### Question --- What is the “Faber-Jackson relation” for elliptical galaxies? How is this different than the "fundamental plane" for elliptical galaxies? ### Answer --- ##### What is the “Faber-Jackson relation” for elliptical galaxies? ![[Velocity Dispersion#Faber-Jackson Relation]] ##### How is this different than the "fundamental plane" for elliptical galaxies? Large scatter in the Faber-Jackson relationship for different types of population lead to the development of the "fundamental plane" which incorporates a 3rd independent parameter $R_e$ called the "effective radius". FJ is then a projection of this relationship down the $R_e$ axis. The [[Velocity Dispersion#Faber-Jackson Relation]] has a large scatter ($L-\sigma$ plot) for different types of populations (ranges of galaxy luminosities), where the power ($\gamma$) is dependent on the data fitted. This lead to the development of the "fundamental plane", which incorporates a third independent parameter called the "effective radius" ($R_{e}$). $\text{Fundamental Plane:} \hspace{2cm} L^{\alpha} \; R_{e}^{\beta} \; \sigma^\gamma \propto \text{const}$ The [[Velocity Dispersion#Faber-Jackson Relation]] is then a projection of this plane onto the $R_e$ axis, where $\alpha=1$, $\beta=0$, and $\gamma=\tfrac{1}{4}$ . > [!note] > Different band measurements give slightly different fit values for $\alpha$, $\beta$, and $\gamma$.