Radial modes of pressure bumps and dips in astrophysical discs Leclerc, Armand Laibe, Guillaume Lynch, Elliot Perez, Nicolas accretion accretion disks hydrodynamics instabilities waves protoplanetary disks ddc:520 Aims. We investigate signatures of pressure extrema on global oscillations in discs. Methods. We used the framework of wave topology to establish a generalised local dispersion relation that includes pressure gradients. We highlight the influence of a previously unrecognised epicyclic–acoustic frequency, and we derive an analytical criterion for the existence of a branch of modes transiting between the inertial and the pressure bands, known as topological modes. Results. We find that pressure extrema consist of wave guides in which such topological modes propagate. The fundamental mode trapped at a pressure bump can propagate at any frequency, allowing it to resonate with any temporal forcing. Conversely, the fundamental mode associated with a pressure dip propagates at any vertical phase velocity. These specific features make them attractive candidates for future discoseismology. EDP Sciences 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/23047 https://research-explorer.ista.ac.at/download/23047/23075 Leclerc A, Laibe G, Lynch E, Perez N. Radial modes of pressure bumps and dips in astrophysical discs. <i>Astronomy and Astrophysics</i>. 2026;708. doi:<a href="https://doi.org/10.1051/0004-6361/202558428">10.1051/0004-6361/202558428</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1051/0004-6361/202558428 info:eu-repo/semantics/altIdentifier/issn/0004-6361 info:eu-repo/semantics/altIdentifier/e-issn/1432-0746 info:eu-repo/semantics/altIdentifier/arxiv/2512.05737 info:eu-repo/semantics/openAccess