Galactic Scaling Rules in a Modified Dynamical Model
  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.
