Large-scale galactic-dust-cleaned cosmic infrared background maps from \textit{Planck} PR4 and HI4PI with \texttt{pyilc}

The cosmic infrared background (CIB) traces star-forming galaxies throughout cosmic history, with emission peaking at $z\sim1-2$. CIB anisotropies are present at the far-infrared frequencies observed by cosmic microwave background (CMB) experiments such as $\textit{Planck}$. These contain a lot of astrophysical and cosmological information, but are hard to separate from the dust emission in our own Milky Way galaxy, especially on large scales where the Milky Way contamination severely dominates. This galactic component is often cleaned using information from other galactic tracers such as neutral hydrogen (HI). In this work we use HI data from the HI4PI survey to clean the 353, 545, and 857 GHz $\textit{Planck}$ NPIPE single-frequency maps using a needlet internal linear combination (NILC) method, with $\texttt{pyilc}$. This allows us to preserve the CIB anisotropy information on $\textit{all}$ scales, while reducing the variance sourced by the galactic contamination. We also create a NILC CMB map from the $\textit{Planck}$ NPIPE data, to subtract a CMB template from the 353 GHz map. Our resulting CIB maps are appropriate for cross-correlation studies with cosmological tracers such as CMB lensing maps down to very low $\ell$ ($\ell\sim10$), while achieving similar performance to previous works on intermediate scales. The use of the NPIPE data additionally allows us to achieve lower instrumental noise in the maps than in previous works. We use our maps, in combination with the $\textit{Planck}$ NPIPE CMB lensing reconstruction, to measure the CIB-CMB lensing cross correlation down to $\ell\sim10$. We make various versions of our maps publicly available to the community for further use in cross-correlation studies, along with a script (and the intermediate data products required) to produce dust-cleaned CIB maps on an arbitrary region of sky.