Investigating the vertical distribution of the disk as a function of radial action: Results from simulations

Aims. Previous research has established a relationship between radial action and scale height in Galactic disks, unveiling a correlation between radial and vertical heating. This finding poses a challenge to our existing comprehension of heating theories and consequently encodes crucial insights into the formation and heating history of Galactic disks. In this study, we perform N-body simulations with the aim of verifying the existence of this correlation between radial action and scale height, thereby enhancing our comprehension of the heating history of Galactic disks. Methods. We conducted a simulation featuring a disk embedded within a static dark matter halo potential, and systematically analyzed the correlation between radial action and scale height across every snapshot. Furthermore, we augmented this simulation by incorporating massive, long-lasting particles to examine their impact on the aforementioned relationship. Results. We find that the relationship between radial action and scale height in our simulations can be described by the same functional form observed in previous work. Furthermore, the relationships derived from our simulations align well with those of the Galactic thin disk. However, they do not coincide with the inner thick disk but exhibit a rough correspondence with the outer thick disk, suggesting the possibility that additional heating mechanisms may be required to explain the inner thick disk. We also find that the mean radial action and scale height undergo rapid increases during the initial stages of the simulation, yet remain relatively unchanged as the disk evolves further. By tracing example particles, we uncover a correlation between radial and vertical heating in our simulation: as a particle in the disk gains or loses radial action, its vertical motion tends to oscillate on a more or less extended orbit, accompanied by a tendency to migrate outward or inward, respectively. The massive, long-lasting particles in our simulation contribute to disk heating by solely enhancing the rate of increase in scale height with radial action, while maintaining the functional form that describes the relationship between these two variables. Conclusions. We have successfully replicated the functional form previously reported in research, thereby confirming a correlation between radial and vertical heating. This achievement enhances our understanding of heating theories in galactic disks.