Spectropolarimetric studies of stellar magnetic fields usually deal with extremely weak line polarisation signatures. The amplitudes of Stokes signals, even in magnetically sensitive spectral lines, are often well below the noise level realistically achievable with the current instrumentation. Consequently, a detection of these polarisation signatures and their meaningful analysis is impossible without combining information from multiple spectral lines. Here I review basic theoretical foundations of the multi-line spectropolarimetric diagnostic methods employed in stellar magnetometry, give examples of their application, and discuss recent efforts to interpret mean polarisation profiles with the help of detailed radiative transfer calculations.

The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) provides continuous monitoring of the Sun's vector magnetic field through full-disk photospheric data with both high cadence and high spatial resolution. Here we investigate the evolution of AR 11249 from March 6 to March 7, 2012. We make use of HMI Stokes imaging, SDO/SHARPs, the HMI magnetic field line-of-sight (LOS) maps and the transverse components of the magnetic field as well as LOS velocity maps in order to detect regions with significant flux emergence and/or cancellation. In addition, we apply the Local Correlation Tracking (LCT) technique to the total and signed magnetic flux data and derive maps of horizontal velocity. From this analysis, we were able to pinpoint localized shear regions (and a shear channel) where penumbrae and pore formation areas, with strong linear polarization signals, are stretched and squeezed, showing also important downflows and upflows. We have also utilized Hinode/SP data and compared them to the HMI-SHARPs and the HMI-Stokes spectrograms. The aforementioned shear channel seems to correspond well with the X-class flare main channel of March 7 2012, as observed in AIA/SDO 171, 304 and 1600 Å.

PolarBase contains stellar spectropolarimetric data collected with the NARVAL & ESPaDOnS instruments (Petit et al. 2014). Their respective spectral resolutions are 65 000 and 68 000, in spectropolarimetric mode. As the first part of this work, we use the NARVAL spectropolarimetric repositories. We selected spectra from a sample of cool stars with effective Temperature (T eff) ranging between 4900 to 6000 K. This sample contains stellar systems with and without reported exoplanets. We exploit the full wavelength range from 380 to 900 nm in order to obtain chromospheric indexes such as the Ca ii H&K S-Index, and a Ca ii IRT and Hα index. We calibrated our measurements using the Mount Wilson S-Index values. Furthermore, we employ lithium (Li) abundance measurements from the literature (Gonzalez et al. 2010; Delgado Mena et al. 2014; Israelian et al. 2004), investigating in this way a possible correlation between the chromospheric activity measurements and the Li abundance in 32 selected cool stars.

In our previous attempt to model the Stokes profiles of the Cr i triplet at 5204-5208 Å and the Ba ii D2 at 4554 Å, we found it necessary to slightly modify the standard FAL model atmospheres to fit the observed polarization profiles. In the case of Cr i triplet, this modification was done to reduce the theoretical continuum polarization, and in the case of Ba ii D2, it was needed to reproduce the central peak in Q/I. In this work, we revisit both these cases using different standard model atmospheres whose temperature structures closely resemble those of the modified FAL models, and explore the possibility of synthesizing the line profiles without the need for small modifications of the model atmosphere.

It is well-known that partial frequency redistribution (PRD) is the basic physical mechanism to correctly describe radiative transfer in spectral lines. In the case of polarized line scattering, the PRD becomes particularly important to describe the line-wing polarization, instead of the well-known mechanism of complete redistribution (CRD). Historically, the two-level atom PRD scattering matrices for polarized line scattering were first derived in the 1970's, and later generalized to the case of arbitrary fields in 1997. The latter formulation of the PRD matrices have subsequently been used in the solution of the line transfer equation to successfully model the non-magnetic (resonance scattering) and the magnetic (Hanle scattering) polarization observations. In recent years, using the Kramers-Heisenberg approach, we formulated PRD matrices for various physical mechanisms like quantum interference involving fine- and hyperfine-structure states in a two-term atom. The effect of collisions is included in an approximate way. We have used these PRD matrices to model the observed linear polarization in several interesting lines of the Second Solar Spectrum. In this paper I present a few results which highlight the importance of PRD in the interpretation of the polarized Stokes profiles.

The ϵ Aurigae system is a single–line spectroscopic binary system that consists of a variable F0 supergiant star and an occulting disk surrounding an unseen object, probably a B star. The eclipse occurs every 27 years and lasts for almost 2 years. Spectral features attributed to the disk exhibit line shifts due to the rotation of the disk that are easily observed in spectra. We obtained 50+ epochs of high dispersion optical spectropolarimetric data from the ESPaDOnS instrument at the Canada–France–Hawaii Telescope before, during, and after the most recent eclipse (2009–2011). We found numerous 3–sigma (or greater) linear polarization features in the spectra and associated these with atomic absorption features also present in the spectra. We observed dramatic changes to polarization and position angles with time during eclipse, particularly around 3rd contact. The increased polarization could be due to a localized increased number of scatterers.

Continuum scattering by free electrons can be significant in early type stars, while in late type stars Rayleigh scattering by hydrogen atoms or molecules may be important. Computer programs used to construct models of stellar atmospheres generally treat the scattering of the continuum radiation as isotropic and unpolarized, but this scattering has a dipole angular dependence and will produce polarization. We review an accurate method for evaluating the polarization and limb darkening of the radiation from model stellar atmospheres. We use this method to obtain results for: (i) Late type stars, based on the MARCS code models (Gustafsson et al. 2008), and (ii) Early type stars, based on the NLTE code TLUSTY (Lanz and Hubeny 2003). These results are tabulated at http://www.astro.umd.edu/~jph/Stellar_Polarization.html While the net polarization vanishes for an unresolved spherical star, this symmetry is broken by rapid rotation or by the masking of part of the star by a binary companion or during the transit of an exoplanet. We give some numerical results for these last cases.

The Solar Orbiter is the next solar physics mission of the European Space Agency, ESA, in collaboration with NASA, with a launch planned in 2018. The spacecraft is designed to approach the Sun to within 0.28 AU at perihelion of a highly eccentric orbit. The proximity with the Sun will also allow its observation at uniformly high resolution at EUV and visible wavelengths. Such observations are central for learning more about the magnetic coupling of the solar atmosphere. At a later phase in the mission the spacecraft will leave the ecliptic and study the enigmatic poles of the Sun from a heliographic latitude of up to 33○.

A central instrument of Solar Orbiter} is the Polarimetric and Helioseismic Imager, SO/PHI. It will do full Stokes imaging in the Landé g = 2.5 Fe I 617.3 nm line. It is composed of two telescopes, a full-disk telescope and a high-resolution telescope, that will allow observations at a resolution as high as 200 km on the solar surface. SO/PHI will also be the first solar polarimeter to leave the Sun-Earth line, opening up new possibilities, such as stereoscopic polarimetry (besides stereoscopic imaging of the photosphere and stereoscopic helioseismology). Finally, SO/PHI will have a unique view of the solar poles, allowing not just more precise and exact measurements of the polar field than possible so far, but also enabling us to follow the dynamics of individual magnetic features at high latitudes and to determine solar surface and sub-surface flows right up to the poles.

In this paper an introduction to the science goals and the capabilities of SO/PHI will be given, as well as a brief overview of the instrument and of the current status of its development.

DUSTPol is a dual-beam polarimeter that operates in optical wavelengths, and was built to promote the study of linear polarimetry with smaller telescopes. DUSTPol's performance has demonstrated low instrumental polarization at 0.05 ± 0.02%. This poster presents commissioning results as well as early science observations, and describes software used for data reduction. Recent polarimetric results of RS CVn systems and Wolf-Rayet stars, discussed herein, indicate shape and interaction parameters. By promoting the development of similar polarimeters at other institutions, DUSTPol will serve to establish new collaborative surveys of cool active stars, as well as systems showing evidence of containing complex stellar environments.

We present the results of a numerical simulation of the corona and wind structure of the Sun-like exoplanet-host GJ 3021 using a global magnetohydrodynamic (MHD) model. The simulation is driven by the radial component of the surface magnetic field recovered with the Zeeman Doppler Imaging (ZDI) technique. We consider two different ZDI input maps, which have similar large-scale structures but different spatial resolutions and field strengths. These maps arise from different but comparable models used to fit the observed circularly polarised spectra of the star. Our simulations show that the structure of the inner corona is consistent among the considered cases. Larger discrepancies are found in the wind structure, in particular in the radial wind speed and the Alfvén surface topology. These elements can have a significant impact on the mass loss and angular momentum loss predicted for this system and in other studies based on this numerical data-driven approach.

Red supergiant stars (RSGs) are not only a key evolutionary stage of massive stars participating in the chemical evolution of galaxies, they also represent a fantastic and challenging laboratory of (magneto-)hydrodynamics. We present recent results and on-going research on mass loss, atmospheres, and polarimetric studies of RSGs that reveal a magnetic field of unknown origin. We discuss the potential interplay between these different processes.

The Ca i 4227 Å is a chromospheric line exhibiting the largest degree of linear polarization near the limb, in the visible spectrum of the Sun. Modeling the observations of the center-to-limb variations (CLV) of different lines in the Second Solar Spectrum helps to sample the height dependence of the magnetic field, as the observations made at different lines of sight sample different heights in the solar atmosphere. Supriya et al. (2014) attempted to simultaneously model the CLV of the (I, Q/I) spectra of the Ca i 4227 Å line using the standard 1-D FAL model atmospheres. They found that the standard FAL model atmospheres and also any appropriate combination of them, fail to simultaneously fit the observed Stokes (I, Q/I) profiles at all the limb distances (μ) satisfying at the same time all the observational constraints. This failure of 1-D modeling approach can probably be overcome by using multi-dimensional modeling which is computationally expensive. To eliminate an even wider choice of 1-D models, we attempt here to simultaneously model the CLV of the (I, Q/I) spectra using the FCHHT solar model atmospheres which are updated and recent versions of the FAL models. The details of our modeling efforts and the results are presented.

Observations of stable mainly dipolar magnetic fields at the surface of ~7% of single hot stars indicate that these fields are of fossil origin, i.e. they descend from the seed field in the molecular clouds from which the stars were formed. The recent results confirm this theory. First, theoretical work and numerical simulations confirm that the properties of the observed fields correspond to those expected from fossil fields. They also showed that rapid rotation does not modify the surface dipolar magnetic configurations, but hinders the stability of fossil fields. This explains the lack of correlation between the magnetic field properties and stellar properties in massive stars. It may also explain the lack of detections of magnetic fields in Be stars, which rotate close to their break-up velocity. In addition, observations by the BinaMIcS collaboration of hot stars in binary systems show that the fraction of those hosting detectable magnetic fields is much smaller than for single hot stars. This could be related to results obtained in simulations of massive star formation, which show that the stronger the magnetic field in the original molecular cloud, the more difficult it is to fragment massive cores to form several stars. Therefore, more and more arguments support the fossil field theory.

We present the innovative soft X-ray spectro-polarimeter, SolpeX. This instrument consists of three functionally independent blocks. They are to be included into the Russian instrument KORTES, to be mounted onboard the ISS. The three SolpeX units are: a simple pin-hole X-ray spectral imager, a polarimeter, and a fast-rotating drum multiple-flat-crystal Bragg spectrometer. Such a combination of measuring blocks will offer a new opportunity to reliably measure possible X-ray polarization and spectra of solar flares, in particular during the impulsive phase. Polarized Bremsstrahlung and line emission due to the presence of directed particle beams will be detected, and measurements of the velocities of evaporated hot plasma will be made. In this paper we discuss the details of the construction of the SolpeX units. The delivery of KORTES with SolpeX to the ISS is expected to happen in 2017/2018.

The unification model of active galactic nuclei postulates an accreting supermassive black hole as the central engine, surrounded by a putative dusty torus. This dust absorbs the incoming radiation, re-emits it in the infrared and obscures our view of the central region at certain inclinations. We present a new set of AGN models, in which the torus is modelled as a 3D multiphase medium. These new models can explain the observed spectral energy distribution of AGNs over the entire infrared domain, including the observed silicate feature strength and the level of near-infrared continuum. A new generation of multi-phase models, based on hydrodynamical simulations, is being constructed. We will compute the polarisation structure of these physically motivated 3D torus models, and compare them to simpler smooth torus models and to the available observational data.

Flux emergence phenomena are relevant at different temporal and spatial scales. We have studied a flux emergence region underneath a filament. This filament elevated itself smoothly, and the associated CME reached the Earth. In this study we investigate the size and the amount of flux in the emergence event. The flux emergence site appeared just beneath a filament. The emergence acquired a size of 24 Mm in half a day. The unsigned magnetic flux density from LOS-magnetograms was around 1 kG at its maximum. The transverse field as well as the filament eruption were also analysed.

The linear polarization in spectral lines produced by coherent scattering is significantly modified by the quantum interference between the atomic states in the presence of a magnetic field. When magnetic fields produce a splitting which is of the order of or greater than the fine or hyperfine structure splittings, we enter the Paschen-Back effect (PBE) regime, in which the magnetic field dependence of the Zeeman splittings and transition amplitudes becomes non-linear. In general, PBE occurs for sufficiently strong fields when the fine structure states are involved and for weak fields in the case of hyperfine structure states. In this work, we apply the recently developed theory of PBE in the atomic fine and hyperfine structure states including the effects of partial frequency redistribution to the case of Li i 6708 Å doublet. We explore the signatures of PBE in a single scattering event and their applicability to the solar magnetic field diagnostics.

The spectropolarimeter dimaPol measures circular polarization in spectral lines of stellar objects. The instrument is used to simultaneously detect polarization signals in the hydrogen Hβ line as well as nearby metallic lines. A fast switching ferro-electric liquid crystal waveplate synchronized with charge shuffling on the CCD is employed to greatly reduce instrumental systematics. dimaPol has been in use on the DAO 1.8-m Plaskett telescope since 2007. In this presentation we show the capabilities of the instrument as well as some of the main results obtained with it to date.

Full Stokes spectropolarimetric observations of a Mira star (χ Cyg) and a RV Tauri star (R Sct) are presented and analyzed comparatively. From their Stokes V data (circular polarization), we report the detection of a weak magnetic field at the surface of these cool and evolved radially pulsating stars. For both stars, we analyse this detection in the framework of their complex atmospheric dynamics, with the possibility that shock waves may imprint an efficient compressive effect on the surface magnetic field. We also report strong Stokes U and Stokes Q signatures associated to metallic lines (as a global trend), those linear polarimetric features appear to be time variable along the pulsating phase. More surprising, in the Stokes U and Stokes Q data, we also detect signatures associated to individual metallic lines (such as Sr i 460.7 nm, Na D2588.9 nm), that are known (from the solar case) to be easily polarizable in case of a global asymmetry at the photospheric level.

The synoptic observations of the magnetic field of the Sun have continued at the National Solar Observatory (NSO) since 1970s. The daily full-disk maps of the longitudinal magnetic field are regularly combined to form Carrington maps of the photospheric magnetic flux per solar rotation. These maps continue to be used by the international research community for a variety of studies related to solar magnetism as well as for space weather studies. The current NSO synoptic facility is the Synoptic Optical Long-term Investigation of the Sun (SOLIS), which regularly provides photospheric vector and chromospheric longitudinal full-disk magnetograms, among other data products. In the near future, an upgrade of SOLIS to produce chromospheric vector magnetograms is planned. We present the design of a new polarization modulator package for full Stokes polarimetry of the chromospheric Ca II 854.2 nm spectral line.