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| Fundamental Plane | |
|---|---|
| Name | Fundamental Plane |
| Type | Empirical relation |
| Epoch | J2000 |
| Major axes | effective radius |
| Velocity dispersion | central velocity dispersion |
| Surface brightness | mean surface brightness within effective radius |
Fundamental Plane The Fundamental Plane is an empirical relation connecting the effective radius, central velocity dispersion, and mean surface brightness of elliptical galaxies and bulges of lenticular galaxies. First identified through observational studies, it provides a tight three-parameter correlation that informs models of galaxy structure, stellar populations, and dark matter. Applications span distance estimation, tests of galaxy formation scenarios, and constraints on scaling relations used in extragalactic surveys.
The Fundamental Plane was revealed by observational programs using instruments at observatories such as the Palomar Observatory, Kitt Peak National Observatory, and the European Southern Observatory and was formalized through analyses by teams associated with institutions like the Harvard–Smithsonian Center for Astrophysics, Max Planck Institute for Astronomy, and California Institute of Technology. Early surveys including the Dressler et al. 1987 sample and the Faber–Jackson relation studies established related two-parameter trends that complemented results from the Sloan Digital Sky Survey and the Two Micron All Sky Survey. Subsequent work by research groups at the University of Cambridge, Princeton University, and University of Oxford refined the plane using samples from the Hubble Space Telescope and ground-based spectrographs.
Observationally, the plane is described using the effective radius (Re), the central stellar velocity dispersion (σ), and the mean surface brightness within Re (⟨I⟩e). Measurements typically exploit imaging from facilities such as the Hubble Space Telescope, Very Large Telescope, and Subaru Telescope combined with spectroscopy from instruments on the Keck Observatory and the Gemini Observatory. Empirical fits often adopt parameterizations in logarithmic form and employ statistical tools developed at institutions like Yale University, Columbia University, and the University of Chicago to derive coefficients and intrinsic scatter. Calibration efforts reference standards from the Cepheid variable distance ladder work associated with the Hubble Space Telescope Key Project and samples from the Local Group and the Virgo Cluster.
Interpretations connect the plane to the virial theorem in the context of collisionless systems described in simulations run on supercomputers at centers like the National Center for Supercomputing Applications and the Lawrence Berkeley National Laboratory. Theoretical models incorporate ideas from researchers affiliated with the Institute for Advanced Study, Princeton Plasma Physics Laboratory, and Los Alamos National Laboratory exploring the roles of dissipative collapse, dry mergers, feedback from Active galactic nucleuss studied by groups at MIT and Columbia University, and secular evolution investigated by teams at the Max Planck Institute for Astrophysics. Stellar population synthesis models by groups at the Padova Observatory and Geneva Observatory address mass-to-light ratio variations, while cosmological hydrodynamical simulations from collaborations like the Illustris Project and EAGLE project examine dark matter halo influence.
Measurement pipelines employ photometric reductions using software developed at laboratories such as the Space Telescope Science Institute and spectral fitting packages from groups at Johns Hopkins University and University of California, Berkeley. Techniques include two-dimensional surface photometry applied in studies by teams at the National Astronomical Observatory of Japan and line-of-sight velocity dispersion measurements from surveys like the ATLAS3D and SAURON projects. Statistical analyses utilize methods from the Carnegie Mellon University and University of Washington communities, including principal component analysis, maximum-likelihood estimation, and Bayesian hierarchical models championed by researchers at University College London and the University of Toronto.
The plane’s coefficients and scatter vary with environment, luminosity, and redshift, with notable differences reported for galaxies in clusters such as the Coma Cluster, Fornax Cluster, and Perseus Cluster versus field samples from the COSMOS survey and DEEP2 Redshift Survey. Studies by teams at the University of Hawaiʻi and Australian National University highlight morphological dependencies between ellipticals cataloged in the Third Reference Catalogue of Bright Galaxies and bulges in lenticular systems examined by researchers at the Max Planck Institute for Extraterrestrial Physics. Environmental trends have been explored in the context of assembly bias discussed at conferences like the American Astronomical Society meetings and workshops hosted by the International Astronomical Union.
The Fundamental Plane serves as a distance indicator used in peculiar velocity studies conducted by collaborations at the Observatoire de Paris and the European Space Agency, aids in constraining mass-to-light ratios relevant to dark matter inferences pursued by researchers at the Kavli Institute for Cosmology, and informs semi-analytic models developed at institutions like the University of Durham and Tel Aviv University. It is exploited in evolutionary studies leveraging deep surveys from the James Webb Space Telescope, Chandra X-ray Observatory, and Spitzer Space Telescope to trace stellar population aging, gas accretion history, and merger-driven growth described in papers from teams at the Carnegie Institution for Science.
Limitations arise from sample selection effects in catalogues such as the Sloan Digital Sky Survey and photometric calibration uncertainties tied to instruments from the European Southern Observatory and National Optical Astronomy Observatory. Systematics include aperture effects in spectroscopy addressed by groups at the Max Planck Institute for Astronomy, stellar initial mass function uncertainties debated in symposia at the Royal Astronomical Society, and projection effects emphasized by theorists at the Institute of Astronomy, Cambridge. Ongoing work by consortia including SDSS-IV and teams at the Harvard & Smithsonian aims to quantify biases and reduce scatter to improve cosmological and evolutionary inferences.
Category:Extragalactic astronomy