J. Trujillo Bueno

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 ∼1 per cent of the complex magnetism of the quiet Sun, which highlights the need to develop a reliable way to investigate the remaining 99 per cent. Here we report three-dimensional radiative transfer 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 ∼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.

Quiet-Sun inter-network magnetic fields observed in the infrared

This paper presents the results of an investigation of the quiet Suns magnetic field based on high-resolution infrared spectropolarimetric observations obtained with the Tenerife Infrared Polarimeter (TIP) at the German VTT of the Observatorio del Teide. We observed two very quiet regions at disc centre. The seeing was exceptionally good during both observing runs, being excellent during one of them. In both cases the network was intentionally avoided to the extent possible, to focus the analysis on the characteristics of the weak polarization signals of the inter-network regions. We find that the Stokes V profile of Fe  15648 A line in almost 50% of the pixels and Stokes Q and/or U in 20% of the pixels have a signal above 10 −3 (in units of continuum intensity Ic), which is significantly above the noise level of 2−3 × 10 −4 . This implies that we detect fluxes as low as 2 × 10 15 Mx/px. We find evidence that we have detected most of the net flux that is in principle detectable at 1 �� resolution with the Zeeman effect. The observed linear polarization resulting from the transverse Zeeman effect indicates that the magnetic fields have a broad range of inclinations, although most of the pixels show polarization signatures which imply an inclination of about 20 ◦ . Nearly 30% of the selected V-profiles have irregular shapes with 3 or more lobes, suggesting mixed polarities with different LOS velocity within the resolution element. The profiles are classified using a single value decomposition approach. The spatial distribution of the magnetic signal shows that profiles of different classes (having different velocities, splitting, asymmetries) are clustered together and form patches, close to the spatial resolution in size. Most of the field is found to be located in intergranular lanes. The statistical properties of the mainly inter-network field sampled by these observations are presented, showing that most of the observed fields are weak with relatively few kG features. The field strength distribution peaks at 350 G and has a FWHM of 300 G. Other parameters, such as profile asymmetries, filling factors and line-of-sight velocities are also determined and discussed.

ADVANCED FORWARD MODELING AND INVERSION OF STOKES PROFILES RESULTING FROM THE JOINT ACTION OF THE HANLE AND ZEEMAN EFFECTS

A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. Here we present a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He I 10830 A and 5876 A (or D3) multiplets. It is based on the quantum theory of spectral line polarization, which takes into account in a rigorous way all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, level crossings and repulsions, Zeeman, Paschen-Back, and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods. The reliability of the forward modeling and inversion code presented here is demonstrated through several applications, which range from the inference of the magnetic field vector in solar active regions to determining whether or not it is canopy-like in quiet chromospheric regions. This user-friendly diagnostic tool called HAZEL (from HAnle and ZEeman Light) is offered to the astrophysical community, with the hope that it will facilitate new advances in solar and stellar physics.

Channeling 5 Minute Photospheric Oscillations into the Solar Outer Atmosphere through Small-Scale Vertical Magnetic Flux Tubes

We report two-dimensional MHD simulations which demonstrate that photospheric 5 minute oscillations can leak into the chromosphere inside small-scale vertical magnetic flux tubes. The results of our numerical experiments are compatible with those inferred from simultaneous spectropolarimetric observations of the photosphere and chromosphere obtained with the Tenerife Infrared Polarimeter (TIP) at 10830 A. We conclude that the efficiency of energy exchange by radiation in the solar photosphere can lead to a significant reduction of the cutoff frequency and may allow for the propagation of the 5 minute waves vertically into the chromosphere.

Determination of the Magnetic Field Vector via the Hanle and Zeeman Effects in the He I λ10830 Multiplet: Evidence for Nearly Vertical Magnetic Fields in a Polar Crown Prominence

The magnetic field is the key physical quantity responsible for the formation, stability, and evolution of solar prominences (ribbons of cool dense gas embedded in the hot tenuous corona). Therefore, it is important to obtain good empirical knowledge of the three-dimensional structure of prominence magnetic fields. Here we show how the magnetic field vector can be inferred via the physical interpretation of spectropolarimetric observations in the He I λ10830 multiplet. To this end, we have developed an inversion code based on the quantum theory of the Hanle and Zeeman effects and on a few modeling assumptions. We show an application to full Stokes vector observations of a polar crown prominence that, in the slit-jaw Hα image, showed nearly vertical plasma structures. Our results provide evidence for magnetic fields on the order of 30 G inclined by about 25° with respect to the local solar vertical direction. Of additional interest is that the inferred nearly vertical magnetic field vector appears to be slightly rotating around a fixed direction in space as one proceeds along the direction of the spectrographs slit. While these results provide new light on the three-dimensional geometry of the magnetic fields that confine the plasma of polar crown prominences, they also urge us to develop improved solar prominence models and to pursue new diagnostic investigations.

G-Band Spectral Synthesis in Solar Magnetic Concentrations

Narrowband imaging in the G band is commonly used to trace the small magnetic field concentrations of the Sun, although the mechanism that makes them bright has remained unclear. We carry out LTE syntheses of the G band in an assorted set of semiempirical model magnetic concentrations. The syntheses include all CH lines as well as the main atomic lines within the bandpass. The model atmospheres produce bright G-band spectra having many properties in common with the observed G-band bright points. In particular, the contrast referring to the quiet Sun is about twice the contrast in continuum wavelengths. The agreement with observations does not depend on the specificities of the model atmosphere; rather, it holds from single flux tubes to microstructured magnetic atmospheres. However, the agreement requires that the real G-band bright points are not spatially resolved, even in the best observations. Since the predicted G-band intensities exceed by far the observed values, we foresee a notable increase of contrast of the G-band images upon improvement of the angular resolution. According to the LTE modeling, the G-band spectrum emerges from the deep photosphere that produces the continuum. Our syntheses also predict solar magnetic concentrations showing up in continuum images but not in the G band. Finally, we have examined the importance of the CH photodissociation in setting the amount of G-band absorption. It turns out to play a minor role.

The Hanle and Zeeman Effects in Solar Spicules: A Novel Diagnostic Window on Chromospheric Magnetism

A large set of high precision full-Stokes spectropolarimetric observations of the He-D3 line in spicules has been recorded with the ZIMPOL polarimeter at the Gregory-Coude Telescope in Locarno. The observational technique allow us to obtain measurements free from seeing induced spurious effects. The instrumental polarization is well under control and taken into account in the data analysis. The observed Stokes profiles are interpreted according to the quantum theory of the Hanle and Zeeman effects with the aim of obtaining information on the magnetic field vector. To this end, we make use of a suitable Stokes inversion technique. The results are presented giving emphasis on a few particularly interesting measurements which show clearly the operation of the Hanle and Zeeman effects in solar chromospheric spicules.

An Open Source, Massively Parallel Code for Non-LTE Synthesis and Inversion of Spectral Lines and Zeeman-induced Stokes Profiles

With the advent of a new generation of solar telescopes and instrumentation, interpreting chromospheric observations (in particular, spectropolarimetry) requires new, suitable diagnostic tools. This paper describes a new code, NICOLE, that has been designed for Stokes non-LTE radiative transfer, for synthesis and inversion of spectral lines and Zeeman-induced polarization profiles, spanning a wide range of atmospheric heights from the photosphere to the chromosphere. The code features a number of unique features and capabilities and has been built from scratch with a powerful parallelization scheme that makes it suitable for application on massive datasets using large supercomputers. The source code is written entirely in Fortran 90/2003 and complies strictly with the ANSI standards to ensure maximum compatibility and portability. It is being publicly released, with the idea of facilitating future branching by other groups to augment its capabilities.

The Influence of Coronal EUV Irradiance on the Emission in the He I 10830 Å and D3 Multiplets

Two of the most attractive spectral windows for spectropolarimetric investigations of the physical properties of the plasma structures in the solar chromosphere and corona are the ones provided by the spectral lines of the He I 10830 and 5876 A (or D3) multiplets, whose polarization signals are sensitive to the Hanle and Zeeman effects. However, in order to be able to carry out reliable diagnostics, it is crucial to have a good physical understanding of the sensitivity of the observed spectral line radiation to the various competing driving mechanisms. Here we report a series of off-the-limb non-LTE calculations of the He I D3 and 10830 A emission profiles, focusing our investigation on their sensitivity to the EUV coronal irradiation and the model atmosphere used in the calculations. We show in particular that the intensity ratio of the blue to the red components in the emission profiles of the He I 10830 A multiplet turns out to be a good candidate as a diagnostic tool for the coronal irradiance. Measurements of this observable as a function of the distance to the limb and its confrontation with radiative transfer modeling might give us valuable information on the physical properties of the solar atmosphere and on the amount of EUV radiation at relevant wavelengths penetrating the chromosphere from above.

Non-LTE Inversion of Line Profiles

In this paper we address the problem of the non-LTE (NLTE) inversion of line profiles by means of a nonlinear least-squares minimization procedure combined with very efficient multilevel transfer methods. Our approach is based on the concept of response functions, which measure the first-order response of the emergent profiles to changes in the atmospheric conditions. We introduce the fixed departure coefficients (FDC) approximation in order to compute these response functions in a fast and straightforward manner. The accuracy of this approximation is checked comparing FDC response functions with those obtained from full NLTE computations. An NLTE inversion code based on these response functions has been developed and extensively tested. Reference synthetic profiles, similar to those expected from real observations, are given as input to the inversion algorithm and the recovered models are shown to be compatible with the reference models within the error bars. Our NLTE inversion code thus provides a new tool for the investigation of the chromospheres of the Sun and other stars.