Tully-Fisher relation
Encyclopedia
In astronomy
, the Tully–Fisher relation, published by astronomers R. Brent Tully
and J. Richard Fisher
in 1977, is an empirical
relationship between the intrinsic luminosity
(proportional to the stellar mass) of a spiral galaxy
and its velocity width (the amplitude of its rotation curve
). The luminosity is the amount of light energy emitted by the galaxy per unit time; it can be measured using the galaxy's apparent brightness when the distance to the galaxy is known. The velocity width is measured via the width or shift of spectral line
s using long-slit spectroscopy
.
The term Baryonic Tully–Fisher relation is used when the mass being considered is the baryonic mass
of the galaxy, as opposed to the mass value inferred from luminosity alone.
The quantitative relationship between luminosity and velocity width is a function of the wavelength
at which the luminosity is measured, but roughly speaking, luminosity is proportional to velocity to the fourth power.
The relation enables the difficult-to-observe intrinsic luminosity to be calculated from the relatively easily-observable velocity. Use of the observed apparent brightness and the inverse square law enables the distance to the object to be estimated. In astronomical parlance this distance measurement is known as a "secondary standard candle".
Internal dynamics of star
s in galaxies are driven by gravity. For this reason, the amplitude of the galaxy rotation curve is related to the galaxy's mass
; the Tully-Fisher relation is a direct observation of a close relationship between galaxy stellar mass (which sets the luminosity) and total gravitational mass (which sets the amplitude of the rotation curve).
The relation is measured and calibrated using primary standard candles.
The relation does not apply to elliptical galaxies which are in general not rotationally supported. However, similar methods exist for them, such as the Faber-Jackson relation
and the fundamental plane
.
One potential explanation for the existence of this empirical relation lies in so-called Modified Newtonian Dynamics
, or MOND theory.
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, the Tully–Fisher relation, published by astronomers R. Brent Tully
R. Brent Tully
R. Brent Tully is an astronomer at the Institute for Astronomy in Honolulu, Hawaii.Tully's specialty is astrophysics of galaxies. He, along with J. Richard Fisher, proposed the now-famous Tully-Fisher relation in a paper, A New Method of Determining Distances to Galaxies, published in Astronomy...
and J. Richard Fisher
J. Richard Fisher
J. Richard Fisher is an astronomer at the National Radio Astronomy Observatory at Charlottesville, VA. He received his Ph.D. in Astronomy from the University of Maryland, College Park and his B.S. in Physics from the Pennsylvania State University.Fisher, along with R...
in 1977, is an empirical
Empiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...
relationship between the intrinsic luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
(proportional to the stellar mass) of a spiral galaxy
Spiral galaxy
A spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
and its velocity width (the amplitude of its rotation curve
Galaxy rotation curve
The rotation curve of a galaxy can be represented by a graph that plots the orbital velocity of the stars or gas in the galaxy on the y-axis against the distance from the center of the galaxy on the x-axis....
). The luminosity is the amount of light energy emitted by the galaxy per unit time; it can be measured using the galaxy's apparent brightness when the distance to the galaxy is known. The velocity width is measured via the width or shift of spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...
s using long-slit spectroscopy
Long-slit spectroscopy
In astronomy, Long-slit spectroscopy involves observing an elongated celestial object through an elongated slit aperture, and refracting this light with a prism or diffraction grating...
.
The term Baryonic Tully–Fisher relation is used when the mass being considered is the baryonic mass
Baryonic dark matter
In astronomy and cosmology, baryonic dark matter is dark matter composed of baryons, i.e. protons and neutrons and combinations of these, such as non-emitting ordinary atoms...
of the galaxy, as opposed to the mass value inferred from luminosity alone.
The quantitative relationship between luminosity and velocity width is a function of the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
at which the luminosity is measured, but roughly speaking, luminosity is proportional to velocity to the fourth power.
The relation enables the difficult-to-observe intrinsic luminosity to be calculated from the relatively easily-observable velocity. Use of the observed apparent brightness and the inverse square law enables the distance to the object to be estimated. In astronomical parlance this distance measurement is known as a "secondary standard candle".
Internal dynamics of star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s in galaxies are driven by gravity. For this reason, the amplitude of the galaxy rotation curve is related to the galaxy's mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
; the Tully-Fisher relation is a direct observation of a close relationship between galaxy stellar mass (which sets the luminosity) and total gravitational mass (which sets the amplitude of the rotation curve).
The relation is measured and calibrated using primary standard candles.
The relation does not apply to elliptical galaxies which are in general not rotationally supported. However, similar methods exist for them, such as the Faber-Jackson relation
Faber-Jackson relation
The Faber–Jackson relation is an early empirical power-law relation between the luminosity L and the central stellar velocity dispersion \sigma of elliptical galaxies, first noted by the astronomers Sandra M. Faber and Robert Earl Jackson in 1976...
and the fundamental plane
Fundamental plane (elliptical galaxies)
The fundamental plane is a relationship between the effective radius, average surface brightness and central velocity dispersion of normal elliptical galaxies. Any one of the three parameters may be estimated from the other two, as together they describe a plane that falls within their more...
.
One potential explanation for the existence of this empirical relation lies in so-called Modified Newtonian Dynamics
Modified Newtonian dynamics
In physics, Modified Newtonian dynamics is a hypothesis that proposes a modification of Newton's law of gravity to explain the galaxy rotation problem. When the uniform velocity of rotation of galaxies was first observed, it was unexpected because Newtonian theory of gravity predicts that objects...
, or MOND theory.
See also
- Distance modulusDistance modulus-Definition:The distance modulus \mu=m-M is the difference between the apparent magnitude m and the absolute magnitude M of an astronomical object...
- Modified Newtonian dynamicsModified Newtonian dynamicsIn physics, Modified Newtonian dynamics is a hypothesis that proposes a modification of Newton's law of gravity to explain the galaxy rotation problem. When the uniform velocity of rotation of galaxies was first observed, it was unexpected because Newtonian theory of gravity predicts that objects...
- Standard candle
- Cosmic distance ladderCosmic distance ladderThe cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" to Earth...
- Fundamental plane (elliptical galaxies)Fundamental plane (elliptical galaxies)The fundamental plane is a relationship between the effective radius, average surface brightness and central velocity dispersion of normal elliptical galaxies. Any one of the three parameters may be estimated from the other two, as together they describe a plane that falls within their more...
- Faber–Jackson relation
- Extragalactic Distance Scale