4 Results

   
4.1 Model-free photometric parameters and radial profiles

The global photometric parameters of our objects are listed in Table 3, and the columns represent: the galaxies number ordered by increasing right ascension (1), name of the galaxy (2), total apparent magnitude in the B band (3), total apparent magnitude in the R band (4), effective radius in B in arcsec(5), effective radius in R in arcsec (6), effective surface brightness in B $[\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobreak\hfi... ... \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$ }}]$ (7), effective surface brightness in R $[\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobreak\hfi... ... \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$ }}]$ (8) , total B-Rcolor index (9) and galactic absorption in B from the NED (10).

The total apparent magnitude of a galaxy was read off the growth curve at a sufficiently large radius, i.e. where the growth curve becomes asymptotically flat. The model-free effective radius was then read at half of the total growth curve intensity. The effective surface brightness is then given by

$$\mathopen{<} \mu \mathclose{>}_\mathrm{ eff}[\mathrm{mag}/\if... ... M + 5 \log(R_\mathrm{ eff}[{\hbox{$^{\prime\prime}$ }}]) + 2.$$ (1)

All radii refer to equivalent radii, $r = \sqrt {ab}$, where a and bare the major and minor axis of the galaxy, respectively. Surface brightness profiles were obtained by differentiating the growth curves with respect to equivalent radius. The resulting B and R surface brightness profiles are shown in Fig. 3. The profiles are traced down to the level where the uncertainties owing to the fluctuations in the sky level on the profile become dominant. As discussed in Sect. 4.3, this represents approx. $28.5\,\mathrm{mag}/ \ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobre... ...} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$ }}$ in B and $27.5\,\mathrm{mag}/ \ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobre... ...} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$ }}$ in R. Galactic absorption values were taken from the NED database. A correction for internal extinction was not applied, as it is not well known in the case if dwarf galaxies. The profiles drawn in the figures have been slightly smoothed with a running window of width $\approx 5 \hbox{$^{\prime\prime}$ }$ and are plotted on a linear radius scale.

 

 

Table 3: Global photometric properties. See text for explanations

No.	Galaxy	BT	RT	rB</I> eff	rR</I> eff	$\mathopen{<} \mu \mathclose{>}^B_\mathrm{ eff}$	$\mathopen{<} \mu \mathclose{>}^R_\mathrm{ eff}$	B-R	AB
1.	UGC 06541	14.32	13.46	14.99	17.98	22.20	21.74	0.86	0.00
2.	UGC 06565	11.92	10.94	28.60	37.12	21.20	20.79	0.98	0.00
3.	UGC 06572	14.38	13.57	16.30	19.92	22.44	22.07	0.81	0.00
4.	UGC 06817	13.45	12.61	53.41	61.37	24.09	23.55	0.85	0.00
5.	UGC 07047	12.93	11.93	42.00	46.14	23.05	22.25	1.00	0.00
6.	UGC 07165	12.41	11.11	16.09	15.52	20.44	19.06	1.30	0.04
7.	UGC 07199	13.66	12.65	22.92	27.39	22.46	21.83	1.02	0.00
8.	UGCA 276	15.70	14.58	38.24	37.69	25.62	24.46	1.13	0.00
9.	UGC 07298	15.96	15.25	13.46	15.70	23.61	23.23	0.72	0.04
10.	UGC 07335	13.13	11.87	29.66	31.01	22.49	21.33	1.26	0.00
11.	UGC 07356	15.58	14.21	23.78	26.61	24.46	23.33	1.37	0.00
12.	UGC 07369	14.84	13.46	16.07	17.30	22.87	21.65	1.38	0.07
13.	UGC 07559		13.55		35.86		23.32		0.00
14.	UGC 07599	14.80		22.15		23.52			0.00
15.	UGC 07639	13.94	12.93	26.11	31.64	23.02	22.43	1.01	0.00

Figure 3: Radial surface brightness profiles of the observed dwarf galaxies in B (filled circles) and R (open circles) except forUGC 7559 (only R) and UGC 7599 (only B). The central data point for UGC 7165 in R is at $17.05\,\mathrm{mag}$. The dotted lines represent the exponential fits, as described in Sect. 4.2, and the fitting region is marked by triangles on the x-axis. The error-bars are drawn with hats for the B band data points and without for the R band data points. These are calculated for (as described in Sect. 4.3), and are centered on the best-fitting exponentials. The radii are all equivalent radii ( $r = \sqrt {ab}$)

Color profiles obtained by subtracting the R from the B surface brightness profiles, together with the difference between the slopes of exponential fits (dotted line, see Sect. 4.2) are plotted in Fig. 4.

Figure 4: Radial B-R color profiles. The dotted lines represent the exponential fits, as described in Sect. 4.2. The error-bars have been computed as described in Sect. 4.3

   
4.2 The exponential model: Fits and parameters

It is well accepted that the radial intensity profiles of dwarf galaxies can be reasonably well fitted by a simple exponential (De Vaucouleurs 1959; Binggeli & Cameron 1993). This applies not only for dwarf ellipticals, but also for irregulars, if one looks aside from the brighter star-forming regions and considers the underlying older populations. These profiles can be written as

$$I(r) = I_0 \:\exp{\left(-{r\over r_0}\right)}\equiv I_0\:{\rm e}^{-\alpha r},$$ (2)

that in surface brightness representation becomes a straight line

$$\mu (r)= \mu_0 + 1.086\: \alpha r.$$ (3)

The central extrapolated surface brightness $\mu_0$ and the exponential scale length $1/\alpha$ are the two free parameters of the exponential fit. In this work the fits to the profiles were done on the outer parts of the profiles by a least squares fitting procedure. The best-fitting parameters are listed in Table 4. The best-fitting exponential profiles are plotted as dash-dotted lines along with the observed profiles in Fig. 3. The deviation from a pure exponential law is expressed by the difference $\Delta M$ between the total magnitude of an exponential intensity law given by

$$M_{\exp}=\mu_0^{\exp} + 5\log\alpha -2.0,$$ (4)

and the actual measured total magnitude. The results are shown in Table 4. The difference shows the goodness of fit of the exponential intensity profile. The columns of Table 4 are as follows: (1) as Col. 1 of Table 3, (2) as Col. 2 of Table 3, extrapolated central surface brightness according to Eq. (3) in $B \,[\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\nobreak... ... \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$ }}]$ (3), same in R (4), exponential scale length in $B\,[\hbox{$^{\prime\prime}$ }]$ (5), same in R (6), difference between the total magnitude as derived from the exponential model and the true total magnitude in B (7), same in R (8), radial color gradient determined from the difference in the slopes of the model fits as described in Sect. 4 $[\mathrm{mag}/\hbox{$^{\prime\prime}$ }]$ (9). dD..3

 

 

Table 4: Model parameters. See text for explanations

No.	Galaxy	$(\mu^{\exp}_0)_B$	$(\mu^{\exp}_0)_R$	$1/{\alpha_B}$	$1/{\alpha_R}$	$\Delta M_B$	$\Delta M_R$	$\mathrm{ d}(B-R)\over \mathrm{ d}r$
1.	UGC 06541	22.49	21.97	12.60	15.53	0.67	0.55	0.016
2.	UGC 06565	22.40	21.29	35.88	36.31	0.71	0.55	0.000
3.	UGC 06572	21.71	21.25	10.73	12.37	0.18	0.22	0.013
4.	UGC 06817	23.09	22.55	32.83	38.56	0.05	0.01	0.005
5.	UGC 07047	22.89	22.57	27.93	35.46	0.73	0.89	0.008
6.	UGC 07165	20.29	18.94	12.54	12.36	0.39	0.37	-0.001
7.	UGC 07199	22.68	21.41	20.23	19.71	0.48	0.29	-0.001
8.	UGCA 276	24.12	22.95	19.75	20.10	-0.06	-0.14	0.001
9.	UGC 07298	22.54	22.44	8.05	9.93	0.05	0.21	0.026
10.	UGC 07335	21.57	20.38	18.48	19.01	0.10	0.12	0.002
11.	UGC 07356	23.37	22.82	13.65	18.03	0.11	0.33	0.019
12.	UGC 07369	22.47	21.24	11.82	12.34	0.27	0.32	0.004
13.	UGC 07559		22.14		21.75		-0.09
14.	UGC 07599	24.72		21.41		1.27
15.	UGC 07639	22.57	21.79	19.24	21.56	0.21	0.20	0.006

   
4.3 Photometric uncertainties

The photometric calibration represents the greatest source of error on the global parameters. The nights were not photometric, so calibrations were done with fields close on the sky to the actual objects, see Sect. 3. Some nights were rejected altogether because of the changing transparency on short time scales. The combined (zero point and slope of the extinction curve) statistical uncertainty on the photometric calibration is estimated to be about 0.1 mag. The uncertainties on the surface brightness profiles (SBP) are a combination of Poisson noise and, at low levels, the large-scale sky fluctuations, owing to flat fielding and sky subtraction imprecision. The uncertainties shown in Fig. 3 have been calculated assuming the galaxies have pure exponential SBPs. To the Poisson noise caused by the photons we added a constant contribution corresponding to $0.5\%$ of the actual measured sky background, that combines the flat field and sky subtraction terms mentioned above. This level of accuracy for the flat fielding and sky subtraction was conservatively estimated by inspecting many frames. Most frames show better flat fielding accuracy. The uncertainties on the profiles were then calculated for azimuthally averaged annuli of one arc second width. For the actual calculations, we considered circles instead of ellipses and compared equivalent radii when determining the error at a given point on a SBP. The galaxy surface brightness and the fluctuations in the sky background reach similar levels at $\sim 28.5$ in B and $\sim 27.5 \,\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$ }$\sqcup$ }\else{\unskip\... ...} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$ }}$ in R. The errors on the color profiles, shown in Fig. 4, were estimated using the error term as described above for each color and applying usual error formulae for logarithms and combining the errors thus obtained for each color by quadrature.

Comparing the B magnitudes from this paper with RC3 data from the NED, one sees that our photometry agrees well with the RC3 for ten galaxies, see Fig. 5. Three galaxies, namely UGC 07199, UGC 07356 and UGC 07559 have brighter magnitudes and one, UGC 7298, has a fainter magnitude in this paper as compared to the values in the RC3. For a subsample of our galaxies, there are total magnitudes calculated by Makarova et al. (1997, 1998). Their data is shown in Fig. 5 as lozenges. The agreement between both photometries is better than for the RC3 data, especially for UGC 7356.

Figure 5: Comparison between the photometry of the present paper and data from the RC3 catalog (crosses) and from Makarova et al. (lozenges). The B magnitudes are from the present paper, and delta mag is the difference between our photometry and RC3 or Makarova et al. (1997, 1998)