astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
, the Tully–Fisher relation (TFR) is an
empirical relationship
In science, an empirical relationship or phenomenological relationship is a relationship or correlation that is supported by experiment and observation but not necessarily supported by theory.
Analytical solutions without a theory
An empirical rel ...
between the mass or intrinsic
luminosity
Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a st ...
of a
spiral galaxy
Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''asymptotic rotation velocity or
emission line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
width. It 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
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's lig ...
by , where is its distance from us, and the spectral-line width is measured using
long-slit spectroscopy
In astronomy, long-slit spectroscopy involves observing a celestial object using a spectrograph in which the entrance aperture is an elongated, narrow slit. Light entering the slit is then refracted using a prism, diffraction grating, or grism. ...
.
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
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
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
Stellar mass is a phrase that is used by astronomers to describe the mass of a star. It is usually enumerated in terms of the Sun's mass as a proportion of a solar mass (). Hence, the bright star Sirius has around . A star's mass will vary over its ...
), and even tighter when luminosity is replaced by the galaxy's 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.
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
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
, 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
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ab ...
paradigm, a galaxy's rotation velocity (and hence line width) is primarily determined by the mass of the
dark matter halo
According to modern models of physical cosmology, a dark matter halo is a basic unit of cosmological structure. It is a hypothetical region that has decoupled from cosmic expansion and contains gravitationally bound matter.
A single dark matte ...
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
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
.
The analogues of the TFR for non-rotationally-supported galaxies, such as ellipticals, are known as the
Faber–Jackson relation
The Faber–Jackson relation provided the first empirical power-law relation between the luminosity L and the central stellar velocity dispersion \sigma of elliptical galaxy, and was presented by the astronomers Sandra M. Faber and Robert Earl ...
Distance modulus The distance modulus is a way of expressing distances that is often used in astronomy. It describes distances on a logarithmic scale based on the astronomical magnitude system.
Definition
The distance modulus \mu=m-M is the difference between the ...
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Standard candle
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
*
Cosmic distance ladder
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
*
Faber–Jackson relation
The Faber–Jackson relation provided the first empirical power-law relation between the luminosity L and the central stellar velocity dispersion \sigma of elliptical galaxy, and was presented by the astronomers Sandra M. Faber and Robert Earl ...
Dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ab ...
Modified Newtonian dynamics
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining ...