2.1. The luminosity-surface brightness plane

The luminosity-surface brightness plane (LSP) is of particular interest because it enables one to compensate for both luminosity (Malmquist bias) and surface brightness selection effects (aka "Disney bias"). In Driver et al. 2004 the LSP is derived for the MGC, which provides the most robust current estimate. The MGC LSP analysis used the joint luminosity-surface brightness Step-Wise Maximum Likelihood method of Sodré & Lahav 1993 and incorporate into this tracking of 5 selection boundaries relevant to each individual galaxy (i.e., maximum & minimum observable size & flux and minimum observable central surface brightness for detection, see Driver 1999). An additional feature is the derivation of individual K-corrections using the combined MGC and SDSS-DR1 colours (uBgriz). Fig. 2 shows the data as a series of Gaussian fits across the LSP at progressive intervals of absolute magnitude. The thicker weighted lines shows the surface brightness distribution for the most luminous galaxies and the fainter lines for the dwarf regime. Two facts leap out. Firstly that the distributions are bounded (the Gaussian fits have good ²'s) broadening towards lower luminosity. Secondly the peak of the distribution moves towards lower surface brightness for lower luminosity systems. In other words low luminosity systems apparently show greater surface brightness diversity than giant systems. However this can also be interpreted in terms of the Kormendy relation for spheriods (Kormendy 1977) and Freeman's Law for disks (Freeman 1970). These two classic studies unveiled distinct relations for the structural properties of spheroid and disk components. The Kormendy study found that the more luminous the spheroid the lower its central surface brightness. Conversely Freeman's study found that all disks, regardless of luminosity, have a constant central surface brightness of µ^o_BMGC = 21.65 ± 0.3 mag arcsec^-2. The MGC result shown on Fig. 2 are for the combined bulge+disk systems. Around L^* the effective surface brightness for spheriods and disks is fairly close - a long-time nagging coincidence. However moving towards lower luminosity the trends for spheriods and disks diverge leading to the broadening of the global surface brightness distribution. To investigate further hence requires separating out these two structural components via 2D bulge-disk decomposition. Here we use GIM2D (Simard et al. 2002) and Fig. 3 shows the data of Fig. 2 subdivided by structural component. The dotted line shows the original Freeman distribution which remains relevant today, albeit with a far broader dispersion than originally reported (see Freeman 1970). It would seem that galaxies consist of two principle components (presumably formed via two mechanisms: merging and accretion/collapse ?) and to unravel these two phases in detail must require robust bulge-disk decompositions of extensive samples over a variety of epochs.

Figure 2. The surface brightness distribution of galaxies at various luminosity intervals (as indicated). The curves show the Gaussian fits to the recovered joint luminosity-surface brightness distribution of Driver et al. (2004). The shaded region denotes the limits at which strong selection effects are likely to impact upon the observed distributions. Generally the distribution is narrow and constant for the brightest galaxies (aka Freeman's Law) and then broadens towards lower surface brightness for lower luminosity systems.

Figure 3. The surface brightness distributions of bulge (upper) and disk (lower) components. The vertical dashed line shows the expected surface brightness for spheriods at L* (MB - 19.6 mag) and the dotted curve the Freeman distribution for disks systems. The shaded regions show the approximate selection boundaries. (lower) as above but for the disk components.