Abstract
We have identified 7824 radio sources from the 1.4GHz NRAO VLA Sky Survey (NVSS) with galaxies brighter than K=12.75 mag. in the Second Incremental Data Release of the 6dF Galaxy Survey (6dFGS DR2). The resulting sample of redshifts and optical spectra for radio sources over an effective sky area of 7076 square degrees (about 17% of the celestial sphere) is the largest of its kind ever obtained. NVSS radio sources associated with galaxies in the 6dFGS span a redshift range 0.003<z<0.3 and have median z=0.043. Through visual examination of 6dF spectra we have identified the dominant mechanism for radio emission from each galaxy. 60% are fuelled by star-formation and 40% are fuelled by an active galactic nucleus powered by a supermassive black hole. We have accurately determined the local radio luminosity function at 1.4GHz for both classes of radio source and have found it to agree well with other recent determinations. From the radio luminosity function of star-forming galaxies we derive a local star formation density of 0.022+/-0.001 M_sun/yr/Mpc^3, in broad agreement with recent determinations at radio and other wavelengths. We have split the radio luminosity function of radio-loud AGN into bins of absolute K-band magnitude (M_K) and compared this with the underlying K-band galaxy luminosity function of all 6dFGS galaxies to determine the bivariate radio-$K$-band luminosity function. We verify that radio-loud AGN preferentially inhabit the brightest and hence most massive host galaxies and show that the fraction of all galaxies which host a radio-loud AGN scales as L_K^2.1, indicative of a similarly strong scaling with black hole mass and stellar mass.

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