GALACTICNUCLEUS: A high-angular-resolution JHKs imaging survey of the Galactic center. V. Toward the GNS second data release: Methodology and photometric and astrometric performance

The center of the Milky Way presents a unique environment of fundamental astrophysical interest. However, its extreme crowding and extinction make this region particularly challenging to study. The GALACTICNUCLEUS survey, a high-angular-resolution near-infrared imaging program, was designed to overcome these difficulties. Its first data release provides a powerful resource for exploring the Galactic center and enables key discoveries in this extreme environment. We present the methodology and first results of a second data release of the GALACTICNUCLEUS survey, which incorporates significant improvements in data reduction, calibration, and methodology as well as a second epoch. In particular, we aim to provide deeper photometry, improved astrometry, and high-precision proper motion for the test fields analyzed in this study. Observations were obtained with VLT/HAWK-I over two epochs separated by approximately seven years for most pointings and by four to five years for others. The data were acquired using speckle holography, and in the case of the second epoch, a ground-layer adaptive optics system was also employed. We have developed a new reduction pipeline with key improvements, including enhanced distortion corrections and jackknife-based error estimation. For the test fields presented in this work, proper motions were derived using two complementary approaches: (i) relative proper motions, aligning epochs within the survey itself, and (ii) absolute proper motions, tied to the reference frame. Validation was performed on two representative test fields: one in the Galactic bar and one in the crowded nuclear stellar disk, overlapping with the Arches cluster. Gaia -1 relative to despite being based solely on two ground-based epochs. Both relative and absolute approaches deliver consistent results. In the Arches field, we recovered the cluster with mean velocities consistent with previous HST-based studies. The proper-motion distributions reveal distinct kinematic behavior between the bulge and nuclear stellar disk fields, suggesting that the latter constitutes a dynamically distinct component. Comparisons with previous catalogs confirmed the robustness of our methodology. Gaia The data analyzed in this study provide ground-based proper motions measurements of the Galactic center that are among the most precise currently available for bright stars and that stand out among other ground-based catalogs at red clump and fainter magnitudes. In this pilot analysis, the proper-motion distributions already reveal a distinct kinematic behavior between the bulge and nuclear stellar disk fields. Once the full survey has been analyzed, it will enable detailed studies of the structure and dynamics of the nuclear stellar disk. The expected quality of the final catalogs will also make them well suited for combination with observations from space-based missions, such as JWST and the Space Telescope. Roman