Fourier-space combination of Planck and Herschel images

Herschel has revolutionized our ability to measure column densities (N$_{\rm H}$) and temperatures (T) of molecular clouds thanks to its far infrared multiwavelength coverage. However, the lack of a well defined background intensity level in the Herschel data limits the accuracy of the N$_{\rm H}$ and T maps. We provide a method that corrects the missing Herschel background intensity levels using the Planck model for foreground Galactic thermal dust emission. We present a Fourier method that combines the publicly available Planck model on large angular scales with the Herschel images on smaller angular scales. We apply our method to two regions spanning a range of Galactic environments: Perseus and the Galactic plane region around $l = 11\deg$ (HiGal--11). We post-process the combined dust continuum emission images to generate column density and temperature maps. We compare these to previously adopted constant--offset corrections. We find significant differences ($\gtrsim$20\%) over significant ($\sim$15\%) areas of the maps, at low column densities ($N_{\rm H}\lesssim10^{22}$\,cm$^{-2}$) and relatively high temperatures ($T\gtrsim20$\,K). We also apply our method to synthetic observations of a simulated molecular cloud to validate our method. Our method successfully corrects the Herschel images, including both the constant--offset intensity level and the scale-dependent background variations measured by Planck. Our method improves the previous constant--offset corrections, which did not account for variations in the background emission levels.