Fundamental plane (elliptical galaxies)

Lore & Background

The fundamental plane emerged from empirical correlations among normal elliptical galaxies. An early correlation showed that larger galaxies have fainter effective surface brightnesses, expressed as R_e ∝ ⟨I⟩_e^{-0.83±0.08} (Djorgovski & Davis 1987). The Faber–Jackson relation (Faber & Jackson 1976) demonstrated that more luminous elliptical galaxies have larger central velocity dispersions, with L_e ∼ σ_o^4. Because luminosity correlates with effective radius, central velocity dispersion is positively correlated with effective radius. An early use of the fundamental plane is the D_n−σ_o correlation (Dressler et al. 1987), which relates the diameter within which the mean surface brightness is 20.75 μ_B to the central velocity dispersion, with a scatter of 15% between galaxies.

Reader's Guide

The fundamental plane is useful because it allows astronomers to estimate the distance to elliptical galaxies. By measuring observable quantities such as surface brightness and velocity dispersion—both independent of the observer's distance—one can estimate the effective radius in kiloparsecs. Knowing the linear size of the effective radius and measuring its angular size, the distance can be determined through the small-angle approximation. This is significant because determining distances to galaxies is a difficult task in astronomy. The plane also provides a framework for understanding how properties like luminosity, mass, and metallicity are interconnected in normal elliptical galaxies, and it serves as a tool for testing theories of galaxy formation and evolution.

Did You Know?

• The fundamental plane is usually expressed as a relationship between effective radius, average surface brightness, and central velocity dispersion.
• The D_n−σ_o correlation has a scatter of 15% between galaxies.
• By measuring surface brightness and velocity dispersion, one can estimate the effective radius of a galaxy in kiloparsecs.

Hubble's Classification and the Elongation Puzzle

Edwin Hubble introduced elliptical galaxies as one of three principal galaxy classes in his 1936 work The Realm of the Nebulae, placing them alongside spirals and lenticulars. Within the elliptical family, Hubble devised a numerical system based on how stretched a galaxy's image appears. The classification number is calculated by multiplying ten by one minus the ratio of the minor axis to the major axis of the galaxy's isophotes. A perfectly round galaxy scores zero, earning the designation E0, while increasingly elongated specimens climb toward E7. Hubble himself acknowledged that this shape-based scheme conflates a galaxy's true geometry with the viewing angle from Earth, meaning some objects labeled E0 might actually be elongated structures seen face-on. Decades later, spectral observations revealed that galaxies classified as E4 through E7 are frequently misidentified lenticular galaxies whose disks are tilted relative to our line of sight, showing measurable stellar rotation. This discovery complicated the clean three-class picture Hubble originally proposed and highlighted the difficulty of distinguishing genuinely featureless ellipsoids from disk systems seen at unfavorable angles.

Stellar Populations and the Globular Cluster Connection

Elliptical galaxies are overwhelmingly dominated by old, low-mass stars, giving them a distinctly reddish hue compared to the bluer populations found in spiral systems. Their interstellar medium is remarkably sparse, containing very little gas or dust, which means star formation is essentially dormant under normal conditions. This scarcity of raw material also explains why open star clusters and young stellar groups are nearly absent. The one notable exception to this quiescence occurs during galactic mergers, when brief bursts of star formation can be triggered. Large ellipticals are typically encircled by extensive systems of globular clusters, and these clusters tend to fall into two distinct populations: one group is redder and metal-rich, while the other is bluer and metal-poor. This bimodal distribution hints at complex formation histories, possibly involving the accretion of smaller galaxies over cosmic time. The overall dynamical behavior of ellipticals resembles that of the bulges found in disk galaxies, and both populations are well described by Sersic's law for luminosity profiles, suggesting they may share common physical origins, though this connection remains debated among astronomers.

Central Black Holes and the M–sigma Relation

A defining feature of massive elliptical galaxies is the presence of a supermassive black hole at their core. Systematic observations spanning 46 elliptical galaxies, 20 classical bulges, and 22 pseudobulges have confirmed that each of these objects harbors a central black hole, making this association remarkably universal. The mass of the black hole is not arbitrary; it is tightly correlated with the mass of the host galaxy. This relationship is captured by the M–sigma relation, which links the velocity dispersion of stars orbiting the galactic center to the mass of the black hole they encircle. One of the most celebrated examples is M87 (NGC 4486), whose central supermassive black hole became the first black hole ever directly imaged by the Event Horizon Telescope. The stars within elliptical galaxies follow somewhat random, three-dimensional orbits around this central mass, in stark contrast to the orderly, flat disk orbits characteristic of spiral galaxies. This structural difference underscores that ellipticals are fundamentally three-dimensional systems without the organized, flat structure seen in spirals.

Extraordinary Range of Size and Cosmic Distribution

Elliptical galaxies span an extraordinary range of sizes, broader than any other galaxy class. At the small end, dwarf ellipticals may contain only tens of millions of stars and can be no larger than a typical globular cluster, yet they still harbor considerable dark matter absent in those clusters. At the opposite extreme, supergiant ellipticals—classified as type cD—can exceed one hundred trillion stars, with diameters stretching beyond 700,000 light years and masses approaching 10 to the 13th solar masses. Examples include Hercules A, IC 1101 as the central galaxy of Abell 2029, and ESO 383-76, one of the largest known galaxies. In terms of cosmic distribution, ellipticals are not the dominant galaxy type overall but are preferentially concentrated near the centers of galaxy clusters and in compact groups. In the Virgo Supercluster, they account for roughly 10 to 15 percent of all galaxies. Maffei 1 stands out as the closest giant elliptical to our own Milky Way, while NeVe 1 is the source of the Ophiuchus Supercluster eruption, the most powerful astronomical event yet identified.

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