Inferring magnetic helicity spectrum in spherical domains
| openaire: EC/H2020/818665/EU//UniSDyn Funding Information: Acknowledgements. MJK acknowledges the support of the Academy of Finland ReSoLVE Centre of Excellence (grant No. 307411). AP was funded by the International Max Planck Research School for Solar System Science at the University of Göttingen. This project has received funding from the European Research Council under the European Union's Horizon 2020 research and innovation programme (project "UniSDyn", grant agreement n:o 818665). SOLIS data used here are produced cooperatively by NSF/NSO and NASA/LWS. Publisher Copyright: © A. P. Prabhu et al. 2021. ; Context. Obtaining observational constraints on the role of turbulent effects for the solar dynamo is a difficult, yet crucial, task. Without such knowledge, the full picture of the operation mechanism of the solar dynamo cannot be formed. Aims. The magnetic helicity spectrum provides important information about the α effect. Here we demonstrate a formalism in spherical geometry to infer magnetic helicity spectra directly from observations of the magnetic field, taking into account the sign change of magnetic helicity across the Sun's equator. Methods. Using an angular correlation function of the magnetic field, we develop a method to infer spectra for magnetic energy and helicity. The retrieval of the latter relies on a fundamental definition of helicity in terms of linkage of magnetic flux. We apply the two-scale approach, previously used in Cartesian geometry, to spherical geometry for systems where a sign reversal of helicity is expected across the equator on both small and large scales. Results. We test the method by applying it to an analytical model of a fully helical field, and to magneto-hydrodynamic simulations of a turbulent dynamo. The helicity spectra computed from the vector potential available in the models are in excellent agreement with the spectra computed solely from the magnetic field using our method. In a next test, we use our method to obtain the helicity spectrum from a synoptic magnetic field map corresponding to a Carrington rotation. We observe clear signs of a bihelical spectrum of magnetic helicity, which is in complete accordance to the previously reported spectra in literature from the same map. Conclusions. Our formalism makes it possible to infer magnetic helicity in spherical geometry, without the necessity of computing the magnetic vector potential. It has many applications in solar and stellar observations, but can also be used to analyse global magnetoconvection models of stars and to compare them with observations. ; Peer reviewed