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

Rogue waves in the atmosphere

The appearance of rogue waves is well known in oceanographics, optics, and cold matter systems. Here we show a possibility for the existence of atmospheric rogue waves.Comment: 2 pages, 1 figur

Horizontal or vertical magnetic fields on the quiet Sun: Angular distributions and their height variations

Different analyses of identical Hinode SOT/SP data of quiet-sun magnetic fields have in the past led to contradictory answers to the question of whether the angular distribution of field vectors is preferentially horizontal or vertical. These answers have been obtained by combining the measured circular and linear polarizations in different ways to derive the field inclinations. A problem with these combinations is that the circular and linear polarizations scale with field strength in profoundly different ways. Here, we avoid these problems by using an entirely different approach that is based exclusively on the fundamental symmetry properties of the transverse Zeeman effect for observations away from the disk center without any dependence on the circular polarization. Systematic errors are suppressed by the application of a doubly differential technique with the 5247-5250 \AA\ line pair for observations with the ZIMPOL-2 imaging polarimeter on the French THEMIS telescope on Tenerife. This allows us to determine in a model- and resolution-independent way how the angular distribution of the intranetwork magnetic fields changes from being preferentially vertical in the lower and middle photosphere to become preferentially horizontal in the upper photosphere

On the physical origin of the second solar spectrum of the Sc II line at 4247 A

The peculiar three-peak structure of the linear polarization profile shown in the second solar spectrum by the Ba II line at 4554 A has been interpreted as the result of the different contributions coming from the barium isotopes with and without hyperfine structure (HFS). In the same spectrum, a triple peak polarization signal is also observed in the Sc II line at 4247 A. Scandium has a single stable isotope (^{45}Sc), which shows HFS due to a nuclear spin I=7/2. We investigate the possibility of interpreting the linear polarization profile shown in the second solar spectrum by this Sc II line in terms of HFS. A two-level model atom with HFS is assumed. Adopting an optically thin slab model, the role of atomic polarization and of HFS is investigated, avoiding the complications caused by radiative transfer effects. The slab is assumed to be illuminated from below by the photospheric continuum, and the polarization of the radiation scattered at 90 degrees is investigated. The three-peak structure of the scattering polarization profile observed in this Sc II line cannot be fully explained in terms of HFS. Given the similarities between the Sc II line at 4247 A and the Ba II line at 4554 A, it is not clear why, within the same modeling assumptions, only the three-peak Q/I profile of the barium line can be fully interpreted in terms of HFS. The failure to interpret this Sc II polarization signal raises important questions, whose resolution might lead to significant improvements in our understanding of the second solar spectrum. In particular, if the three-peak structure of the Sc II signal is actually produced by a physical mechanism neglected within the approach considered here, it will be extremely interesting not only to identify this mechanism, but also to understand why it seems to be less important in the case of the barium line.Comment: 8 pages, 8 figures, and 1 table. Accepted for publication in Astronomy and Astrophysic

Scaling laws for magnetic fields on the quiet Sun

The Sun's magnetic field is structured over a range of scales that span approximately seven orders of magnitudes, four of which lie beyond the resolving power of current telescopes. Here we have used a Hinode SOT/SP deep mode data set for the quiet-sun disk center in combination with constraints from the Hanle effect to derive scaling laws that describe how the magnetic structuring varies from the resolved scales down to the magnetic diffusion limit, where the field ceases to be frozen-in. The focus of the analysis is a derivation of the magnetic energy spectrum, but we also discuss the scale dependence of the probability density function (PDF) for the flux densities and the role of the cancellation function for the average unsigned flux density. Analysis of the Hinode data set with the line-ratio method reveals a collapsed flux population in the form of flux tubes with a size distribution that is peaked in the 10-100 km range. Magnetic energy is injected into this scale range by the instability mechanism of flux tube collapse, which is driven by the external gas pressure in the superadiabatic region at the top of the convection zone. This elevates the magnetic energy spectrum just beyond the telescope resolution limit. Flux tube decay feeds an inertial range that cascades down the scale spectrum to the magnetic diffusion limit, and which contains the tangled, "hidden" flux that is known to exist from observations of the Hanle effect. The observational constraints demand that the total magnetic energy in the hidden flux must be of the same order as the total energy in the kG flux tubes. Both the flux tubes and the hidden flux are found to be preferentially located in the intergranular lanes, which is to be expected since they are physically related.Comment: accepted for publication in Astronomy & Astrophysic

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

The Scattering Polarization of the Sr I 4607 \AA Line at the Diffraction Limit Resolution of a 1-m Telescope

One of the greatest challenges in solar and stellar physics in coming years will be to observe the Second Solar Spectrum with a spatial resolution significantly better than 1 arcsec. This type of scattering polarization observations would probably allow us to discover hitherto unknown aspects of the Sun's hidden magnetism. Here we report on some theoretical predictions for the photospheric line of Sr I at 4607 \AA, which we have obtained by solving the three-dimensional (3D) radiative transfer problem of scattering line polarization in a realistic hydrodynamical model of the solar photosphere. We have taken into account not only the anisotropy of the radiation field in the 3D medium and the Hanle effect of a tangled magnetic field, but also the symmetry breaking effects caused by the horizontal atmospheric inhomogeneities produced by the solar surface convection. Interestingly, the Q/I and U/I linear polarization signals of the emergent spectral line radiation have sizable values and fluctuations, even at the very center of the solar disk where we meet the forward scattering case. The ensuing small-scale patterns in Q/I and U/I turn out to be sensitive to the assumed magnetic field model, and are of great diagnostic value. We argue that it should be possible to observe them with the help of a 1-m telescope equipped with adaptive optics and a suitable polarimeter.Comment: Accepted for publication in The Astrophysical Journal Letters (12 pages and 2 color figures

Spectral Properties of Acoustic Gravity Wave Turbulence

The nonlinear turbulent interactions between acoustic gravity waves are investigated using two dimensional nonlinear fluid simulations. The acoustic gravity waves consist of velocity and density perturbations and propagate across the density gradients in the vertical direction in the Earth's atmosphere. We find that the coupled two component model exhibits generation of large scale velocity potential flows along the vertical direction, while the density perturbations relax towards an isotropic random distribution. The characteristic turbulent spectrum associated with the system has a Kolmogorov-like feature and tends to relax towards a $k^{-5/3}$ spectrum, where $k$ is a typical wavenumber. The cross field diffusion associated with the velocity potential grows linearly and saturates in the nonlinear phase

Iterated function systems with a given continuous stationary distribution

For any continuous probability measure $\mu$ on ${\mathbb R}$ we construct an IFS with probabilities having $\mu$ as its unique measure-attractor.Comment: 7 pages, 3 figure