The luminosity function of ringed galaxies

We perform an analysis of the luminosity functions (LFs) of two types of ringed galaxies -- polar-ring galaxies and collisional ring galaxies -- using data from the Sloan Digital Sky Survey (SDSS). Both classes of galaxies were formed as a result of interaction with their environment and they are very rare objects. We constructed LFs of galaxies by different methods and found their approximations by the Schechter function. The luminosity functions of both types of galaxies show a systematic fall-off at low luminosities. The polar structures around bright ($M_r \leq -20^m$) and red ($g-r > +0.8$) galaxies are about twice as common as around blue ones. The LF of collisional rings is shifted towards brighter luminosities compared to polar-ring galaxies. We analysed the published data on the ringed galaxies in several deep fields and confirmed the increase in their volume density with redshift: up to z$\sim$1 their density grows as $(1+z)^m$, where $m \gtrsim 5$.