4 Results

 

4.1 Model-free photometric parameters and radial profiles

 

  

Table 3: Global photometric properties. See text for explanations

The global photometric parameters of our objects are listed in Table 3, and the columns represent:
Column 1: number of the galaxy ordered by increasing right ascension.
Column 2: name of the galaxy.
Column 3: total apparent magnitude in the B band.
Column 4: total apparent magnitude in the R band.
Column 5: effective radius in B $[\hbox{$^{\prime\prime}$}]$.
Column 6: effective radius in R $[\hbox{$^{\prime\prime}$}]$.
Column 7: effective surface brightness in B $[\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\unskip\nobreak\hfil ... ...} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}]$.
Column 8: effective surface brightness in R $[\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\unskip\nobreak\hfil ... ...} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}]$.
Column 9: radius where $< \mu \gt\ = 25 \, \mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\u... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$ in the B band $[\hbox{$^{\prime\prime}$}]$.
Column 10: as above, except $< \mu \gt\ = 26 \, \mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\un... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$.
Column 11: as above, except $< \mu \gt\ = 27 \, \mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\un... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$.
Column 12: radius where $< \mu \gt\ = 25 \, \mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\u... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$ in the R band $[\hbox{$^{\prime\prime}$}]$.
Column 13: as above, except $< \mu \gt\ = 26 \, \mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\un... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$.
Column 14: as above, except $< \mu \gt\ = 27 \, \mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\un... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$.
Column 15: total B-R $[\mathrm{mag}]$.

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 simply read at half of the total growth curve intensity. The effective surface brightness is then given by

$$\begin{eqnarray} < \mu \gt _\mathrm{ eff}[\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqc... ...$}}]= M + 5 \log(R_\mathrm{ eff}[{\hbox{$^{\prime\prime}$}}]) + 2.\end{eqnarray}$$ (1)

All radii refer to equivalent radii ($r=\sqrt{ab}$, where a and b are the major and minor axes of the galaxy, respectively).

Surface brightness profiles were obtained by differentiating the growth curves with respect to radius. For 20 of our sample galaxies the resulting B and R profiles are shown in Fig. 3. No profile could be constructed for UGCA 342 due to a bright nearby star (cf. Sect. 6 and Fig. 2). The profiles have been slightly smoothed (with a running window of width $\approx 3 \hbox{$^{\prime\prime}$}$) and are plotted on a linear radius scale.

  

Figure 3: Radial surface brightness profiles of the observed dwarf galaxies in B (lower) and R (upper) except for NGC5204 (only R) and DDO181 and MCG 9-23-21 for which only B data are available. The dash-dotted lines represent the exponential fits, as described in Sect. 4.2 and the dashed and dotted lines represent the error envelopes as described in Sect. 4.4. The radii are all equivalent radii ($r=\sqrt{ab}$)

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

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

which in surface brightness representation becomes a straight line

$$\begin{eqnarray} \mu (r)= \mu_0 + 1.086\: \alpha r.\end{eqnarray}$$ (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 (note, however, that the very outermost parts were not considered in the fitting, as they are often "flaring up'', see below Sect. 5). 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.

  

Table 4: Model parameters. See text for explanations

The deviation from a pure exponential law is expressed by the difference between the total magnitude of an exponential intensity law given by

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

and the actual measured total magnitude. The results are shown in Table 4. The difference is an indication of the goodness of fit of the exponential intensity profile. The columns of Table 4 are as follows:
Column 1: as Col. 1 of Table 3.
Column 2: as Col. 2 of Table 3.
Column 3: extrapolated central surface brightness according to equation 3 in $B \,[\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\unskip\nobreak\h... ...} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}]$.
Column 4: as above but in R.
Column 5: exponential scale length in $B\,[\hbox{$^{\prime\prime}$}]$.
Column 6: as above but in R.
Column 7: difference between the total magnitude as derived from the exponential model and the true total magnitude in B.
Column 8: as above but in R.
Column 9: radial colour gradient determined from the difference in the slopes of the model fits as described in Sect. 4.3 $[\mathrm{mag}/\hbox{$^{\prime\prime}$}]$.

4.3 Colour gradients

 As one can see in Table 4, the colour gradients of the galaxies are very small, if not zero ($< {\mathrm{ d}(B-R)/ \mathrm{ d}r}\gt\ = 0.012\,\pm 0.013\,\mathrm{mag}/\hbox{$^{\prime\prime}$}$). Many authors report that colour profiles show very small gradients or are flat in the case of dwarf galaxies (Paper I, Patterson & Thuan 1996). We find that if the galaxies do show a trend in their colour profiles, they become slightly redder with increasing radius. The actual colour profiles together with the difference between the slopes of exponential fits (dash-dotted) are plotted in Fig. 4.

  

Figure 4: Radial B-R colour profiles. The dot dashed lines represent the exponential fits, as described in Sect. 4.2 and the dotted lines represent the error envelopes as described in Sect. 4.4

4.4 Photometric uncertainties

 Uncertainties in the photometry have multiple sources: calibration errors, flatfielding and sky subtraction, photon shot noise, readout noise, contamination by cosmic rays, foreground stars and background galaxies.

The largest contribution to the uncertainties in the global photometric parameters is from the photometric calibration. As the nights were non-photometric, one must beware of uncontrollable errors in the zero-point and the extinction coefficient. The statistical uncertainty on the photometric calibration is of the order of 0.1 mag, due to an uncertainty of $\sim 0.08$ mag and $\sim 0.05$ on the zero-point and the extinction coefficient, respectively.

The uncertainties on the photometric profiles at low levels are dominated by the non-flatness of the sky background. The pixel-to-pixel fluctuations caused by photon shot noise are averaged out by measuring azimuthally averaged profiles. At typical sky levels of the order of $\sim 22.7 \,\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\unskip\no... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$ in B, and $\sim 21.7 \,{\rm mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\unskip\nobre... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$ in R, and a flat-fielding accurate to $\mathrel{\hbox{\rlap{\lower.55ex \hbox {$\sim$}} \kern-.3em \raise.4ex \hbox{$<$}}}0.5\%$ of the sky background, the sky fluctuations reach values similar to the the galaxy profiles at respectively $\sim 28.5$ and $\sim 27.5 \,\mathrm{mag}/\ifmmode\hbox{\rlap{$\sqcap$}$\sqcup$}\else{\unskip\no... ...$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi{\hbox{$^{\prime\prime}$}}$.

To have a handle on this error along a profile, we have calculated error envelopes for all our profiles based on their best-fitting exponentials. The combined uncertainty caused by photon shot noise from the sky and the galaxy, calculated for azimuthally averaged $1\hbox{$^{\prime\prime}$}$ annuli, has been added in quadrature with a large-scale sky flatness and subtraction error term set to a constant $0.5\%$ of the actual sky electron counts. The error term obtained this way has been added or subtracted, respectively, from the intensity profiles corresponding to exponential surface brightness profiles and then converted to magnitudes to produce the upper and lower error envelopes. These error envelopes are shown in Fig. 3 along with the observed and model profiles. The colour profile error envelopes, shown in Fig. 4 as dotted lines, have been calculated by using the error term as described above for each colour and applying usual error formulae for logarithms and combining the errors thus obtained for each colour by quadrature. It is to be noted that the large scale fluctuation level of $0.5\%$ of the sky background is an upper limit, most frames showing less variation, i.e. these error estimates are rather conservative . The calibration zero-point uncertainty is not included in the plots.

The errors on the profiles at low luminosity do not influence the total magnitude to a large extent, but sources projected onto or near the galaxies do. We masked out such objects, trying not to eliminate HII regions from the galaxy. An overall assessment of our photometric accuracy is provided by a comparison with external data. In Fig. 5 photometry from this paper is compared to data published in Schmidt & Boller (1992a). The agreement is quite good, $\sigma_{\rm m} \sim 0.13\,\mathrm{mag}$ in the B band.

  

Figure 5: Comparison between the photometry of the present paper and the data published in Schmidt & Boller (1992a)