The Kormendy Relation

Correlation between re, the radius that contains half of the luminosity in a de Vaucouleurs law fit to the surface brightness profile of an elliptical galaxy and Be, the surface brightness at re. A least-squares fit to the points is shown by the straight line and equation. This is the original version of the correlation found in Kormendy (1977). A later version based on more galaxies is shown in Hamabe & Kormendy (1987).

A major theme of my work has been the structure and dynamics of bulges and elliptical galaxies. One early aim was the search for correlations between parameters measuring the characteristic sizes, densities, and velocity dispersions of galaxies. Elliptical galaxies are now known to populate a tilted ``fundamental plane'' in the space of these parameters (Djorgovski & Davis 1987; Faber et al. 1987; Kormendy & Djorgovski 1989). These correlations were initially found via their projections. The first discovered was the Faber-Jackson (1976) correlation between luminosity and velocity dispersion. The second was the above correlation between the de Vaucouleurs (1948) effective radius r_e and surface brightness B_e (or, equivalently, the mean surface brightness inside r_e). It says that larger elliptical galaxies have lower densities. Since brighter galaxies are bigger, a more general statement is that more luminous ellipticals are fluffier: they have larger sizes and lower densities. This is a correlation that galaxy formation theories must explain. One implication is that low-luminosity elliptical galaxies formed with more gaseous dissipation than did giant ellipticals.

The above correlation was found in my thesis (Kormendy 1977) and is now often referred to as the Kormendy relation. Because it does not require velocity dispersion measurements, it is useful for Tolman surface brightness and galaxy evolution tests as a function of redshift (e. g., Pahre et al. 1996; Fasano et al. 1997; Moles et al. 1998; Barger et al. 1998; Ziegler et al. 1999). The fundamental plane is a result of the Virial theorem, the shallow dependence of mass-to-light ratio on luminosity, and several minor effects (see Kormendy & Djorgovski 1989 for a review).

Barger, A. J., et al. 1998, ApJ, 501, 522
de Vaucouleurs, G.~1948, Ann. d'Astrophys., 11, 267
Djorgovski, S., & Davis, M. 1987, ApJ, 313, 59
Faber, S. M., & Jackson, R. E. 1976, ApJ, 204, 668
Faber, S. M., et al. 1987, in Nearly Normal Galaxies: From the Planck Time to the Present, ed. S. M. Faber (New York: Springer), 175
Fasano, G., Christiani, S., & Arnouts, S. 1997, in The Hubble Deep Field, ed. M. Livio, S. M. Fall, & P. Madau (Baltimore: STScI), 26
Hamabe, M., & Kormendy, J. 1987, in IAU Symposium 127, Structure and Dynamics of Elliptical Galaxies, ed. T. de Zeeuw (Dordrecht: Reidel), 379
Kormendy, J. 1977, ApJ, 218, 333
Kormendy, J., & Djorgovski, S. 1989, ARA&A, 27, 235
Moles, M., et al. 1998, ApJ, 495, L31
Pahre, M. A., Djorgovski, S. G., & de Carvalho, R. R. 1996, ApJ, 456, L79
Ziegler, B. L., et al. 1999, A&A, 346, 13

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