A fast method for deriving relative small-scale magnetic field variations from high-resolution spectroscopy

¹ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
² Center for Astrophysics | Havard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA

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

Received: 12 January 2026
Accepted: 27 February 2026

Abstract

Context. Setting observational constraints on stellar magnetic fields is essential for both stellar and planetary physics. They play a key role in the formation and evolution of stars and planets, and they are responsible for spurious signals in radial velocity curves that impact the detection and characterization of exoplanets. Recent observations have revealed the diversity and evolution of large-scale magnetic fields in low-mass stars. However, these large-scale fields only account for a small fraction of the observed unsigned magnetic flux. The other crucial stellar magnetism information originates from (spatially) small-scale magnetic fields, which account for most of the surface magnetic flux and exhibit a clear temporal evolution on timescales of many years.

Aims. With this work, we aim to develop new fast techniques to extract small-scale magnetic field estimates from time series of observed high-resolution spectra. One objective is to develop tools that will enable the community to take full advantage of the upcoming monitoring surveys carried out with various high-resolution spectrometers. Our ultimate goal is to study the temporal evolution of small-scale magnetic fields and offer insights into the magnetic properties of low-mass stars and their magnetic cycles.

Methods. We implemented a process to capture relative pixel variations caused by changes in magnetic field strengths, relying on synthetic spectra computed with ZeeTurbo. This approach provides extremely fast and reliable estimates of relative magnetic field strength variations from series of high-resolution spectra, mitigating the impact of systematics between models and observations. We assessed the performance of the proposed method through its application to simulated data and publicly available observed spectra recorded with SPIRou, Narval, and ESPaDOnS. In addition, we implemented a model-driven process to derive relative temperature variations and we explored the influence magnetic fields have on these measurements.

Results. Our results are in excellent agreement with the magnetic field estimates previously obtained from spectra recorded with SPIRou. This method provides robust constraints on the structure of the magnetic field variations and proves to be relatively insensitive to small changes in the assumed atmospheric parameters and broadening. We find that magnetic field variations have the potential of introducing biases in relative temperature estimates. This is particularly relevant in the case of the Narval/ESPaDOnS spectral domains, which contain a large number of magnetically sensitive transitions and where contrast is more important. Our application to archival data provides new constraints on the evolution of small-scale magnetic fields and underscores the potential of the proposed method for analyzing data in the context of large observation programs.

Conclusions. By reducing the problem to a set of linear equations, our method offers extremely fast results, making it viable for integration in future pipelines developed for large spectroscopic surveys. These estimates will provide much needed information to correct radial velocity curves and constrain dynamo processes.