A model of umbral oscillations inherited from subphotospheric fast-body modes Juhyung Kang, Jongchul Chae, Kyuhyoun Cho, Soosang Kang and Eun-Kyung Lim A&A, 686 (2024) A293 Published online: 20 June 2024 DOI: 10.1051/0004-6361/202449887