Researchers perform numerical simulations of the BEC wave function based on first principles to determine if quantized vortices exist in these systems.

In this study, the BEC images did indeed show the presence of quantized vortices. In addition, the visualization also discovered an unanticipated structure of concentric vortex rings, shown in Fig.

Because it can be shown using standard definition of Hubble law that redshift quantization implies quantized distance between galaxies in the same cluster, then one could say that this equation of quantized distance (11) is a result of topological quantized vortices (9) in astrophysical scale [5]; and it agrees with Gross-Pitaevskii (quantum phion condensate) description of CMB spectrum [1].

Now it is clear from (15) that quantized vortices could be formed by different source of flux.

And because it corresponds to graph kinematic [25], generalized Bohr-Sommerfeld quantization rule for quantized vortices (22) in astrophysical scale could be viewed as signature of "super-graph"quantization.

It is worth noting here, because vortices could be defined as elementary objects in the form of stable topological excitations [4], then equation (6) could be interpreted as Bohr-Sommerfeld-type quantization from topological quantized vortices. Fischer [4] also remarks that equation (6) is quite interesting for the study of superfluid rotation in the context of gravitation.

Their argument was based on propagation torsion model for quantized vortices [23].