4. Results

4.1. Model-free photometric parameters and radial profiles

  Model-free photometric parameters as well as radial brightness profiles can easily be derived from the GC's. Indeed, by definition the GC is the function defined by the radial integral of the flux per unit area for increasing radius, that is
 

where, f(r') is the average flux per unit area at radius r'. For instance the total apparent luminosity M is the asymptotic value of the total flux converted into astronomical magnitudes. The effective radius , or half light radius, is the radius where . The effective surface brightness is then the average surface brightness within the effective radius, which can be written as
 
Finally, the azimuthally averaged surface brightness profiles are obtained by differentiating the GC's with respect to radius. Indeed , as one measures F(r) by the procedure described above, and not f(r), one has
 
where C is a calibration constant. It is then possible to obtain R₂₅, R₂₆ and R₂₇, radii at which the surface brightness equals 25, 26 and 27 respectively.

The global photometric parameters are listed in Table 2 (click here), and the columns represent:
: number of the galaxy ordered by increasing right ascension
: name of the galaxy
: total apparent magnitude in the B band
: total apparent magnitude in the R band
: effective radius in B (arcsecs)
: effective radius in R (arcsecs)
: effective surface brightness in B ()
: effective surface brightness in R ()
: radius where in the B band (arcsecs)
: as above, except
: as above, except
: radius where in the R band (arcsecs)
: as above, except
: as above, except
: total B-R in magnitudes.

 

Number Galaxy R^B₂₅ R^B₂₆ R^B₂₇ R^R₂₅ R^R₂₆ R^R₂₇ B-R

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

3 DDO 53 14.62 13.60 32.3 40.8 24.17 23.66 36.2 51.6 63.1 52.4 71.6 95.5 1.02

4 UGC 4483 15.12 14.70 19.2 17.7 23.54 22.94 33.1 37.0 43.9 34.6 38.5 42.4 0.42

5 KAR 54 15.75 14.35 22.33 29.3 24.50 23.68 23.9 34.6 40.8 35.4 53.1 67.8 1.41

6 UGC 4998 14.47 13.24 25.4 28.5 23.49 22.52 34.6 49.3 65.4 54.7 80.1 104.7 1.23

7 HoI 13.69 12.69 69.3 79.3 24.90 24.19 64.3 93.2 118.6 92.4 132.4 174.8 1.00

8 BK 1N 17.41 15.97 16.17 16.6 25.45 24.08 - 16.2 25.4 19.2 26.9 40.8 1.43

9 NGC 2976 10.94 9.66 55.0 57.0 21.64 20.44 134.0 164.0 - - - - 1.28

10 BK 2N 18.14 16.99 10 10.4 25.14 24.08 5.4 10.8 18.5 11.5 19.2 25.4 1.14

11 KAR 59 - - - - - - - - - - - - -

12 BK 3N 18.89 18.44 7.7 7.3 25.23 24.76 - 10.0 12.3 - 10.8 18.5 0.45

16 KAR 61 15.17 13.64 50.8 56.2 25.70 24.39 12.3 35.4 72.4 53.1 94.7 120.1 1.53

17 Ho IX - - - - - - - - - - - - -

20 BK 5N 17.46 16.27 19.25 19.2 25.89 24.69 - 13.1 26.9 16.2 31.6 37.7 1.19

21 DDO 71 15.95 14.27 29.25 33.1 25.28 23.87 12.3 31.6 50.0 42.3 59.3 74.7 1.68

22 UGC 5423 - - - - - - - - - - - - -

23 KAR 64 15.46 14.04 36.19 40.0 25.25 24.05 16.9 34.6 54.7 41.6 66.2 101.6 1.41

25 UGC 5658 - - 13.8 12.3 - - - - - - - - -

27 DDO 82 13.52 12.18 42.35 45.9 23.65 22.49 55.4 80.8 107.0 92.4 117.8 144.8 1.33

28 BK 6N - - 32.3 35.4 - - - - - - - - -

30 UGCA 220 16.77 15.30 26.18 32.3 25.86 24.84 - 17.7 38.5 22.3 50.0 61.6 1.48

31 DDO 87 15.17 14.23 37.7 40.4 25.05 24.26 20.8 43.1 68.5 42.3 69.3 84.7 0.95

36 KAR 73 17.20 15.79 18.5 30.8 25.53 25.24 6.2 15.4 28.5 13.9 31.6 43.9 1.41

39 BK 8N 16.50 14.74 43.1 51.6 26.67 25.31 - 6.2 37.0 13.9 61.6 90.1 1.76

41 KAR 74 17.93 16.64 9.2 10.8 24.76 23.80 6.9 13.9 18.5 14.6 20.8 28.5 1.29

 

For various reasons (sky-background problem, extremely bright foreground star, etc.) it was not possible to construct a reliable GC for Kar 59, Ho IX, and UGC 5423, which appear without data in Table 2 (click here). For UGC 5658 and BK 6N we were unable to set a proper magnitude scale; here we can only give the effective radii and show the arbitrarily scaled brightness profiles.

The radial brightness profiles in both colours are presented in Figs. 2 (click here) and 3 (click here).

  
Figure 2: Radial surface brightness profiles of the dwarf elliptical galaxies in B (lower) and R (upper). The dotted lines represent the exponential fits, as described in Sect. 4.2 (click here)

  
Figure 3: Radial surface brightness profiles of the dwarf irregular galaxies in B (lower) and R (upper). The dotted lines represent the exponential fits, as described in Sect. 4.2 (click here). Note: The profiles of NGC 2976 are shifted one magnitude downward (fainter) in the plot. BK 6N, UGC 5423 and UGC 5658 are arbitrarily shifted in surface brightness

The error caused by the poissonian nature of the photons may be evaluated according to Gilliland (1992). Applied to our profiles we find typically in the central part and at the faint end. and an eror in total magnitudes of the order of less than . It is clear that the main contributor to the errors is not photon shot noise but the magnitude zero-point as mentioned in Sect. 3.2 (click here), and the fluctuations of the sky background itself. The background indeed shows fluctuations of the order of 0.5 - 1 ADU over large scales in the images. A wrong sky determination of 0.5 ADU implies an error on the total magnitude of the order of . Hence the total errors remain about . A comparison with the independently derived profiles from Paper II for galaxies in common shows agreement within this level of uncertainty.

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 star-forming regions and considers the underlying older population. These profiles can be written as
 
which in surface brightness representation becomes a straight line
 
The central extrapolated surface brightness and the exponential scale length 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 3 (click here). No exponentials could be fitted to Kar 52 and BK 3N.

The deviation from a pure exponential law is expressed by the difference between the total magnitude of an exponential intensity law given by
 
and the actual measured total magnitude. The results are shown in Table 3 (click here). The difference is an indication of the goodness of fit of the exponential intensity profile. The columns of Table 3 (click here) are as follows:
: as Col. 1 of Table 2 (click here)
: as Col. 2 of Table 2 (click here)
: extrapolated central surface brightness according to Eq. (6 (click here)) in the B band, in
: as above, in the R band
: exponential scale length in arc seconds, in the B band
: as above, in the R band
: difference between the total magnitude as derived from the exponential model and the true total magnitude, in the B band
: as above, in the R band
: radial colour gradient determined from the difference in the slopes of the model fits, in magnitudes, as described below in Sect. 4.3 (click here).

4.3. Colour gradients

  The colour gradients are listed in the last column of Table 3 (click here) as calculated from the difference in the slopes in the surface brightness representation, i.e.
 
and are given in magnitudes per arcsec. The colour gradients, from Table 3 (click here), as well as the true observed gradients obtained by subtracting the two colour surface brightness profiles are plotted in Figs. 4 (click here) and 5 (click here).

 

Number Galaxy

(1) (2) (3) (4) (5) (6) (7) (8) (9)

2 KAR 52 - - - - - - -

3 DDO 53 23.06 22.54 18.72 23.11 0.08 0.12 0.011

4 UGC 4483 22.15 21.36 10.54 8.98 -0.08 -0.11 -0.018

5 KAR 54 23.89 22.81 21.72 18.41 -0.54 0.13 -0.009

6 UGC 4998 22.50 21.51 15.53 17.21 0.08 0.09 0.007

7 HoI 22.75 22.58 31.03 41.77 -0.40 -0.21 0.009

8 BK 1N 24.49 23.00 10.44 9.87 -0.02 0.06 -0.006

9 NGC 2976 20.52 19.33 36.2 37.45 -0.18 -0.09 0.002

10 BK 2N 24.06 23.09 5.75 6.35 0.12 0.09 0.018

11 KAR 59 - - - - - - -

12 BK 3N - - - - - - -

16 KAR 61 24.71 23.39 31.94 37.45 0.02 -0.12 0.005

17 HoIX - - - - - - -

20 BK 5N 25.23 23.98 16.21 16.71 -0.28 -0.40 0.002

21 DDO 71 24.32 22.98 20.11 22.63 -0.15 -0.06 0.006

22 UGC 5423 - - 12.25 13.53 - - 0.008

23 KAR 64 24.19 22.98 20.88 23.11 0.13 0.12 0.005

25 UGC 5658 - - 9.10 8.04 - - -0.016

27 DDO 82 22.73 21.43 27.15 27.85 0.04 0.03 0.001

28 BK 6N - - 24.90 23.73 - - -0.002

30 UGCA 220 25.16 23.95 22.16 24.68 -0.34 -0.31 0.005

31 DDO 87 24.13 23.26 25.86 27.15 -0.10 -0.14 0.002

36 KAR 73 24.53 24.04 11.80 15.97 -0.03 0.23 0.024

39 BK 8N 25.98 24.51 49.36 45.25 -0.99 -0.50 -0.002

41 KAR 74 23.97 23.05 7.34 8.47 -0.29 -0.23 0.021

 

  
Figure 4: Radial colour profiles of the dwarf elliptical galaxies. The solid and dotted lines represent the measured difference between the B and R profiles and the difference between the fitted exponentials, respectively

  
Figure 5: Radial colour profiles of the dwarf irregular galaxies. The solid and dotted lines represent the measured difference between the B and R profiles and the difference between the fitted exponentials, respectively