Faberjackson RelationEdit
The Faber–Jackson relation is an empirical scaling relation in extragalactic astronomy that links the luminosity of an elliptical galaxy to the velocity dispersion of its stars in the central regions. In its classic form, brighter galaxies tend to have higher stellar velocity dispersions, often summarized by a power-law form L ∝ σ^4, though the precise slope depends on the sample, wavelength, and measurement aperture. This relationship provides a window into how mass, light, and the dynamical state of a galaxy are connected, and it serves as a practical constraint for models of galaxy formation and evolution. Throughout this article, the key quantities are the luminosity luminosity of an elliptical galaxy and the stellar velocity dispersion velocity dispersion that characterizes motions within the galaxy’s core.
Historically, the relation was quantified by S. M. Faber and R. E. Jackson in 1976, based on spectroscopic observations of bright, nearby early-type galaxies. Their work showed that as the central brightness of an elliptical galaxy increases, its stars move faster on average, yielding a higher velocity dispersion. This finding—now known as the Faber–Jackson relation—became a foundational piece of the broader effort to map how galaxy structure reflects dynamical mass and stellar populations. The original study and subsequent refinements drew on data from local galaxy samples and established a benchmark against which theories of galaxy assembly could be tested. For context and historical development, see the pages on Sandra M. Faber and Robert E. Jackson as well as the broader topic of how early-type galaxies were understood in the late 20th century.
The Faber–Jackson relation is closely connected to the broader framework of the fundamental plane of elliptical galaxies, which links three observables: effective radius, surface brightness, and velocity dispersion. The FJR can be viewed as a projection of this plane onto the luminosity–dispersion plane. Several physical factors contribute to the observed relation and its scatter, including the distribution of stellar orbits, variations in the stellar mass-to-light ratio mass-to-light ratio, and structural differences among galaxies (non-homology) that affect how light traces mass. In warm terms, the relation encodes a link between dynamical mass and emitted light, with implies about how efficiently galaxies convert baryons into stars and how dark matter contributes to the inner potential. See also the concept of the virial theorem virial theorem and its role in connecting kinematics to mass.
Observationally, the FJR has been measured across a range of environments and cosmic epochs, though its exact form depends on the passband used for the luminosity, the aperture over which σ is measured, and the selection of the galaxy sample. In general, measurements in the optical bands yield a steeper slope than those in the near-infrared, reflecting differences in the stellar populations contributing to the light. Modern surveys, such as the Sloan Digital Sky Survey, have expanded the number of galaxies with well-determined L and σ by orders of magnitude, enabling more precise calibrations and exploration of environmental dependencies. The relation remains a useful check on models of galaxy formation, and it continues to be examined in relation to the broader mass–size–luminosity scaling relations that describe early-type galaxies.
Variants and extensions of the Faber–Jackson relation shed light on how galaxies of different masses, ages, and structural properties conform to or diverge from the simple L ∝ σ^4 picture. For example, the relation is often discussed alongside the Tully–Fisher relation, which describes a similar luminosity–kinematic coupling for rotating disk galaxies, highlighting a common theme in galaxy scaling laws. Studies also consider how the FJR integrates with the fundamental plane and how the inclusion of rotation, anisotropic pressure support, and dark matter influences the interpretation of σ as a tracer of total dynamical mass. Observationally, dwarfs and some lenticulars can depart from the bright-end trend, illustrating that the relationship is most robust for a specific class of early-type systems.
Controversies and debates surrounding the Faber–Jackson relation focus on its physical interpretation and its universality. Key questions include how much of the slope and scatter are driven by variations in the stellar mass-to-light ratio, by dark matter content in the inner regions, or by non-homology in galaxy structure. Some researchers emphasize that the relation is a projection of a more comprehensive dynamical plane and must be read in the context of the fundamental plane, while others explore how the relation evolves with redshift, offering clues about the formation histories of massive galaxies. Differences in results can arise from sample selection, wavelength band, and the aperture used to measure σ, underscoring that the FJR is a diagnostic tool whose exact form is contingent on observational choices and galaxy demographics.
Beyond its role as a scaling relation, the Faber–Jackson relation informs several practical and theoretical avenues. It serves as a cross-check for dynamical models of early-type galaxies, constrains the mass-to-light ratio in different stellar populations, and provides a legacy for calibrating distance indicators in systems where independent distance measurements are available. In the ongoing effort to connect photometric properties to dynamical mass, the FJR remains a touchstone for comparing theory with observations and for testing how well current galaxy-formation models reproduce the observed coupling between light and stellar kinematics.