Orion's veil consists of several layers of largely neutral gas lying between us and the main ionizing stars of the Orion nebula. It is visible in 21cm H I absorption and in optical and UV absorption lines of H I and other species. Toward the Trapezium, the veil has two remarkable properties, high magnetic field (~100 microGauss) and a surprising lack of molecular hydrogen given its total hydrogen column density. Here we compute photoionization models of the veil to establish its gas density and its distance from the Trapezium. We use a greatly improved model of the hydrogen molecule that determines level populations in ~1e5 rotational/vibrational levels and provides improved estimates of molecular hydrogen destruction via the Lyman-Werner bands. Our best fit photoionization models place the veil 1-3 pc in front of the star at a density of 1e3-1e4 cubic centimeters. Magnetic energy dominates the energy of non-thermal motions in at least one of the 21cm H I velocity components. Therefore, the veil is the first interstellar environment where magnetic dominance appears to exist. We find that the low ratio of molecular to atomic hydrogen (< 1e-4) is a consequence of high UV flux incident upon the veil due to its proximity to the Trapezium stars and the absence of small grains in the region.

45 pages, 20 figures, accepted for publication in ApJ