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Next: A..4 Bulge+Disk Profile Up: A. Galaxy Surface Brightness Previous: A..2 Bulge Profile


A..3 Disk Profile

For $ n=1$, Equation 17 can be rewritten as the exponential law

\begin{displaymath}\begin{split}\Sigma_d(r) & = \Sigma_e \,\exp\left[-1.6783 \le...
...ght) = \Sigma_0 \,\exp\left(-\frac{r}{r_s}\right)~, \end{split}\end{displaymath} (26)

which characterizes the profile of disk components of disk galaxies, where $ \Sigma_0$ is the central surface brightness and $ r_s$ is referred to as the disk scale length. The relations between these two quantities and $ \Sigma_e$ and $ r_e$ are respectively

$\displaystyle \Sigma_0 = 5.3567 \,\Sigma_e~,~~~~~~r_s=\frac{r_e}{1.6783}~.$ (27)

According to this profile, the total brightness of the galaxy can be written as

$\displaystyle F_{d,tot} = 11.948 \,\Sigma_e \,r_e^2~,$ (28)

while the average surface brightness inside the effective radius $ <\Sigma>_e$ is related to $ \Sigma_e$ by

$\displaystyle <\Sigma>_e=\frac{F_{d,tot}/2}{\pi\,r_e^2}=1.9016\,\Sigma_e~.$ (29)

When put on a magnitude scale, the disk profile given by Equation 26 becomes

\begin{displaymath}\begin{split}\mu_d(r)&=-2.5\,\log\left(\frac{\Sigma_d(r)}{\Si...
...frac{r}{r_e}-1\right) ~\mathrm{[mag~arcsec^{-2}]}~, \end{split}\end{displaymath} (30)

while Equation 28 can be trivially manipulated to obtain for $ \Sigma_e$ the expression

\begin{displaymath}\begin{split}\mu_e&=-2.5\,\log\left(\frac{\Sigma_e}{\Sigma_{z...
... +I_{\mathrm{[mag]}}~~~\mathrm{[mag~arcsec^{-2}]}~. \end{split}\end{displaymath} (31)


next up previous
Next: A..4 Bulge+Disk Profile Up: A. Galaxy Surface Brightness Previous: A..2 Bulge Profile
Mattia Vaccari 2002-01-31