The NGC 5846 Group: Dynamics and the Luminosity Function to M_R=-12

We conduct a photometric and spectroscopic survey of a 10 sq. deg. region surrounding the nearby NGC 5846 group of galaxies, using the Canada-France-Hawaii and Keck I telescopes to study the population of dwarf galaxies as faint as M_R=-10. Candidates are identified on the basis of quantitative surface brightness and qualitative morphological criteria. Spectroscopic follow up and a spatial correlation analysis provide the basis for affirming group memberships. Altogether, 324 candidates are identified and 83 have spectroscopic membership confirmation. We argue on statistical grounds that a total 251 +/- 10 galaxies in our sample are group members. The observations, together with archival Sloan Digital Sky Survey, ROSAT, XMM-Newton, and ASCA data, suggest that the giant ellipticals NGC 5846 and NGC 5813 are the dominant components of subgroups separated by 600 kpc in projection and embedded in a 1.6 Mpc diameter dynamically evolved halo. The galaxy population is overwhelmingly early type. The group velocity dispersion is 322 km/s, its virial mass is 8.4 x 10^13 M_sun, and M/L_R = 320 M_sun/L_sun. The ratio of dwarfs to giants is large compared with other environments in the Local Supercluster studied and, correspondingly, the luminosity function is relatively steep, with a faint end Schechter function slope of \alpha_d = -1.3 +/- 0.1 (statistical) +/- 0.1 (systematic) at our completeness limit of M_R = -12.