On the Sensitivity of Partial Redistribution Scattering Polarization Profiles to Various Atmospheric Parameters

This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of several atmospheric parameters on the emergent fractional linear polarization profiles. The shapes of these $Q/I$ profiles are interpreted in terms of the anisotropy of the radiation field, which in turn depends on the source function gradient that sets the angular variation of the specific intensity. We define a suitable frequency integrated anisotropy factor for PRD that can be directly related to the emergent linear polarization. We show that complete frequency redistribution is a good approximation to model weak resonance lines. We also show that the emergent linear polarization profiles can be very sensitive to the thermal structure of the solar atmosphere and, in particular, to spatial variations of the damping parameter.Comment: 45 pages, 16 figures, accepted for publication in the Astrophysical Journal (2010

Hanle effect in the solar Ba II D2 line: a diagnostic tool for chromospheric weak magnetic fields

The physics of the solar chromosphere depends in a crucial way on its magnetic structure. However there are presently very few direct magnetic field diagnostics available for this region. Here we investigate the diagnostic potential of the Hanle effect on the Ba II D2 line resonance polarization for the determination of weak chromospheric turbulent magnetic fields......Comment: In press in astronomy and astrophysic

Magnetic flux in the inter-network quiet Sun from comparison with numerical simulations

Khomenko et al. estimate the mean magnetic field strength of the quiet Sun to be 20 G. The figure is smaller than several existing estimates, and it comes from the comparison between observed Zeeman polarization signals and synthetic signals from numerical simulations of magneto-convection. The numerical simulations require an artificially large magnetic diffusivity, which smears out magnetic structures smaller than the grid scale. Assuming a turbulent cascade for the unresolved artificially smeared magnetic fields, we find that their unsigned magnetic flux is at least as important as that explicitly shown in the simulation. The unresolved fields do not produce Zeeman polarization but contribute to the unsigned flux.Since they are not considered by Khomenko et al., their mean magnetic field strength has to be regarded as a lower limit. This kind of bias is not specific of a particular numerical simulation or a spectral line. It is to be expected when observed quiet Sun Zeeman signals are compared with synthetic signals from simulations.Comment: Accepted A&A. 4 pages, 0 figure

Hanle effect in the CN violet system with LTE modeling

Weak entangled magnetic fields with mixed polarity occupy the main part of the quiet Sun. The Zeeman effect diagnostics fails to measure such fields because of cancellation in circular polarization. However, the Hanle effect diagnostics, accessible through the second solar spectrum, provides us with a very sensitive tool for studying the distribution of weak magnetic fields on the Sun. Molecular lines are very strong and even dominate in some regions of the second solar spectrum. The CN $B {}^{2} \Sigma - X {}^{2} \Sigma$ system is one of the richest and most promising systems for molecular diagnostics and well suited for the application of the differential Hanle effect method. The aim is to interpret observations of the CN $B {}^{2} \Sigma - X {}^{2} \Sigma$ system using the Hanle effect and to obtain an estimation of the magnetic field strength. We assume that the CN molecular layer is situated above the region where the continuum radiation is formed and employ the single-scattering approximation. Together with the Hanle effect theory this provides us with a model that can diagnose turbulent magnetic fields. We have succeeded in fitting modeled CN lines in several regions of the second solar spectrum to observations and obtained a magnetic field strength in the range from 10--30 G in the upper solar photosphere depending on the considered lines.Comment: Accepted for publication in Astronomy and Astrophysic

Origin of spatial variations of scattering polarization in the wings of the Ca {\sc i} 4227 \AA line

Polarization that is produced by coherent scattering can be modified by magnetic fields via the Hanle effect. According to standard theory the Hanle effect should only be operating in the Doppler core of spectral lines but not in the wings. In contrast, our observations of the scattering polarization in the Ca {\sc i} 4227 \AA line reveals the existence of spatial variations of the scattering polarization throughout the far line wings. This raises the question whether the observed spatial variations in wing polarization have a magnetic or non-magnetic origin. A magnetic origin may be possible if elastic collisions are able to cause sufficient frequency redistribution to make the Hanle effect effective in the wings without causing excessive collisional depolarization, as suggested by recent theories for partial frequency redistribution with coherent scattering in magnetic fields. To model the wing polarization we apply an extended version of the technique based on the "last scattering approximation". This model is highly successful in reproducing the observed Stokes $Q/I$ polarization (linear polarization parallel to the nearest solar limb), including the location of the wing polarization maxima and the minima around the Doppler core, but it fails to reproduce the observed spatial variations of the wing polarization in terms of magnetic field effects with frequency redistribution. This null result points in the direction of a non-magnetic origin in terms of local inhomogeneities (varying collisional depolarization, radiation-field anisotropies, and deviations from a plane-parallel atmospheric stratification).Comment: Accepted in May 2009 for publication in The Astrophysical Journa

Quiet Sun Magnetic Field Measurements Based on Lines with Hyperfine Structure

The Zeeman pattern of MnI lines is sensitive to hyperfine structure (HFS) and, they respond to hG magnetic field strengths differently from the lines used in solar magnetometry. This peculiarity has been employed to measure magnetic field strengths in quiet Sun regions. However, the methods applied so far assume the magnetic field to be constant in the resolution element. The assumption is clearly insufficient to describe the complex quiet Sun magnetic fields, biasing the results of the measurements. We present the first syntheses of MnI lines in realistic quiet Sun model atmospheres. The syntheses show how the MnI lines weaken with increasing field strength. In particular, kG magnetic concentrations produce NnI 5538 circular polarization signals (Stokes V) which can be up to two orders of magnitude smaller than the weak magnetic field approximation prediction. Consequently, (1) the polarization emerging from an atmosphere having weak and strong fields is biased towards the weak fields, and (2) HFS features characteristic of weak fields show up even when the magnetic flux and energy are dominated by kG fields. For the HFS feature of MnI 5538 to disappear the filling factor of kG fields has to be larger than the filling factor of sub-kG fields. Stokes V depends on magnetic field inclination according to the simple consine law. Atmospheres with unresolved velocities produce asymmetric line profiles, which cannot be reproduced by simple one-component model atmospheres. The uncertainty of the HFS constants do not limit the use of MnI lines for magnetometry.Comment: Accepted for publication in ApJ. 10 pages, 14 figure

A Substantial Amount of Hidden Magnetic Energy in the Quiet Sun

Deciphering and understanding the small-scale magnetic activity of the quiet solar photosphere should help to solve many of the key problems of solar and stellar physics, such as the magnetic coupling to the outer atmosphere and the coronal heating. At present, we can see only ${\sim}1$ of the complex magnetism of the quiet Sun, which highlights the need to develop a reliable way to investigate the remaining 99%. Here we report three-dimensional radiative tranfer modelling of scattering polarization in atomic and molecular lines that indicates the presence of hidden, mixed-polarity fields on subresolution scales. Combining this modelling with recent observational data we find a ubiquitous tangled magnetic field with an average strength of ${\sim}130$ G, which is much stronger in the intergranular regions of solar surface convection than in the granular regions. So the average magnetic energy density in the quiet solar photosphere is at least two orders of magnitude greater than that derived from simplistic one-dimensional investigations, and sufficient to balance radiative energy losses from the solar chromosphere.Comment: 21 pages and 2 figures (letter published in Nature on July 15, 2004

Time-Dependent Behavior of Linear Polarization in Unresolved Photospheres, With Applications for The Hanle Effect

Aims: This paper extends previous studies in modeling time varying linear polarization due to axisymmetric magnetic fields in rotating stars. We use the Hanle effect to predict variations in net line polarization, and use geometric arguments to generalize these results to linear polarization due to other mechanisms. Methods: Building on the work of Lopez Ariste et al., we use simple analytic models of rotating stars that are symmetric except for an axisymmetric magnetic field to predict the polarization lightcurve due to the Hanle effect. We highlight the effects for the variable line polarization as a function of viewing inclination and field axis obliquity. Finally, we use geometric arguments to generalize our results to linear polarization from the weak transverse Zeeman effect. Results: We derive analytic expressions to demonstrate that the variable polarization lightcurve for an oblique magnetic rotator is symmetric. This holds for any axisymmetric field distribution and arbitrary viewing inclination to the rotation axis. Conclusions: For the situation under consideration, the amplitude of the polarization variation is set by the Hanle effect, but the shape of the variation in polarization with phase depends largely on geometrical projection effects. Our work generalizes the applicability of results described in Lopez Ariste et al., inasmuch as the assumptions of a spherical star and an axisymmetric field are true, and provides a strategy for separating the effects of perspective from the Hanle effect itself for interpreting polarimetric lightcurves.Comment: 6 pages; 4 figures. Includes an extra figure found only in this preprint versio

Measuring the Hidden Aspects of Solar Magnetism

2008 marks the 100th anniversary of the discovery of astrophysical magnetic fields, when George Ellery Hale recorded the Zeeman splitting of spectral lines in sunspots. With the introduction of Babcock's photoelectric magnetograph it soon became clear that the Sun's magnetic field outside sunspots is extremely structured. The field strengths that were measured were found to get larger when the spatial resolution was improved. It was therefore necessary to come up with methods to go beyond the spatial resolution limit and diagnose the intrinsic magnetic-field properties without dependence on the quality of the telescope used. The line-ratio technique that was developed in the early 1970s revealed a picture where most flux that we see in magnetograms originates in highly bundled, kG fields with a tiny volume filling factor. This led to interpretations in terms of discrete, strong-field magnetic flux tubes embedded in a rather field-free medium, and a whole industry of flux tube models at increasing levels of sophistication. This magnetic-field paradigm has now been shattered with the advent of high-precision imaging polarimeters that allow us to apply the so-called "Second Solar Spectrum" to diagnose aspects of solar magnetism that have been hidden to Zeeman diagnostics. It is found that the bulk of the photospheric volume is seething with intermediately strong, tangled fields. In the new paradigm the field behaves like a fractal with a high degree of self-similarity, spanning about 8 orders of magnitude in scale size, down to scales of order 10 m.Comment: To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200

Magnetic Coupling in the Quiet Solar Atmosphere

Three kinds of magnetic couplings in the quiet solar atmosphere are highlighted and discussed, all fundamentally connected to the Lorentz force. First the coupling of the convecting and overshooting fluid in the surface layers of the Sun with the magnetic field. Here, the plasma motion provides the dominant force, which shapes the magnetic field and drives the surface dynamo. Progress in the understanding of the horizontal magnetic field is summarized and discussed. Second, the coupling between acoustic waves and the magnetic field, in particular the phenomenon of wave conversion and wave refraction. It is described how measurements of wave travel times in the atmosphere can provide information about the topography of the wave conversion zone, i.e., the surface of equal Alfv\'en and sound speed. In quiet regions, this surface separates a highly dynamic magnetic field with fast moving magnetosonic waves and shocks around and above it from the more slowly evolving field of high-beta plasma below it. Third, the magnetic field also couples to the radiation field, which leads to radiative flux channeling and increased anisotropy in the radiation field. It is shown how faculae can be understood in terms of this effect. The article starts with an introduction to the magnetic field of the quiet Sun in the light of new results from the Hinode space observatory and with a brief survey of measurements of the turbulent magnetic field with the help of the Hanle effect.Comment: To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200