1 Introduction

In recent years, deep galaxy surveys of the vicinity of the Local Group (Côté et al. 1997; Karachentseva & Karachentsev 1998; Jerjen et al. 2000) revealed a significant number of very low surface brightness galaxies. As these most elusive stellar systems in the universe have been identified primarily on morphological grounds their distances remain generally unknown. However, many of them are expected to be nearby dwarf galaxies and as such preferred targets for studies related to galaxy formation and evolution or dark matter.

While the gas-rich dwarfs, the dwarf irregulars (Irrs), can be located relatively easily in space from 21cm radio observations (Huchtmeier et al. 2000), dwarf elliptical galaxies (hereafter dEs, subsuming "dwarf spheroidals'', see Ferguson & Binggeli 1994) have a low gas content and thus remain undetected in H I. Moreover, their low surface brightness makes optical spectroscopy feasible only for the few brightest objects (Jerjen et al. 2000, hereafter JFB00). Hence, the only way to identify nearby diffuse dEs and to unveil their physical nature is to estimate their distances from their stellar contents.

In principal, the distance of a dE can be obtained via the colour-magnitude diagram (Armandroff et al. 1999), the tip of the red giant branch (TRGB) magnitude (e.g. Karachentsev et al. 2000, hereafter K00), or the RR Lyrae stars (Saha & Hoessel 1990). But the requirement of resolving the galaxy into stars makes these methods costly and time consuming. A more practical and similarly accurate distance indicator would be required if distances for a larger number of dE candidates shall be measured in an efficient way. Such a distance indicator provides a powerful tool to explore the spatial distribution of a statistically meaningful sample of nearby dEs out to a distance $D\approx 10$Mpc and beyond. As dEs are the best tracers of high-density regions (known as the morphology-density relation, Binggeli et al. 1990) they flag the gravitational centres in the Local Volume and thus hold valuable information on the substructure of the Supergalactic plane where most of the nearby galaxies are concentrated (e.g. Jerjen et al. 1998, hereafter JFB98; Binggeli 2001 and references therein).

In search for an efficient and accurate distance indicator for dEs, Jerjen and collaborators (JFB98; JFB00) tested the Surface Brightness Fluctuation (SBF) method. This method was introduced by Tonry & Schneider (1988) to measure distances to high surface brightness giant ellipticals. It is based on the discrete sampling of a galaxy image with the CCD detector and the resulting pixel-to-pixel variance due to the light of unresolved RGB stars. Analysing CCD data obtained at the 2.3 m SSO telescope, JFB98 and JFB00 successfully measured R-band SBF magnitudes in dwarf galaxies found in the nearby Sculptor and CenA groups (2<D<5Mpc).

While JFB00 showed convincingly that it is technically feasible to quantify surface brightness fluctuations in dEs, there is no empirical calibration of the SBF method as distance indicator for this galaxy type available yet due to the lack of calibrators. All reported SBF distances had to rely on the theoretical relationship between (B-R) colour and absolute fluctuation magnitude $\overline {M}_{R}$ that was calculated from Worthey's (1994) population synthesis models and the Padova isochrones (Bertelli et al. 1994). First results found good qualitative agreements between SBF distances for dEs in the CenA group and the mean group distance. However, the SBF distance for the Sculptor group dwarf ESO540-032 turned out to be significantly shorter than the value derived from the RGB tip magnitude (Jerjen & Rejkuba 2000). The existing results thus pose the questions about the reliability of the theoretical models to predict $\overline {M}_{R}$, the accuracy of the SBF method for dEs and about the limits of the method. The latter issue is related to the fact that ESO540-032 was morphologically classified as an intermediate type dwarf with optical properties of both dEs and Irrs. The mixed morphology indicates the presence of a more complex underlying stellar population (i.e. recent star formation activities and a wider spread in age and metallicity) than the predominantly old, metal-poor populations observed in genuine dEs.

To improve our understanding of the surface brightness fluctuations in dwarf elliptical galaxies we studied six nearby dEs in the northern hemisphere. DDO 44 (Karachentsev et al. 1999, hereafter K99) is a member of the NGC 2403 group, UGC 4998 (Bremnes et al. 1998) is a dwarf in the background of the M 81 group, KK98 77 and DDO 71 (K00) are true members of the M 81 group, and the two dwarfs DDO 113 and UGC 7356 are found in the direction of the Canes Venatici I (CVn I) cloud (Tully & Fisher 1987; Binggeli et al. 1990; Bremnes et al. 2000). Of particular interest for the present study are DDO 44, KK98 77, and DDO 71 for which independent TRGB distances have been reported (K98; K00). In Table 1 we give a complete list of our galaxy sample including galaxy name, associated group, morphological type within the extended Hubble classification system (Sandage & Binggeli 1984), and coordinates.

Figure 1: Cleaned R-band master images of the six dwarf galaxies with the analysed square SBF fields overlaid. The FOV is $2\hbox {$.\mkern -4mu^\prime $ }5 \times 2\hbox {$.\mkern -4mu^\prime $ }5$. North is up, East to the left.

In Sect. 2, we describe the observations and data reduction. The SBF analysis is presented in Sect. 3. We develop the semiempirical calibration of the SBF method for dEs in Sect. 4 and compare it with the model predictions based on synthetic stellar population models. We then discuss the implications of our results and derive in Sect. 5 distances for UGC 4998, DDO 113, and UGC 7356. Finally, we present the integral properties of the dwarfs in Sect. 6 and draw the conclusions of this work in Sect. 7.

 

 

Table 1: Selected sample of nearby early-type dwarf galaxies.

			RA	Dec
Name	Group	Type	(J2000.0)	(J2000.0)
DDO 44	NGC 2403	dE	07 34 11.4	66 53 10
UGC 4998	M 81 BG	dS0	09 25 12.1	68 22 59
KK 98 77	M 81	dE	09 50 10.5	67 30 24
DDO 71	M 81	dE	10 05 06.4	66 33 32
DDO 113	CVn I	dE	12 14 57.9	36 13 08
UGC 7356	CVn I	dE, N:	12 19 09.1	47 05 23

 

 

Table 2: Summary of observations.

		t			FWHM
Name	Date	(s)	F	AM	( $\hbox{$^{\prime\prime}$ }$)
DDO 44	22 Jan.	6$\times$600	B	1.78	1.6
DDO 44	22 Jan.	7$\times$600	R	1.53	1.3
KK98 77	22 Jan.	6$\times$600	B	1.29	1.0
KK98 77	22 Jan.	5$\times$600	R	1.33	0.9
DDO 113	22 Jan.	6$\times$600	B	1.01	1.1
DDO 113	22 Jan.	6$\times$600	R	1.09	0.9
UGC 4998	23 Jan.	6$\times$600	B	1.41	1.0
UGC 4998	23 Jan.	6$\times$600	R	1.32	0.9
DDO 71	23 Jan.	6$\times$600	B	1.27	0.9
DDO 71	23 Jan.	6$\times$600	R	1.27	0.8
UGC 7356	23 Jan.	6$\times$600	B	1.08	1.2
UGC 7356	23 Jan.	4$\times$600	R	1.05	1.0

 

 

Table 3: Photometric calibration coefficients.

Date	F	ZP	k	c
22 Jan.	B	$-25.54\pm0.02$	$0.22\pm0.01$	$-0.040\pm0.004$
22 Jan.	R	$-25.41\pm0.02$	$0.09\pm0.02$	$0.031\pm0.006$
23 Jan.	B	$-25.54\pm0.02$	$0.22\pm0.01$	$-0.037\pm0.004$
23 Jan.	R	$-25.42\pm0.02$	$0.09\pm0.02$	$0.033\pm0.006$
24 Jan.	B	$-25.53\pm0.02$	$0.22\pm0.01$	$-0.042\pm0.003$
24 Jan.	R	$-25.41\pm0.02$	$0.09\pm0.02$	$0.030\pm0.006$