Evolution of superthin galaxies under Milgromian dynamics
This work investigates the long-term evolution of the vertical structure of superthin galaxies within the framework of Milgromian dynamics (MOND). By constructing an observationally constrained model of UGC 7321, we test whether its disc can maintain an extremely flattened structure in a MOND gravitational field. We also construct models with different values of the MOND depth index $D_{\rm M}$ to study how the global MOND depth affects disc evolution. We perform three-dimensional hydrodynamical $N$-body simulations using the code Phantom of RAMSES. The evolution of the disc is quantified using $(h_z/R_{\rm D})$, Fourier amplitudes characterizing non-axisymmetric structures and vertical buckling, measures of vertical heating, and the vertical restoring force. In the observationally constrained model of UGC 7321, the galaxy develops a strong bar and undergoes a buckling instability during the early stages of the simulation. The bar strength then decreases, and the system eventually exhibits a weak bar structure. The stellar disc undergoes only limited vertical thickening, and most of the disc remains largely within the superthin regime, $h_z/R_{\rm D}<0.1$, after 5 Gyr. The comparison of models with different $D_{\rm M}$ values suggests that models with lower $D_{\rm M}$ values, associated in our model suite with higher baryonic masses or more compact discs, exhibit stronger vertical heating and more significant disc thickening. By contrast, models with higher $D_{\rm M}$ values, corresponding to lower masses or more diffuse structures, tend to maintain a superthin structure. Overall, the simulation results indicate that superthin discs can remain vertically thin during long-term isolated evolution in MOND, and that the long-term maintenance of superthin structures is influenced, at least partly, by the degree to which a galaxy lies in the low-acceleration regime.