Astron. Astrophys. 321, 111-122 (1997)

The fundamental plane of early-type galaxies: non-homology of the spatial structure ^*

Ph. Prugniel and F. Simien

CRAL-Observatoire de Lyon (CNRS: UMR 142), F-69561 St-Genis-Laval Cedex, France

Received 26 April 1996 / Accepted 12 September 1996

Abstract

Parametrizing their light distribution with a Sérsic profile, we show that the non-homology in the structure of early-type galaxies has a measurable incidence on their scaling relations. Indeed, the Sérsic exponent (i.e., the shape of the photometric profile) correlates with the residuals to the Fundamental Plane. This correlation is in excellent agreement with the theoretical expectation for isotropic galaxies.

Adding together the contributions of: (i) the stellar population, (ii) the rotational support, and (iii) the non-homology, fully accounts for the tilt of the Fundamental Plane. This supports the hypothesis of a constant stellar to dynamical mass ratio in the luminous region of early-type galaxies.

We confirm the existence of relations between the Sérsic exponent, n, and the effective radius or the absolute magnitude, and we give indications for a saturation of this index for the bright () or large ( kpc) galaxies at a value compatible with the de Vaucouleurs law ().

Key words: galaxies: elliptical & lenticular, cD galaxies: fundamental parameters galaxies: general galaxies: photometry galaxies: kinematics and dynamics

* Based in part on observations collected at the Observatoire de Haute-Provence.

Send offprint requests to: F. Simien

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Contents

• 1. Introduction
  • 1.1. non-linearity of the scaling relations
  • 1.2. Coupling between the scaling relations
  • 1.3. Outline of the paper
• 2. Sample and data
  • 2.1. Sample
  • 2.2. The photometric parameters
• 3. Standard equation of the Fundamental Plane
  • 3.1. Combined stellar-population indicator
  • 3.2. The Fundamental-Plane equation including the stellar-population effect
• 4. Effect of the non-homology
  • 4.1. Correlations between , and n
  • 4.2. Correlation between the FP residuals and n
  • 4.3. The tilt of the Fundamental Plane
• 5. Expected effect of the non-homology
• 6. Discussion and conclusions
  • 6.1. The scaling relations for galaxies
  • 6.2. The compact and diffuse elliptical galaxies
  • 6.3. The Fundamental Plane of globular clusters
  • 6.4. Conclusion
• Acknowledgements
• Appendix A
• • Appendix A: circular-aperture growth curves for a Sérsic profile
  • Appendix B: deprojection and binding energy of the Sérsic profile
    • B.1. Deprojection of the density profile
    • B.2. Scaling relation for the gravitational energy
    • B.3. Scaling relation for the kinetic energy
• References

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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