The Sérsic ( 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 Sérsic 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 cent per galaxy ( the higher values arising from the inclusion of the S0 galaxies ) .
The corresponding Fundamental Plane yielded a 33-37 per cent error in distance for the same galaxy ( sub- ) samples ( i.e . \sim 15-30 per cent less scatter ) .
The gains in using a hyperplane ( i.e .
adding the Sérsic index to the Fundamental Plane as a fourth parameter ) were small , giving a 27-33 per cent 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 \pm 0.30 mag ( cf .
0.51 \pm 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 cent per galaxy .