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Appendix A: Error estimation

To obtain a better insight into the errors of the derived parameters of the BCDs, we created a set of artificial BCDs. To mimick the real Virgo BCDs, we combined the light distribution from two components, representing the LSB and starburst component. Firstly, the LSB-components were divided into a bright version (M_r, LSB =  −17.0mag), with half-light semi-major axes of a_hl = 7.6arcsec and a_hl = 15.1arcsec, and a faint version (M_r,LSB =  −15.0mag), with a_hl = 6.3arcsec and a_hl = 12.6arcsec. Secondly, two different Sérsic indices n were used, with n = 1.0 (pure exponential) and n = 1.3. We chose three different axis ratios (b/a = 0.5,0.7,0.9) and two position angles (pa = 60, 90) for the LSB component; the starburst component was chosen to be circular.

To mimick the additional outer tail of the LSB-component of some of the real Virgo-BCDs (see Sect. 3.5) at larger radii, we optionally added an exponential outer tail to the exponential LSB-component, having the same axis ratio and position angle. The tail has twice the half-light semi-major axis of the LSB-component, and can be weak (Δm = 1.2 mag fainter in total brightness) or strong (Δm = 0.75mag). Note that we did not add a tail to the LSB component with n = 1.3, since our intention was to test whether our approach to assume an exponential shape for the LSB component’s analysis, and to account for a possible outer tail, would be able to approximate the n = 1.3 case reasonably well.

For the starburst component, two different effective radii (2.0 and 4.0arcsec) were used to account for the various extents of the starbursts. We created one version in which the starburst is co-aligned with the LSB component, and another version in which it is offset by 0.5a_hl, since a fraction of the real BCDs show a clear offset between starburst and LSB component (see Table 1).

With these different parameters we end up with 384 artificial BCDs. We first created noise-free images without the starburst component, to determine the true total (two-Petrosian) magnitude M_r,LSB of the LSB+tail component, as well as the true value of a_hl, using the input axis ratios and position angles. We then created images with realistic noise and seeing characteristics, which were analysed in the same manner as the Virgo BCDs (see Sect. 3). The magnitudes and radii derived with LAZY for the LSB+tail component were then compared to the true values, thereby yielding estimates for systematic errors of magnitude and relative radius, as well as for their statistical errors (standard deviation) σ_Mr and σ_Reff. Note that here and in the remainder of this section, we omit the subscript “LSB” from all quantities, for better readability.

Table A.1 summarises the results, subdivided by LSB component brightness and profile shape. Based on this approach, the final systematic and statistical errors that we adopt for our BCD analysis are provided in Table A.2, subdivided into bright

and faint LSB components. We refrain here from differentiating between the different Sérsic indices n and between the cases with/without a tail component, as the resulting values were very similar.

The mean effective surface brightness ⟨μ⟩_eff can be derived directly from M_r and R_eff: (A.3)Its statistical error was calculated assuming independent errors on magnitude and radius: The systematic surface brightness error was calculated by (A.6)The average differences between the input magnitudes and radii and the ones measured by LAZY are almost negligible for the bright galaxies (0.03 mag / 1%) and moderate for the faint galaxies (0.15 mag/11%). However, both add up to a significant systematic effect on the surface brightness of 0.41 mag/arcsec² for the faint galaxies, while being negligible (0.01 mag/arcsec²) for the bright galaxies. The statistical errors are reasonably small for all quantities, with 0.10 mag for M_r, 6% for R_eff, and 0.16 mag/arcsec² for ⟨μ⟩_eff.

We point out that, due to our parameter setup, the fraction of artificial BCDs with inner flattening (see Sect. 3.4) was much larger than for the real Virgo BCDs, where only three BCDs were fitted with a inner flattening. We therefore calculated the above quantities only from those BCDs without inner flattening, to avoid an overestimation of the errors.

© ESO, 2014