On the use of the first-order moment approach for measurements of Heff from LSD profiles

Abstract

ABSTRACT The big majority of the reported measurements of the stellar magnetic fields that have analysed spectropolarimetric data have employed the least-squares deconvolution method (LSD) and the first-order moment approach. We present a series of numerical tests in which we review some important aspects of this technique. First, we show that the selection of the profile widths, i.e. integration range in the first-order moment equation, is independent of the accuracy of the magnetic measurements, meaning that for any arbitrary profile width it is always possible to properly determine the longitudinal magnetic field. We also study the interplay between the line depth limit adopted in the line mask and the normalization values of the LSD profiles. We finally show that the rotation of the stars has to be considered to correctly infer the intensity of the magnetic field, something that has been neglected up to now. We show that the latter consideration is crucial, and our test shows that the magnetic intensities differ by a factor close to 3 for a moderate fast rotator star with vsini of 50 ${\rm km\, s^{-1}}$. Therefore, it is expected that in general the stellar magnetic fields reported for fast rotators are stronger than what was believed. All the previous results shows that the first-order moment can be a very robust tool for measurements of magnetic fields, provided that the weak magnetic field approximation is secured. We also show that when the magnetic field regime breaks down, the use of the first-order moment method becomes uncertain.