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.