Effective radius

The effective radius R _e shows the region of the galaxy in which half the light is emitted.

Effective radius ( $R_{e}$ ${\ displaystyle R_ {e}}$ $R_ {e}$ ) galaxies - the radius within which half of all light emitted by the galaxy is emitted. ^[1] ^[2] This definition implies that a galaxy has spherical symmetry or at least circular symmetry in projection onto the celestial sphere. For objects that do not have these symmetries, you can use the contour or isophotes inside which half the light is emitted.

The effective radius is an important parameter in de Vaucouler’s law , showing the dependence of surface brightness on the apparent distance to the center of the galaxy

I(R)=I_{e}\cdot e^{-7.67\left({\sqrt[{4}]{\frac {R}{R_{e}}}}-1\right)},

{\ displaystyle I (R) = I_ {e} \ cdot e ^ {- 7.67 \ left ({\ sqrt [{4}] {\ frac {R} {R_ {e}}}} - 1 \ right)} ,}

{\ displaystyle I (R) = I_ {e} \ cdot e ^ {- 7.67 \ left ({\ sqrt [{4}] {\ frac {R} {R_ {e}}}} - 1 \ right)} ,}

Where $I_{e}$ ${\ displaystyle I_ {e}}$ $I_ {e}$ equal to surface brightness at $R=R_{e}$ ${\ displaystyle R = R_ {e}}$ ${\ displaystyle R = R_ {e}}$ . At $R=0$ ${\ displaystyle R = 0}$ $R = 0$

I(R=0)=I_{e}\cdot e^{7.67}\approx 2000\cdot I_{e},

{\ displaystyle I (R = 0) = I_ {e} \ cdot e ^ {7.67} \ approx 2000 \ cdot I_ {e},}

{\ displaystyle I (R = 0) = I_ {e} \ cdot e ^ {7.67} \ approx 2000 \ cdot I_ {e},}

that is, the surface brightness of the center of the galaxy is approximately $2000\cdot I_{e}$ ${\ displaystyle 2000 \ cdot I_ {e}}$ ${\ displaystyle 2000 \ cdot I_ {e}}$ .

Notes

↑ Half-light Radius (neopr.) . Swinburne University. Date of treatment May 22, 2013.
↑ Binney, James. Galactic Dynamics / James Binney, Scott Tremaine. - Second. - Princeton Series in Astrophysics, 2008 .-- P. 21. - ISBN 9780691130279 .

[1] Half-light Radius (neopr.) . Swinburne University. Date of treatment May 22, 2013.

[2] Binney, James. Galactic Dynamics / James Binney, Scott Tremaine. - Second. - Princeton Series in Astrophysics, 2008 .-- P. 21. - ISBN 9780691130279 .

Effective radius

Notes

More articles: