next previous
Up: m (H-band) surface photometry


4 Profile decomposition procedures

The 2-dimensional light distribution of each galaxy was fitted with elliptical isophotes, using a procedure based on the task ${\it
ellipse}$, (STSDAS ${\it ISOPHOTE}$ package; Jedrzejewski 1987; Busko 1996), which allows the interactive masking of unwanted superposed sources. Starting from an interactively centered ellipse, the fit maintains as free parameters the ellipse center, ellipticity, and position angle. The ellipse semi-major axis is incremented by a fixed fraction of its value at each step of the fitting procedure. The routine halts when the surface brightness found in a given corona equals the sky rms, and then restarts decrementing the initial semi-major axis toward the center. Isophotes whose rms is greater than their mean value are discarded. The fit fails to converge for some galaxies with very irregular light distributions. In these cases we kept fixed one or more of the ellipse parameters.

The resulting radial light profiles were fitted using one of four models of light distributions:
1) a de Vaucouleurs r1/4 law (de Vaucouleurs 1948);
2) an exponential law;
3) a "mixed'' profile consisting of the sum (in flux) of an exponential law, dominating at large radii ("disk''), and an exponential or a de Vaucouleurs r1/4 law, dominating at small radii ("bulge'');
4) a "truncated'' profile consisting of an exponential or a de Vaucouleurs r1/4 law, truncated by a steeper exponential law beyond a certain critical radius $r_{\rm t}$, according to either of the following:

$\displaystyle I(r)=c_1\cdot {\exp\big[-\frac{1}{c_2}({r-r_{\rm t}}-\vert{r-r_{\...
...!r_{\rm t}}\!+\!\vert{r\!-\!r_{\rm t}}\vert\big]}~{\rm (Truncated~exponential)}$      
$\displaystyle I(r)=c_1\cdot{\exp\big[-\frac{1}{c_2}({r^{1/4}-r_{\rm t}^{1/4}}-\...
...{1}{c_3}({r-r_{\rm t}}+\vert{r-r_{\rm t}}\vert\big]}~{\rm (Tr.~DeVaucouleurs)}.$      

For pure de Vaucouleurs and exponential laws, the fit was performed using a weighted least squares method. For the mixed and truncated profiles, the fit was performed using the Levemberg-Marquardt algorithm implemented in the task ${\it nfit1d}$ (STSDAS ${\it FITTING}$ package). This algorithm is implemented within an interactive procedure which requires some initial set of parameters i.e. 4 markers delimiting the outer or exponential dominated region, and the inner or bulge dominated region. The former is fitted with an exponential law. For mixed profiles, the external exponential fit is extrapolated to the inner region and subtracted. The resulting inner profile is then fitted either with an exponential or a de Vaucouleurs r1/4 law, according to a $\chi^2$ test. Fitting parameters are then assumed as initial guess for the Levemberg-Marquardt algorithm. For truncated profiles, the inner region is fitted either with an exponential or a de Vaucouleurs r1/4 law, according to a $\chi^2$ test, and the fitting parameters are then used as initial guess, along with the external exponential slope and the inner edge of the outer region as $r_{\rm t}$.

The fits are performed from a radius equal to twice the seeing disk, out to the outermost significant isophotes.

Total magnitudes $H_{\rm T}$ are then obtained by adding to the flux measured within the outermost significant isophote the flux extrapolated to infinity along the fitted profile. The $1-\sigma$ error attached to the total magnitude $H_{\rm T}$ combines the statistical error on the flux at the outermost isophote with that on the fit parameters.

The effective radius $r_{\rm e}$ (the radius containing half of the total light) and the effective surface brightness $\mu_{\rm e}$ (the mean surface brightness within $r_{\rm e}$) of each galaxy are "empirically'' computed (see Paper V). The relative errors are obtained combining the uncertainty on $H_{\rm T}$, as described above, with the scatter $\sigma_{\rm r}$ along the integrated-light growth curve.

Finally we compute other useful parameters: the concentration index (C31), defined in de Vaucouleurs (1977) as the model-independent ratio between the radii that enclose 75% and 25% of the total light $H_{\rm T}$, and, for galaxies fitted with a two component model, the bulge to total flux ratio (B/T).

The derived surface brightness profiles are shown in Fig. 3: each galaxy is labelled with a prefix denoting the telescope (N00 for ESO-NTT or G99 for TNG), followed by its catalogue name and by the type of decomposition (see Table 4).


next previous
Up: m (H-band) surface photometry

Copyright ESO 2001