The Photometric Plane of Elliptical Galaxies
  The Sersic r^(1/n) index n of an elliptical galaxy (or bulge) has recently been shown to correlate strongly (r=0.8) with a galaxy's central velocity dispersion. This index could therefore prove extremely useful and cost-effective (in terms of both telescope time and data reduction) for many fields of extragalactic research. It is a purely photometric quantity which apparently not only traces the mass of a bulge but has additionally been shown to reflect the degree of bulge concentration. This paper explores the affect of replacing the central velocity dispersion term in the Fundamental Plane with the Sersic index n. Using a sample of early-type galaxies from the Virgo and Fornax clusters, various (B-band) `Photometric Planes' were constructed and found to have a scatter of 0.14-0.17 dex in log(r_e), or a distance error of 38-48% per galaxy (the higher values arising from the inclusion of the S0 galaxies). The corresponding Fundamental Plane yielded a 33-37% error in distance for the same galaxy (sub-)samples (i.e. ~15-30% less scatter). The gains in using a hyperplane (i.e. adding the Sersic index to the Fundamental Plane as a fourth parameter) were small, giving a 27-33% error in distance, depending on the galaxy sample used. The Photometric Plane has been used here to estimate the Virgo-Fornax distance modulus; giving a value of \Delta\mu=0.62(+/-0.30) mag (cf. 0.51(+/-0.21), HST Key Project on the Extragalactic distance Scale). The prospects for using the Photometric Plane at higher redshift appears promising. Using published data on the intermediate redshift cluster Cl 1358+62 (z=0.33) gave a Photometric Plane distance error of 35-41% per galaxy. 
Alister W. Graham