Herschel-Planck dust optical-depth and column-density maps: I. Method description and results for Orion

We present high-resolution, high dynamic range column-density and color-temperature maps of the Orion complex using a combination of Planck dust-emission maps, Herschel dust-emission maps, and 2MASS NIR dust-extinction maps. The column-density maps combine the robustness of the 2MASS NIR extinction maps with the resolution and coverage of the Herschel and Planck dust-emission maps and constitute the highest dynamic range column-density maps ever constructed for the entire Orion complex, covering $0.01 \, \mathrm{mag} < A_K < 30 \,\mathrm{mag}$, or $2 \times 10^{20} \, \mathrm{cm}^{-2} < N < 5 \times 10^{23} \,\mathrm{cm}^{-2}$. We determined the ratio of the 2.2 microns extinction coefficient to the 850 microns opacity and found that the values obtained for both Orion A and B are significantly lower than the predictions of standard dust models, but agree with newer models that incorporate icy silicate-graphite conglomerates for the grain population. We show that the cloud projected pdf, over a large range of column densities, can be well fitted by a simple power law. Moreover, we considered the local Schmidt-law for star formation, and confirm earlier results, showing that the protostar surface density $\Sigma_*$ follows a simple law $\Sigma_* \propto \Sigma_{gas}^\beta$, with $\beta \sim 2$.