An Economical Technique for the Estimate of Galaxy Distances: the Photometric Fundamental Plane

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 ∼ 0.10 in logRe 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. Present address: European Southern Observatory, Karl-Schwarzschild-Straβe 2, D-85748, Garching bei München, Germany. The National Astronomy and Ionosphere Center is operated by Cornell University under a cooperative agreement with the National Science Foundation.