We apply order statistics (OS) to the bright end ($M_r < -22$) of the luminosity distribution of early-type galaxies spectroscopically identified in the SDSS DR7 catalog. We calculate the typical OS quantities of this distribution numerically, measur
ing the expectation value and variance of the $k^{th}$ most luminous galaxy in a sample with cardinality $N$ over a large ensemble of such samples. From these statistical quantities we explain why and in what limit the $k^{th}$ most luminous galaxies can be used as standard candles for cosmological studies. Since our sample contains all bright galaxies including the brightest cluster galaxies (BCG), based on OS we argue that BCGs can be considered as statistical extremes of a well-established Schechter luminosity distribution when galaxies are binned by redshift and not cluster-by-cluster. We presume that the reason behind this might be that luminous red ellipticals in galaxy clusters are em not random em samples of an overall luminosity distribution but biased by the fact that they are in a cluster containing the BCG. We show that a simple statistical toy model can reproduce the well-known magnitude gap between the BCG and the second brightest galaxy of the clusters.
We determine the evolution of the co-moving density of the most massive ($M_* geq 10^{12} M_odot$) early-type galaxy population in the redshift range of $z = 0.15$ - 0.45 in different stellar mass ranges using data from the Sloan Digital Sky Survey D
ata Release 7 (SDSS DR7) catalog. We find that the co-moving number density of these galaxies grew exponentially, weakly depending on the stellar mass range, as a function of cosmic time with a time-scale of $tau simeq 1.16 pm 0.16$ Gyr for at least 4 Gyr ending around $z simeq 0.15$. This is about a factor of ten of growth between $z=0.5$ - 0.15. Since $z simeq 0.15$ a constant co-moving number density can be measured. According to theoretical models the most massive early-type galaxies gain most of their stellar mass via dry merging but the major merger rate measured by others cannot account for the high growth in number density we measured thus, stellar mass gain from minor mergers and slow, smooth accretion seems to play an important role. We outline a simple analytic model that explains the observed evolution based on the exponential decline of the luminosity function and sets constraints on the time dependence of the close-pair fraction of merger candidate galaxies.
