Faber Jackson RelationEdit

The Faber–Jackson relation is a foundational empirical link in extragalactic astronomy between how bright an elliptical galaxy is and how fast stars orbit in its core. It shows that luminosity and stellar motions move together in a relatively tight pattern, suggesting that the same gravity that binds a galaxy also governs how its stars shine. In practical terms, brighter elliptical galaxies tend to exhibit higher central velocity dispersions. The relation is typically summarized as a power-law, roughly L ∝ σ^4, where L is the luminosity and σ is the stellar velocity dispersion measured in the galaxy’s inner regions. As a compact, data-driven relation, it has long served as a touchstone for understanding galaxy structure and evolution, and as a stepping stone toward more comprehensive scaling relations. From a pragmatic, results-focused perspective, it demonstrates how a relatively simple observational pattern can constrain the complex physics of galaxy formation without requiring a full, detailed model of every star and gas cloud.

The Faber–Jackson relation sits among the most important scaling relations in astronomy, alongside the fundamental plane and the Tully–Fisher relation for spirals. It encapsulates how photometric properties (like luminosity) connect to dynamical properties (like velocity dispersion) in early-type galaxies, and it helps astronomers infer masses and evolutionary histories from observable quantities. In this sense, it provides a bridge between what we can see directly—the light from stars—and what we infer about the gravitational potential that shapes that light.

Overview

Origin and form: The relation was identified in the mid-1970s from a survey of bright elliptical galaxies, revealing a tight correlation between their luminosity and central stellar velocity dispersion. Although the exact slope varies with sample and wavelength, the qualitative outcome—that brighter galaxies tend to have larger σ values—has held up across decades of observations.
Observables and measurements: The luminosity L is measured from photometric data, usually in a specified band, corrected for distance and extinction. The velocity dispersion σ is obtained from spectroscopy, representing the spread of stellar velocities near the galaxy’s center. The combination of these measurements makes the Faber–Jackson relation a practical tool for estimating dynamical mass and testing models of galaxy structure.
Role within larger frameworks: The relation is often described as a projection of the Fundamental Plane, a three-parameter relationship involving luminosity, effective radius, and velocity dispersion that captures the equilibrium structure of early-type galaxies. As a result, L–σ is a simpler, two-parameter cousin of a more complete, multi-dimensional description of galaxy properties.

Key concepts linked to the topic include the central questions of how mass-to-light ratios vary among galaxies, how dark matter and stellar populations influence observed properties, and how the relation evolves over cosmic time and across environments. Related terms to explore include elliptical galaxy, velocity dispersion, luminosity, virial theorem, fundamental plane and mass-to-light ratio.

Historical background

The Faber–Jackson relation arose from early work in the 1970s that sought to connect visible light output with the internal dynamics of galaxies. By compiling spectroscopic velocity dispersions for bright ellipticals and comparing them to their luminosities, Faber and Jackson demonstrated a clear trend: the more luminous a galaxy, the higher the typical velocities of its stars in the central regions. This empirical finding provided strong evidence that the gravitational potential of a galaxy—set by its total mass and concentration—plays a decisive role in shaping both its light and its stellar motions. The discovery has since become a standard reference point in studying how early-type galaxies form and evolve.

In the decades since, large surveys and more sophisticated modeling have refined the relation, quantified its scatter, and tested its applicability across different galaxy cohorts. The basic relationship remains a cornerstone in the broader effort to map how galaxies acquire mass, regulate star formation, and respond to their larger-scale environments.

Physical interpretation

Interpreting the Faber–Jackson relation rests on the virial theorem, which relates a system’s kinetic energy to its gravitational potential energy in a state of dynamical equilibrium. A simplified reading goes as follows: - The dynamical mass within a characteristic radius scales roughly as M ∝ σ^2 R, where R is a measure of the galaxy’s size (for example, the effective radius). - The luminosity L traces the stellar content and, through the mass-to-light ratio, the stellar mass M_*. - If the mass-to-light ratio does not vary dramatically with luminosity, brighter galaxies (larger L) tend to have larger σ because they live in deeper potential wells.

Under these assumptions, one expects a roughly L ∝ σ^4 relation, consistent with the observed trend. In practice, the slope and zero-point depend on various factors: - The stellar population: age and metallicity affect L at fixed mass, altering M/L and shifting the relation. - The mass-to-light ratio: galaxies with higher dark matter fractions or different stellar remnants can change the link between σ and L. - Structural differences: galaxies with different light profiles, anisotropies, or merger histories can exhibit departures from a single universal slope. - Wavelength dependence: measuring L in different photometric bands can yield slightly different slopes because of population and dust effects.

Consequently, the Faber–Jackson relation is best viewed as a robust trend with measurable scatter, not a perfectly universal law. It is a powerful empirical constraint on galaxy formation models, forcing simulations to reproduce both the dynamical structure and the stellar content of early-type systems.

Extensions and related relations

Fundamental plane: The Faber–Jackson relation is one projection of the Fundamental Plane, which ties together luminosity, effective radius, and velocity dispersion into a plane in a three-dimensional parameter space. This broader relation captures more of the structural diversity of early-type galaxies and provides deeper insights into their formation histories.
Mass-to-light ratio variations: Studies of the Faber–Jackson relation motivate investigations into how M/L changes with luminosity and color, informing models of stellar populations and dark matter distribution within galaxies.
High-redshift behavior: Observations indicate evolution in the L–σ relation with cosmic time, reflecting changes in star formation histories, stellar populations, and assembly processes in the early universe.
Dwarf ellipticals and outliers: Not all galaxies follow the same slope. Faint or structurally distinct ellipticals, especially dwarfs, can deviate, revealing a more complex picture of galaxy growth at low masses and in different environments.
Connections to black hole scaling relations: The velocity dispersion that drives the Faber–Jackson relation also features in the M–σ relation, which links the mass of a central supermassive black hole to the host galaxy’s bulge velocity dispersion. These relationships together illuminate how galactic centers coevolve with their host systems.

Controversies and debates

Universality vs. diversity: A central debate concerns how universal the Faber–Jackson relation is across environments (clusters vs fields), galaxy ages, and metallicities. Some studies find systematic departures in certain populations, suggesting that a single power-law cannot capture all elliptical systems.
Role of the IMF and stellar populations: If the initial mass function (IMF) varies with galaxy mass or environment, the resulting mass-to-light ratios could bias the inferred L–σ slope. Critics argue that what looks like a clean dynamical trend might partly reflect population effects rather than pure dynamical structure.
Apparent simplicity vs. underlying complexity: The relation’s elegance stands in tension with the messy reality of galaxy formation, which involves mergers, feedback, gas accretion, and non-spherical dynamics. Some theorists emphasize that a two-parameter or multi-parameter description (as in the Fundamental Plane) better captures observed diversity than a single L–σ scaling, especially when precision is required for distance estimates or mass budgeting.
Selection effects and measurement biases: As with many empirical relations, the slope and scatter can be sensitive to how galaxies are selected, how luminosities are measured, and how σ is aperture-corrected. Critics caution that incomplete or biased samples can masquerade as a genuine trend or mask real physical variation.
Alternative theories and interpretive frameworks: While the standard picture uses dark matter and cold gas physics to explain the relation, some alternative gravity frameworks propose different dynamical interpretations. Proponents of such approaches sometimes argue that careful scrutiny of scaling relations can illuminate fundamental physics, though mainstream cosmology already fits the data well across a broad range of galaxy scales.

Across these debates, the mainstream view remains that the Faber–Jackson relation is a robust, informative empirical relation that constrains models of elliptical galaxies and their evolution. It is not the final word on galaxy structure, but it is a remarkably durable tool for connecting observable light to the gravitational potential that shapes stellar motions.