We show that it is possible to define a purely Photometric Fundamental Plane ( PFP ) for early–type galaxies .
This relation is similar to the standard Fundamental Plane ( FP ) , and is obtained by replacing the velocity dispersion parameter with the difference between the magnitude of a galaxy and that of the mode of the Gaussian luminosity function of E and S0 galaxies .
The use of magnitude differences as a third parameter allows a significant reduction in the dispersion of the PFP relation when compared to the Kormendy relation between effective radius and effective surface brightness , but limits the application of this method to galaxies in clusters .
The dispersion of \sim 0.10 in \log R _ { e } about the mean plane in the PFP is comparable to that of the standard FP .
However , the use of the mode of the luminosity function to compute the magnitude differences introduces a systematic uncertainty in the derivation of the PFP relation zero-point , so that its accuracy for distance determinations does not scale with the square root of the number of objects used to perform the fit .
The method is also vulnerable to any bias that might affect the estimate of the mode of the luminosity function .
If however the mode of the luminosity function can be reliably determined , the PFP relation can provide distance estimates with an accuracy comparable to the FP relation , with the advantage that the use of photometric parameters alone reduces drastically the observational requirements of the PFP , in comparison with those of the FP relation .
This practical advantage makes the PFP a very economical distance indication method .