Letter to the Editor

Towards inertial-mode helioseismology: Direct sensing of solar rotation at 75° latitude and 0.8 R_⊙

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
² Institut für Astrophysik und Geophysik, Georg-August-Universtät Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
³ Center for Astrophysics and Space Science, NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 25 April 2026
Accepted: 6 May 2026

Abstract

Context. Because solar global inertial modes are highly sensitive to differential rotation, they may provide new diagnostics of internal rotation at high latitudes, where acoustic-mode helioseismology provides only weak constraints.

Aims. Our aim was to constrain solar rotation using the measured frequency of the m = 1 high-latitude inertial mode, starting from the HMI/SDO reference rotation profile given by p-mode helioseismology for 2010–2024.

Methods. Using a validated and accurate eigenvalue solver, we computed the perturbation to the mode frequency resulting from localized changes in the differential rotation rate throughout the solar interior.

Results. We find that the linear sensitivity kernel of the m = 1 high-latitude mode peaks at a latitude of 75° and a radius of 0.8 R_⊙, with full widths of 7° and 0.13 R_⊙. From the observed mode frequency in the Carrington frame, −87.9 ± 1.9 nHz (retrograde, averaged over 2010–2024), we infer that the solar rotation rate near this location is 365.3 ± 2.0 nHz, which exceeds the reference p-mode estimate by 8.1 nHz. Additionally, we propose a latitudinally smooth, radially independent modification to the rotation rate at high latitudes beyond the linear (small-perturbation) regime.

Conclusions. This work demonstrates that individual inertial modes can provide direct constraints on rotation in the bulk of the solar convection zone, well below the surface, representing the first example of spatially resolved inertial-mode helioseismology.