GALACTICNUCLEUS: A high-angular-resolution $JHK_s$ imaging survey of the Galactic centre. IV. Extinction maps and de-reddened photometry

The extreme extinction ($A_V\sim30$\,mag) and its variation on arc-second scales towards the Galactic centre hamper the study of its stars. Their analysis is restricted to the near infrared (NIR) regime, where the extinction curve can be approximated by a broken power law. Therefore, correcting for extinction is fundamental to analyse the structure and stellar population of the central regions of our Galaxy. We aim to, (1) discuss different strategies to de-redden the photometry and check the usefulness of extinction; (2) build extinction maps for the NIR bands $JHK_s$ and make them publicly available; (3) create a de-reddened catalogue of the GALACTICNUCLEUS (GNS) survey, identifying foreground stars; and (4) perform a preliminary analysis of the de-reddened $K_s$ luminosity functions (KLFs). We used photometry from the GNS survey to create extinction maps for the whole catalogue. We took red clump (RC) and red giant stars of similar brightnesses as a reference to build the maps and de-reddened the GNS photometry. We discussed the limitations of the process and analysed non-linear effects of the de-reddening. We obtained high resolution ($\sim3''$) extinction maps with low uncertainties ($\lesssim5$\,\%) and computed average extinctions for each of the regions covered by the GNS. We checked that our maps effectively correct the differential extinction reducing the spread of the RC features by a factor of $\sim2$. We assessed the validity of the broken power law approach computing two equivalent extinction maps $A_H$ using either $JH$ and $HK_s$ photometry for the same reference stars and obtained compatible average extinctions within the uncertainties. Finally, we analysed de-reddened KLFs for different lines of sight and found that the regions belonging to the NSD contain a homogeneous stellar population that is significantly different from that in the innermost bulge regions.