4 Discussion

Hereafter, we discuss the properties of our complete sample of northern and southern galaxies. This accounts for 44 objects, including the UM 465 companion. Five objects are not "dwarfs'' according to the criterion of having a luminosity $M_B \ge -16.5$: SBS 0136+328, Tololo 0513-393, Tololo 0645-376, Tololo 1924-416, and Tololo 1937-423. These brighter galaxies are included in the discussion to compare with our low-luminosity star-forming galaxies. The companion of Tololo 1924-416 is not included. We assume H₀ = 80 km s^-1 Mpc^-1 for the derivation of distance-dependent quantities based on the Galactocentric corrected recession velocities. Table 7 summarizes the absolute parameters: absolute magnitudes and linear radii, for the southern sample (see Paper I, for the Northern sample values).

  

Table 7: Absolute magnitudes and linear radii

 

Figure 4:  B-R color distribution. a) B-R asymptotic total color distribution for the whole sample (44 galaxies) in solid lines. b) B-R color distribution as a function of the galaxy type. The top box shows the distribution for the elliptical-like objects, the bottom box shows the distribution for disk galaxies (dash) and for composite profile galaxies (solid line)

4.1 Color distribution

The asymptotic mean B-R color of the present sample is 1.13 $\pm$ 0.35, consistent with that reported for the Northern sample (B-R = 1.07 $\pm$ 0.09). The spread in asymptotic color for the southern sample is due to the fact that we have redder objects, and that our photometry is deeper in R band - therefore we reach the reddest parts of the galaxies. The observed colors span the range 0.34 to 1.63. We have one object bluer than 0.5, Tol 0954-293, an exponential-dominated galaxy. Figure 4a shows the distribution of the B-R color for the 41 objects with mean and median B-R = 1.1 $\pm$ 0.4.

Figure 4b shows separate color distributions for the three main surface brightness profile types. The average B - R colors are: 1.32 $\pm$ 0.4 for the r^1/4 BCDGs, 1.10 $\pm$ 0.2 for the exponential BCDGs and 1.09 $\pm$ 0.3 for the composite profile BCDGs (composite r^1/4: B-R = 1.08 $\pm$ 0.3, and exponential composite: B-R = 1.09 $\pm$ 0.4).

There is a tendency for the pure r^1/4 BCDGs to be redder than the exponential ones. However, composite profile objects have the same average asymptotic color as the pure exponential ones, whatever the nature of the dominant component.

 

Figure 5:  Luminosity-Radius relationship. a) Relationship between the effective radius in B and R, and the absolute magnitude for the whole sample. The solid line has a slope of -5 and the dashed line represents the least-square fit to the data. b) Relationship between the absolute magnitude in B (empty circle) and R (filled circle) but using 2 different isophotal radii: at $\mu$ = 24 B mag/arcsec2 from the sample in Paper I (top), and $\mu$ = 26 B mag/arcsec2 from the present sample (bottom). The solid line has a slope of -5

4.2 Radius-luminosity relations

Figure 5a shows the relation between the effective radius in pc and the absolute magnitude (corrected for foreground Galactic absorption). We confirm the findings of Paper I, that there is a tendency for the observed relation to depart significantly from the expected relation:

$$M_{\rm abs} = -5\times \log{r_{\rm e}} + C^{\rm st}.$$ (6)

The observed slopes are -3.86 $\pm$ 1.13 in B, and -4.84 $\pm$ 1.48 in R. After a 1-sigma rejection iteration, the slopes become -3.72 $\pm$ 0.9 in B and -4.45 $\pm$  0.9 in R. The departure from the empiric relation is clear in B but there is a large scatter in the data. Part of this scatter may be due to errors in the extrapolation process used to derive asymptotic magnitudes and effective radii. In Paper I, we have already explained this effect in terms of a selection bias towards compact and centrally located starbursts inside our galaxies.

In the R band, there is no significant difference between the empirical value of the luminosity-radius relation and the observed value for our sample. This is due to the fact that the starburst does not dominate in the R band (except if H$_\alpha$ dominates the spectrum, the effect would then be similar to the compactness bias, but smaller and lost in the scatter due to magnitude errors), causing the properties of the "host'' galaxy to dominate.

Figure 5b shows the relation between the absolute magnitude and the isophotal radius at $\mu$ = 26 mag/arcsec² for the present sample. For comparison, we have also reproduced the corresponding plot from Paper I, but at $\mu$ = 24 mag/arcsec². The values of the slope are not significantly different from the empirical value of -5. At these low levels of surface brightness, the dominant component is obviously the underlying galaxy. If the underlying galaxy of the BCDGs is composed of evolved stars of several Gyrs (i.e. if the scatter in the mass-to-light ratio is small; [Thuan1983]; [Hunter & Gallagher1985]; [Doublier et al.1999]), the intensity at a given radius is proportional to the stellar volume density integrated along the line of sight. The scatter is much reduced indicating that the stellar overall density properties of the host galaxy may be quite similar for all BCDGs.

4.3 Compactness

The compactness of a galaxy is a visual impression translating a combination of small angular size and "high'' surface brightness. Therefore, to provide quantitative estimators of compactness, one is led to use the value of some quantity resulting from a combination of these observables. Two such indicators are discussed in the following:

The mean surface brightnesses are measured inside a given "metric'' radius (as compared to the sky brightness, around 22 mag arcsec^-2  in B band, 21.5 in R band), which we choose to be the effective radius. For our total sample, the average value of the effective mean surface brightness is 21.6 $\pm$ 1.2 mag arcsec^-2 in B band (corrected from Galactic extinction). Note that this is slightly brighter than the canonical central value of the surface brightness of giant disk galaxies derived by [Freeman(1970)], but compares well with Papaderos et al. (1996a) derived from their BCDG sample. It translates into an apparent projected luminosity density on the line-of-sight of 150 $L_\odot$ pc^-2.

 

Figure 6:  Mean Effective Surface Brightness Distribution. a) Distribution of the mean effective surface brightness for the whole sample (solid line), the Northern sample (short dash) and the Southern sample (long dash). b) Mean effective surface brightness distribution for different galaxy types. Top: r1/4 dominated BCDGs, bottom: exponential dominated BCDGs (long dash), and composite profile BCDGs (short dash)

Figures 6a and b show that there is a marked difference between the exponential objects and the r^1/4 ones. The latter have a symmetric distribution around $<\mu_{\rm eff}\gt$ = 21.03 $\pm$ 0.9 mag arcsec^-2 (238 $L_\odot$ pc^-2) while the exponential dominated galaxies have a very flat distribution of mean effective brightness with $<\mu_{\rm eff}\gt$ = 22.2 $\pm$ 0.9 mag arcsec^-2 yielding a clearly fainter 87 $L_\odot$ pc^-2. Among composite objects, those dominated by a r^1/4 are one magnitude brighter in average than those dominated by an exponential.

 

Figure 7:  Concentration Index distribution. a) Concentration index distribution in B band (solid line), and in R band (dash). b) C21 distribution for two galaxy types: elliptical-like BCDGs (dash) and Magellanic-like BCDG (solid line), in B (top) and R (bottom) bands. In B, the elliptical-like are more compact than the disk-like ones. There is no difference in R

Figures 7a and b show the distribution of the distance independent concentration index defined by the ratio of the effective radius to the radius containing 1/4 of the total luminosity ([De Vaucouleurs & Aguero1973]; [Fraser1977]). Another compactness index has been used by Papaderos et al. (1996b): it is based on the ratio of the starburst component projected area to the total area of the galaxy seen at the isophote 25 mag arcsec^-2 in B; it was derived from the profile decomposition for a sample that exhibits a "plateau'' component in B, presumably caused by the starburst population. We have not used this definition, because very few of our BCDGs profiles exhibit such a clear-cut plateau allowing a three-component decomposition. [James(1991)] or [Doi et al.(1995)] use concentration index definitions that are basically similar to de Vaucouleurs' definition.

Figure 7a shows the distribution of the concentration index (CI) in B and R displayed on the same graph for comparison. The mean values in B and R are very similar with a value of 2.25 $\pm$ 0.5, that is larger than the value we obtained for the northern sample. We should note that the southern sample contains slightly more luminous BCDGs. The CI in B and R are basically consistent, but their correlation coefficient is low, only 0.5. Our observations in the near-infrared will allow to extend the study of the CI to J, H and K bands that are in principle more sensitive to the underlying evolved stellar populations.

Figure 7b shows the distribution of the CI for the disk BCDGs and the elliptical BCDGs in both B and R bands. The CI is similar for the exponential galaxies (2.27 $\pm$ 0.5 in R and B) and for the r^1/4 (2.25 $\pm$ 0.1 in B and R). There is a slight difference between the pure r^1/4 (CI(B) = 2.3 $\pm$ 0.3) and the pure exponential dominated BCDG (CI(B) = 2.1 $\pm$ 0.4), but the scatter remains large and it is difficult to conclude.

 

Figure 8:  "Compactness'' indexes versus Asymptotic B-R. a) Mean surface brightness in B band versus asymptotic B-R for the 4 photometric classes of BCDGs. b) Concentration index C21 versus asymptotic B-R for the 4 photometric classes of BCDGs

Let us underline that the two compactness indicators studied above do not pertain to the same physical quantities. The concentration index is a dimensionless number that is the ratio of two metric radii, physically associated with the scale length of the projected brightness distribution, regardless of any assumption on the shape of the surface brightness distribution. On the other hand, $<\mu_{\rm eff}\gt$ which is a logarithmic projected luminosity, is rather directly linked to the visual aspect of the central region of the galaxies. The differences in compactness interpretation are illustrated in Figs. 8a and 8b in which C₂₁(B) and $<\mu_{\rm eff}\gt$ are plotted versus the asymptotic B-R. Obviously $<\mu_{\rm eff}\gt$ is not correlated with B-R whatever the photometric type of the BCDGs (elliptical-like, disk-like or composite). On the contrary, CI(B) exhibits a weak correlation (t-coefficient of Student's test: 9.54, with a probability of exceeding this value of 10^-11) with B-R for exponential dominated objects only. This correlation almost vanishes for the r^1/4 dominated BCDGs, even when Mk 324 and Mk 1450 deviant values are included.

It is tempting to interpret this as a result of differences in the evolutionary history of the two photometric classes of BCDGs: disk-dominated systems evolving possibly with recurrent bursts due to accretion of HI clouds but keeping their overall dynamical structures and hence their basic scale length parameters, while the elliptical-like BCDGs would be the products of violent dynamical events that bring fundamental changes in their structure: merging, interaction with an HI cloud, or a larger galaxy.

However, it might be that the concentration index depends strongly on the presence of the starburst, since the mean B-R color ($<B-R\gt _{\rm eff}\ = 0.65$ $\pm$ 0.12) within the effective radius is much bluer than the integrated B-R color by 0.4 mag. It is most likely, once the starburst has faded, that the concentration index will change, i.e. decrease significantly as the light density decreases. Thus, the differences we see for the C₂₁ might disappear after the BCDG phase.

Table 8 summarizes the average values of some photometric parameters for the two BCDG populations of our sample.

  

Table 8: Average values of photometric parameters

4.4 Blue neighbours and companions for BCDGs

The study of the environment of HII galaxies reported by Telles & Terlevich (1997) showed that less than 10% of these galaxies (including BCDGs) have larger companions (normal, giant galaxies within a cylinder of 200 km s^-1 in depth and a hundred kiloparsec in projected radius). A recent study of Pustil'nik et al. (1995) showed also that the dwarf emission line galaxies of the Second Byurakan Survey do not show any clustering tendency within regions of more than 5 Mpc^-3. The BCDGs selected for observation in the present work have no neighbouring larger units. Except for Mk 1308, Mk 1480 and Mk 1481, and II SZ 34, our objects are "isolated''. However, galaxy formation theories using hierarchical models predict that the bulk of the galaxy population formed out from proto clouds of small mass ([Kauffmann et al.1997]). Indeed, if the BCDGs, as isolated as they appear to be, have formed out of density fluctuations independent from the larger ones responsible for the formation of giant spirals and ellipticals, the power spectrum associated to these fluctuations implies that these BCDGs should be surrounded by smaller mass units, somehow larger than globular clusters, like fragments or galactic debris. Although merging should have happened frequently among the debris, some of them might still be found around the BCDGs.

Following this argument, we examined our frames closely, in B, R and especially the B-R maps. We could detect (S/N > 10 in R, S/N $\sim$ 3 in B-R) some extended (FWHM $\ge$ 1.5'', with a seeing $\le$ 1'') objects with B-R colors ranging from 0.5 to >3. Among these, we selected the objects showing the "bluest'' colors: 0.5-2.0, in order to sort out the closest ones, therefore with lowest k-correction. Only few objects in the fields met the requirements, and the selection was done visually using the B-R maps. Selecting out blue stars was straightforward: when we constructed the color maps, we did not take into account the slight variation of the PSF from one filter to another, as the differences are not significant for extended objects. But they are, indeed, clearcut on the star images: on the B-R maps, the stars show a wavelet (or "sombrero'') profile due to the difference in the PSF shape (the seeing is generally worse in B than in R). For the faintest stars, the PSF differences are not significant and therefore one has to check directly the FWHM. We set a lower limit of 4'' on the size of the detected objects assumed to be "extragalactic blue sources'', to avoid effects due to image aberrations.

 

Figure 9:  Apparent B magnitude versus B-R color diagram for faint extended objects observed in the neighbourhood of BCDGs. See detailed explanation in the text (Sect. 4.4)

Figure 9 shows the B-R colors vs. apparent B magnitude diagram of the selected objects with our BCDGs for comparison, and summarizes how we define "candidate'' companions. The overplotted lines represent the variation of the [magnitude, color] location of different galaxy types with redshift (derived from Frei & Gunn 1994 (FG94), and Pence 1976 (P76)). First of all, we followed P76's tracks establishing the values of the apparent magnitudes for different galaxy types (E-S0, Sbc, Scd and Im: H₀ = 75 km s^-1/Mpc) at the various redshifts given by FG94 (including K-correction) in the B band. From FG94, we derive B-R colors at a given redshift for apparent B magnitudes of various galaxy types. Most selected objects (empty squares) fall beyond the redshift of 0.1, and therefore are probably background galaxies. Indeed, almost all of them appear on the frames to lie in "groups'' close (few 10'') to a much redder object ($\ge3$). Likely, in these cases, we are detecting late type galaxies in small clusters or groups.

For the few objects suspected to be at low redshift ($z\le0.1$) from their position in the [magnitude, color] plane, in term of absolute values, their sizes range between 5'' and 20'' in diameter, i.e. 10 - 40 kpc (at z= 0.1) or 1 - 4 kpc at z=0.01 (highest redshift of the BCDGs in our sample). We are thus led to speculate whether these objects are background late type galaxies, or physical "neighbours'' of our BCDGs (stars). The apparent magnitudes range from B = 24 to 17 mag i.e. M_B = -9 to -16 at z=0.01 and -14 to -21 at z = 0.1. Only if the redshift is 0.1 or larger, the objects would lie in the luminosity range of the Scd and Sbc; indeed, a few "large'' objects do show some inner structures very close to those of spirals or large irregulars when seen face-on. For smaller redshifts, the objects would lie in the "dwarf'' zone (M_B $\ge$ -17).

In the fields, we found a population of objects that lies below the line defined by the Im galaxies in terms of color (Fig. 9). We do not have redshift measurement to identify their origin. Only 3 of them have diameters of 4'' and could be faint blue stars, but all others have diameters larger than 8'' and could not be mistaken for stars.

The galaxies identified with filled circles are objects found close to the BCDGs ($\le$ 20'' from their outermost isophotes) with a low average surface brightness (<SB>_B $\sim$ 25.5 mag arcsec^-2). These objects are likely to be companions because they are not associated with other galaxies in the fields except the nearby BCDG; they do not show marked internal structures. Most interesting, 4 of them (in the field of Tol 1924-416, Tol 0610-387, Mk 600 and UM 461) seem to lie in the direction of the distortions seen in these BCDGs. As seen in Fig. 9, these objects lurk across the area populated by other galaxies and do not define a specific sequence.

[Östlin et al.(1998)] recently confirmed the association between Tololo 1924-416 and the faint blue companion located NE of this galaxy. This result strengths our hypothesis that some of our faint neighbours could be indeed companions.

Moreover, recent studies using HI mapping around BCDGs and other Low Surface Brightness Dwarf galaxies, showed that many of them do have "HI'' companions that have no detected optical counterparts on deep plates (< 50%, [Taylor et al.1994]; [Taylor et al.1995]; [Taylor et al.1996]). It would be worthwhile to search for HI companions around our BCDGs. It would also be of interest to compare the spatial distribution of the faint optical companions.

More observations, among which, obviously, redshift determinations, are needed to ascertain the physical association of these candidates with the BCDGs.