Context. The determination of the relative frequency of active galactic nuclei (AGN) versus other spectral classes, for example, HII region-like (HII), transition objects (TRAN), passive (PAS), and retired (RET), in a complete set of galaxies in the local Universe is of primary importance to discriminate the source of ionization in the nuclear region of galaxies. Aims. Here we aim to provide a spectroscopic characterization of the nuclei of galaxies belonging to the Herschel Reference Survey (HRS), a volume and magnitude limited sample representative of the local Universe, which has become a benchmark for local and high-z studies, for semianalytical models and cosmological simulations. The comparison between the nuclear spectral classification and the one determined on the global galactic scale provides information about how galaxy properties change from the nuclear to the outer regions. Moreover, the extrapolation of the global star formation (SF) properties from the SDSS fiber spectroscopy compared to the one computed by Halpha photometry can be useful for testing the method based on aperture correction for determining the global star formation rate (SFR) for local galaxies. Methods. By collecting the existing nuclear spectroscopy available from the literature, complemented with new observations obtained using the Loiano 1.52m telescope, we analyze the 322 nuclear spectra of HRS galaxies. Results. Using two diagnostic diagrams (the BPT and the WHAN) we provide a nuclear and an integrated spectral classification for the HRS galaxies. Conclusions. We find that the fraction of AGNs increases with stellar mass, such that at logM > 10.0 Modot or 66% of the LTGs are AGNs or TRAN.
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