[Paper Review] Normalization of polarized spectral contours for high-accuracy magnetic field measurements

S. I. Plachinda, D. Shulyak+1 more|arXiv (Cornell University)|Oct 2, 2019

Astronomical Observations and Instrumentation4 citations

TL;DR

This paper introduces the COALA method for normalizing polarized spectral line profiles to enable high-accuracy magnetic field measurements in stars. By modeling the residual intensity of polarized profiles as a function of central residual intensity, COALA enables consistent normalization across spectral lines, improving the reliability of magnetic field measurements from individual lines, as validated on synthetic data and observations of β Aql (2014 October 6).

ABSTRACT

Designed at the Crimean Astrophysical Observatory the SL-method of stellar magnetic field measurement is based on the calculation of the distance between the centers of gravity of the left and right circularly polarized components of the spectral line. The SL-method is free from the limitations of the LSD-method, namely its requirement for weak magnetic fields, weak spectral lines, the same shape of polarized profiles. Also, this method is free from model limitations of the PCA, NDD and ZCD methods also. The SL-method involves the calculation of the magnetic field using individual spectral lines and the subsequent formation of uniform arrays of the magnetic field measurements. The formation of the arrays is based on different criteria, e.g. using spectral lines of a chemical element, assumption of the same physical conditions in the areas of the spectral line formation, a statistically significant difference between the values of the magnetic field calculated from different arrays of spectral lines etc. If there are several arrays of spectral lines, it is necessary to obtain normalized polarized profiles using predetermined parameters for each array: the magnitude of the field, wavelength for normalization, Lande factor and the central residual intensity of the line. In this paper, we present a method of normalization of polarized profiles based on the dependence of the residual intensity of the observed polarized profiles on their central residual intensity (COntour Algorithm of the Line Approximation: COALA). The SL and COALA methods strong depend on the signal-to-noise ratio and a number of used unblended spectral lines. In this work the application of the proposed method is demonstrated for synthetic polarized spectra and for circularly polarized spectra of the yellow subgiant $\\beta$ Aql (Sp G8 IV) obtained on 2014 October 06.

Motivation & Objective

• To address inconsistencies in polarized spectral line profiles caused by varying central residual intensities and line blending in stellar spectropolarimetry.
• To enable high-accuracy magnetic field measurements by normalizing individual spectral line profiles using a functional dependence on residual intensity.
• To support the formation of homogeneous arrays of magnetic field measurements from unblended spectral lines, overcoming limitations of traditional multiline methods like LSD.
• To improve the reliability of magnetic field topology modeling by ensuring consistent input profiles for global and local field analysis.
• To validate the method on both synthetic spectra and real observations of the yellow subgiant β Aql (2014 October 6).

Proposed method

• The COALA method models the dependence of observed polarized profile residual intensity on the central residual intensity of the line, using a functional system (1) to derive normalized profiles.
• Normalization is performed using key parameters: central residual intensity (Rc = 0.700), Landé factor (g = 1.5), and reference wavelength (5116.0427 Å) for alignment.
• The method selects 527 unblended spectral lines to solve the system of functional dependencies, ensuring robustness against noise and blending effects.
• Normalized profiles are derived by adjusting each line’s polarization to a common reference, minimizing systematic shifts due to line depth or blending.
• The approach is applied to both synthetic spectra (100 G longitudinal field) and real spectropolarimetric data of β Aql, using 19 lines for averaging.
• The method is integrated with the SL-method, which computes magnetic fields from individual lines before array formation, enhancing accuracy over LSD and PCA methods.

Experimental results

Research questions

• RQ1 How can polarized spectral line profiles be normalized to ensure consistency across lines with varying residual intensities and blending?
• RQ2 Can a functional dependence between residual intensity and central residual intensity improve the accuracy of magnetic field measurements from individual spectral lines?
• RQ3 To what extent does the COALA method reduce systematic biases in magnetic field measurements caused by line depth and blending?
• RQ4 How does the normalized profile performance compare between synthetic data and real observations of β Aql?
• RQ5 Can the COALA-normalized profiles support more accurate modeling of global and local magnetic field topologies in stars?

Key findings

• The COALA method successfully normalizes polarized spectral profiles using a functional dependence on central residual intensity, reducing inconsistencies across lines.
• For the synthetic spectrum with 100 G longitudinal field, the method produced normalized profiles with mean errors σ ≤ 0.0003 in circular polarization (Stokes V).
• In the β Aql observations (2014 October 6), the normalized profiles showed consistent polarization patterns with σ ≤ 0.0004 for weak-field lines.
• The average polarization curve for the strong-field case (B ≈ 43.98 G) was broader and asymmetric compared to the weak-field case (B ≈ 11.96 G), indicating distinct magnetic configurations.
• Lines with Rc = 0.68–0.72 were selected to minimize averaging bias; these yielded consistent field values (43.98 ± 5.59 G and 11.96 ± 7.90 G, respectively).
• The method demonstrated that classical LSD is unsuitable for such cases due to significant profile asymmetries and sign changes in polarization, which COALA resolves via normalization.