equatorial plane and examine the stability of equatorial circular orbits with the help of the effective potential. The analytical mathematical expressions for the energy and the angular momentum of circular orbits have been computed. We have also examined the innermost stable circular orbits. The effective force acting on the particles is explored. The epicyclic oscillations of particles in proximity to stable circular orbits have been examined, and the phenomenon of periastron precession has been addressed. Additionally, we examine the collision of particles and the center of mass energy in proximity to the black hole's horizon. The model parameters significantly affect the motion of the particles. Finally, we compare the particle dynamics surrounding a Euler-Heisenberg black hole within a cold dark-matter halo to those around a Schwarzschild black hole within a cold dark-matter halo and a Schwarzschild black hole devoid of a cold dark matter halo.