en>Jason Quinn: /* See also */ rm red link from See also... it's also generally a bad idea to pipe non-existing wikilinks asking for their creation

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See also: rm red link from See also... it's also generally a bad idea to pipe non-existing wikilinks asking for their creation

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	~~Hello~~ and ~~welcome~~. ~~My title~~ is ~~Irwin~~ and ~~I totally dig~~ that title. ~~I am~~ a ~~meter reader but I plan on changing it~~. ~~Puerto Rico~~ is ~~exactly where he~~ and ~~his spouse reside~~. ~~One~~ of the ~~extremely very best issues~~ in the ~~globe for me~~ is ~~to do aerobics~~ and ~~now I~~'~~m attempting to earn cash with it~~.<br><br>~~my weblog home std test kit~~ [[http://~~fillyloo~~.~~com~~/~~profile~~/~~MCronin view site…~~]]		The '''distance modulus''' is a way of expressing distances that is often used in [[astronomy]].

			==Definition==

			The distance modulus <math>\mu=m-M</math> is the difference between the [[apparent magnitude]] <math>m</math> (ideally, corrected from the effects of [[interstellar reddening\|interstellar absorption]]) and the [[absolute magnitude]] <math>M</math> of an [[astronomical object]]. It is related to the distance <math>d</math> in parsecs by:

			:<math>\log_{10}(d) = 1 + \frac{\mu}{5}</math>

			:<math>\mu=5\log_{10}(d)-5</math>

			This definition is convenient because the observed brightness of a light source is related to its distance by the [[inverse square law]] (a source twice as far away appears one quarter as bright) and because brightnesses are usually expressed not directly, but in [[apparent magnitude\|magnitudes]].

			Absolute magnitude <math>M</math> is defined as the apparent magnitude of an object when seen at a distance of 10 [[parsec]]s. Suppose a light source has luminosity L(d) when observed from a distance of <math>d</math> parsecs, and luminosity L(10) when observed from a distance of 10 parsecs. The inverse-square law is then written like:

			:<math>L(d) = \frac{L(10)}{(\frac{d}{10})^2} </math>

			The magnitudes and luminosities are related by:

			:<math>m = -2.5 \log_{10}L(d) </math>
			:<math>M = -2.5 \log_{10}L(10) </math>

			Substituting and rearranging, we get:

			:<math>m - M = 5 \log_{10}(d) - 5 = \mu </math>

			which means that the apparent magnitude is the absolute magnitude plus the distance modulus.

			Isolating <math>d</math> from the equation <math>5 \log_{10}(d) - 5 = \mu </math>, we find that the distance in parsecs is given by

			:<math>d = 10^{\frac{\mu}{5}+1} </math>

			The uncertainty in the distance in parsecs (δd) can be computed from the uncertainty in the distance modulus (δμ) using

			:<math> \delta d = 0.2 \ln(10) 10^{0.2\mu+1} \delta\mu = 0.461 d \ \delta\mu</math>

			which is derived using standard error analysis.<ref name="taylor1982">{{cite book
			\| author=J. R. Taylor
			\| year=1982
			\| title=An introduction to Error Analysis
			\| edition=
			\| publisher=University Science Books
			\| location=Mill Valley, California
			\| isbn=0-935702-07-5 }}</ref>

			== Different kinds of distance moduli ==
			Distance is not the only quantity relevant in determining the difference between absolute and apparent magnitude. Absorption is another important factor and it may even be a dominant one in particular cases (e. g. in the direction of the galactic center).

			Thus a distinction is made between distance moduli uncorrected for [[interstellar reddening\|interstellar absorption]] (whose values would overestimate the distance if used naively) and absorption-corrected moduli.

			The first ones are termed ''visual distance moduli'' and are denoted by <math>{(m - M)}_{v}</math> while the second ones are called ''true distance moduli'' and denoted by <math>{(m - M)}_{0}</math>.

			Visual distance moduli are computed by calculating the difference between the observed apparent magnitude and some theoretical estimate of the absolute magnitude. True distance moduli require a further theoretical step, that is the estimation of the [[interstellar absorption coefficient]].

			==Usage==

			Distance moduli are most commonly used when expressing the distance to other galaxies in the relatively nearby universe. For example, the [[Large Magellanic Cloud]] is at a distance modulus of 18.5,<ref name="alvez2--4">{{cite journal
			\| author=D. R. Alvez
			\| title=A review of the distance and structure of the Large Magellanic Cloud
			\| year=2004
			\| volume=48
			\| issue=9
			\| pages=659–665
			\| bibcode=2004NewAR..48..659A
			\| doi=10.1016/j.newar.2004.03.001
			\| format=abstract
			\| journal=New Astronomy Reviews\|arxiv = astro-ph/0310673 }}</ref> the [[Andromeda Galaxy]]'s distance modulus is 24.4,<ref name="alvez2005">{{cite journal
			\| author=I. Ribas, C. Jordi, F. Vilardell, E. L. Fitzpatrick, R. W. Hilditch, E. F. Guinan
			\| title=First Determination of the Distance and Fundamental Properties of an Eclipsing Binary in the Andromeda Galaxy
			\| year=2005
			\| volume=635
			\| issue=1
			\| pages=L37–L40
			\| bibcode=2005ApJ...635L..37R
			\| doi=10.1086/499161
			\| format=abstract
			\| journal=The Astrophysical Journal\|arxiv = astro-ph/0511045 }}</ref> and the galaxy [[NGC 4548]] in the [[Virgo Cluster]] has a DM of 31.0.<ref name="graham1999">{{cite journal
			\| author=J. A. Graham, L. Ferrarese, W. L. Freedman, R. C. Kennicutt Jr., J. R. Mould, A. Saha, P. B. Stetson, B. F. Madore, F. Bresolin, H. C. Ford, B. K. Gibson, M. Han, J. G. Hoessel, J. Huchra, S. M. Hughes, G. D. Illingworth, D. D. Kelson, L. Macri, R. Phelps, S. Sakai, N. A. Silbermann, A. Turner
			\| title=The Hubble Space Telescope Key Project on the Extragalactic Distance Scale. XX. The Discovery of Cepheids in the Virgo Cluster Galaxy NGC 4548
			\| year=1999
			\| volume=516
			\| issue=2
			\| pages=626–646
			\| bibcode=1999ApJ...516..626G
			\| doi=10.1086/307151
			\| format=abstract
			\| journal=The Astrophysical Journal}}</ref> In the case of the LMC, this means that the [[supernova]] [[SN1987A]], with a peak apparent magnitude of 2.8, had an absolute magnitude of -15.7, which is low by supernova standards.

			Using distance moduli makes computing magnitudes easy. As for instance, a solar type star (M=5) in Andromeda galaxy (DM=24.4) would have an apparent magnitude (m) of 5 + 24.4 = 29.4, so it would be barely visible in the [[Hubble Space Telescope\|HST]], which has a limiting magnitude of about 30 [http://www.astro.uu.nl/~strous/AA/en/antwoorden/magnituden.html]. This calculation can be done quickly in one's head. Since it is apparent magnitudes which are actually measured at a telescope, this way of looking at things serves to highlight the fact that many discussions about distances in astronomy are really discussions about the putative or derived absolute magnitudes of the distant objects being observed.

			==References==

			* Zeilik, Gregory and Smith, ''Introductory Astronomy and Astrophysics'' (1992, Thomson Learning)
			{{reflist}}

			{{DEFAULTSORT:Distance Modulus}}
			[[Category:Physical quantities]]

			[[de:Absolute Helligkeit#Entfernungsmodul]]

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2012-05-09T17:50:49Z

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Hello and welcome. My title is Irwin and I totally dig that title. I am a meter reader but I plan on changing it. Puerto Rico is exactly where he and his spouse reside. One of the extremely very best issues in the globe for me is to do aerobics and now I'm attempting to earn cash with it.<br><br>my weblog home std test kit [[http://fillyloo.com/profile/MCronin view site…]]

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en>Jason Quinn: /* See also */ rm red link from See also... it's also generally a bad idea to pipe non-existing wikilinks asking for their creation

en>Helpful Pixie Bot: ISBNs (Build KE)