Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds

The Aschenbach effect, the increasing behavior of the angular velocity of a timelike circular orbit with its radius coordinate, is found to extensively exist in rapidly spinning black holes to a zero-angular-momentum observer. It also has potential observation in the high-frequency quasi-periodic oscillations of X-ray flux. However, observing such effect remains to be a challenge in static and spherically symmetric black hole backgrounds. In this paper, we mainly focus on such issue. Starting with the geodesics, we analytically study the underlying properties of the timelike circular orbits, and show the conditions under which the Aschenbach effect survives. It is shown that the presence of the static point orbits and stable photon spheres would be the indicator of the Aschenbach effect. We then apply it to three characteristic black holes exhibiting different features. The results state that this effect is absent for both the Schwarzschild and Reissner-Nordstr\"{o}m black holes. While, for the dyonic black hole in quasi-topological electromagnetics, there indeed exists the Aschenbach effect. This provides a first example that such effect exists in a non-spinning black hole background. Moreover, it also uncovers an intriguing property for understanding the black holes in nonlinear electrodynamics.