A fast method to derive relative small-scale magnetic field variations from high resolution spectroscopy

Abstract

Observational constraints on stellar magnetic fields are essential to both stellar and planetary physics. Recent studies revealed the diversity and evolution of large-scale magnetic fields in low-mass stars. These large-scale fields only account for a small fraction of the observed unsigned magnetic flux. Most of the surface magnetic flux if accounted for by small (spatial) scale magnetic fields, which exhibit clear temporal evolution of time scales of years. We aim at developing new techniques to extract small-scale magnetic field estimates from time series of observed spectra. Our ultimate goal is to study the temporal evolution of small-scale magnetic fields which will provide insight into the magnetic properties of low-mass stars and their magnetic cycles. We implement 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 assess the performance of the proposed method through its application to simulated data and publicly available spectra. In addition, we implement a model-driven process to derive relative temperature variations and explore the influence magnetic fields have on these measurements. Our results are in excellent agreement with previous magnetic field estimates. The method provides robust constraints 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, in particular for domains containing a large number of magnetically-sensitive transitions.

Figures (17)

• Figure 1: Comparison between the retrieved (y-axis) and input (x-axis) relative magnetic field strengths ($\delta\langle B \rangle$). The synthetic observations were normalized to the template using a rolling median with a window of 100 $\rm km\,s^{-1}$. The red squares and green plus symbols ('+') show the results obtained before and after re-normalizing the models used to computed $\vec{F}_k-\vec{F}_0$ (equation \ref{['eq:eq_linear_ff']}) with a 100 $\rm km\,s^{-1}$ median filter, respectively (see text). The black line marks the equality. This figure illustrates the need for careful re-normalization of the models to avoid biases in the results.
• Figure 2: Comparison between the retrieved $\delta T$ (y-axis) and the input $\delta T$ used to generate the synthetic observations (x-axis). Synthetic observations were computed on the wavelength range covered by Narval/ESPaDOnS, accounting for magnetic field variations (red squares), or fixing the value of the magnetic fields to 0 kG (green circles). This figure illustrates how magnetic fields can impact the $\delta T$ estimates.
• Figure 3: Comparison between $\delta\langle B \rangle$ obtained in this work and the values of cristofari-2025b. The average $\langle B \rangle$ was removed from the estimates of cristofari-2025b for comparison. The red line shows the equality. The Pearson correlation coefficient ($\rho$) is shown on the figure. Our process allows us to retrieve $\delta\langle B \rangle$ in very good agreement with those obtained from fits of synthetic spectra to the data.
• Figure 4: Best Quasi Periodic Gaussian Process (GP) fit (green) obtained on relative small-scale magnetic field estimates derived from ESPaDOnS and Narval spectra for EV Lac. The top panel shows the fit over the entire data set, while the middle and bottom panels show segments of the data set. The residuals (Res.) between data points and GP fit are shown on each panel.
• Figure 5: Same as Fig. \ref{['fig:narval-gl873-gp']} for DS Leo.