Distribution of Radio Spectral Slopes of Galaxies in Optical Diagnostic
  Diagrams
  For about 500 intermediate-redshift sources ($0.04<z<0.4$), whose radio flux
densities at $1.4\,{\rm GHz}$ are larger than 10 mJy, we performed additional
observations at 4.85 GHz and 10.45 GHz using 100-m Effelsberg telescope. Our
radio-optical galaxies are located preferentially in the composite and AGN
spectral classes in the narrow line optical diagnostic diagrams (ODD). In the
analysis, we focused on the distribution of radio spectral indices of radio
synchrotron power-law profiles, $S_{\nu}\propto \nu^{+\alpha}$, in the ODDs.
Using different analysis techniques, both observationally motivated and
machine-learning based, we found three distinct groups--clusters in the radio
loudness, [OIII]/H$\beta$ ratio, and spectral index volume: (1) sources with
steep radio spectral index, large radio loudness and large [OIII]/H$\beta$
ratio; (2) sources with flat radio spectral index, intermediate radio loudness
and lower [OIII]/H$\beta$ ratio; (3) sources with inverted radio spectral
index, low radio loudness and low [OIII]/H$\beta$. The groups (1), (2), and (3)
are located along the Seyfert-LINER spectral classes towards lower ionization
ratios in the ODDs and hence can represent different activity cycles/accretion
modes of AGNs, which could be in some cases associated with different merger
stages.
