The distance-independent "fluctuation count" is defined as = - mtot = +2.5 log[Ltot ] (Tonry et al. 2001), where Ltot is the galaxy total luminosity and is the mean "fluctuation luminosity" corresponding to magnitude , which depends on the stellar population. The ratio Ltot / is a distance-independent galaxy luminosity in units of and scales with the number of stars in the galaxy (and thus with stellar mass). Figure 5 shows the correlation of with color from Blakeslee et al. (2009), a consequence of the mass-metallicity relation. also shows a good correlation with velocity dispersion , tighter than even the Mg2- relation (Blakeslee et al. 2002).
Figure 5. Galaxy (g475 - z850) color is plotted as a function of the "fluctuation count" z, the difference between SBF magnitude 850 and total z magnitude of the galaxy, for galaxies in Virgo (open circles) Fornax (filled circles). Note that z, like (g475 - z850), is distance-independent and can therefore be used for an alternative calibration of the SBF method (see Blakeslee et al. 2009). Unlike color, is also independent of Galactic extinction. The dashed and solid lines show the best-fit linear and quadratic relations, respectively. is closely related to the stellar mass of the galaxy, and the correlation with color results from the mass-metallicity scaling relation; the scatter increases at blue colors and low luminosities.
The correlation with color means that can also be used to calibrate SBF distances. Depending on the color baseline and properties of the data sample, the SBF calibration based on may show less scatter than that from color (Blakeslee et al. 2002, 2009). However, the calibration is then no longer based purely on stellar population properties, but involves a galaxy mass scaling relation. Thus, luminous blue galaxies and small red galaxies deviate from the calibration, and there may be systematic environmental effects similar those of the fundamental plane. For these reasons, the preferred calibration uses galaxy color, but the behavior of itself would be interesting to examine with semi-analytic galaxy modeling.