Editing Tully–Fisher relation

{{Short description|Trend in astronomy}}
[[Image:OffsetTF.png|thumb|right|280px|The Tully–Fisher relation for spiral and [[lenticular galaxy|lenticular]] galaxies]]

In [[astronomy]], the '''Tully–Fisher relation''' ('''TFR''') is a widely verified [[empirical relationship]] between the mass or intrinsic [[luminosity]] of a [[spiral galaxy]] and its [[galaxy rotation curve|asymptotic rotation velocity]] or [[emission line]] width. Since the observed brightness of a galaxy is distance-dependent, the relationship can be used to estimate distances to galaxies from measurements of their rotational velocity.<ref name=SaidTF>{{Cite book |last=Said |first=Khaled |title=Hubble Constant Tension |date=2023-10-24 |editor-last=Di Valentino |editor-first=E |chapter=Tully–Fisher relation |arxiv=2310.16053 |editor-last2=Brout |editor-first2=D. }}</ref>

==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]].<ref name=SaidTF/><ref>Opik, Ernst. "An estimate of the distance of the Andromeda Nebula." Astrophysical Journal, 55, 406–410 (1922) 55 (1922).</ref> In the 1970s, Balkowski, C., et al. measured 13 galaxies but focused on using the data to distinguish galaxy shapes rather than extract distances.<ref name=SaidTF/><ref>Balkowski, C., et al. "Neutral hydrogen study of spiral and irregular dwarf galaxies." Astronomy and Astrophysics, Vol. 34, p. 43–52 34 (1974): 43–52.</ref>
The relationship was first published in 1977 by astronomers [[R. Brent Tully]] and [[J. Richard Fisher]].<ref>{{cite journal |last1=Tully |first1=R. B. |last2=Fisher |first2=J. R. |title=A New Method of Determining Distances to Galaxies |journal=[[Astronomy and Astrophysics]] |volume=54 |issue=3 |year=1977 |pages=661–673 |bibcode=1977A&A....54..661T }}</ref> The luminosity is calculated by multiplying the galaxy's [[apparent brightness]] by <math>4\pi d^2</math>, where <math>d</math> 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.<ref>{{Cite journal |last1=Kourkchi |first1=Ehsan |last2=Tully |first2=R. Brent |last3=Eftekharzadeh |first3=Sarah |last4=Llop |first4=Jordan |last5=Courtois |first5=Hélène M. |last6=Guinet |first6=Daniel |last7=Dupuy |first7=Alexandra |last8=Neill |first8=James D. |last9=Seibert |first9=Mark |last10=Andrews |first10=Michael |last11=Chuang |first11=Juana |last12=Danesh |first12=Arash |last13=Gonzalez |first13=Randy |last14=Holthaus |first14=Alexandria |last15=Mokelke |first15=Amber |date=2020-10-23 |title=Cosmicflows-4: The Catalog of ∼10,000 Tully–Fisher Distances |journal=The Astrophysical Journal |volume=902 |issue=2 |pages=145 |doi=10.3847/1538-4357/abb66b |doi-access=free |arxiv=2009.00733 |bibcode=2020ApJ...902..145K |issn=1538-4357}}</ref> Many values of the [[Hubble constant]] have been derived from Tully–Fisher analysis, starting with the first paper and continuing through 2024.<ref name=SaidTF/>

==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 [[visible light|optical]] luminosity, but subsequent work showed the relation to be tighter when defined using microwave to infrared ([[K band (infrared)|K band]]) radiation (a good proxy for [[stellar mass]]), and even tighter when luminosity is replaced by the galaxy's total stellar mass.<ref>{{cite journal |last1=Ristea |first1=Andrei |title= The Tully–Fisher relation from SDSS-MaNGA: physical causes of scatter and variation at different radii |journal=[[MNRAS]] |volume=527 |issue=3 |year=2023 |pages=7438–7458 |doi=10.1093/mnras/stad3638 |url=https://academic.oup.com/mnras/article/527/3/7438/7450469 |doi-access=free |arxiv=2311.13251 }}</ref> 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).<ref>{{cite journal |last1=McGaugh |first1=S. S. |last2=Schombert |first2=J. M. |last3=Bothun |first3=G. D. |last4=de Blok |first4=W. J. G |title=The Baryonic Tully-Fisher Relation |journal=The Astrophysical Journal Letters |date=2000 |volume=533 |issue=2 |pages=L99–L102 |doi=10.1086/312628 |pmid=10770699 |bibcode=2000ApJ...533L..99M|arxiv=astro-ph/0003001 |s2cid=103865 }}</ref> 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.<ref>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}}</ref>

The TFR can be used to estimate the distance to spiral galaxies by allowing the luminosity of a galaxy to be derived from its directly measurable line width. The distance can then be found by comparing the luminosity to the apparent brightness. Thus the TFR constitutes a rung of the [[cosmic distance ladder]], where it is calibrated using more direct distance measurement techniques and used in turn to calibrate methods extending to larger distance.

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 [[MOND|Modified Newtonian dynamics (MOND)]], the BTFR (with power-law index exactly 4) is a direct consequence of the [[gravitational force| gravitational force law]] effective at low [[acceleration]].<ref>{{cite journal |first=S. |last=McGaugh |year=2012 |title=The Baryonic Tully–Fisher Relation of Gas-Rich Galaxies as a Test of ΛCDM and MOND |journal=Astrophysical Journal |volume=143 |issue=2 |pages= 40|doi=10.1088/0004-6256/143/2/40 |arxiv=1107.2934 |bibcode=2012AJ....143...40M |s2cid=38472632 }}</ref>

The analogues of the TFR for non-rotationally-supported galaxies, such as [[elliptical galaxy|ellipticals]], are known as the [[Faber–Jackson relation]] and the [[Fundamental plane (elliptical galaxies)|fundamental plane]].

== See also ==
{{div col|colwidth=22em}}
* [[Distance modulus]]
* [[Standard candle]]
* [[Cosmic distance ladder]]
* [[Faber–Jackson relation]]
* [[Fundamental plane (elliptical galaxies)|Fundamental plane]]
* [[Dark matter]]
* [[Lambda-CDM model|Standard model of cosmology]]
* [[Modified Newtonian dynamics]]
* [[Freeman law]]
{{div col end}}

==References==
{{Reflist|2}}

==External links==
* [http://www.scholarpedia.org/article/Tully-Fisher_Relation Scholarpedia article on the subject] written by [[R. Brent Tully]]

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[[Category:Extragalactic astronomy]]
[[Category:Physical cosmological concepts]]
[[Category:Spiral galaxies]]