Spectropolarimetric analysis of an active region filament. I. Magnetic and dynamical properties from single component inversions

The determination of the magnetic filed vector in solar filaments is possible by interpreting the Hanle and Zeeman effects in suitable chromospheric spectral lines like those of the He I multiplet at 10830 A. We study the vector magnetic field of an active region filament (NOAA 12087). Spectropolarimetric data of this active region was acquired with the GRIS instrument at the GREGOR telescope and studied simultaneously in the chromosphere with the He I 10830 A multiplet and in the photosphere with the Si I 10827 A line. As it is usual from previous studies, only a single component model is used to infer the magnetic properties of the filament. The results are put into a solar context with the help of the Solar Dynamic Observatory images. Some results clearly point out that a more complex inversion had to be done. Firstly, the Stokes $V$ map of He I does not show any clear signature of the presence of the filament. Secondly, the local azimuth map follows the same pattern than Stokes $V$ as if the polarity of Stokes $V$ were conditioning the inference to very different magnetic field even with similar linear polarization signals. This indication suggests that the Stokes $V$ could be dominated by the below magnetic field coming from the active region, and not, from the filament itself. Those and more evidences will be analyzed in depth and a more complex inversion will be attempted in the second part of this series.Comment: 18 pages, 19 figures, accepted for publication in A&

A search for magnetic fields on central stars in planetary nebulae

One of the possible mechanisms responsible for the panoply of shapes in planetary nebulae is the presence of magnetic fields that drive the ejection of ionized material during the proto-planetary nebula phase. Therefore, detecting magnetic fields in such objects is of key importance for understanding their dynamics. Still, magnetic fields have not been detected using polarimetry in the central stars of planetary nebulae. Circularly polarized light spectra have been obtained with the Focal Reducer and Low Dispersion Spectrograph at the Very Large Telescope of the European Southern Observatory and the Intermediate dispersion Spectrograph and Imaging System at the William Herschel Telescope. Nineteen planetary nebulae spanning very different morphology and evolutionary stages have been selected. Most of central stars have been observed at different rotation phases to point out evidence of magnetic variability. In this paper, we present the result of two observational campaigns aimed to detect and measure the magnetic field in the central stars of planetary nebulae on the basis of low resolution spectropolarimetry. In the limit of the adopted method, we can state that large scale fields of kG order are not hosted on the central star of planetary nebulae.Comment: Paper accepted to be published in Astronomy and Astrophysics on 20/01/201

Analytical maximum likelihood estimation of stellar magnetic fields

The polarised spectrum of stellar radiation encodes valuable information on the conditions of stellar atmospheres and the magnetic fields that permeate them. In this paper, we give explicit expressions to estimate the magnetic field vector and its associated error from the observed Stokes parameters. We study the solar case where specific intensities are observed and then the stellar case, where we receive the polarised flux. In this second case, we concentrate on the explicit expression for the case of a slow rotator with a dipolar magnetic field geometry. Moreover, we also give explicit formulae to retrieve the magnetic field vector from the LSD profiles without assuming mean values for the LSD artificial spectral line. The formulae have been obtained assuming that the spectral lines can be described in the weak field regime and using a maximum likelihood approach. The errors are recovered by means of the hermitian matrix. The bias of the estimators are analysed in depth.Comment: accepted for publication in MNRA

Hierarchical analysis of the quiet Sun magnetism

Standard statistical analysis of the magnetic properties of the quiet Sun rely on simple histograms of quantities inferred from maximum-likelihood estimations. Because of the inherent degeneracies, either intrinsic or induced by the noise, this approach is not optimal and can lead to highly biased results. We carry out a meta-analysis of the magnetism of the quiet Sun from Hinode observations using a hierarchical probabilistic method. This model allows us to infer the statistical properties of the magnetic field vector over the observed field-of-view consistently taking into account the uncertainties in each pixel due to noise and degeneracies. Our results point out that the magnetic fields are very weak, below 275 G with 95% credibility, with a slight preference for horizontal fields, although the distribution is not far from a quasi-isotropic distribution.Comment: 9 pages, 4 figures, accepted for publication in A&

PCA detection and denoising of Zeeman signatures in stellar polarised spectra

Our main objective is to develop a denoising strategy to increase the signal to noise ratio of individual spectral lines of stellar spectropolarimetric observations. We use a multivariate statistics technique called Principal Component Analysis. The cross-product matrix of the observations is diagonalized to obtain the eigenvectors in which the original observations can be developed. This basis is such that the first eigenvectors contain the greatest variance. Assuming that the noise is uncorrelated a denoising is possible by reconstructing the data with a truncated basis. We propose a method to identify the number of eigenvectors for an efficient noise filtering. Numerical simulations are used to demonstrate that an important increase of the signal to noise ratio per spectral line is possible using PCA denoising techniques. It can be also applied for detection of magnetic fields in stellar atmospheres. We analyze the relation between PCA and commonly used well-known techniques like line addition and least-squares deconvolution. Moreover, PCA is very robust and easy to compute.Comment: accepted to be published in A&

New results on q-positivity

In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original bilinear form. The notion of q-positivity generalizes the classical notion of the monotonicity of a subset of a product of a Banach space and its dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss concepts generalizing the representations of monotone sets by convex functions, as well as the number of maximally q-positive extensions of a q-positive set. We also discuss symmetrically self-dual Banach spaces, in which we add a Banach space structure, giving new characterizations of maximal q-positivity. The paper finishes with two new examples.Comment: 18 page