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Radiogalaxies in the Sloan Digital Sky Survey: spectral index-environment correlations

We analyze optical and radio properties of radiogalaxies detected in the Sloan Digital Sky Survey (SDSS). The sample of radio sources are selected from the catalogue of Kimball & Ivezić (2008) with flux densities at 325, 1400 and 4850 MHz, using WENSS, NVSS and GB6 radio surveys and from flux measurements at 74 MHz taken from VLA Low-frequency Sky Survey \citep{cohen}. We study radiogalaxy spectral properties using radio colour-colour diagrams and find that our sample follows a single power law from 74 to 4850 MHz. The spectral index vs. spectroscopic redshift relation ($α-z$) is not significant for our sample of radio sources. We analyze a subsample of radio sources associated with clusters of galaxies identified from the maxBCG catalogue and find that about 40% of radio sources with ultra steep spectra (USS, $α<-1$, where $S_ν\propto ν^α$) are associated with galaxy clusters or groups of galaxies. We construct a Hubble diagram of USS radio sources in the optical $r$ band up to $z\sim0$.8 and compare our results with those for normal galaxies selected from different optical surveys and find that USS radio sources are around as luminous as the central galaxies in the maxBCG cluster sample and typically more than 4 magnitudes brighter than normal galaxies at $z\sim0$.3. We study correlations between spectral index, richness and luminosity of clusters associated with radio sources. We find that USS at low redshift are rare, most of them reside in regions of unusually high ambient density, such of those found in rich cluster of galaxies. Our results also suggest that clusters of galaxies associated with steeper than the average spectra have higher richness counts and are populated by luminous galaxies in comparison with those environments associated to radio sources with flatter than the average spectra. A plausible explanation for our results is that radio emission is more pressure confined in higher gas density environments such as those found in rich clusters of galaxies and as a consequence radio lobes in rich galaxy clusters will expand adiabatically and lose energy via synchrotron and inverse Compton losses, resulting in a steeper radio spectra.