4 Radius - absolute magnitude relation

Table 4 summarizes the absolute magnitudes and linear radii for the BCDGs in the near infrared. The values were computed using H₀=80 Mpc km^-1s^-1. No k-correction was applied since at such low recession velocities, it is largely negligible.

We saw in the previous section that the light distribution in the near infrared is less sensitive to the starburst than in the optical, especially in K band. We have investigated the relation between the absolute magnitude and the radius in the three bands. Figure 8a shows the relations for the radius at 50% ( $r_{\rm eff}$) of the total infrared light and Fig. 8b shows the relations for the radius at 75% (r_0.75) of the total infrared light. Table 5 summarizes the coefficients of the relations and the correlation coefficients in the three bands for both radii.

Figure 9: a) Color-Metallicity relation for the BCDGs compared to the relation described by the globular clusters (continuous line). The r1/4 BCDGs are represented in filled lozenge, the exponential BCDGs are represented in open circles; b) upper panel: color - metallicity relation in an 8'' aperture. The continuous line represents the relation followed by the Globular Clusters. Lower panel: effect of the integration in an aperture on the color metallicity relation. We plotted the ratio between the 8''aperture and the size of the BCDGs at 75% of light as a function of the metallicity. The r1/4 BCDGs are represented in filled lozenge and the exponential BCDGs are represented in open circles

The coefficients of the $r_{\rm eff}$ relation are significantly smaller than the -5.0 empirical value after 1 sigma rejection, possibly due to a systematic effect as in the B band (Papers I and II) but the size of the sample is small and the statistical significance is low. Moreover the slope of the relation depends strongly on the quality of the determination of the effective radius based on the extrapolation to estimate the asymptotic magnitudes, although this would mainly affect the scatter of the points. It depends also on the intrinsic morphology of the objects, e.g. the compactness. For example, in the cases of Tol 0957-297 and Fairall 301. Both have about the same physical size ( $R_{26} \sim$ 2 kpc), but they have very different compactness indexes in B and R bands: Tol 0957-279 shows a very steep decreasing luminosity gradient in the R band, about twice the gradient observed in Fairall 301. If the stellar densities drop so much in Tol 0957-297 compared to Fairall 301, we do not expect to be able to detect the emission very far out from the starburst in K (we detect the K emission to 30'' compared to the 50'' radius of the galaxy in B). Hence, the determination of the radii will be strongly affected by the presence of the burst. The starburst affects the relation such that the smaller galaxies show a central excess in the near infrared compared to the larger galaxies.

In the case of r_0.75, the values in all three bands are significantly closer to the empirical value, supporting the idea that the near infrared bands are much less affected by the starburst than in the optical. At large radii, the evolved host galaxy dominates in all bands, confirming the previous results obtained in the R bands (Papers I and II).

We are interested in understanding the relations between the photometric class and the intrinsic parameters. Table 6 summarizes the absolute magnitude-radius relation in all 5 bands (B, R, J, Hand K) for both classes of BCDGs.

The slope of the relation is very different between the two classes. The smaller r^1/4 BCDGs show a significant excess of light dominated by the starburst, especially in the B and Rbands, but not in K band. On the other hand, the exponential BCDGs follow loosely the empirical relation as indicated by the low correlation coefficients. The scatter in the relation may be due to the fact that in our exponential BCDGs, the star formation is spread throughout the galaxy, while in r^1/4 BCDGs the star formation takes place mostly in the central regions.

   

Table 6: Relation between the absolute magnitude and r_0.75 for the two photometric classes

r1/4		Exponentials
r0.75	A	$\rho$	A	$\rho$
B	-3.71(0.10)	0.98	-6.48(0.71)	0.38
R	-3.52(0.17)	0.94	-5.83(0.61)	0.44
J	-3.78(0.86)	0.76	-5.71(0.61)	0.79
H	-4.10(0.52)	0.90	-5.56(0.65)	0.77
K	-4.20(0.40)	0.94	-5.39(0.64)	0.77

A: slope of the relation after 1 sigma rejection.
$\rho$: correlation coefficient.

The scatter, in the relations, is smaller for the r^1/4BCDGs. Again, it is probable that the steepness of the slope is due to the fact that the starburst dominates the smaller BCDGs, and the small scatter may be due to the fact that the star formation appears to take place in localized and compact regions.