Search

We extend the spherical tensorial formalism for polarization to the treatment of electric- and magnetic-multipole transitions of any order. We rely on the spherical-wave expansion to derive the tensor form of the operator describing the interaction of the atomic system with a polarized radiation field, which naturally leads to the introduction of spherical tensors describing the polarization properties of the interacting field. As a direct application, the formalism is used to model the radiation anisotropy affecting the scattering of radiation in an electric-quadrupole transition, and the associated Hanle effect in the presence of a magnetic field., Comment: 23 pages, 4 figures

The Observatorio Astrof\'isico de Javalambre (OAJ{\dag}1) in Spain is a young astronomical facility, conceived and developed from the beginning as a fully automated observatory with the main goal of optimizing the processes in the scientific and general operation of the Observatory. The OAJ has been particularly conceived for carrying out large sky surveys with two unprecedented telescopes of unusually large fields of view (FoV): the JST/T250, a 2.55m telescope of 3deg field of view, and the JAST/T80, an 83cm telescope of 2deg field of view. The most immediate objective of the two telescopes for the next years is carrying out two unique photometric surveys of several thousands square degrees, J-PAS{\dag}2 and J-PLUS{\dag}3, each of them with a wide range of scientific applications, like e.g. large structure cosmology and Dark Energy, galaxy evolution, supernovae, Milky Way structure, exoplanets, among many others. To do that, JST and JAST are equipped with panoramic cameras under development within the J-PAS collaboration, JPCam and T80Cam respectively, which make use of large format (~ 10k x 10k) CCDs covering the entire focal plane. This paper describes in detail, from operations point of view, a comparison between the detailed cost of the global automation of the Observatory and the standard automation cost for astronomical facilities, in reference to the total investment and highlighting all benefits obtained from this approach and difficulties encountered. The paper also describes the engineering development of the overall facilities and infrastructures for the fully automated observatory and a global overview of current status, pinpointing lessons learned in order to boost observatory operations performance, achieving scientific targets, maintaining quality requirements, but also minimizing operation cost and human resources., Comment: Global Observatory Control System GOCS

Magnetic fields are important for stellar photospheres and magnetospheres, influencing photospheric physics and sculpting stellar winds. Observations of stellar magnetic fields are typically made in the visible, although infrared observations are becoming common. Here we consider the possibility of directly detecting magnetic fields at ultraviolet (UV) wavelengths using high resolution spectropolarimetry, specifically considering the capabilities of the proposed Polstar mission. UV observations are particularly advantageous for studying wind resonance lines not available in the visible, but they can also provide many photospheric lines in hot stars. Detecting photospheric magnetic fields using the Zeeman effect and Least Squares Deconvolution is potentially more effective in the UV due to the much higher density of strong lines. We investigate detecting magnetic fields in the magnetosphere of a star using the Zeeman effect in wind lines, and find that this could be detectable at high S/N in an O or B star with a strong magnetic field. We consider detecting magnetic fields using the Hanle effect in linear polarization, which is complementary to the Zeeman effect, and could be more sensitive in photospheric lines of rapid rotators. The Hanle effect can also be used to infer circumstellar magnetism in winds. Detecting the Hanle effect requires UV observations, and a multi-line approach is key for inferring magnetic field properties. This demonstrates that high resolution spectropolarimetry in the UV, and the proposed Polstar mission, has the potential to greatly expand our ability to detect and characterize magnetic fields in and around hot stars., Comment: Accepted for publication in Astrophysics and Space Science; updated to accepted version. arXiv admin note: text overlap with arXiv:2111.06434

We investigate the warm ionized gas in the blue compact galaxy (BCG) Haro 14 by means of integral field spectroscopic observations taken with the MUSE/VLT. The large FoV of MUSE and its unprecedented sensitivity enable observations of the galaxy nebular emission up to large galactocentric distances. This allowed us to trace the ionized gas morphology and ionization structure up to kiloparsec scales and, for the first time, to accurately investigate the excitation mechanism operating in the outskirts of a typical BCG. The intensity and diagnostic maps reveal at least two highly distinct components of ionized gas: the bright central regions, mostly made of individual clumps, and a faint component which extends up to kiloparsec scales and consists of widespread diffuse emission, well-delineated filamentary structures, and faint knots. Noteworthy are the two curvilinear filaments extending up to 2 and 2.3 kpc southwest, which likely trace the edges of supergiant expanding bubbles driven by galactic outflows. We find that while the central clumps in Haro 14 are HII-region complexes, the morphology and line ratios of the whole low-surface-brightness component are not compatible with star formation photoionization. In the spatially resolved emission-line-ratio diagnostic diagrams, spaxels above the maximum starburst line form the majority. Moreover, our findings suggest that more than one alternative mechanism is ionizing the outer galaxy regions. The properties of the diffuse component are consistent with ionization by diluted radiation and the large filaments and shells are most probably shocked areas at the edge of bubbles. The mechanism responsible for the ionization of the faint individual clumps observed in the galaxy periphery is more difficult to assess. These clumps could be the shocked debris of fragmented shells or regions where star formation is proceeding under extreme conditions., Comment: 27 pages, 13 figures. Accepted in A&A

(Abriged) Blue compact galaxies (BCGs) are low-luminosity, metal-poor, gas-rich objects that form stars at high rates, excellent analogs to the high-redshift star-forming galaxy population. Being low-mass starbursts, they also constitute ideal laboratories for investigating star formation and massive stellar feedback. This work presents results from integral field spectroscopic observations of the BCG Haro 14 taken with the Multi Unit Spectroscopic Explorer (MUSE). The large MUSE field of view enables simultaneous observations of the starburst and the host galaxy. We built galaxy maps in continuum and in emission lines and generated synthetic VRI images, from which we produced color index maps and surface brightness profiles. We detected numerous clumps spread throughout the galaxy, both in continuum and in emission lines, and produced a catalog with their position, size, and photometry. This analysis allowed us to study the morphology and stellar populations of Haro 14 in detail. The stellar distribution shows a pronounced asymmetry; the intensity peak in continuum is not centered with respect to the stellar host but is displaced by about 500 pc southwest. At the position of the continuum peak we find a bright stellar cluster that with M$_{V}=-12.18$ appears as a strong super stellar cluster candidate. We also find a highly asymmetric, blue, but nonionizing stellar component that occupies almost the whole eastern part of the galaxy. We conclude that there are at least three different stellar populations in Haro 14: the current starburst of about 6 Myr; an intermediate-age component of between ten and several hundred million years; and a red and regular host of several gigayears. The pronounced lopsidedness in the continuum and also in the color maps, and the presence of numerous stellar clusters, are consistent with a scenario of mergers or interactions acting in Haro 14., Comment: 20 pages, 6 figures. Accepted in A&A

We carry out a theoretical study of the polarization of the solar Mg II h-k doublet (including its extended wings) and the subordinate UV triplet around 280 nm. These lines are of great diagnostic interest, as they encode information on the physical properties of the solar atmosphere from the upper photosphere to the chromosphere-corona transition region. We base our study on radiative transfer calculations of spectral line polarization in one-dimensional models of quiet and plage regions of the solar atmosphere. Our calculations take into account the combined action of atomic polarization, quantum level interference, frequency redistribution, and magnetic fields of arbitrary strength. In particular, we study the sensitivity of the emergent Stokes profiles to changes in the magnetic field through the Zeeman and Hanle effects. We also study the impact of the chromospheric plasma dynamics on the emergent Stokes profiles, taking into account the angle-dependent frequency redistribution in the h-k resonance transitions. The results presented here are of interest for the interpretation of spectropolarimetric observations in this important region of the solar ultraviolet spectrum.

The European Solar Telescope (EST) is a research infrastructure for solar physics. It is planned to be an on-axis solar telescope with an aperture of 4 m and equipped with an innovative suite of spectro-polarimetric and imaging post-focus instrumentation. The EST project was initiated and is driven by EAST, the European Association for Solar Telescopes. EAST was founded in 2006 as an association of 14 European countries. Today, as of December 2019, EAST consists of 26 European research institutes from 18 European countries. The Preliminary Design Phase of EST was accomplished between 2008 and 2011. During this phase, in 2010, the first version of the EST Science Requirement Document (SRD) was published. After EST became a project on the ESFRI roadmap 2016, the preparatory phase started. The goal of the preparatory phase is to accomplish a final design for the telescope and the legal governance structure of EST. A major milestone on this path is to revisit and update the Science Requirement Document (SRD). The EST Science Advisory Group (SAG) has been constituted by EAST and the Board of the PRE-EST EU project in November 2017 and has been charged with the task of providing with a final statement on the science requirements for EST. Based on the conceptual design, the SRD update takes into account recent technical and scientific developments, to ensure that EST provides significant advancement beyond the current state-of-the-art. The present update of the EST SRD has been developed and discussed during a series of EST SAG meetings. The SRD develops the top-level science objectives of EST into individual science cases. Identifying critical science requirements is one of its main goals. Those requirements will define the capabilities of EST and the post-focus instrument suite. The technical requirements for the final design of EST will be derived from the SRD., Comment: 2nd edition, December 2019, 138 pages

We report on spectropolarimetric observations across the Mg II h and k-lines at 2800 angstrom made by the Ultraviolet Spectrometer and Polarimeter onboard the Solar Maximum Mission satellite. Our analysis confirms the strong linear polarization in the wings of both lines observed near the limb, as previously reported, but also demonstrates the presence of a negatively (i.e., radially oriented) polarized signal between the two lines. We find evidence for fluctuations of the polarization pattern over a broad spectral range, resulting in some depolarization with respect to the pure scattering case when observed at very low spatial and temporal resolutions. This is consistent with recent theoretical modeling that predicts this to be the result of redistribution effects, quantum interference between the atomic levels of the upper term, and magneto-optical effects. A first attempt at a quantitative exploitation of these signals for the diagnosis of magnetic fields in the chromosphere is attempted. In active regions, we present observations of circular polarization dominated by the Zeeman effect. We are able to constrain the magnetic field strength in the upper active chromosphere using an analysis based on the magnetograph formula, as justified by theoretical modeling. We inferred a significantly strong magnetic field (~500 G) at the 2.5 sigma level on an exceptionally active, flaring region., Comment: (12 pages, 5 figures)

The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a suborbital rocket experiment that on 3rd September 2015 measured the linear polarization produced by scattering processes in the hydrogen Ly-$\alpha$ line of the solar disk radiation, whose line-center photons stem from the chromosphere-corona transition region (TR). These unprecedented spectropolarimetric observations revealed an interesting surprise, namely that there is practically no center-to-limb variation (CLV) in the $Q/I$ line-center signals. Using an analytical model, we first show that the geometrical complexity of the corrugated surface that delineates the TR has a crucial impact on the CLV of the $Q/I$ and $U/I$ line-center signals. Secondly, we introduce a statistical description of the solar atmosphere based on a three-dimensional (3D) model derived from a state-of-the-art radiation magneto-hydrodynamic simulation. Each realization of the statistical ensemble is a 3D model characterized by a given degree of magnetization and corrugation of the TR, and for each such realization we solve the full 3D radiative transfer problem taking into account the impact of the CLASP instrument degradation on the calculated polarization signals. Finally, we apply the statistical inference method presented in a previous paper to show that the TR of the 3D model that produces the best agreement with the CLASP observations has a relatively weak magnetic field and a relatively high degree of corrugation. We emphasize that a suitable way to validate or refute numerical models of the upper solar chromosphere is by confronting calculations and observations of the scattering polarization in ultraviolet lines sensitive to the Hanle effect., Comment: Accepted for publication in The Astrophysical Journal Letters

On 3rd September 2015, the Chromospheric Lyman-Alpha SpectroPolarimeter (CLASP) successfully measured the linear polarization produced by scattering processes in the hydrogen Lyman-$\alpha$ line of the solar disk radiation, revealing conspicuous spatial variations in the $Q/I$ and $U/I$ signals. Via the Hanle effect the line-center $Q/I$ and $U/I$ amplitudes encode information on the magnetic field of the chromosphere-corona transition region (TR), but they are also sensitive to the three-dimensional structure of this corrugated interface region. With the help of a simple line formation model, here we propose a statistical inference method for interpreting the Lyman-$\alpha$ line-center polarization observed by CLASP., Comment: Accepted for publication in The Astrophysical Journal

We derive a formalism to describe the scattering of polarized radiation over the full spectral range encompassed by atomic transitions belonging to the same spectral series (e.g., the H I Lyman and Balmer series, the UV multiplets of Fe I and Fe II). This allows us to study the role of radiation-induced coherence among the upper terms of the spectral series, and its contribution to Rayleigh scattering and the polarization of the solar continuum. We rely on previous theoretical results for the emissivity of a three-term atom of the $\Lambda$-type taking into account partially coherent scattering, and generalize its expression in order to describe a "multiple $\Lambda$" atomic system underlying the formation of a spectral series. Our study shows that important polarization effects must be expected because of the combined action of partial frequency redistribution and radiation-induced coherence among the terms of the series. In particular, our model predicts the correct asymptotic limit of 100% polarization in the far wings of a \emph{complete} (i.e., $\Delta L=0,\pm 1$) group of transitions, which must be expected on the basis of the principle of spectroscopic stability.

The complex spectropolarimetric patterns around strong chromospheric lines, the result of subtle spectroscopic and transport mechanisms, are sensitive, sometimes in unexpected ways, to the presence of magnetic fields in the chromosphere, which may be exploited for diagnostics. We apply numerical polarization radiative transfer implementing partially coherent scattering by polarized multi-term atoms, in the presence of arbitrary magnetic fields, in planeparallel stellar atmospheres to study a few important spectroscopic features: Mg II h-k doublet; Ca II H-K doublet and IR triplet. We confirm the importance of partial redistribution effects in the formation of the Mg II h-k doublet in magnetized atmospheres, as previously pointed out for the non-magnetic case. Morevover, we show, numerically and analytically, that a magnetic field produces measurable modications of the broadband linear polarization even for relatively small field strengths, while circular polarization remains well represented by the magnetograph formula. We note that this phenomenon has already (unknowingly) been observed by UVSP/SMM, and the interest and possibility of its observation in stars other than the Sun. The interplay between partial redistribution in the H-K doublet of Ca II and metastable level polarization in its IR triplet allow diagnosing the chromospheric magnetic field at different layers and strengths. Our results suggest several new avenues to investigate empirically the magnetism of the solar and stellar chromospheres., Comment: Solar Polarization Workshop 8

We consider the vector emissivity of the polarized radiation transfer in a $\Lambda$-type atomic transition, which we recently proposed in order to account for both CRD and PRD contributions to the scattered radiation. This expression can concisely be written as $$\varepsilon=\left(\varepsilon^{(1)} -\varepsilon^{(2)}_{\rm f.s.} \right) +\varepsilon^{(2)}\;$$ where $\varepsilon^{(1)}$ and $\varepsilon^{(2)}$ are the emissivity terms describing, respectively, one-photon and two-photon processes in a $\Lambda$-type atom, %the fully and partially redistributed radiations, and where "f.s." means that the corresponding term must be evaluated assuming an appropriate "flat spectrum" average of the incident radiation across the spectral line. In this follow up study, we explicitly consider the expressions of these various terms for the case of a polarized multi-term atom, in order to derive the algebraic forms of the branching ratios between the CRD and PRD contributions to the emissivity. In the limit of a two-term atom with non-coherent lower-term, our results are shown to be in full agreement with those recently derived by Bommier (2017)

There is a thin transition region (TR) in the solar atmosphere where the temperature rises from 10,000 K in the chromosphere to millions of degrees in the corona. Little is known about the mechanisms that dominate this enigmatic region other than the magnetic field plays a key role. The magnetism of the TR can only be detected by polarimetric measurements of a few ultraviolet (UV) spectral lines, the Lyman-$\alpha$ line of neutral hydrogen at 121.6 nm (the strongest line of the solar UV spectrum) being of particular interest given its sensitivity to the Hanle effect (the magnetic-field-induced modification of the scattering line polarization). We report the discovery of linear polarization produced by scattering processes in the Lyman-$\alpha$ line, obtained with the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) rocket experiment. The Stokes profiles observed by CLASP in quiet regions of the solar disk show that the $Q/I$ and $U/I$ linear polarization signals are of the order of 0.1 % in the line core and up to a few percent in the nearby wings, and that both have conspicuous spatial variations with scales of $\sim 10$ arcsec. These observations help constrain theoretical models of the chromosphere-corona TR and extrapolations of the magnetic field from photospheric magnetograms. In fact, the observed spatial variation from disk to limb of polarization at the line core and wings already challenge the predictions from three-dimensional magnetohydrodynamical models of the upper solar chromosphere.

We present the frequency redistribution function for the polarized three-term atom of the $\Lambda$-type in the collisionless regime, and we specialize it to the case where both the initial and final terms of the three-state transition are metastable (i.e., with infinitely sharp levels). This redistribution function represents a generalization of the well-known $R_{\rm II}$ function to the case where the lower terms of the transition can be polarized and carry atomic coherence, and it can be applied to the investigation of polarized line formation in tenuous plasmas, where collisional rates may be low enough that anisotropy induced atomic polarization survives even in the case of metastable levels.

We discuss the implementation of physically meaningful branching ratios between the CRD and PRD contributions to the emissivity of a polarized multi-term atom in the presence of both inelastic and elastic collisions. Our derivation is based on a recent theoretical formulation of partially coherent scattering, and it relies on a heuristic diagrammatic analysis of the various radiative and collisional processes to determine the proper form of the branching ratios. The expression we obtain for the emissivity is $\varepsilon=\left[\varepsilon^{\tiny (1)}-\varepsilon^{\tiny (2)}_{\rm f.s.} \right]+\varepsilon^{\tiny (2)}$, where $\varepsilon^{\tiny (1)}$ and $\varepsilon^{\tiny (2)}$ are the emissivity terms for the redistributed and partially coherent radiation, respectively, and where "f.s." implies that the corresponding term must be evaluated assuming a flat-spectrum average of the incident radiation.

We study the effects of Rayleigh and Raman scattering on the formation of polarized spectral lines in a $\Lambda$-type multi-term atom. We fully take into account the partial redistribution of frequency and the presence of atomic polarization in the lower states of the atomic model. Problems that can be modeled with this formalism include, for example, the formation of the Ca II H-K and IR triplet, the analogous system of Ba II, and the Ly$\beta$-H$\alpha$ system of hydrogenic ions., Comment: 18 pages, 8 figures; in press for the Astrophysical Journal

A properly calibrated longitudinal magnetograph is an instrument that measures circular polarization and gives an estimation of the magnetic flux density in each observed resolution element. This usually constitutes a lower bound of the field strength in the resolution element, given that it can be made arbitrarily large as long as it occupies a proportionally smaller area of the resolution element and/or becomes more transversal to the observer and still produce the same magnetic signal. Yet, we know that arbitrarily stronger fields are less likely --hG fields are more probable than kG fields, with fields above several kG virtually absent-- and we may even have partial information about its angular distribution. Based on a set of sensible considerations, we derive simple formulae based on a Bayesian analysis to give an improved estimation of the magnetic field strength for magnetographs., Comment: 8 pages, 7 figures, accepted for publication in A&A

We present an exceptional data set acquired with the Vacuum Tower Telescope (Tenerife, Spain) covering the pre-flare, flare, and post-flare stages of an M3.2 flare. The full Stokes spectropolarimetric observations were recorded with the Tenerife Infrared Polarimeter in the He I 1083.0 nm spectral region. The object under study was active region NOAA 11748 on 2013 May 17. During the flare the chomospheric He I 1083.0 nm intensity goes strongly into emission. However, the nearby photospheric Si I 1082.7 nm spectral line profile only gets shallower and stays in absorption. Linear polarization (Stokes Q and U) is detected in all lines of the He I triplet during the flare. Moreover, the circular polarization (Stokes V) is dominant during the flare, being the blue component of the He I triplet much stronger than the red component, and both are stronger than the Si I Stokes V profile. The Si I inversions reveal enormous changes of the photospheric magnetic field during the flare. Before the flare magnetic field concentrations of up to 1500 G are inferred. During the flare the magnetic field strength globally decreases and in some cases it is even absent. After the flare the magnetic field recovers its strength and initial configuration., Comment: 6 pages, 3 figures, to appear in the conference proceedings of the IAUS 305: "Polarimetry: From the Sun to Stars and Stellar Environments"

This letter reports on a set of full-Stokes spectropolarimetric observations in the near infrared He I 10830 A spectral region covering the pre-, flare, and post-flare phases of an M3.2 class solar flare. The flare originated on 2013 May 17 and belonged to active region NOAA 11748. We detected strong He I 10830 A emission in the flare. The red component of the He I triplet peaks at an intensity ratio to the continuum of about 1.86. During the flare, He I Stokes V is substantially larger and appears reversed compared to the usually larger Si I Stokes V profile. The photospheric Si I inversions of the four Stokes profiles reveal the following: (1) the magnetic field strength in the photosphere decreases or is even absent during the flare phase, as compared to the pre-flare phase. However, this decrease is not permanent. After the flare the magnetic field recovers its pre-flare configuration in a short time (i.e., in 30 minutes after the flare). (2) In the photosphere, the line-of-sight velocities show a regular granular up- and down-flow pattern before the flare erupts. During the flare, upflows (blueshifts) dominate the area where the flare is produced. Evaporation rates of ~ $10^{-3}$ and ~ $10^{-4}$ g cm$^{-2}$ s$^{-1}$ have been derived in the deep and high photosphere, respectively, capable of increasing the chromospheric density by a factor of two in about 400 seconds., Comment: 5 pages, 3 figures, accepted for publication in ApJ Letters

Solar prominences are clouds of cool plasma levitating above the solar surface and insulated from the million-degree corona by magnetic fields. They form in regions of complex magnetic topology, characterized by non-potential fields, which can evolve abruptly, disintegrating the prominence and ejecting magnetized material into the heliosphere. However, their physics is not yet fully understood because mapping such complex magnetic configurations and their evolution is extremely challenging, and must often be guessed by proxy from photometric observations.Using state-of-the-art spectro-polarimetric data, we reconstruct the structure of the magnetic field in a prominence. We find that prominence feet harbor helical magnetic fields connecting the prominence to the solar surface below., Comment: Accepted for publication in ApJ

We carried out high-sensitivity spectropolarimetric observations of the central star of the Red Rectangle proto-planetary nebula with the aim of constraining the mechanism that gives its biconical shape. The stellar light of the central binary system is linearly polarised since it is scattered on the dust particles of the nebula. Surprisingly, the linear polarisation in the continuum is aligned with one of the spikes of the biconical outflow. Also, the observed Balmer lines as well as the Ca II K lines are polarised. These observational constraints are used to confirm or reject current theoretical models for the shaping mechanism of the Red Rectangle. We propose that the observed polarisation is very unlikely generated by a uniform biconical stellar wind. Also, the hypothesis of a precessing jet does not completely match the observations since it will require a jet aperture larger than that of the nebula., Comment: accepted in A&A

We present a generalized frequency redistribution function for the polarized two-term atom in an arbitrary magnetic field. This result is derived within a new formulation of the quantum problem of coherent scattering of polarized radiation by atoms in the collisionless regime. The general theory, which is based on a diagrammatic treatment of the atom-photon interaction, is still work in progress. However, the results anticipated here are relevant enough for the study of the magnetism of the solar chromosphere and of interest for astrophysics in general., Comment: ApJ, in press

More than about twenty central stars of planetary nebulae (CSPN) have been observed spectropolarimetrically, yet no clear, unambiguous signal of the presence of a magnetic field in these objects has been found. We perform a statistical (Bayesian) analysis of all the available spectropolarimetric observations of CSPN to constrain the magnetic fields on these objects. Assuming that the stellar field is dipolar and that the dipole axis of the objects are oriented randomly (isotropically), we find that the dipole magnetic field strength is smaller than 400 G with 95% probability using all available observations. The analysis introduced allows integration of future observations to further constrain the parameters of the distribution, and it is general, so that it can be easily applied to other classes of magnetic objects. We propose several ways to improve the upper limits found here., Comment: 7 pages, 3 figures, accepted for publication in ApJ

Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio $\beta$ is lower than unity, are essential for understanding the thermal structure and dynamical activity of the solar atmosphere. Recent developments in the theory and numerical modeling of polarization in spectral lines have suggested that information on the magnetic field of the chromosphere-corona transition region could be obtained by measuring the linear polarization of the solar disk radiation at the core of the hydrogen Lyman-$\alpha$ line at 121.6~nm, which is produced by scattering processes and the Hanle effect. The Chromospheric Lyman-$\alpha$ Spectropolarimeter (CLASP) sounding rocket experiment aims to measure the intensity (Stokes $I$) and the linear polarization profiles ($Q/I$ and $U/I$) of the hydrogen Lyman-$\alpha$ line. In this paper we clarify the information that the Hanle effect can provide by applying a Stokes inversion technique based on a database search. The database contains all theoretical $Q/I$ and $U/I$ profiles calculated in a one-dimensional semi-empirical model of the solar atmosphere for all possible values of the strength, inclination, and azimuth of the magnetic field vector, though this atmospheric region is highly inhomogeneous and dynamic. We focus on understanding the sensitivity of the inversion results to the noise and spectral resolution of the synthetic observations as well as the ambiguities and limitation inherent to the Hanle effect when only the hydrogen Lyman-$\alpha$ is used. We conclude that spectropolarimetric observations with CLASP can indeed be a suitable diagnostic tool for probing the magnetism of the transition region, especially when complemented with information on the magnetic field azimuth that can be obtained from other instruments., Comment: 34 pages, 10 figures, accepted for publication in ApJ

Line scattering polarization can be strongly affected by Rayleigh scattering by neutral hydrogen and Thompson scattering by free electrons. Often a continuum depolarization results, but the Doppler redistribution produced by the continuum scatterers, which are light (hence, fast), induces more complex interactions between the polarization in spectral lines and in the continuum. Here we formulate and solve the radiative transfer problem of scattering line polarization with non coherent continumm scattering consistently. The problem is formulated within the spherical tensor representation of atomic and light polarization. The numerical method of solution is a generalization of the Accelerated Lambda Iteration that is applied to both, the atomic system and the radiation field. We show that the redistribution of the spectral line radiation due to the non coherence of the continuum scattering may modify significantly the shape of the emergent fractional linear polarization patterns, even yielding polarization signals above the continuum level in intrinsically unpolarizable lines., Comment: Accepted for publication in The Astrophysical Journal

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 20/01/2014

The analysis of high spectral resolution spectroscopic and spectropolarimetric observations constitute a very powerful way of inferring the dynamical, thermodynamical, and magnetic properties of distant objects. However, these techniques are photon-starving, making it difficult to use them for all purposes. One of the problems commonly found is just detecting the presence of a signal that is buried on the noise at the wavelength of some interesting spectral feature. This is specially relevant for spectropolarimetric observations because typically, only a small fraction of the received light is polarized. We present in this note a Bayesian technique for the detection of spectropolarimetric signals. The technique is based on the application of the non-parametric relevance vector machine to the observations, which allows us to compute the evidence for the presence of the signal and compute the more probable signal. The method would be suited for analyzing data from experimental instruments onboard space missions and rockets aiming at detecting spectropolarimetric signals in unexplored regions of the spectrum such as the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) sounding rocket experiment., Comment: 10 pages, 5 figures, accepted for publication in A&A

We derive exact expressions for the degree of lineal polarization over a resolved or integrated stellar disc due to resonance scattering and the Hanle effect from a dipolar or quadrupolar distribution of magnetic fields. We apply the theory of scattering polarization within the formalism of the spherical tensors representation for the density matrix and radiation field. The distribution of linear polarization over the stellar disk for different configurations of the magnetic field is studied and its topology discussed. For an unresolved dipole, the resulting polarization can be expressed in terms of just three functions (of the inclination angle and effective dipole strength), that are calculated numerically and their behaviour discussed. Dipolar and (aligned) quadrupoles are considered in some detail, but the techniques here ---in particular, the extensive use of the spherical tensor formalism for polarization---, can easily be applied to more general field configurations., Comment: To appear in ApJ

We report Stokes vector observations of solar spicules and a prominence in the He I 1083 nm multiplet carried out with the Tenerife Infrared Polarimeter. The observations show linear polarization profiles that are produced by scattering processes in the presence of a magnetic field. After a careful data reduction, we demonstrate the existence of extremely asymmetric Stokes V profiles in the spicular material that we are able to model with two magnetic components along the line of sight, and under the presence of atomic orientation in the energy levels that give rise to the multiplet. We discuss some possible scenarios that can generate the atomic orientation in spicules. We stress the importance of spectropolarimetric observations across the limb to distinguish such signals from observational artifacts., Comment: accepted for publication in ApJ

We analyze two regions of the quiet Sun (35.6 x 35.6 Mm^2) observed at high spatial resolution (~100 km) in polarized light by the IMaX spectropolarimeter onboard the Sunrise balloon. We identify 497 small-scale (~400 km) magnetic loops, appearing at an effective rate of 0.25 loop h^{-1} arcsec^{-2}; further, we argue that this number and rate are underestimated by ~30%. However, we find that these small dipoles do not appear uniformly on the solar surface: their spatial distribution is rather filamentary and clumpy, creating dead calm areas, characterized by a very low magnetic signal and a lack of organized loop-like structures at the detection level of our instruments, that cannot be explained as just statistical fluctuations of a Poisson spatial process. We argue that this is an intrinsic characteristic of the mechanism that generates the magnetic fields in the very quiet Sun. The spatio-temporal coherences and the clumpy structure of the phenomenon suggest a recurrent, intermittent mechanism for the generation of magnetic fields in the quietest areas of the Sun., Comment: accepted in ApJ

Magnetic field topology, thermal structure and plasma motions are the three main factors affecting the polarization signals used to understand our star. In this theoretical investigation, we focus on the effect that gradients in the macroscopic vertical velocity field have on the non-magnetic scattering polarization signals, establishing the basis for general cases. We demonstrate that the solar plasma velocity gradients have a significant effect on the linear polarization produced by scattering in chromospheric spectral lines. In particular, we show the impact of velocity gradients on the anisotropy of the radiation field and on the ensuing fractional alignment of the CaII levels, and how they can lead to an enhancement of the zero-field linear polarization signals. This investigation remarks the importance of knowing the dynamical state of the solar atmosphere in order to correctly interpret spectropolarimetric measurements, which is important, among other things, for establishing a suitable zero field reference case to infer magnetic fields via the Hanle effect., Comment: 14 pages, 10 figures, 3 appendixes, accepted for publication in ApJ

Inferring magnetic and thermodynamic information from spectropolarimetric observations relies on the assumption of a parameterized model atmosphere whose parameters are tuned by comparison with observations. Often, the choice of the underlying atmospheric model is based on subjective reasons. In other cases, complex models are chosen based on objective reasons (for instance, the necessity to explain asymmetries in the Stokes profiles) but it is not clear what degree of complexity is needed. The lack of an objective way of comparing models has, sometimes, led to opposing views of the solar magnetism because the inferred physical scenarios are essentially different. We present the first quantitative model comparison based on the computation of the Bayesian evidence ratios for spectropolarimetric observations. Our results show that there is not a single model appropriate for all profiles simultaneously. Data with moderate signal-to-noise ratios favor models without gradients along the line-of-sight. If the observations shows clear circular and linear polarization signals above the noise level, models with gradients along the line are preferred. As a general rule, observations with large signal-to-noise ratios favor more complex models. We demonstrate that the evidence ratios correlate well with simple proxies. Therefore, we propose to calculate these proxies when carrying out standard least-squares inversions to allow for model comparison in the future., Comment: 16 pages, 2 figures, 8 tables, accepted for publication in ApJ

The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona -- that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. Solmex integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations., Comment: Submitted to Experimental Astronomy. 30 pages, 19 figures

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 MNRAS

The presence of magnetic fields is an attractive hypothesis for shaping PNe. We report on observations of the central star of the two Planetary Nebulae NGC1360 and LSS1326. We performed spectroscopy on circularly polarized light with the FOcal Reducer and low dispersion Spectrograph at the Very Large Telescope of the European Southern Observatory. Contrary to previous reports (Jordan et al. 2005, A&A, 432, 273), we find that the effective magnetic field, that is the average over the visible stellar disk of longitudinal components of the magnetic fields, is null within errors for both stars. We conclude that a direct evidence of magnetic fields on the central stars of PNe is still missing --- either the magnetic field is much weaker (< 600 G) than previously reported, or more complex (thus leading to cancellations), or both. Certainly, indirect evidences (e.g., MASER emission) fully justify further efforts to study the strength and morphology of such magnetic fields., Comment: Published in ApJ letters: Leone et al. 2011, ApJ, 731, 33L

We present observational evidence for oscillations of magnetic flux density in the quiet areas of the Sun. The majority of magnetic fields on the solar surface have strengths of the order of or lower than the equipartition field (300-500 G). This results in a myriad of magnetic fields whose evolution is largely determined by the turbulent plasma motions. When granules evolve they squash the magnetic field lines together or pull them apart. Here we report on the periodic deformation of the shapes of features in circular polarization observed at high resolution with Sunrise. In particular, we note that the area of patches with constant magnetic flux oscillates with time, which implies that the apparent magnetic field intensity oscillates in antiphase. The periods associated to this oscillatory pattern is compatible with the granular life-time and change abruptly, which suggests that these oscillations might not correspond to characteristic oscillatory modes of magnetic structures, but to the forcing by granular motions. In one particular case, we find three patches around the same granule oscillating in phase, which means that the spatial coherence of these oscillations can reach 1600 km. Interestingly, the same kind of oscillatory phenomenon is found also in the upper photosphere., Comment: accepted for publication in ApJ letters

Obtaining the magnetic properties of non-resolved structures in the solar photosphere is always challenging and problems arise because the inversion is carried out through the numerical minimization of a merit function that depends on the proposed model. We investigate the reliability of inversions in which the stray-light contamination is obtained from the same observations as a local average. In this case, we show that it is fundamental to include the covariance between the observed Stokes profiles and the stray-light contamination. The ensuing modified merit function of the inversion process penalizes large stray-light contaminations simply because of the presence of positive correlations between the observables and the stray-light, fundamentally produced by spatially variable systematics. We caution that using the wrong merit function, artificially large stray-light contaminations might be inferred. Since this effect disappears if the stray-light contamination is obtained as an average over the full field-of-view, we recommend to take into account stray-light contamination using a global approach., Comment: 5 pages, 3 figures, accepted for publication in ApJ

The chromosphere of the quiet Sun is an important stellar atmospheric region whose thermal and magnetic structure we need to decipher for unlocking new discoveries in solar and stellar physics. To this end, we must identify and exploit observables sensitive to weak magnetic fields (B<100 G) and to the presence of cool and hot gas in the bulk of the solar chromosphere. Here we report on an investigation of the Hanle effect in two semi-empirical models of the quiet solar atmosphere with different chromospheric thermal structures. Our study reveals that scattering polarization in the Ca II IR triplet has thermal and magnetic sensitivities potentially of great diagnostic value. The linear polarization in the 8498 A line shows a strong sensitivity to inclined magnetic fields with strengths between 0.001 and 10 G, while the emergent linear polarization in the 8542 A and 8662 A lines is mainly sensitive to magnetic fields with strengths between 0.001 and 0.1 G. The reason for this is that the scattering polarization of the 8542 A and 8662 A lines, unlike the 8498 A line, is controlled mainly by the Hanle effect in their (metastable) lower levels. Therefore, in regions with magnetic strengths sensibly larger than 1 G, their Stokes Q and U profiles are sensitive only to the orientation of the magnetic field vector. We also find that for given magnetic field configurations the sign of the Q/I and U/I profiles of the 8542 A and 8662 A lines is the same in both atmospheric models, while the sign of the linear polarization profile of the 8498 A line turns out to be very sensitive to the thermal structure of the lower chromosphere. We suggest that spectropolarimetric observations providing information on the relative scattering polarization amplitudes of the Ca II IR triplet will be very useful to improve our empirical understanding of the thermal and magnetic structure of the quiet chromosphere., Comment: 27 pages, 16 figures, to appear in ApJ

Sunspots are the most spectacular manifestation of solar magnetism, yet, 99% of the solar surface remains 'quiet' at any time of the solar cycle. The quiet sun is not void of magnetic fields, though; they are organized at smaller spatial scales and evolve relatively fast, which makes them difficult to detect. Thus, although extensive quiet Sun magnetism would be a natural driver to a uniform, steady heating of the outer solar atmosphere, it is not clear what the physical processes involved would be due to lack of observational evidence. We report the topology and dynamics of the magnetic field in very quiet regions of the Sun from spectropolarimetric observations of the Hinode satellite, showing a continuous injection of magnetic flux with a well organized topology of Omega-loop from below the solar surface into the upper layers. At first stages, when the loop travels across the photosphere, it has a flattened (staple-like) geometry and a mean velocity ascent of $\sim3$ km/s. When the loop crosses the minimum temperature region, the magnetic fields at the footpoints become almost vertical and the loop topology ressembles a potential field. The mean ascent velocity at chromospheric height is $\sim12$ km/s. The energy input rate of these small-scale loops in the lower boundary of the chromosphere is (at least) of 1.4x10^6-2.2x10^7 erg cm-2 s-1. Our findings provide empirical evidence for solar magnetism as a multi-scale system, in which small-scale low-flux magnetism plays a crucial role, at least as important as active regions, coupling different layers of the solar atmosphere and being an important ingredient for chromospheric and coronal heating models., Comment: to appear in ApJ letters (better quality figures will be available in the published version)

The behavior of the observed polarization amplitudes with spatial resolution is a strong constraint on the nature and organization of solar magnetic fields below the resolution limit. We study the polarization of the very quiet Sun at different spatial resolutions using ground- and space-based observations. It is shown that 80% of the observed polarization signals do not change with spatial resolution, suggesting that, observationally, the very quiet Sun magnetism remains the same despite the high spatial resolution of space-based observations. Our analysis also reveals a cascade of spatial scales for the magnetic field within the resolution element. It is manifest that the Zeeman effect is sensitive to the microturbulent field usually associated to Hanle diagnostics. This demonstrates that Zeeman and Hanle studies show complementary perspectives of the same magnetism., Comment: Accepted for publication in ApJ

We study the vector magnetic field of a filament observed over a compact Active Region Neutral Line. Spectropolarimetric data acquired with TIP-II (VTT, Tenerife, Spain) of the 10830 \AA spectral region provide full Stokes vectors which were analyzed using three different methods: magnetograph analysis, Milne-Eddington inversions and PCA-based atomic polarization inversions. The inferred magnetic field strengths in the filament are of the order of 600 - 700 G by all these three methods. Longitudinal fields are found in the range of 100 - 200 G whereas the transverse components become dominant, with fields as large as 500 - 600 G. We find strong transverse fields near the Neutral Line also at photospheric levels. Our analysis indicates that strong (higher than 500 G, but below kG) transverse magnetic fields are present in Active Region filaments. This corresponds to the highest field strengths reliably measured in these structures. The profiles of the Helium 10830 \AA lines observed in this Active Region filament are dominated by the Zeeman effect., Comment: Accepted for publication in Astronomy and Astrophysics, 9 pages, 4 figures

For about a decade, spectro-polarimetry of HeI 10830 has been applied to the magnetic diagnostics of the solar chromosphere. This resonance line is very versatile, as it is visible both on disk and in off-limb structures, and it has a good sensitivity to both the weak-field Hanle effect and the strong-field Zeeman effect. Recent observations of an active-region filament showed that the linear polarization was dominated by the transverse Zeeman effect, with very little or no hint of scattering polarization. This is surprising, since the HeI levels should be significantly polarized in a conventional scattering scenario. To explain the observed level of atomic depolarization by collisional or radiative processes, one must invoke plasma densities larger by several orders of magnitude than currently known values for prominences. We show that such depolarization can be explained quite naturally by the presence of an unresolved, highly entangled magnetic field, which averages to give the ordered field inferred from spectro-polarimetric data, over the typical temporal and spatial scales of the observations. We present a modeling of the polarized HeI 10830 in this scenario, and discuss its implications for the magnetic diagnostics of prominences and spicules, and for the general study of unresolved magnetic field distributions in the solar atmosphere.

The only way to obtain reliable empirical information on the intensity and topology of the weak magnetic fields of the quiet solar chromosphere is via the measurement and rigorous physical interpretation of polarization signals in chromospheric spectral lines. The observed Stokes profiles reported here are due to the Hanle and Zeeman effects operating in a weakly magnetized plasma that is in a state far from local thermodynamic equilibrium. The physical origin of their enigmatic linear polarization Q and U components is the existence of atomic polarization in their metastable lower-levels, which permits the action of a dichroism mechanism that has nothing to do with the transverse Zeeman effect. It is also pointed out that the population imbalances and coherences among the Zeeman sublevels of such long-lived atomic levels can survive in the presence of horizontal magnetic fields having intensities in the gauss range, and produce significant polarization signals. Finally, it is shown how the most recent developments in the observation and theoretical modelling of weak polarization signals are facilitating fundamental new advances in our ability to investigate the magnetism of the outer solar atmosphere via spectropolarimetry., Comment: Invited keynote paper (14 pages and 5 figures)

This paper addresses the problem of scattering line polarization and the Hanle effect in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) media for the case of a two-level model atom without lower-level polarization and assuming complete frequency redistribution. The theoretical framework chosen for its formulation is the QED theory of Landi Degl'Innocenti (1983), which specifies the excitation state of the atoms in terms of the irreducible tensor components of the atomic density matrix. The self-consistent values of these density-matrix elements is to be determined by solving jointly the kinetic and radiative transfer equations for the Stokes parameters. We show how to achieve this by generalizing to Non-LTE polarization transfer the Jacobi-based ALI method of Olson et al. (1986) and the iterative schemes based on Gauss-Seidel iteration of Trujillo Bueno and Fabiani Bendicho (1995). These methods essentially maintain the simplicity of the Lambda-iteration method, but their convergence rate is extremely high. Finally, some 1D and 2D model calculations are presented that illustrate the effect of horizontal atmospheric inhomogeneities on magnetic and non-magnetic resonance line polarization signals., Comment: 14 pages and 5 figures

The analysis of near infrared spectropolarimetric data at the internetwork at different regions on the solar surface could offer constraints to reject current modeling of these quiet areas. We present spectro-polarimetric observations of very quiet regions for different values of the heliocentric angle for the Fe I lines at 1.56 micron, from disc centre to positions close to the limb. The spatial resolution of the data is 0.7-1". We analyze direct observable properties of the Stokes profiles as the amplitude of circular and linear polarization as well as the total degree of polarization. Also the area and amplitude asymmetries are studied. We do not find any significant variation of the properties of the polarimetric signals with the heliocentric angle. This means that the magnetism of the solar internetwork remains the same regardless of the position on the solar disc. This observational fact discards the possibility of modeling the internetwork as a Network-like scenario. The magnetic elements of internetwork areas seem to be isotropically distributed when observed at our spatial resolution., Comment: Sorry, this is the version with the correct bibliography. Some figures had to be compressed. Accepted for publication in A&A

We consider a gas of hydrogen atoms illuminated by a broadband, unpolarized radiation with zero anisotropy. In the absence of external fields, the atomic J-levels are thus isotropically populated. While this condition persists in the presence of a magnetic field, we show instead that electric fields can induce the alignment of those levels. We also show that this electric alignment cannot occur in a two-term model of hydrogen (e.g., if only the Ly-alpha transition is excited), or if the level populations are distributed according to Boltzmann's law., Comment: 10 pages, 4 figures. Accepted by J.Phys.B: At.Mol.Opt.Phys

The physical interpretation of scattering line polarization offers a novel diagnostic window for exploring the thermal and magnetic structure of the quiet regions of the solar atmosphere. Here we evaluate the impact of isotropic collisions with neutral hydrogen atoms on the scattering polarization signals of the 13 lines of multiplet 42 of Ti I and on those of the K line and of the IR triplet of Ca II, with emphasis on the collisional transfer rates between nearby J-levels. To this end, we calculate the linear polarization produced by scattering processes considering realistic multilevel models and solving the statistical equilibrium equations for the multipolar components of the atomic density matrix. We confirm that the lower levels of the 13 lines of multiplet 42 of Ti I are completely depolarized by elastic collisions. We find that upper-level collisional depolarization turns out to have an unnoticeable impact on the emergent linear polarization amplitudes, except for the ${\lambda 4536$ line for which it is possible to notice a rather small depolarization caused by the collisional transfer rates. Concerning the Ca II lines, we show that the collisional rates play no role on the polarization of the upper level of the K line, while they have a rather small depolarizing effect on the atomic polarization of the metastable lower levels of the Ca II IR triplet., Comment: Accepted for publication in Astronomy and Astrophysics

context heading (optional) {With the development of new polarimeters for large telescopes, the spectro-polarimetric study of astrophysical bodies is becoming feasible and, indeed, more frequent. In particular, this is permitting the observational study of stellar magnetic fields} % aims heading (mandatory) {With the aim to optimize and interpret this kind of observations, we have produced a spectral atlas of circular polarization in a grid of stellar atmospheric models with effective temperatures between 3500 and 10000 K, surface gravities $\log(g)=3.5-5$, metallicities between 10$^{-2}$ and 1, and magnetic field strengths of 100, 1000 and 5000~G} % methods heading (mandatory) {We have computed the emergent Stokes $I$ and $V$ flux spectra in LTE of more than 10$^5$ spectral lines} % results heading (mandatory) {The atlas and several numerical tools are available in electronic format and may be downloaded from http://download.hao.ucar.edu/pub/PSA/. In this paper we review and discuss some of its most relevant features, such as which spectral regions and individual lines harbor the strongest signals, what are interesting lines to observe, how to disentangle field strength from filling factor, etc.}, Comment: To appear in A&A

We study the broadband polarization of hydrogen lines produced by scattering of radiation, in the presence of isotropic electric fields. In this paper, we focus on two distinct problems: a) the possibility of detecting the presence of turbulent electric fields by polarimetric methods, and b) the influence of such fields on the polarization due to a macroscopic, deterministic magnetic field. We found that isotropic electric fields decrease the degree of linear polarization in the scattered radiation, with respect to the zero-field case. On the other hand, a distribution of isotropic electric fields superimposed onto a deterministic magnetic field can generate a significant increase of the degree of magnetic-induced, net circular polarization. This phenomenon has important implications for the diagnostics of magnetic fields in plasmas using hydrogen lines, because of the ubiquitous presence of the Holtsmark, microscopic electric field from neighbouring ions. In particular, previous solar magnetographic studies of the Balmer lines of hydrogen may need to be revised because they neglected the effect of turbulent electric fields on the polarization signals. In this work, we give explicit results for the Lyman-alpha and Balmer-alpha lines., Comment: 15 pages, 6 figures