Galactic Scaling Rules in a Modified Dynamical Model

Abstract: Schulz (2017) galactic scaling rules, which include baryonic Tully-Fisher relation, have been surveyed in this work within the context of a modified dynamical model. These scaling relations are derived by employing the virial theorem and applying equilibrium and stability conditions. The scaling rules are also obtained by dimensional analysis of an integral relation between surface density and circular velocity of disk galaxies. To check the validity of the scaling relations based on observational data, we have defined, based on the properties of the model, the proper equilibrium size $R_{eq}$ and equilibrium velocity $V_{eq}$ of systems. By employing these measures of length and velocity, SPARC data ( Lelli et al. 2016a ) is used to analyze the results. The viability of the scaling relations is tested and it is shown that, compared to some other measures of length and velocity, $R_{eq}$ and $V_{eq}$ provide the closest fits to the theoretical predictions. We have compared our results with prior works and have concluded that the set of baryonic Tully-Fisher relation plus mass-size relation ( or mass-velocity ) provides an appropriate description of the general characteristics of the systems. Lastly, it is shown that these scaling relations predict a certain evolution of galactic properties with redshift. This behavior provides a chance to examine the cosmic evolution of the present modified dynamical model in future works.