next up previous contents
Next: 4.4.2 Disk Galaxies Up: 4.4 Surface Brightness Distribution Previous: 4.4 Surface Brightness Distribution   Contents


4.4.1 Elliptical Galaxies

The surface brightness radial profiles of elliptical galaxies are in general reasonably well described by de Vaucouleurs, or $ r^{1/4}$, law, first introduced by [de Vaucouleurs 1948]

$\displaystyle \Sigma_E(r) = \Sigma_{E,e} \,\exp\left(-7.6692 \left[\left(\frac{r}{r_e}\right) ^{1/4}-1\right] \right)~,$ (4.6)

where the effective surface brightness is labelled with an additional ``$ E$'' because in our model this quantity, unlike the effective radius, will in general be different for E and D galaxies. This law has succeeded in reproducing, with a remarkable accuracy, the profiles of quite a few E galaxies. For instance, [Capaccioli et al. 1990] found that the $ r^{1/4}$ fit of the surface brightness radial profile of the nearby standard elliptical NGC 3379 give residuals smaller than 0.08 mag over a 10 magnitude range. [Makino et al. 1990], however, found from dynamical arguments that the $ r^{1/4}$ law bore little physical significance, though it is the best-fitting function, and that $ r^{1/n}$ laws with $ n$ in the range 3-10 gave almost as good fits for a range of $ r$ of about 100. More recently, [Caon et al. 1993] showed that the best-fitting $ n$ correlates with the galaxy linear effective radius and luminosity, while [Andredakis et al. 1995] found that the light profiles of the bulges of disk galaxies, which are also usually modelled with an $ r^{1/4}$ law, are in fact best-fitted by $ r^{1/n}$ profiles with an $ n$ correlating with the galaxy morphological type. Nevertheless, the empirical fitting function given by Equation 4.6 is useful for characterizing the global properties of galaxies, and by that token in this study elliptical galaxies and bulges of disk galaxies will both be modelled with $ r^{1/4}$ laws.

On a magnitude scale, Equation 4.6 becomes

$\displaystyle \mu_E(r)=\mu_{E,e}+8.3268\,\left[\left(\frac{r}{r_e}\right)^{1/4}-1\right]~,$ (4.7)

where $ \mu_{E,e}$ is the effective surface brightness of Es expressed in mag/arcsec$ ^2$. This latter quantity can be expressed as function of $ r_e$ and $ I$, and thus, via Equation 4.3, of $ I$ only, obtaining

$\displaystyle \mu_{E,e}=2.5\,\log\left(22.665\right)+5\,\log\left(r_{e,\mathrm{[as]}}(I) \right)+I_{\mathrm{[mag]}}~~~\mathrm{[number~deg^{-2}~mag^{-1}]}~.$ (4.8)

Values of $ \mu_{E,e}$ are given in Table 4.5.
next up previous contents
Next: 4.4.2 Disk Galaxies Up: 4.4 Surface Brightness Distribution Previous: 4.4 Surface Brightness Distribution   Contents
Mattia Vaccari 2000-12-05