On the atlas of profiles, (Fig. 1 (click here)), a classical flat (disk) distribution of light, following the well-known exponential law, translates into a linear relation. Alternatively, a plot of the surface brightness versus the 0.25 power of the equivalent radius allows to recognize the objects having a light distribution of "spheroidal galaxy'' type. One would expect the occurrence of "mixed'' profiles indicating the probable presence of two dynamically different populations, the disk-like one and the spheroidal one, making such objects low luminosity equivalents of normal giant flattened galaxies.

**Table 3:** Exponential profiles

name	(R)[pc]	(B)[pc]	]	]


sbs0940	308	525	1.12	1.11	21.78	22.39
mrk1308	407	317	1.31	1.20	19.60	21.09
sbs1006	430	338	0.40	0.51	20.07	20.64
mrk1416	478	518	1.19	1.04	20.11	20.61
sbs1428	555	597	1.03	0.98	18.9	20.37
sbs1533	684	-	0.97	-	18.38	-
mrk1423	779	-	0.65	-	15.06	-

In the following we discuss some characteristics of the derived surface brightness profiles.

Figure 3 (click here) shows, in (

) coordinates, the observed brightness distribution of the 10 objects exhibiting a linear r^1/4 law across a substantial range of equivalent radius. We assume that the surface brightness profile follows the empirical law as given by De Vaucouleurs (1948, 1953)

where I is the intensity at a given r and

is the intensity at the effective radius. This relation is more convenient to use in terms of surface brightness

Genuinely fitting a linear relation on the (

versus (

) plot of the surface brightness in the range of

not affected by seeing effects, we get the slope and the deviation of the profile from the pure r ^1/4 law. It appears that for some galaxies (Mk 1450, Mk 1480 and SBS 1147+520) the slope is different in the two bands. Note that the 8.327 slope is intrinsic to the r^1/4 law, as written in terms of normalized coordinates (

). A value of the slope differing significantly from the canonical 8.327 usually implies that the adopted

is not correct. Since the determination of

is made through an extrapolation process (in order to derive the asymptotic magnitude from the cumulated magnitude growth curve) the errors are quite difficult to control, especially when the frames are insufficiently deep. However, another effect is also responsible for the deviation from a pure r^1/4 law: if the galaxy houses a population dynamically different from an isothermal spheroid (King 1966) that contaminates the light of the latter, departure from the r^1/4 law will be quickly visible. This is the obvious case for extended envelopes that show up as excess light above the r^1/4 (e.g. SBS0136+328, Mk 324 and Mk 1426). It should be underlined that these outer envelopes differ in color from that of more central regions, suggesting a different stellar content. Also, if the [

, (

] relationship is linear but with a slope different from 8.327, on frames sufficiently deep such as to rule out significant errors on

, it could be suggested that a non-spherical population is quite continuously superimposed to the spherical one, (but with a moderate contribution to the total light) so that the scale length is changed (as could be the case for Mk 324).

Figure 3: Reduced surface brightness distributions of the 10 galaxies obeying an r^1/4 law. The abscissa is the quantity

, the ordinate is the surface brightness in magnitudes per square arc second. The tick marks in abscissa represent a 0.5 interval. The dashed line has a slope of 8.327 and represents the "pure'' de Vaucouleurs' law. The various curves, translated from each other to ensure legibility, are for: a) SBS 0136+328, b) SBS 1054+504, c) SBS 1147+520, d) Mk 324, e) Mk 996, f) Mk 1434, g) Mk 1450, h) Mk 1480, i) Mk 1418, j) Mk 1426

4.1.2. Exponential profiles

In most cases, the exponential law (de Vaucouleurs 1959) applies right after the seeing limit (

to 3'').

or, in terms of surface brightness:

where 1/r₀ is the scaling factor in

and

is the central value of the surface brightness. In other cases, there is a significant contribution of a small brighter central component. See also the case of SBS 1006+578 in Sect. 3.5. Table 4 (click here) gives the resulting numerical values of the linear regression.

**Table 4:** Absolute magnitudes and linear radii
Object name	d [Mpc]	M_B	[pc](B)	r₂₄[pc](B)
			[pc](R)	r₂₄[pc](R)
SBS 0136	84.5	-17.72	1910	2181
			1184	3472
SBS 0940	23.0	-14.34	643	577
			503	638
SBS 1006	18.6	-14.80	362	655
			473	864
SBS 1054	18.6	-15.16	348	661
			411	1070
SBS 1147	15.0	-13.60	197	332
			205	559
SBS 1331	10.8	-15.14	616	761
			635	988
SBS 1413	11.1	-13.83	803	505
			505	512
SBS 1428	32.1	-16.51	653	1376
			665	1948
SBS 1533	44.2	-	-	-
			825	2065
Mk 324	23.9	-16.98	1131	1041
			536	1405
Mk 900	17.5	-16.83	1286	1137
			1729	2888
Mk 996	21.4	-	558	1532
			1454	1913
Mk 1131	27.3	-17.24	2453	1316
			911	2808
Mk 1308	13.6	-15.80	505	931
			460	1392
Mk 1416	28.7	-15.31	541	881
			586	1281
Mk 1418	6.3	-14.62	223	484
			260	803
Mk 1423	15.5	-	-	-
		-17.17	948	1441
Mk 1426	25.2	-	-	-
		-17.23	561	1658
Mk 1434	27.6	-14.84	251	601
			264	866
Mk 1450	12.6	-13.52	127	306
			141	641
Mk 1480	24.3	-15.36	358	738
			465	1144
Mk 1481	25.1	-15.21	737	917
			812	1154
Mk 1499	36.7	-16.29	650	1138
			926	2068

4.1.3. Mixed law profiles

4 galaxies show a profile reminiscent of the classical superimposition of a central bulge component with an underlying exponential law extending to the outer parts where this latter becomes dominant. The exponential is easily interpreted as showing up the presence of a disk. Only 2 cases show a slight systematic blueing outwards. (SBS 1413+495 and SBS 0940+544C)

4.2. Integral relationships

Table 4 (click here) lists the integrated parameters on the observed galaxies together with metric observables deduced from the photometry. The distance dependent quantities have been derived using

, the redshifts of Table 2 (click here) corrected from Galactic rotation (using

) and from the Virgo-centric infall model of Aaronson et al. (1981) as reformulated by Bottinelli et al. (1986) using the recent Virgo distance based on Cepheid photometry by Freedman et al. (1994).

Table 4 (click here) is arranged as follows:
Column 1: Name of the galaxy
Column 2: Distance in Mpc.
Column 3: Absolute B magnitude from our asymptotic magnitude.
Column 4: Effective equivalent radius in pc, in B and R colors.
Column 5: Isophotal equivalent radius at

in pc, in B and R colors.

4.2.1. Color distributions

The asymptotic B-R color ranges from 0.22 to 2.16. The mean color of the sample is 1.09 (with no correction for reddening due to Galactic or internal absorption) which places the sample among the blue galaxy population. Fukugita et al. (1995) have recently revised the integrated colors of various galaxy types and show that normal field galaxies of elliptical types have B-R = 1.6 while the bluest spirals of type Scd have B-R = 1.0 (from synthetic color computation, perhaps a little redder from observations). 2 objects in our sample are very blue with

: SBS 1413+495 (B-R = 0.22) and Mk 324 (B-R = 0.44). We note that the galaxies whose brightness distribution obey an r^1/4 law follow the same distribution of colors as that of the whole sample.

4.2.2. Radius-luminosity relations

Figure 5 (click here)a shows relations between the logarithm of the effective radius and the absolute magnitude in B, uncorrected for Galactic and internal absorption. The two quantities are correlated (correlation coefficient of 0.82 in B and 0.66 in R) as expected, with a slope of

in B and

in R.

In B, there is a clear deviation from the expected slope of -5 implied by a dependence of the luminosity on the square of the radius. It should be remembered that Heidmann (1969) found a dependence of the luminosity on r^k with k = 1.9 for giant ellipticals and k = 2.8 for giant spirals. However Fraser (1977) found k = 2.1 for Virgo spirals). The tendency in our sample is towards an excess B luminosity for the less luminous objects, for a given effective radius. Although the dispersion in both colors may be explained partly by the extrapolation errors in the determination of

(see Sect. 4.1.2) and the errors on the distance moduli, the trend would rather be due to the selection bias of the sample. The most extreme blue compact dwarfs are selected in the Byurakan surveys because their central surface brightness in the blue part of the spectrum, reinforced by the starburst, is intrinsically high. The use of

favours the weight of the central regions where the burst dominates the light (see Table 4 (click here)), and this bias is stronger on the intrinsically faint objects.

In R band, there is a large dispersion of the representative points, but, as expected, the "blue'' selection bias as explained above is much less apparent.

Figure 5: Absolute magnitude-radius relations: a) at

, (effective) in B band, b) at r = r₂₄, (isophotal at

) in B band

Figure 5 (click here)b shows the same relationship using the isophotal radius r₂₄. This radius is systematically larger than

, and therefore integrates light largely emitted by the underlying evolved population, hence reducing the weight of the starburst component. The dispersions are much reduced, the slopes are

in B and

in R with respective correlation coefficients of 0.90 and 0.96. The slope in B is significantly different from -5, but in the opposite sense as observed in the (M_B,

) plot. Most of the discrepancy comes from Mk 324 and Mk 1131 which both exhibit an extended envelope that contributes significantly to the light beyond r₂₄. Excluding these galaxies, we find a slope of

(correlation coefficient: 0.97) for the (M_B, r₂₄) diagram, and hence an almost identical behaviour in B and R, and consistency with a luminosity proportional to the square of the isophotal radius.

Huchra (1977) found that the luminosity of Markaryan galaxies, irrespective of their morphological type, closely follows a r² dependence (r being an estimate of the isophotal radius), "indicating approximate constancy of mean surface brightness over the absolute magnitude interval studied''. However, there is only a small number of dwarf Markaryan (

) in Huchra's study, and the selection effects towards compact, i.e. high surface brightness objects, in our sample are certainly different from those present in an all-type Markaryan galaxy sample.

4.2.3. Compactness

Compact galaxies were defined by Zwicky (1967, 1971) as being galaxies for which the central surface brightness is brighter than

in B. But this definition applies, at least partly, to almost all galaxies having giant star-forming regions and/or a bright nuclear component. It is usually assumed that a dwarf "compact'' galaxy associates two basic features: a short scale length of the brightness distribution and a high "average'' surface brightness, this latter being the observable translation of a higher than normal stellar luminosity density.

Figure 6 (click here) displays the histogram of the mean surface brightness inside the effective radius measured in B band. The average surface brightness of the night sky is around

. The median value, (uncorrected for Galactic foreground extinction) observed for our sample is

and several objects have especially bright values (namely Mk 996, Mk 1418, Mk 1434 and Mk 1450). Compared to a sample of DDO dwarf galaxies (de Vaucouleurs et al. 1981) that exhibit low or moderate star formation rates in the average, and is largely dominated by disk late-type systems, the Byurakan dwarf blue compacts are brighter in

by some two magnitudes. From Ichakawa et al. (1986), we get that the average of

in 69 dwarf ellipticals of the Virgo Cluster is

. The Byurakan BCDGs among which we find a high proportion of dwarf elliptical galaxy analogs (but with r^1/4 laws while dE's of Virgo are claimed to have exponential brightness distributions: Ichikawa et al. 1986) are again some two magnitudes brighter.

Figure 7 (click here) displays the histogram of the concentration index C₂₁(B) as defined in Sect. 3.4.1. This index averages from 1.6 to 1.9 for diffuse late-type spirals, and reaches about 2.5 to 2.8 for normal ellipticals (Fraser 1972, 1977; de Vaucouleurs & Aguero 1973) while diffuse dwarf magellanic have

(Ables 1971). The present sample peaks at 1.9 and one may notice three anomalously "concentrated'' objects (namely Mk 324, Mk 900 and Mk 1308).

Finally, Fig. 7 (click here) shows the histogram of the effective radii in pc measured in B band. The bulk of our galaxies have indeed small effective radii with 9 objects below 500 pc.

4. Discussion