Shaping the Milky Way: The interplay of mergers and cosmic filaments

Time evolution of the quadrupole-environment view (columns 1 and 3), reconstructed for the two identified frequency groups: filament frequency (first two columns) and LMC frequency (last two columns) PCs in the m12b halo. The first and third columns show the global view (within 1 Mpc), while the second and fourth columns focus on the local region (within 100 kpc). Open contours represent the quadrupole density field (vertical color bar), with the LMC-analog trajectory (dashed black curve and a magenta star for the current position) overlaid for reference. In the global view, the background highlights filamentary structures with the main halo and LMC-analog subtracted. In the local view, the background shows the main halo and LMC-analog subtracted surface densities. The reported values in the local regions are scaled down by a factor of 100 for clarity. The dominant frequency quadrupole components align with large-scale filamentary structures, while the subdominant components capture the localized impact of the satellite's passage.