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| - I. Optical characterization of the CIG catalog
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| - The AMIGA project (Analysis of the Interstellar Medium of Isolated Galaxies) is compiling a multiwavelength database of isolated galaxies that includes optical (B and H α), infrared (FIR and NIR) and radio (continuum plus HI and CO lines) properties. It involves a refinement of the pioneering Catalog of Isolated Galaxies. This paper is the first in a series and begins with analysis of the global properties of the nearly redshift-complete CIG with emphasis on the Optical Luminosity Function (OLF) which we compare with other recent estimates of the OLF for a variety of environments. The CIG redshift distribution for $n=$ 956 galaxies re-enforces the evidence for a bimodal structure seen earlier in smaller samples. The peaks at redshift near 1500 and 6000 km s -1, corresponding respectively to galaxies in the local supercluster and those in more distant large-scale components (particularly Perseus-Pisces). The two peaks in the redshift distribution are superimposed on 50% or more of the sample that is distributed in a much more homogeneous way. The CIG probably represents the most homogeneous local field example that has ever been compiled. Our derivation of the CIG OLF is consistent with other studies of the OLF for lower density environments. This comparison via the Schechter parameter formalization shows that: 1) M * increases with galaxy surface density on the sky and 2) α shows a weaker tendency to do the same. The CIG represents the largest and most complete foundation for studies of isolated galaxies and is likely as close as we can come to a field sample.
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