6 Decomposition parameters

The decomposition of a galaxy profile into a bulge and a disk component requires the profile to be fitted by the sum of two empirical laws. The presence of structures like bars, dust lanes, lenses and rings render such a straightforward two component fit very difficult. The luminosity profiles of the program galaxies are complex in nature. The burst of star formation in the nuclear region manifests itself as a sharp rise in intensity in this region. The burst luminosity completely dominates the light output in this region particularly and the estimation of a bulge component becomes very difficult. Hence we characterize the light distribution by parameters like the half-light radius, the central disk surface brightness and the disk scale lengths.

6.1 Scale lengths and central disk surface brightness

In the Markarian starburst galaxies, the luminosity profiles are complex in nature. In the inner region, the profile falls steeply up to about 10$^{\prime\prime}$ where the light is completely dominated by the burst component. The outer parts of the luminosity profile in most cases can be well described by an exponential scaling law viz.

$$\begin{eqnarray} \mu(r)& =& \mu_0 + 1.086{\left(r\over h\right)}. \nonumber\end{eqnarray}$$

The outer exponential nature is also seen in case of dwarf ellipticals dwarf irregulars and HII galaxies (Telles [1995]). This outer part is likely to represent the old underlying population of the parent galaxy. Structural properties like scale lengths and central disk surface brightnesses can be derived from these profiles. We fit a exponential law to the outer part of the profile down to where the signal falls to 3$\sigma$ of the background noise level. Figure 8 depicts the fits to the outer regions. Good fits to the observed profiles are obtained for the galaxies Mrk 14, Mrk 743, Mrk 1002, Mrk 1308 and Mrk 1379. In case of Mrk 449, the luminosity profile shows a sharp dip due to the presence of the dust lane and hence the fitted values are higher than the observed values for surface brightness in this region. We have deliberately included a part of the bar into the range of fit for Mrk 213, Mrk 781 and Mrk 1379 since we found that excluding the bar region tends to overestimate the intensity in the inner regions of the galaxies. The results of exponential fits to each filter are tabulated in Table 4. A plot of the scale length in B versus the scale length in R (Fig. 9) indicates that the blue scale lengths are comparable to the red scale lengths in all the cases except for Mrk 87. The exponential law fails to fit very well in the outer regions for Mrk 87 and the departures seen could be a result of this improper fit. The total magnitudes $B_{\rm T}$, $V_{\rm T}$, $R_{\rm T}$ and $I_{\rm T}$ were derived by extrapolating the fitted disk to infinity and summing over the flux.

  

Figure 9: Comparison of the scale lengths in B ($h_{\rm b}$) and R in ($h_{\rm r}$). The points are the derived values and the solid line is the locus of $h_{\rm b}=h_{\rm r}$

  

Figure 10: Comparison of the half-light radius in B ($a_{\rm eb}$) and in R ($a_{\rm er}$). The points denote the derived values and the solid line is the locus of $a_{\rm eb}=a_{\rm er}$

  

Figure 11: Plots of the blue central disk surface brightness versus the blue scale length. For comparison with the values obtained by de Jong, the scale lengths have been transformed appropriately

 

Table 4: Distribution of half-light radii ($a_{\rm e}$), scale lengths (h) and the central disk surface brightnesses ($\mu_{\rm o}$). The subscripts b, v, r, i denote the filters for which the values are presented. The half-light radii and scale lengths are in kpc, the surface brightness in mag/sq arcsec and the range of fit in arcsec. The first row gives the derived values and the second row gives the errors on the corresponding quantities

6.2 Half-light radius

The growth curve in each filter band was used to determine the half-light radius, $a_{\rm e}$ namely the radius within which half of the total light of the galaxy is contained.

$$\begin{eqnarray} m_{\rm hl}& =& m_{\rm T} + 0.7525. \nonumber\end{eqnarray}$$

The values for the total magnitudes were taken from Table 3. to compute the half-light radii. The half-light radii derived for the sample galaxies in each of the filter bands are presented in Table 4. Figure 10 shows the plot of the half light radius in B versus the half-light radius in R. The plot does not show any clear trends, however there are indications of $a_{\rm eb}$ being smaller than $a_{\rm er}$in most cases. This suggests that the blue light is more centrally concentrated then the red light in most of these objects within the surface brightness limits reached by our data. This is to be expected in case of starburst galaxies as the starburst activity is nuclear or circumnuclear in most of the galaxies.