In this paper we discuss the X-ray properties of 49 local (z<0.035) Seyfert 2 galaxies with HST/WFC2 high-resolution optical coverage. It includes the results of 26 still unpublished Chandra and XMM-Newton observations, which yield 25 (22) new X-ray detections in the 0.5-2 keV (2-10 keV) energy band. Our sample covers a range in the 2-10 keV observed flux from 3x10^{-11} to 6x10^{-15} erg cm$^{-2}$ s$^{-1}$. The percentage of the objects which are likely obscured by Compton-thick matter (column density, N_H>1.6x10^{24} atoms/cm/cm) is ~50%, and reaches ~80% for log(F_{2-10})<12.3. Hence, K-alpha fluorescent iron lines with large Equivalent Width (EW > 0.6 keV) are common in our sample (6 new detections at a confidence level >2 sigma). They are explained as due to reflection off the illuminated side of optically thick material. We confirm a correlation between the presence of a ~100-pc scale nuclear dust in the WFC2 images and Compton-thin obscuration. We interpret this correlation as due to the large covering fraction of gas associated with the dust lanes following an idea originally proposed by Malkan et al. 1998, and Matt 2000). The X-ray spectra of highly obscured AGN invariably present a prominent soft excess emission above the extrapolation of the hard X-ray component. This soft component can account for a very large fraction of the overall X-ray energy budget. As this component is generally unobscured - and therefore likely produced in extended gas structures - it may lead to a severe underestimation of the nuclear obscuration in z~1 absorbed AGN, if standard X-ray colors are used to classify them. As a by-product of our study, we report the discovery of a soft X-ray, luminous (~7x10^{40} erg/s) halo embedding the interacting galaxy pair Mkn266.
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