Effective radius

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This article is about astronomy. For cloud drops, see Cloud drop effective radius.



Half light radius Re encloses half of the total light emitted by an object


The effective radius (Re{displaystyle R_{e}}R_e) of a galaxy is the radius at which half of the total light of the system is emitted.[1][2] This assumes the galaxy has either intrinsic spherical symmetry or is at least circularly symmetric as viewed in the plane of the sky. Alternatively, a half-light contour, or isophote, may be used for spherically and circularly asymmetric objects.


Re{displaystyle R_{e}}R_e is an important length scale in de Vaucouleurs R4{displaystyle {sqrt[{4}]{R}}}{sqrt[ {4}]R} law, which characterizes a specific rate at which surface brightness decreases as a function of radius:


I(R)=Ie⋅e−7.67(RRe4−1){displaystyle I(R)=I_{e}cdot e^{-7.67left({sqrt[{4}]{frac {R}{R_{e}}}}-1right)}}I(R)=I_{e}cdot e^{{-7.67left({sqrt[ {4}]{{frac R{R_{e}}}}}-1right)}}

where Ie{displaystyle I_{e}}I_e is the surface brightness at R=Re{displaystyle R=R_{e}}R=R_{e}. At R=0{displaystyle R=0}R = 0,


I(R=0)=Ie⋅e7.67≈2000⋅Ie{displaystyle I(R=0)=I_{e}cdot e^{7.67}approx 2000cdot I_{e}}I(R=0)=I_{e}cdot e^{{7.67}}approx 2000cdot I_{e}

Thus, the central surface brightness is approximately 2000⋅Ie{displaystyle 2000cdot I_{e}}2000cdot I_{e}.



See also




  • Airy disk

  • Elliptical galaxy

  • Globular cluster

  • Open cluster

  • Point spread function

  • Sersic profile




References





  1. ^ "Half-light Radius". Swinburne University. Retrieved 22 May 2013..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}


  2. ^ Binney, James; Tremaine, Scott (2008). Galactic Dynamics (Second ed.). Princeton Series in Astrophysics. p. 21. ISBN 9780691130279.











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