Units

With regards to Toomre and Toomre's original paper, the units of measurement that will be used in all calculations will be as follow:

distance -- kiloparsec, where $1 \hspace{2 mm} kpc = 3.08567758e19 \hspace{2 mm} m$

time -- years, where $1 \hspace{2 mm} billion \hspace{1 mm}yr = 3.1556926e16 \hspace{2 mm} s$

mass -- solar mass, where $1 \hspace{2 mm} M_{\odot} = 1.9891e30 \hspace{2 mm}kg$

To have these units work in the equations given, the gravitational constant gamma will also have to be converted:

$\gamma = 6.67384e\text{-}11 \hspace{1 mm} \frac{m^{3}}{kg\cdot s^{2}}\left(\frac{kpc }{3.08567758e19\hspace{1 mm}m}\right)^{3}\left(\frac{1.9891e30\hspace{1 mm}kg}{M_{\odot}}\right)\left(\frac{3.1556926e16\hspace{1 mm}s}{billion \hspace{1 mm}yr}\right)^{2} = 4.4983169634398596e\text{-}06\frac{kpc^{3}}{M_{\odot}\cdot billion \hspace{1 mm} yr^{2}}$