Editing Tully–Fisher relation (section)

==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]].