We concentrate on the following features of the globular cluster candidates: their color distribution, their luminosity function, and their spatial distribution. Due to the small number of candidates found around each dwarf, we will analyze the characteristics of all of them together.

The (C-T₁) color distribution is shown in Fig. 3; it is an histogram smoothed by means of a Gaussian with a dispersion comparable to the errors in (C-T₁). The color-metallicity calibration from Geisler & Forte (1990) has also been included in this figure. In order to take into account the background contamination we have used a comparison field located at $3~\hbox{$.\!\!^\circ$ }5$ north-east from the cluster center, which has already been used by Dirsch et al. (2002b) and whose color distribution is also shown in Fig. 3, after normalizing for the different field sizes corresponding to the dwarfs' images and to the background's one. The comparison field was observed with C and $R_{\rm KC}$ filters instead of C and T₁, but according to Geisler (1996), the Kron-Cousins R and the Washington T₁ magnitudes are similar, to a high degree of accuracy, for the color range considered in this paper. The comparison field is not very far from FCC 76, the dwarf with the largest projected distance from NGC 1399 in the sample; thus, the contribution from the background may be probably overestimated and so we may be underestimating the surface densities obtained after this correction. The surface density of globular cluster candidates for each dwarf field, after the background-correction, is given in the last column of Table 1. The color distribution of the raw data, as can be seen in Fig. 3, is extended and appears to be bimodal (see also the color-magnitude diagram displayed in Fig. 2). In order to quantify this apparent bimodality in a statistical way, we have applied to the raw data the KMM test which helps to detect and evaluate bimodality in datasets (see Ashman et al. 1994 for a description of the test and its application). The results of the test indicate that two Gaussians with means at 1.18 and 1.86 mag can be fit to the set of (C-T₁) values, and assuming that both Gaussians have the same covariance (homoscedastic fitting) we obtain a dispersion $\sigma$ = 0.2 mag for them. The hypothesis that this (C-T₁) distribution is unimodal rather than bimodal is rejected at a confidence level of 100% according to the KMM test. It must be taken into account that the number of candidates is small (75 objects) but, according to the study of the KMM algorithm sensitivity performed by Ashman et al. (1994), there is a sufficient large separation in the means of the two Gaussians (3.4 $\sigma$ ) to be able to obtain a significant rejection of the unimodal hypothesis. The result of the background subtraction is also shown in Fig. 3, where the corrected color distribution appears to be bimodal too, with two possible peaks that would be located at $(C-T_1) \approx$ 1.2 and 1.9 mag, corresponding to metallicities [Fe/H] $\approx -1.6$ and 0.1, respectively (Geisler & Forte 1990). However, it is not possible to apply the KMM test to this corrected distribution because the number of candidates is smaller than 50, and Ashman et al. (1994) state that in this cases the test does not provide a reliable result for detecting bimodality. Anyway, even though we cannot confirm statistically the bimodality, it is clear that we do not find a single population of metal-poor globular cluster candidates around the dwarfs, as happens in the cases already mentioned in the Introduction; instead, an extended distribution that expands over the whole metallicity range, from metal-poor to metal-rich populations, is detected.

In spite of the apparent symmetry in the corrected color distribution displayed in Fig. 3, we cannot be sure that the number of these probable metal-poor and metal-rich candidates are similar because we do not have a complete area sample. Figure 1 shows that there are more dwarfs near to NGC 1399 than far from it. We have not attempted to search for radial globular clusters color gradients with respect to the dwarfs or to the Fornax Cluster center due to the small sample we are considering. Whether or not two globular cluster populations should be expected in dwarf galaxies is still unclear. All the globular clusters around dwarfs in the Local Group studied by Minniti et al. (1996) had metallicities that correspond to a metal-poor population, with [Fe/H] $\leq -1$ . They suggested that the dE galaxies included in their study seem to have formed no metal-rich globular clusters. In turn, Durrell et al. (1996b) found a possible bimodality in the colors of the globular clusters of the Virgo dwarf VCC 1254, which they speculate might correspond to two phases of globular cluster formation.

With regard to the results for the NGC 1399 globular cluster system, Ostrov et al. (1998) identified globular clusters located between $0\farcm5$ and $4\hbox{$^\prime$ }$ from the galaxy center finding two globular cluster populations with $(C-T_1) \approx$ 1.3 and 1.8 mag, respectively. In turn, Dirsch et al. (2002b) performed a wide-field study of this system and showed that the innermost sample, between $1\farcm8$ and $4\farcm5$ , was clearly bimodal with peaks at $(C-T_1) \approx$ 1.3 and 1.75 mag; at larger radii, from $4\farcm5$ up to $22\hbox{$^\prime$ }$ , the metal-poor population became dominant without changing the position of the blue peak.

3.2 Luminosity function

We plot the luminosity function (background-corrected) in Fig. 4: an histogram of the number of globular cluster candidates vs. T₁, where we use an upper limiting magnitude, T₁ = 21.5 mag, omitting the last bin where the completeness of the red candidates is more seriously affected. A Gaussian distribution, calculated with the parameters obtained by Ostrov et al. (1998) fitting the luminosity function of the NGC 1399 globular cluster system, is included for comparison. Our sample covers only 7% of the area under that Gaussian and, after background subtraction, we are left with 37 globular cluster candidates with magnitudes 19 < T₁ < 21.5. Although it is a small sample, we attempt to compare it with the number of globular clusters that we should have found, in a similar area, if they belonged to the dwarf galaxies' globular cluster systems. We calculate the total integrated brightness of our sample's dEs by means of the T₁ total integrated magnitudes of the dwarfs given by Cellone et al. (1994), the adopted distance modulus to the Fornax Cluster and the relation between V and T₁ magnitudes mentioned above; thus, we obtain a total integrated visual brightness for the sample of -18.8 mag. As the range of specific frequencies proposed for dEs is $S_{\rm N} = 2$ -6 (Miller et al. 1998a; Elmegreen 1999), we estimate that we should have found between 4 and 13 dwarfs' globular cluster candidates, within the mentioned T₁ range. By comparison, we have identified three to ten times more globular cluster candidates than what is inferred from the $S_{\rm N}$ values.

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{MS2948f4.eps}}\end{figure}$

Figure 4: Luminosity function (background-corrected) for the globular cluster candidates. The dashed line represents a Gaussian with < T₁ > = 23.3 mag and $\sigma~=~1.2$ mag. Errors are based on Poisson statistics.

3.3 Spatial distribution

3.3.1 Distribution with respect to the dwarf centers

If the globular cluster candidates are bound to the respective dwarf galaxies, the projected density of globular clusters vs. galactocentric distance is expected to increase towards the center. This behavior can be clearly seen in the Fig. 5 of Lotz et al. (2001), which shows the summed radial distribution of globular cluster candidates from a sample of 51 dEs. Figure 5 depicts the surface number density of globular clusters (background-corrected), calculated in concentric annuli around each of the dwarfs and summed over all of them. These surface densities are estimated as follows. First, a set of 20 $^{\prime\prime}$ wide annuli is established around each dwarf, taking into account the different scales of the images. For each image, annuli with more than 60% of their area outside the frame limits were discarded, thus leading to the 160 $^{\prime\prime}$ limit in angular distance. Then, for each dwarf, the number of globular candidates is estimated within each annulus, applying a completeness correction to the annuli lying partly outside the corresponding frame. Afterwards, the counts for each annulus are background-corrected, subtracting the density of the background field multiplied by the area of the corresponding complete annulus. Finally, the background-corrected counts are summed over the annuli defined by the same angular distance from each dwarf, and divided by its complete area. As can be seen in Fig. 5, no concentration towards the center is evident. In order to demonstrate this statistically, we compare this observed distribution with a uniform distribution, that is, one with a constant number density calculated as the same number of globular clusters, scattered across the same total area. The result of a $\chi ^2$ test performed between them, indicates that the observed distribution is statistically consistent with being drawn from a uniform distribution at a significance level of 89%. Under this evidence, it is not possible to assert that these globular cluster candidates are bound to the respective dwarfs as they show no concentration to the dwarf centers, although we cannot confirm this hypothesis without the aid of radial velocities. We must take into account that the studied radial distribution shown in Fig. 5 extends up to 14 kpc from the center of the dEs. The radial density profiles from Lotz et al. (2001) reach almost zero value at shorter distances from the dwarfs, between 1.1 and 8.7 kpc, according to the dwarf's exponential scalelength they use and the distance modulus we have adopted, while the summed radial distribution of the globular cluster system for 11 Virgo dEs by Durrell et al. (1996b) extends to only 2.5 kpc. Both results indicate that the globular cluster systems of dwarfs are rather compact.

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{MS2948f5.eps}}\end{figure}$

Figure 5: Surface density distribution of the globular cluster candidates with respect to the dwarf galaxies. Errors are based on Poisson statistics.

$\begin{figure} \par\resizebox{\hsize}{!}{\includegraphics[clip]{MS2948f6.eps}}\end{figure}$

Figure 6: Surface density of the globular cluster candidates (background-corrected) with respect to the Fornax Cluster center (NGC 1399) grouped according to its angular distance from it (less than or greater than 80 $^\prime$ ). Dotted circles correspond to the nucleated dEs, open triangles to the non-nucleated dEs and filled squares to all the dE galaxies. Errors are based on Poisson statistics.

3 Results

3.1 Color distribution

3.2 Luminosity function

3.3 Spatial distribution

3.3.1 Distribution with respect to the dwarf centers

3.3.2 Distribution with respect to the cluster center