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| Faber–Jackson | |
|---|---|
| Name | Faber–Jackson relation |
| Field | Astrophysics |
| Introduced | 1976 |
| Founders | Sandra M. Faber, Robert Earl Jackson |
| Related | Fundamental Plane (astronomy), Tully–Fisher relation, Virial theorem |
Faber–Jackson
The Faber–Jackson relation is an empirical correlation linking the luminosity of elliptical galaxies to the stellar velocity dispersion measured in their central regions, first reported by Sandra M. Faber and Robert Earl Jackson in 1976. It played a formative role in extragalactic astronomy by providing a distance indicator and a tool for probing galaxy formation and structure, influencing studies connected with the Virial theorem, Fundamental Plane (astronomy), and scaling relations such as the Tully–Fisher relation. The relation has been refined and critiqued through observations involving instruments and facilities including the Hubble Space Telescope, Keck Observatory, and the Sloan Digital Sky Survey.
The relation emerged from analyses comparing global photometric properties cataloged in surveys like the Third Cambridge Catalogue of Radio Sources era photometry and spectroscopic velocity dispersions compiled in early work at observatories such as Lick Observatory and Palomar Observatory. Seminal follow-ups were carried out by researchers at institutions including California Institute of Technology, University of California, Santa Cruz, and Carnegie Observatories. Subsequent large-sample studies leveraged data from the Two Micron All Sky Survey and the Sloan Digital Sky Survey enabling cross-calibration with distance ladders anchored by the Cepheid variable scale and the Type Ia supernova distance modulus. Development of the Fundamental Plane (astronomy) in the 1980s by groups at Max Planck Institute for Astronomy and University of Cambridge expanded the context for the Faber–Jackson relation.
In its canonical form the Faber–Jackson relation asserts that the luminosity L of an elliptical galaxy scales approximately as a power law of the central stellar velocity dispersion σ, commonly expressed as L ∝ σ^γ, with γ empirically near 4 for luminous ellipticals. Early empirical determinations referenced photometric bands used at Palomar Observatory and calibrations tied to the Johnson–Cousins photometric system and near-infrared bands from Infrared Astronomical Satellite. Variants of the relation substitute total stellar mass M⋆ or dynamical mass estimates derived from integrated spectra obtained with spectrographs on European Southern Observatory telescopes, linking M⋆ ∝ σ^α with exponents adjusted to account for stellar population synthesis results from teams at University of Arizona and Massachusetts Institute of Technology.
The theoretical underpinning connects the observed scaling to applications of the Virial theorem under assumptions of dynamical equilibrium and homologous structure among ellipticals. Combining the virial relation M_dyn ∝ R_e σ^2 with surface brightness relations calibrated to photometric work at Mount Wilson Observatory yields power-law scalings that can reproduce the observed γ when plausible mass-to-light ratio trends from stellar population models developed at Institute for Advanced Study and Princeton University are included. Alternative derivations incorporate dissipation during mergers studied in numerical simulations from groups at Harvard–Smithsonian Center for Astrophysics, Max Planck Institute for Astrophysics, and Lawrence Berkeley National Laboratory, as well as feedback processes modeled by researchers at Space Telescope Science Institute and University of California, Berkeley. The influence of supermassive black holes was explored using scaling relations tied to the M–sigma relation from work at Institut d'Astrophysique de Paris and the Kavli Institute for Cosmology.
Empirical tests have used integral-field spectroscopy from instruments such as SAURON and ATLAS3D to map σ profiles and compare luminosities from imaging by the Hubble Space Telescope and ground-based surveys like SDSS. Large compilations by collaborations associated with 2dF Galaxy Redshift Survey and GAMA (galaxy survey) reveal scatter and systematic trends as a function of environment characterized by membership in systems cataloged by Abell catalogue and cluster studies at European Southern Observatory. Measurements across bands from 2MASS to ultraviolet work by GALEX allowed assessment of stellar population effects, while kinematic decompositions referencing catalogs from Keck Observatory and Very Large Telescope provided checks on rotation-supported systems versus pressure-supported systems that depart from the canonical relation.
The relation has been applied as a secondary distance indicator in efforts tied to the Hubble constant and peculiar velocity field mapping undertaken by teams at Johns Hopkins University and University of Hawaii. It informs models of hierarchical assembly in cosmological simulations run by groups at Center for Computational Astrophysics and ETH Zurich, and constrains baryonic processes implemented in semi-analytic models from Max Planck Institute for Astrophysics and Durham University. The Faber–Jackson scaling is used to infer dynamical masses in studies of compact ellipticals found in surveys conducted by CFHT (Canada–France–Hawaii Telescope) and to compare local relations with high-redshift compact quiescent galaxies observed with the James Webb Space Telescope and Subaru Telescope.
Critiques emphasize intrinsic scatter, dependence on wavelength, and sensitivity to non-homology; these issues were raised in analyses by teams at University of Oxford and University of Tokyo. Observational biases from aperture effects and selection functions in surveys like SDSS and 2dFGRS can distort derived slopes, and inclusion of rotational support in lenticulars cataloged in Uppsala General Catalogue complicates interpretation. The relation’s limited predictive power for low-luminosity dwarf ellipticals and ultracompact dwarfs identified in studies at European Southern Observatory and Gemini Observatory has motivated replacement or augmentation by the Fundamental Plane (astronomy) and multi-parameter scaling relations developed at Max Planck Institute for Astronomy and Princeton University.