Tully–Fisher relation

Tully–Fisher relation
Astro533Fa10 · Public domain · source
Name	Tully–Fisher relation
Discovered	1977
Discoverers	Richard Brent Tully, J. Richard Fisher
Domain	Extragalactic astronomy
Related	Faber–Jackson relation, Hubble law, baryonic Tully–Fisher relation

Tully–Fisher relation is an empirical correlation between the intrinsic luminosity of spiral galaxies and their rotational velocity, widely used as a distance indicator and probe of galaxy formation. The relation links observable kinematic measures from rotation curves to photometric measures across bands, informing studies of galaxy scaling relations, dark matter, and cosmological distance ladders. It remains central to observational programs and theoretical models that involve galaxy dynamics, halo structure, and baryonic processes.

History and discovery

The relation was first published by Richard Brent Tully and J. Richard Fisher in 1977 following observational work that drew on prior measurements by Vera Rubin, Kent Ford, Albert Bosma, and Martin Schwarzschild using optical spectroscopy and radio astronomy facilities such as the Arecibo Observatory and the Very Large Array. Early calibrations referenced distance estimates from Edwin Hubble, Walter Baade, Harlow Shapley, and the Cepheid work of Henrietta Leavitt as refined by Allan Sandage and the Hubble Space Telescope Key Project led by Wendy Freedman. Subsequent studies by Sidney van den Bergh, François Schweizer, and Sandra Faber compared the relation to the contemporaneous Faber–Jackson relation for elliptical galaxies, while collaborations involving the Sloan Digital Sky Survey, Two Micron All Sky Survey, and GALEX refined photometric band dependencies. The historical development engaged researchers affiliated with institutions such as the Carnegie Institution, Palomar Observatory, Mount Wilson Observatory, and the Royal Greenwich Observatory.

Physical basis and theoretical interpretations

Interpretations trace to the virial theorem applied within the context of dark matter halos discussed by Vera Rubin, Fritz Zwicky, and Jeremiah Ostriker, and to galaxy formation models by James Peebles and Simon White. Semi-analytic models developed by Carlos Frenk, Marc Davis, and Nick Kaiser tie the scaling to Lambda Cold Dark Matter cosmology explored by the Planck collaboration and the Wilkinson Microwave Anisotropy Probe teams. Feedback processes invoked by researchers including Christopher McKee, Jeremiah Ostriker, and Rachel Somerville, and star formation prescriptions from Robert Kennicutt and Eve Ostriker, modulate the luminous mass that appears in the relation. The role of modified gravity proposals by Mordehai Milgrom and Jacob Bekenstein offers an alternate interpretation that connects the slope and zero point to fundamental dynamics rather than dark matter halos, intersecting debates involving the European Southern Observatory, Harvard–Smithsonian Center for Astrophysics, and Max Planck Institute researchers.

Measurement techniques and observational calibration

Empirical determinations use 21 cm neutral hydrogen spectroscopy from facilities like Arecibo, Green Bank Telescope, and Parkes, alongside optical rotation curves from Keck Observatory, the Very Large Telescope, and the Hubble Space Telescope. Photometric calibration spans bands from the Sloan Digital Sky Survey, 2MASS near-infrared, Spitzer Space Telescope mid-infrared, and GALEX ultraviolet, with zero-point anchoring via Cepheid variables measured by teams including the Hubble Key Project and the Carnegie Hubble Program. Techniques include linewidth measures (W20, W50), resolved rotation curve fitting used by Vera Rubin-era spectrographs, and integral field spectroscopy from instruments on the European Southern Observatory and Gemini Observatory. Calibration efforts often involve distance anchors such as the Large Magellanic Cloud, Andromeda (M31), and nearby groups cataloged by the Local Group studies and the Cosmicflows project led by R. Brent Tully.

Applications in extragalactic astronomy and distance scale

The relation underpins distance measurements for studies by the Hubble Space Telescope teams, the Supernova Cosmology Project, and the Carnegie Supernova Project, contributing to determinations of the Hubble constant pursued by teams at the Space Telescope Science Institute and the National Radio Astronomy Observatory. It aids mapping of peculiar velocities in the Local Group, Virgo Cluster, and Coma Cluster, informing large-scale structure analyses by the 2dF Galaxy Redshift Survey and the Sloan Digital Sky Survey. Applications extend to mass modeling in halos examined by groups at the Kavli Institute and Institute for Advanced Study, to environmental dependence studies in clusters observed by the European Southern Observatory, and to cross-calibration with Type Ia supernova distances used by the High-Z Supernova Search Team and the Supernova Legacy Survey.

Variants and extensions (e.g., baryonic Tully–Fisher)

Variants include the baryonic Tully–Fisher relation developed by Stacy McGaugh and collaborators, which replaces luminosity with total baryonic mass measured through HI surveys like ALFALFA and molecular gas studies from the Atacama Large Millimeter/submillimeter Array. Multi-band and stellar-mass Tully–Fisher relations exploit data from 2MASS, Spitzer, and the Wide-field Infrared Survey Explorer, while modifications addressing low-surface-brightness galaxies and dwarf systems reference observational programs by Michael Disney, Leo Blitz, and Carole Mundy. Theoretical extensions connect to halo abundance matching frameworks formulated by Andrew Benson, Risa Wechsler, and Peter Behroozi and to hydrodynamic simulations by the Illustris, EAGLE, and FIRE collaborations at institutions including MIT, Princeton University, and University of California campuses.

Limitations, uncertainties, and systematic effects

Systematics arise from inclination corrections using morphological studies by Gérard de Vaucouleurs and Allan Sandage, internal extinction corrections tied to dust models from B. T. Draine and astronomers at the Jet Propulsion Laboratory, and sample selection biases traced by the Cosmicflows and SFI++ teams. Environmental effects noted in cluster studies by Giuseppe Bertin and John Huchra, rotation-curve asymmetries documented by Janice Lee and Judith Irwin, and variations in stellar mass-to-light ratios discussed by Scott Trager introduce scatter. Cosmological parameter dependence links uncertainties to results from the Planck Collaboration, Supernova Cosmology Project, and the Dark Energy Survey, while alternative-gravity interpretations engage tests proposed by the European Space Agency and national observatories that continue to probe consistency across surveys.

Category:Extragalactic astronomy