6 Surface brightness profiles

In combination with the morphological appearance of the observed galaxies, the analysis of their SB profiles provides a reliable tool to classify them as cluster dwarf galaxies or background galaxies (e.g. Sandage & Binggeli 1984). In the surface brightness versus magnitude diagram ($\mu -V$ diagram) the dEs follow a well defined sequence.

  

Table 2: Photometric properties and profile fit parameters of dwarf galaxies in Fornax. The classification as dwarf galaxy is based on the morphological appearance, surface brightnesses, and in four cases on radial velocities

A growth curve analysis for each galaxy has been made with increasing elliptical apertures using the position, ellipticity, and position angle of the SExtractor photometry results. As local background the SExtractor value of the interpolated sky map for each individual galaxy was taken (see Sect. 4). In some cases overlapping stars have been removed before the analysis by interpolating the galaxy surface brightness profile from a unaffected ring outside the stellar profile. In other cases, the region of an overlapping star was masked out during the fitting process of the surface brightness profile. Two model-independent parameters have been determined for the galaxies: the effective semi-major axis $a_{\rm eff}$ (major axis of the ellipse that contains half of the total light) and the mean effective surface brightness within the effective semi-major axis, $\langle \mu_{\rm eff} \rangle = V_{\rm tot} + 5~\cdot$ log$(a_{\rm eff}) + 2.5~\cdot$ log$(2\pi(1 - \epsilon))$, with $\epsilon = 1 - b/a$ (b = semi-minor axis, a = semi-major axis). These parameters, as well as the size of the full major axis D₂₆ at the isophote of V = 26 mag arcsec^-2, are given in the photometric catalog (Appendix A).

  

Figure 3: The three panels show surface brightness versus total magnitude plots for all objects in the photometric catalog (small dots). In the upper two panels $\mu_{\rm peak}$ (not seeing corrected) and $\mu_{\rm eff}$ from growth curve analyses are plotted. In the lower panel the corrected central surface brightness (as described in the text) is shown for a subsample of galaxies. $\Delta\mu$ is the difference between the apparent and corrected central surface brightness. In all diagrams the encircled dots indicate Fornax cluster members, as follows from their radial velocity (see Paper II) and/or SB profile (Sect. 6). All other objects that are not encircled are suspected to be background galaxies. In the middle panel definite background galaxies, according to their radial velocities, are symbolised with crosses. In all panels the dotted lines mark the region that is defined by the $\mu -V$ relation of the Local Group and Virgo dEs (the asterisks in the lower panel are Local Group dSphs shifted to the Fornax distance; Kormendy 1985; Mateo et al. 1993)

The $\mu_{\rm eff}-V_{\rm tot}$ - diagram is shown in Fig. 3 (middle panel). Qualitatively, this plot is comparable to the $\mu_{\rm peak}-V_{\rm tot}$ diagram in the upper panel. The sequence of dwarf galaxies is clearly separated from the location of background galaxies. However, the nucleated dEs that are hidden in the $\mu_{\rm peak}$ plot among the background galaxies, fall in the range of the dE sequence when measuring $\mu_{\rm eff}$. In both diagrams, there are some galaxies located below the bulk of background galaxies, falling in the range of dwarf ellipticals. Each individual galaxy in this region has been individually inspected. Most of them are background spirals or galaxies that have close neighbours which disturb the correct $\mu_{\rm eff}$ calculation. Furthermore, radial velocity measurements have shown that nearly all galaxies at the bright $\mu$ limit of the dE sequence are indeed background objects (see crosses in the middle panel of Fig. 3).

The determination of the true central surface brightness $\mu_0$ is critical for objects with small angular diameters. The centrally peaked light distributions are blurred by seeing, which leads to a dimming of $\mu_0$.If the apparent core radius, where the surface intensity has decreased by a factor of 2 from its central apparent value, is smaller than $2\sigma_\ast (\sigma_\ast = FWHM/2.354)$, the SB profile cannot be deconvolved from the seeing profile (Schweizer 1981; Kormendy 1985). In our observations the average seeing dispersion is about $\sigma_\ast = 0\hbox{$.\!\!^{\prime\prime}$}45$.

In the following, the calculations are restricted to a subsample of galaxies, whose apparent core radii $r_{\rm c,app}$ are larger than $0\hbox{$.\!\!^{\prime\prime}$}9$.The corrections given by Kormendy (1985) were applied to derive true core radii and true central surface brightnesses $\mu_{\rm 0,cor}$.Note that for objects with $r_{\rm c,app} = 0\hbox{$.\!\!^{\prime\prime}$}9$ the correction for the true central surface brightness is of the order of 2 magnitudes, and the true core radius is about a third of the apparent one. At the distance of the Fornax cluster $0\hbox{$.\!\!^{\prime\prime}$}9$ corresponds to about 80 pc. The Local Group dSphs, for example, have core radii between 150 and 600 pc (Caldwell et al. 1992; Mateo et al. 1993). Thus, the apparent surface brightnesses of dEs in the Fornax cluster should be nearly identical with their true central surface brightnesses, whereas compact dwarfs (like M 32) and background galaxies are severely underestimated in their measured $\mu_{\rm peak}$. The core radius of M 32, for example, is about 500 times smaller than that of Local Group and Virgo dEs ($\simeq 1-2$ pc, Kormendy 1985). Figure 3 (lower panel) shows the $\mu_{\rm 0,cor}-V_{\rm tot}$ - diagram for all galaxies with corrections less than 1.5 mag. The different symbol sizes divide the sample in degrees of resolution of the core, as given by the ratio $r_{\rm c,app}/\sigma_\ast$, which can directly be translated into the correction in magnitudes $\Delta\mu$: $\Delta\mu < 0.2$ mag corresponds to $r_{\rm c,app}/\sigma_\ast \gt 5$, $\Delta\mu < 0.5$ mag to $r_{\rm c,app}/\sigma_\ast \gt 3$, and $\Delta\mu < 1.5$ mag to $r_{\rm c,app}/\sigma_\ast \gt 2$.

  

Figure 4: Typical SB profiles of different galaxy types are shown in the four panels. For better illustration most profiles are shifted in $\mu$ as indicated by the numbers. The labels are the catalog names of this paper, cross references of the FCC catalog are given in parenthesis. In the upper left panel ellipticals are plotted together with de Vaucouleurs profile fits. The elliptical CGF 1-1 has a cD halo and is the brightest galaxy of a background galaxy cluster behind NGC 1399. The upper right panel shows the profiles of 4 spirals and 2 irregular galaxies with exponential fits to their disk components. In the lower panels, all galaxies that have been classified as nucleated and non-nucleated dEs (see Table 2) are shown

All non-nucleated Fornax cluster dwarfs are clearly separated from the bulk of background galaxies and fit the sequence of the Local Group dSphs. Their parameters are listed in Table 2. However, three well resolved background galaxies between 17 < V < 19 mag also fall in this range. Visual inspection of these objects showed that they all are spirals seen edge-on. The surface brightness of edge-on spirals appears to be very low due to the light absorption by dust in the plane of their disks.

  

Figure 5: The "n'' parameter of the Sérsic profile fits is plotted versus the total absolute V magnitude for early-type galaxies. Filled and open circles indicate ellipticals and S0 galaxies from our spectroscopic sample (Paper II). Crosses are dwarf ellipticals, asterisks nucleated ones. The two filled triangles in the lower right are the two compact objects found in the Fornax cluster. A typical error for the data points is given in the upper left. For the dwarf galaxies a n-luminosity relation is clearly visible

Most of the galaxies that are located in the dwarf region are already listed in the FCC (see Table 4, Appendix A, for cross references). Only 4 additional galaxies are probably dwarfs in the Fornax cluster due to their morphological appearance and their photometric properties. Their catalog names are: CGF 6-5, CGF 1-44, CGF 3-1, and CGF 10-11.

CGF 6-5 is located close to NGC 1387 and is visible only after subtraction of the galaxy light of NGC 1387. It looks like a nucleated dwarf elliptical judged from its surface brightness profile (see Fig. 4 lower left panel). CGF 1-44 is a dwarf elliptical south-east of NGC 1399. CGF 3-1 is listed in the catalog of probable background galaxies by Ferguson (1989). According to our results this galaxy more likely resembles a dwarf elliptical or dwarf spheroidal in the Fornax cluster. CGF 10-11, located about $3\hbox{$.\mkern-4mu^\prime$}5$ north of NGC 1427, has an irregular shape and a quite blue color (V - I) = 0.9 mag. According to its surface brightness it is most likely a dwarf irregular. Nevertheless, this galaxy would be very small if it would belong to the Fornax cluster, and therefore might be a background object.

Two objects with very high surface brightness have been identified as Fornax members due to their radial velocity (see Paper II). As discussed in more detail in Paper II, these objects might be stripped nucleated dwarf ellipticals or very bright globular clusters. These examples show that compact objects at the Fornax distance can hardly be distinguished in their photometric properties from bulges of background spirals or ellipticals. More compact Fornax objects might be hidden in our galaxy sample. The photometric properties and profile fitting parameters of the galaxies that has been classified as Fornax members due to their morphological appearance, surface brightness - magnitude relation or radial velocity are given in Table 2.

Three different light profiles were fitted to a subsample of our galaxies that have major axis diameters larger than $D_{26} = 7\hbox{$^{\prime\prime}$}$.Depending on the shape of the SB profile type, an exponential law, a r^1/4-law (de Vaucouleurs 1948) and/or a generalized exponential law were fitted to the outer part of the profiles, which are nearly unaffected by seeing effects. The innermost radius limit for all fits was $1\hbox{$.\!\!^{\prime\prime}$}5$.In Fig. 4 selected surface brightness profiles and their fits are shown. The upper panels give typical examples for background ellipticals, spirals and irregulars. The lower panels show all profiles of the Fornax cluster nucleated and non-nucleated dEs from Table 2. The morphological types of the galaxies were not only determined on the basis of the profiles themselves, but also on properties like color, ellipticity, small scale structure (i.e. spiral arms, knots, etc.), and spectral informations (see Paper II). However, with decreasing angular diameter of the galaxy the morphological classification becomes more and more uncertain. Therefore, all type classifications with a "?'' behind (Appendix B) should be taken with caution; they are more a guess than a certain determination.

The ellipticals have been fitted by a de Vaucouleurs profile of the form I(r) = I₀exp$(-7.67(r/r_{\rm eff})^{1/4})$ or $\mu(r) = \mu_0 + 8.328(r/r_{\rm eff})^{1/4}$,$\mu_0$ being the central surface brightness and $r_{\rm eff}$ the effective radius where the surface brightness is half the central value. In addition, we fitted the profiles of all early-type galaxies (Es, S0s, and dEs) by the generalized exponential law (Sérsic 1968) I(r) = I₀exp$(-r/\alpha)^n$ or $\mu(r) = \mu_0 + 1.086(r/\alpha)^n$, n > 0, which has been shown to describe the observed profiles much better (e.g. Graham et al. 1996). Furthermore, it is under discussion whether the exponent "n'' of the Sérsic fit can be used as luminosity indicator. Young & Currie (1994) found that an n-luminosity relation exists for early-type dwarf galaxies. Jerjen & Binggeli (1997) suggested that this relation even is continued towards "normal'' ellipticals. In Fig. 5 we show the "n'' parameter plotted versus the absolute luminosity $M_{V_{\rm tot}}$for all Fornax dwarf elliptical in our sample and the early-type galaxies of our spectroscopic sample (see Paper II). The absolute luminosities were determined by adopting a distance modulus of (m-M)₀ = 31.3 mag to the Fornax dwarfs, and using the radial velocity and a Hubble constant of H₀ = 70 for the other galaxies. Whereas the scatter of "n'' for the brighter galaxies is quite large due to the small angular diameter of the surface brightness profiles, the n-luminosity relation for the dwarf galaxies is clearly visible. The two compact Fornax objects do not follow the relation, but have "n'' values comparable to ellipticals.

Spiral galaxies, S0s, dwarf ellipticals, and irregulars were fitted in the outer (disk) part by an exponential law, I(r) = I₀exp$(-r/r\rm _D)$ or $\mu(r) = \mu_0 + 1.086(r/r\rm _D)$,$r\rm _D$ being the characteristic radius where I₀ has decreased by a factor of e^-1. For some galaxies the inner part of the profile exceeds the fitted exponential law in brightness indicating the presence of a bulge or nucleus. Other galaxies show a light deficiency in the center, which might be due to seeing effects or due to dust. All fitting parameters are summarized in a catalog, Appendix B.