A conjugate gradient method for the solution of the non-LTE line radiation transfer problem

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and Successive Over-Relaxation (GS/SOR) schemes. Our study is indeed based on the application of a preconditioned bi-conjugate gradient method (BiCG-P). Standard tests, in 1D plane parallel geometry and in the frame of the two-level atom model, with monochromatic scattering, are discussed. Rates of convergence between the previously mentioned iterative schemes are compared, as well as their respective timing properties. The smoothing capability of the BiCG-P method is also demonstrated.Comment: Research note: 4 pages, 5 figures, accepted to A&

A new formal solution of the radiative transfer in arbitrary velocity fields

We present a new formal solution of the Lagrangian equation of radiative transfer that is useful in solving the equation of radiative transfer in the presence of arbitrary velocity fields. Normally a term due to the inclusion of the wavelength derivative in the Lagrangian equation of radiative transfer is associated with a generalised opacity. In non-monotonic velocity fields, this generalised opacity may become negative. To ensure that the opacity remains positive, this term of the derivative is included in the formal solution of the radiative transfer problem. The new definition of the generalised opacity allows for a new solution of the equation of radiative transfer in the presence of velocity fields. It is especially useful for arbitrary velocity fields, where it effectively prevents the occurrences of negative generalised opacities and still allows the explicit construction of the Lambda-operator of the system needed for an accelerated Lambda-iteration. We performed test calculations, where the results of old, established solutions were compared with the new solution. The relative deviations never exceeded 1% and so the new solution is indeed suitable for use in radiative-transfer modelling. Non-monotonic velocity fields along photon paths frequently occur in three-dimensional hydrodynamical models of astrophysical atmospheres. Therefore, the formal solution will be of use for multidimensional radiative transfer and has immediate applications in the modelling of pulsating stars and astrophysical shock fronts.Comment: Astronomy & Astrophysics, in press 8 figure

The quiet Sun's magnetic flux estimated from CaIIH bright inter-granular G-band structures

We determine the number density and area contribution of small-scale inter-granular calcium-II bright G-band structures in images of the quiet Sun as tracers of kilo-Gauss magnetic flux-concentrations. In a 149" x 117" G-band image of the disk center at the activity minimum, 7593 small inter-granular structures ['IGS']were segmented with the `multiple-level tracking' pattern recognition algorithm ['MLT_4']. The scatter-plot of the continuum versus the G-band brightness shows the known magnetic and non-magnetic branches. These branches are largely disentangled by applying an intrinsic Ca-II excess criterion. The thus obtained 2995 structures contain 1152 G-band bright points ['BP'] and 1843 G-band faint points ['FP']. They show a tendency of increasing size with decreasing G-band excess, as expected from the `hot wall' picture. Their Ca-H and G-band brightness are slightly related, resembling the known relation of Ca-II and magnetic field strength. The magnetic flux density of each individual BP and FP is estimated from their G-band brightness according to MHD-model calculations. The entity of BP and FP covers the total field-of-view ['FOV'] with a number density of 0.32/Mm^2 and a total area contribution of 2.0%. Their individual calibrations yield a mean flux density of 20 Mx/cm^2 in the entire FOV and 13 Mx/cm^2 for inter-network regions

Theoretical Models of Sunspot Structure and Dynamics

Recent progress in theoretical modeling of a sunspot is reviewed. The observed properties of umbral dots are well reproduced by realistic simulations of magnetoconvection in a vertical, monolithic magnetic field. To understand the penumbra, it is useful to distinguish between the inner penumbra, dominated by bright filaments containing slender dark cores, and the outer penumbra, made up of dark and bright filaments of comparable width with corresponding magnetic fields differing in inclination by some 30 degrees and strong Evershed flows in the dark filaments along nearly horizontal or downward-plunging magnetic fields. The role of magnetic flux pumping in submerging magnetic flux in the outer penumbra is examined through numerical experiments, and different geometric models of the penumbral magnetic field are discussed in the light of high-resolution observations. Recent, realistic numerical MHD simulations of an entire sunspot have succeeded in reproducing the salient features of the convective pattern in the umbra and the inner penumbra. The siphon-flow mechanism still provides the best explanation of the Evershed flow, particularly in the outer penumbra where it often consists of cool, supersonic downflows.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

NLTE solar irradiance modeling with the COSI code

Context. The solar irradiance is known to change on time scales of minutes to decades, and it is suspected that its substantial fluctua- tions are partially responsible for climate variations. Aims. We are developing a solar atmosphere code that allows the physical modeling of the entire solar spectrum composed of quiet Sun and active regions. This code is a tool for modeling the variability of the solar irradiance and understanding its influence on Earth. Methods. We exploit further development of the radiative transfer code COSI that now incorporates the calculation of molecular lines. We validated COSI under the conditions of local thermodynamic equilibrium (LTE) against the synthetic spectra calculated with the ATLAS code. The synthetic solar spectra were also calculated in non-local thermodynamic equilibrium (NLTE) and compared to the available measured spectra. In doing so we have defined the main problems of the modeling, e.g., the lack of opacity in the UV part of the spectrum and the inconsistency in the calculations of the visible continuum level, and we describe a solution to these problems. Results. The improved version of COSI allows us to reach good agreement between the calculated and observed solar spectra as measured by SOLSTICE and SIM onboard the SORCE satellite and ATLAS 3 mission operated from the Space Shuttle. We find that NLTE effects are very important for the modeling of the solar spectrum even in the visual part of the spectrum and for its variability over the entire solar spectrum. In addition to the strong effect on the UV part of the spectrum, NLTE effects influence the concentration of the negative ion of hydrogen, which results in a significant change of the visible continuum level and the irradiance variability.Comment: 14 pages, 14 figures, accepted for publication in Astronomy&Astrophysic

New Observations of Subarcsecond Photospheric Bright Points

We have used an interference filter centered at 4305 A within the bandhead of the CH radical (the 'G band') and real-time image selection at the Swedish Vacuum Solar Telescope on La Palma to produce very high contrast images of subarcsecond photospheric bright points at all locations on the solar disk. During the 6 day period of 1993 September 15-20 we observed active region NOAA 7581 from its appearance on the East limb to a near-disk-center position on September 20. A total of 1804 bright points were selected for analysis from the disk center image using feature extraction image processing techniques. The measured Full Width at Half Maximum (FWHM) distribution of the bright points in the image is lognormal with a modal value of 220 km (0 sec .30) and an average value of 250 km (0 sec .35). The smallest measured bright point diameter is 120 km (0 sec .17) and the largest is 600 km (O sec .69). Approximately 60% of the measured bright points are circular (eccentricity approx. 1.0), the average eccentricity is 1.5, and the maximum eccentricity corresponding to filigree in the image is 6.5. The peak contrast of the measured bright points is normally distributed. The contrast distribution variance is much greater than the measurement accuracy, indicating a large spread in intrinsic bright-point contrast. When referenced to an averaged 'quiet-Sun' area in the image, the modal contrast is 29% and the maximum value is 75%; when referenced to an average intergranular lane brightness in the image, the distribution has a modal value of 61% and a maximum of 119%. The bin-averaged contrast of G-band bright points is constant across the entire measured size range. The measured area of the bright points, corrected for pixelation and selection effects, covers about 1.8% of the total image area. Large pores and micropores occupy an additional 2% of the image area, implying a total area fraction of magnetic proxy features in the image of 3.8%. We discuss the implications of this area fraction measurement in the context of previously published measurements which show that typical active region plage has a magnetic filling factor on the order of 10% or greater. The results suggest that in the active region analyzed here, less than 50% of the small-scale magnetic flux tubes are demarcated by visible proxies such as bright points or pores

New Observations of Subarcsecond Photospheric Bright Points

We have used an interference filter centered at 4305 A within the bandhead of the CH radical (the 'G band') and real-time image selection at the Swedish Vacuum Solar Telescope on La Palma to produce very high contrast images of subarcsecond photospheric bright points at all locations on the solar disk. During the 6 day period of 15-20 Sept. 1993 we observed active region NOAA 7581 from its appearance on the East limb to a near-disk-center position on 20 Sept. A total of 1804 bright points were selected for analysis from the disk center image using feature extraction image processing techniques. The measured FWHM distribution of the bright points in the image is lognormal with a modal value of 220 km (0.30 sec) and an average value of 250 km (0.35 sec). The smallest measured bright point diameter is 120 km (0.17 sec) and the largest is 600 km (O.69 sec). Approximately 60% of the measured bright points are circular (eccentricity approx. 1.0), the average eccentricity is 1.5, and the maximum eccentricity corresponding to filigree in the image is 6.5. The peak contrast of the measured bright points is normally distributed. The contrast distribution variance is much greater than the measurement accuracy, indicating a large spread in intrinsic bright-point contrast. When referenced to an averaged 'quiet-Sun' area in the image, the modal contrast is 29% and the maximum value is 75%; when referenced to an average intergranular lane brightness in the image, the distribution has a modal value of 61% and a maximum of 119%. The bin-averaged contrast of G-band bright points is constant across the entire measured size range. The measured area of the bright points, corrected for pixelation and selection effects, covers about 1.8% of the total image area. Large pores and micropores occupy an additional 2% of the image area, implying a total area fraction of magnetic proxy features in the image of 3.8%. We discuss the implications of this area fraction measurement in the context of previously published measurements which show that typical active region plage has a magnetic filling factor on the order of 10% or greater. The results suggest that in the active region analyzed here, less than 50% of the small-scale magnetic flux tubes are demarcated by visible proxies such as bright points or pores

On-disk coronal rain

Small and elongated, cool and dense blob-like structures are being reported with high resolution telescopes in physically different regions throughout the solar atmosphere. Their detection and the understanding of their formation, morphology and thermodynamical characteristics can provide important information on their hosting environment, especially concerning the magnetic field, whose understanding constitutes a major problem in solar physics. An example of such blobs is coronal rain, a phenomenon of thermal non- equilibrium observed in active region loops, which consists of cool and dense chromospheric blobs falling along loop-like paths from coronal heights. So far, only off-limb coronal rain has been observed and few reports on the phenomenon exist. In the present work, several datasets of on-disk H{\alpha} observations with the CRisp Imaging SpectroPolarimeter (CRISP) at the Swedish 1-m Solar Telescope (SST) are analyzed. A special family of on-disk blobs is selected for each dataset and a statistical analysis is carried out on their dynamics, morphology and temperatures. All characteristics present distributions which are very similar to reported coronal rain statistics. We discuss possible interpretations considering other similar blob-like structures reported so far and show that a coronal rain interpretation is the most likely one. Their chromospheric nature and the projection effects (which eliminate all direct possibility of height estimation) on one side, and their small sizes, fast dynamics, and especially, their faint character (offering low contrast with the background intensity) on the other side, are found as the main causes for the absence until now of the detection of this on-disk coronal rain counterpart.Comment: 18 pages, 10 figures. Accepted for Solar Physic

Models and Observations of Sunspot Penumbrae

The mysteries of sunspot penumbrae have been under an intense scrutiny for the past 10 years. During this time, some models have been proposed and refuted, while the surviving ones had to be modified, adapted and evolved to explain the ever-increasing array of observational constraints. In this contribution I will review two of the present models, emphasizing their contributions to this field, but also pinpointing some of their inadequacies to explain a number of recent observations at very high spatial resolution. To help explaining these new observations I propose some modifications to each of them. These modifications bring those two seemingly opposite models closer together into a general picture that agrees well with recent 3D magneto-hydrodynamic simulations.Comment: 9 pages, 1 color figure. Review talk to appear in the proceedings of the International Workshop of 2008 Solar Total Eclipse: Solar Magnetism, Corona and Space Weather--Chinese Space Solar Telescope Scienc

The Imaging Magnetograph eXperiment (IMaX) for the Sunrise balloon-borne solar observatory

The Imaging Magnetograph eXperiment (IMaX) is a spectropolarimeter built by four institutions in Spain that flew on board the Sunrise balloon-borne telesocope in June 2009 for almost six days over the Arctic Circle. As a polarimeter IMaX uses fast polarization modulation (based on the use of two liquid crystal retarders), real-time image accumulation, and dual beam polarimetry to reach polarization sensitivities of 0.1%. As a spectrograph, the instrument uses a LiNbO3 etalon in double pass and a narrow band pre-filter to achieve a spectral resolution of 85 mAA. IMaX uses the high Zeeman sensitive line of Fe I at 5250.2 AA and observes all four Stokes parameters at various points inside the spectral line. This allows vector magnetograms, Dopplergrams, and intensity frames to be produced that, after reconstruction, reach spatial resolutions in the 0.15-0.18 arcsec range over a 50x50 arcsec FOV. Time cadences vary between ten and 33 seconds, although the shortest one only includes longitudinal polarimetry. The spectral line is sampled in various ways depending on the applied observing mode, from just two points inside the line to 11 of them. All observing modes include one extra wavelength point in the nearby continuum. Gauss equivalent sensitivities are four Gauss for longitudinal fields and 80 Gauss for transverse fields per wavelength sample. The LOS velocities are estimated with statistical errors of the order of 5-40 m/s. The design, calibration and integration phases of the instrument, together with the implemented data reduction scheme are described in some detail.Comment: 17 figure