Surface brightness fluctuation (SBF) is a secondary distance indicator used to estimate distances to galaxies. It is useful to 100 Mpc (

parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...

). The method measures the variance in a galaxy's light distribution arising from fluctuations in the numbers of and luminosities of individual stars per resolution element. The SBF technique uses the fact that galaxies are made up of a finite number of stars. The number of stars in any small patch of a galaxy will vary from point to point, creating a noise-like fluctuation in its surface brightness. While the various stars present in a galaxy will cover an enormous range of luminosity, the SBF can be characterized as having an average brightness. A galaxy twice as far away appears twice as smooth as a result of the averaging. Older

elliptical galaxies An elliptical galaxy is a type of galaxy with an approximately ellipsoidal shape and a smooth, nearly featureless image. They are one of the four main classes of galaxy described by Edwin Hubble in his Hubble sequence and 1936 work ''The Real ...

have fairly consistent stellar populations, thus it closely approximates a

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 ...

. In practice, corrections are required to account for variations in age or metallicity from galaxy to galaxy. Calibration of the method is made empirically from Cepheids or theoretically from stellar population models. The SBF pattern is measured from the

power spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of Power (physics), power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discre ...

of the residuals left behind from a deep galaxy image after a smooth model of the galaxy has been subtracted. The SBF pattern is evident as the transform of the point spread function in the

Fourier domain In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signa ...

. The amplitude of the spectrum gives the luminosity of the fluctuation star. Because the technique depends on a precise understanding of the image structure of the galaxy, extraneous sources such as

globular cluster A globular cluster is a spheroidal conglomeration of stars. Globular clusters are bound together by gravity, with a higher concentration of stars towards their centers. They can contain anywhere from tens of thousands to many millions of membe ...

s and background galaxies must be excluded. Corrections for

interstellar dust Cosmic dust, also called extraterrestrial dust, star dust or space dust, is dust which exists in outer space, or has fallen on Earth. Most cosmic dust particles measure between a few molecules and 0.1 mm (100 micrometers). Larger particles are c ...

absorption must also be accounted. In practice this means that SBF works best for

or the bulges of S0 galaxies, and less so for spiral galaxies as they generally have complex morphologies and extensive dust features. SBF is calibrated by use of nearby

Cepheid A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude. A strong direct relationship between a Cepheid varia ...

period-luminosity relation In astronomy, a period-luminosity relation is a relationship linking the bolometric luminosity, luminosity of pulsating variable stars with their pulsation period. The best-known relation is the direct proportionality law holding for Classical Ceph ...

(P-L) based on measurements of SBF magnitudes in the bulges of spiral galaxies with distances measured from

Cepheid variables A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude. A strong direct relationship between a Cepheid vari ...

. SBF is an indicator that uses stars in the old stellar populations (

Population II During 1944, Walter Baade categorized groups of stars within the Milky Way into stellar populations. In the abstract of the article by Baade, he recognizes that Jan Oort originally conceived this type of classification in 1926: Baade noticed th ...

References

{{reflist, refs= {{Citation , author=Ferrarese, Laura , author2=Ford, Holland C. , author3=Huchra, John , author4=Kennicutt, Robert C., Jr. , author5=Mould, Jeremy R. , author6=Sakai, Shoko , author7=Freedman, Wendy L. , author8=Stetson, Peter B. , author9=Madore, Barry F. , author10=Gibson, Brad K. , author11=Graham, John A. , author12=Hughes, Shaun M. , author13=Illingworth, Garth D. , author14=Kelson, Daniel D. , author15=Macri, Lucas , author16=Sebo, Kim , author17=Silbermann, N. A. , title=A Database of Cepheid Distance Moduli and Tip of the Red Giant Branch, Globular Cluster Luminosity Function, Planetary Nebula Luminosity Function, and Surface Brightness Fluctuation Data Useful for Distance Determinations , journal=The Astrophysical Journal Supplement Series , date=2000 , volume=128 , issue=2 , pages=431–459 , bibcode=2000ApJS..128..431F , doi=10.1086/313391 , postscript=. , arxiv = astro-ph/9910501 {{Citation , last1 = Tonry , first1 = John L. , last2 = Dressler , first2 = Alan , last3 = Blakeslee , first3 = John P. , last4 = Ajhar , first4 = Edward A. , last5 = Fletcher , first5 = Andre B. , last6 = Luppino , first6 = Gerard A. , last7 = Metzger , first7 = Mark R. , last8 = Moore , first8 = Christopher B. , title = The SBF Survey of Galaxy Distances. IV. SBF Magnitudes, Colors, and Distances , journal = Astrophysical Journal , date = 2001 , volume = 546 , issue = 2 , pages = 681–693 , bibcode = 2001ApJ...546..681T , doi = 10.1086/318301 , arxiv = astro-ph/0011223 {{Citation , last1 = Macri , first1 = L. M. , last2 = Stanek , first2 = K. Z. , last3 = Bersier , first3 = D. , last4 = Greenhill , first4 = L. J. , last5 = Reid , first5 = M. J. , title = A New Cepheid Distance to the Maser-Host Galaxy NGC 4258 and Its Implications for the Hubble Constant , journal = Astrophysical Journal , date = 2006 , volume = 652 , issue = 2 , pages = 1133–1149 , bibcode = 2006ApJ...652.1133M , doi = 10.1086/508530 , arxiv = astro-ph/0608211 Standard candles