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| Faber–Jackson relation | |
|---|---|
| Name | Faber–Jackson relation |
| Field | Astrophysics |
| Discovered | 1976 |
| Discoverers | Sandra Faber; Robert Jackson |
| Related | Fundamental Plane; Tully–Fisher relation; Virial theorem |
Faber–Jackson relation is an empirical correlation observed between the luminosity of an elliptical galaxy and the stellar velocity dispersion in its central regions. It provides a tool for estimating distances and constraining galaxy formation models by linking photometric properties with kinematic measurements. The relation played a central role in establishing scaling relations for early-type galaxies and remains connected to theoretical frameworks developed by researchers at institutions such as Harvard University, California Institute of Technology, and Institute for Advanced Study.
The relation was first reported by astronomers Sandra Faber and Robert Jackson in 1976 following analyses of data from observatories including Palomar Observatory and Lick Observatory. Early work by teams led by figures such as John Kormendy, Allan Sandage, and Gérard de Vaucouleurs contextualized the correlation within morphological studies of ellipticals cataloged in projects like the Third Reference Catalogue of Bright Galaxies and the Revised Shapley-Ames Catalog. Subsequent surveys from facilities such as the Keck Observatory, Very Large Telescope, and the Sloan Digital Sky Survey expanded samples, while theorists at institutions including Princeton University and University of California, Berkeley linked the relation to the virial theorem and hierarchical models advanced by proponents like Simon White and Carlos Frenk.
Quantitatively, the relation is often expressed as L ∝ σ^γ, where L denotes galaxy luminosity and σ denotes central stellar velocity dispersion measured within a defined aperture. In practice, authors adopt forms such as M = a − b log σ for absolute magnitude M, with coefficients calibrated using distance indicators developed by teams at Carnegie Institution for Science and European Southern Observatory. Typical slopes γ found in optical bands range from ~3 to ~5 depending on sample selection and passband choices influenced by photometric systems established by groups at Royal Observatory, Greenwich and Space Telescope Science Institute. The formulation is tied to fitting techniques including least-squares regressions and Bayesian hierarchical models implemented by groups at Max Planck Society and University of Cambridge.
Measurements of σ derive from spectroscopy using instruments like the Keck Low Resolution Imaging Spectrometer, the Hobby-Eberly Telescope spectrographs, and integral-field units developed at European Southern Observatory and Gemini Observatory. Photometry for L or M uses CCD cameras calibrated with standards from Landolt, processed with pipelines maintained by teams at Sloan Digital Sky Survey and Pan-STARRS. Velocity dispersions require template fitting with stellar libraries such as those compiled by Pickles and the MILES project, while surface brightness profiles rely on imaging from observatories like Hubble Space Telescope and Subaru Telescope. Surveys including the ATLAS3D and SAURON projects provided homogenous datasets combining spectroscopy and imaging to refine measurement systematics.
The relation is interpreted as a manifestation of the virial equilibrium of stellar systems, linking gravitational potential traced in works by Oort and Jeans to observed kinematics. The slope and scatter have been explained in models incorporating stellar population effects studied by research teams at Max Planck Institute for Astrophysics and chemical enrichment histories explored by groups at Institute of Astronomy, Cambridge. Cosmological simulations by groups at Millennium Simulation collaborators including Volker Springel and by efforts at Illustris and EAGLE projects reproduce variants of the relation when feedback processes attributed to Active Galactic Nuclei and supernovae modeled by researchers at Stanford University and Columbia University are included.
The relation connects to the Fundamental Plane and complements the Tully–Fisher relation for spiral galaxies. Extensions include replacements of luminosity with stellar mass calibrated by spectral energy distribution fits from groups at European Southern Observatory and the use of dynamical mass proxies developed at Max Planck Institute for Extraterrestrial Physics. Studies comparing cluster-centric samples from Coma Cluster and Virgo Cluster reveal environmental dependencies investigated by teams at University of Michigan and University of Illinois Urbana-Champaign. Black hole scaling relations, such as the M–σ relation advanced by groups at Caltech and University of Texas at Austin, are conceptually linked through central potential depth considerations.
Practically, the relation has been used for distance estimation in extragalactic catalogs compiled by the Extragalactic Distance Database and to constrain luminosity functions measured by collaborations at Space Telescope Science Institute and European Southern Observatory. It aids in population synthesis comparisons performed by researchers at Johns Hopkins University and informs semi-analytic models of galaxy formation developed at Department of Astronomy, Yale University and Dark Cosmology Centre. Observational programs targeting high-redshift samples with Very Large Telescope and Keck Observatory use the relation to trace the evolution of massive early-type galaxies across cosmic time investigated by groups at University of California, Santa Cruz and Carnegie Observatories.
Systematics arise from aperture effects highlighted by studies at University of Hawaii and from selection biases in magnitude-limited samples cataloged by Two Micron All Sky Survey and Sloan Digital Sky Survey. Stellar population gradients, rotation support identified in integral-field surveys like SAURON and ATLAS3D, and contributions from dark matter halos modeled by groups at University of Zurich affect inferred slopes. Photometric band dependence traced by observers at Mount Palomar Observatory and calibration uncertainties tied to standard-star networks such as those compiled by Landolt introduce additional scatter. Robust interpretation requires joint analyses combining kinematics, stellar population synthesis, and cosmological context developed by international collaborations including teams at Max Planck Society and International Astronomical Union.
Category:Extragalactic astronomy