The µ Herculis system solved after nearly three centuries

¹ Stellar Astrophysics center, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
² Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
³ Department of Astronomy, University of Texas at Austin, 2515 Speedway, Stop C1400 Austin, TX 78712-1205, USA
⁴ Institute for Astronomy, University of Hawai‘i at Mānoa, Hilo, HI 96720, USA
⁵ Instituto de Astrofisica de Canarias, 38205 La Laguna. Tenerife, Spain
⁶ Departamento de Astrofisica. Universidad de La laguna, 38206 La Laguna, Tenerife, Spain
⁷ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁸ Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA

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

Received: 15 January 2026
Accepted: 19 March 2026

Abstract

Context. µ Herculis is a bright, nearby quadruple system. Its brightest member, µ Her Aa, displays solar-like oscillations, establishing the system as a crucial benchmark for asteroseismology, provided that its mass can be determined independently of stellar models.

Aims. We aim to resolve the full hierarchical architecture of the system and determine precise, model-independent dynamical masses for all four components (Aa, Ab, B, and C), along with a consistent astrometric solution for the system’s centre of mass.

Methods. We performed a joint fit of radial velocities, relative astrometry and absolute astrometry from HIPPARCOS, Gaia DR3, and ground-based catalogues, spanning nearly three centuries. Our forward-modelling framework simultaneously constrains the Keplerian orbits of the inner Aa–Ab and B–C subsystems, the wide A–BC orbit, and the sky motion and parallax of the total centre of mass.

Results. Leveraging several complementary datasets and the decisive 2023 periastron passage of the Aa–Ab pair, we precisely determine all orbital parameters and obtain sub-percent precision on the component masses: M_Aa = 1.134 ± 0.007 M_⊙, M_Ab = 0.2286±0.0006 M_⊙, M_C = 0.445±0.005 M_⊙, and M_B = 0.417±0.005 M_⊙. We derive a system parallax of ϖ_CM = 120.069±0.089 mas that reconciles and improves upon the individual HIPPARCOS and Gaia DR3 values.