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We have investigated the physical conditions in the narrow-line region (NLR) of M51 by using long-slit spectra obtained with the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope and 3.6 cm radio continuum observations obtained with the Very Large Array. Emission-line diagnostics were employed for nine NLR clouds, which extend 2 5 (102 pc) from the nucleus, to examine the electron density, temperature, and ionization state of the NLR gas. The emission-line ratios are consistent with those typically found in Seyfert nuclei and indicate that within the inner near-nuclear region ( r ≲ 1'') the ionization decreases with increasing radius. Upper limits to the [O III] electron temperature ( T e ≲ 11,000 K) for the inner NLR clouds indicate that photoionization is the dominant ionization mechanism close to the nucleus. The emission-line fluxes for most of the NLR clouds can be reproduced reasonably well by simple photoionization models using a central power-law continuum source and supersolar nitrogen abundances. Shock+precursor models, however, provide a better fit to the observed fluxes of an NLR cloud ~2 5 south of the nucleus that is identified with the extranuclear cloud. The large [O III] electron temperature of this cloud ( T e = 24,000 K) further suggests the presence of shocks. This cloud is straddled by two radio knots and lies near the location where a weak radio jet, ~2 5 (102 pc) in extent, connects the near-nuclear radio emission with a diffuse lobe structure spanning ~4'' (163 pc). It is plausible that this cloud represents the location where the radio jet impinges on the disk ISM.
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