Nature and completeness of galaxies detected in the Two Micron All Sky Survey

The Two Micron All Sky Survey (2MASS) provides the most comprehensive data set of near-infrared galaxy properties. We cross correlate the well-defined and highly complete spectroscopic selection of over 155000 bright (r <= 17.5 mag) galaxies in the Sloan Digital Sky Survey (SDSS) main galaxy sample (MGS) with 2MASS sources to explore the nature and completeness of the 2MASS (K-band) selection of nearby galaxies. Using estimates of total galaxy brightness direct from the 2MASS and SDSS public catalogues, corrected only for Galactic extinction, we find that 2MASS detects 90 per cent of the MGS brighter than r = 17 mag. We quantify the completeness of 2MASS galaxies in terms of optical properties from SDSS. For r <= 16 mag, 94.6 per cent of the MGS is found in the 2MASS extended source catalogue (XSC). These detections span the representative range of optical and near-infrared galaxy properties, but with a surface brightness-dependent bias to preferentially miss sources at the extreme blue and low-concentration end of parameter space, which are consistent with the most morphologically late-type galaxy population. An XSC completeness of 97.6 per cent is achievable at bright magnitudes, with blue low-surface-brightness galaxies being the only major source of incompleteness, if one follows our careful matching criteria and weeds out spurious SDSS sources. We conclude that the rapid drop in XSC completeness at r > 16 mag reflects the sharp surface-brightness limit of the extended source detection algorithm in 2MASS. As a result, the r > 16 galaxies found in the XSC are over-representative in red early types and under-representative in blue late types. At r > 16 mag, the XSC suffers an additional selection effect from the 2-3 arcsec spatial resolution limit of 2MASS. Therefore, in the range 16 < r <= 17 mag, 2MASS continues to detect 90 per cent of the MGS, but with a growing fraction found in the point-source catalogue (PSC) only. Overall, one-third of the MGS is detected in the 2MASS PSC but not the XSC. Careful consideration of the different selection effects of 2MASS and SDSS are required to produce useful matched samples. A combined K <= 13.57 and r <= 16 mag-limited selection provides the most representative inventory of galaxies in the local cosmos with near-infrared and optical measurements, and 92.2 per cent completeness. Using data from the SDSS Second Data Release, this sample contains 19143 galaxies with a median redshift of 0.052