H

Context.Previous studies have indicated that the 372.4 GHz ground transition of ortho-H2D+ might be a powerful probe of Proto-Planetary Disks. The line could be especially suited for study of the disk mid-plane, where the bulk of the mass resides and where planet formation takes place. Aims.Provide detailed theoretical predictions for the line intensity, profile and maps expected for representative disk models. Methods.We determine the physical and chemical structure of the disks from the model developed by Ceccarelli & Dominik (2005, A&A, 440, 583). The line emission is computed with the new radiative transfer method developed recently by Elitzur & Asensio Ramos (2006, MNRAS, 365, 779). Results.We present intensity maps convolved with the expected ALMA resolution, which delineate the origin of the H2D+ 372.4 GHz line. In the disk inner regions, the line probes the conditions in the mid-plane out to radial distances of a few tens of AU, where Solar-like planetary systems might form. In the disk outermost regions, the line originates from slightly above the mid-plane. When the disk is spatially resolved, the variation of line profile across the image provides important information about the velocity field. Spectral profiles of the entire disk flux show a double peak shape at most inclination angles. Conclusions.Our study confirms that the 372.4 GHz H2D+ line provides powerful diagnostics of the mid-plane of Proto-Planetary Disks. Current submillimeter telescopes are capable of observing this line, though with some difficulties. The future ALMA interferometer will have the sensitivity to observe and even spatially resolve the H2D+ line emission