Tully–Fisher relation

History

The connection between rotational velocity measured spectroscopically and distance was first used in 1922 by Ernst Öpik to estimate the distance to the Andromeda Galaxy. In the 1970s, Balkowski, C., et al. measured 13 galaxies but focused on using the data to distinguish galaxy shapes rather than extract distances. The relationship was first published in 1977 by astronomers R. Brent Tully and J. Richard Fisher. The luminosity is calculated by multiplying the galaxy's apparent brightness by 4\pi d^2, where d is its distance from Earth, and the spectral-line width is measured using long-slit spectroscopy.

A series of collaborative catalogs of galaxy peculiar velocity values called CosmicFlow uses Tully–Fisher analysis; the Cosmicflow-4 catalog has reached 10000 galaxies. Many values of the Hubble constant have been derived from Tully–Fisher analysis, starting with the first paper and continuing through 2024.

Subtypes

Several different forms of the TFR exist, depending on which precise measures of mass, luminosity or rotation velocity one takes it to relate. Tully and Fisher used optical luminosity, but subsequent work showed the relation to be tighter when defined using microwave to infrared (K band) radiation (a good proxy for stellar mass), and even tighter when luminosity is replaced by the galaxy's total stellar mass. The relation in terms of stellar mass is dubbed the "stellar mass Tully Fisher relation" (STFR), and its scatter only shows correlations with the galaxy's kinematic morphology, such that more dispersion-supported systems scatter below the relation. The tightest correlation is recovered when considering the total baryonic mass (the sum of its mass in stars and gas). This latter form of the relation is known as the baryonic Tully–Fisher relation (BTFR), and states that baryonic mass is proportional to velocity to the power of roughly 3.5–4.

In the dark matter paradigm, a galaxy's rotation velocity (and hence line width) is primarily determined by the mass of the dark matter halo in which it lives, making the TFR a manifestation of the connection between visible and dark matter mass. In Modified Newtonian dynamics (MOND), the BTFR (with power-law index exactly 4) is a direct consequence of the gravitational force law effective at low acceleration.

The analogues of the TFR for non-rotationally-supported galaxies, such as ellipticals, are known as the Faber–Jackson relation and the fundamental plane.

References

References

1. Said, Khaled. (2023-10-24). "Hubble Constant Tension".
2. Opik, Ernst. "An estimate of the distance of the Andromeda Nebula." Astrophysical Journal, 55, 406–410 (1922) 55 (1922).
3. (1977). "A New Method of Determining Distances to Galaxies". [[Astronomy and Astrophysics]].
4. (2020-10-23). "Cosmicflows-4: The Catalog of ∼10,000 Tully–Fisher Distances". The Astrophysical Journal.
5. (2022). "The Cen A galaxy group: Dynamical mass and missing baryons". Astronomy & Astrophysics.
6. (2021-11-01). "The Baryonic Tully–Fisher Relation in the Local Group and the Equivalent Circular Velocity of Pressure-supported Dwarfs". The Astronomical Journal.
7. (2019-04-11). "The baryonic Tully–Fisher relation for different velocity definitions and implications for galaxy angular momentum". Monthly Notices of the Royal Astronomical Society.
8. (2021-09-20). "Rotation curves and scaling relations of extremely massive spiral galaxies". Monthly Notices of the Royal Astronomical Society.
9. (2024-07-01). "Indefinitely Flat Circular Velocities and the Baryonic Tully–Fisher Relation from Weak Lensing". The Astrophysical Journal Letters.
10. Milgrom, Mordehai. (2019-02-20). "MOND in galaxy groups: A superior sample". Physical Review D.
11. (2023). "The Tully–Fisher relation from SDSS-MaNGA: physical causes of scatter and variation at different radii". [[MNRAS]].
12. (2000). "The Baryonic Tully-Fisher Relation". The Astrophysical Journal Letters.
13. S. Torres-Flores, B. Epinat, P. Amram, H. Plana, C. Mendes de Oliveira (2011), "GHASP: an Hα kinematic survey of spiral and irregular galaxies – IX. The NIR, stellar and baryonic Tully–Fisher relations", {{arxiv. 1106.0505
14. McGaugh, S.. (2012). "The Baryonic Tully–Fisher Relation of Gas-Rich Galaxies as a Test of ΛCDM and MOND". Astrophysical Journal.