We explore the stability of different galaxy light concentration indices as a function of the outermost observed galaxy radius .
With a series of analytical light-profile models , we show mathematically how varying the radial extent to which one measures a galaxy ’ s light can strongly affect the derived galaxy concentration .
The “ mean concentration index ” , often used for parametrizing high-redshift galaxies , is shown to be horribly unstable , even when modelling one-component systems such as Elliptical , dwarf Elliptical , and pure exponential disk galaxies .
The C _ { 31 } concentration index performs considerably better but is also heavily dependent on the radial extent , and hence exposure depth , of any given galaxy .
We show that the recently defined central concentration index is remarkably stable against changes to the outer radius and observational errors , and provides both a meaningful and reliable estimate of galaxy concentration .
The Sérsic index n from the r ^ { 1 / n } models is shown to be monotonically related with the central concentration of light , giving the index n a second and perhaps more tangible meaning .
With a sample of Elliptical and dwarf Elliptical galaxies we present correlations between the central light concentration and the global parameters : luminosity ( Pearson ’ s r = -0.82 ) , effective radius ( r = 0.67 ) , central surface brightness ( r = -0.88 ) , and velocity dispersion ( r = 0.80 ) .
The more massive Elliptical galaxies are shown to be more centrally concentrated .
We speculate that the physical mechanism behind the recently observed correlation between the central velocity dispersion ( mass ) of a galaxy and the mass of it ’ s central supermassive blackhole may be connected with the central galaxy concentration .
That is , we hypothesize that it may not simply be the amount of mass in a galaxy , but rather how that mass is distributed , which controls the mass of the central blackhole .