Zeeman-Tomography of the Solar Photosphere -- 3-Dimensional Surface Structures Retrieved from Hinode Observations

AIMS :The thermodynamic and magnetic field structure of the solar photosphere is analyzed by means of a novel 3-dimensional spectropolarimetric inversion and reconstruction technique. METHODS : On the basis of high-resolution, mixed-polarity magnetoconvection simulations, we used an artificial neural network (ANN) model to approximate the nonlinear inverse mapping between synthesized Stokes spectra and the underlying stratification of atmospheric parameters like temperature, line-of-sight (LOS) velocity and LOS magnetic field. This approach not only allows us to incorporate more reliable physics into the inversion process, it also enables the inversion on an absolute geometrical height scale, which allows the subsequent combination of individual line-of-sight stratifications to obtain a complete 3-dimensional reconstruction (tomography) of the observed area. RESULTS : The magnetoconvection simulation data, as well as the ANN inversion, have been properly processed to be applicable to spectropolarimetric observations from the Hinode satellite. For the first time, we show 3-dimensional tomographic reconstructions (temperature, LOS velocity, and LOS magnetic field) of a quiet sun region observed by Hinode. The reconstructed area covers a field of approximately 12000 by 12000 km and a height range of 510 km in the photosphere. An enormous variety of small and large scale structures can be identified in the 3-D reconstructions. The low-flux region (B_{mag} = 20G) we analyzed exhibits a number of "tube-like" magnetic structures with field strengths of several hundred Gauss. Most of these structures rapidly loose their strength with height and only a few larger structures can retain a higher field strength to the upper layers of the photosphere.Comment: accepted for A&A Letter

A fast method for Stokes profile synthesis -- Radiative transfer modeling for ZDI and Stokes profile inversion

The major challenges for a fully polarized radiative transfer driven approach to Zeeman-Doppler imaging are still the enormous computational requirements. In every cycle of the iterative interplay between the forward process (spectral synthesis) and the inverse process (derivative based optimization) the Stokes profile synthesis requires several thousand evaluations of the polarized radiative transfer equation for a given stellar surface model. To cope with these computational demands and to allow for the incorporation of a full Stokes profile synthesis into Doppler- and Zeeman-Doppler imaging applications as well as into large scale solar Stokes profile inversions, we present a novel fast and accurate synthesis method for calculating local Stokes profiles. Our approach is based on artificial neural network models, which we use to approximate the complex non-linear mapping between the most important atmospheric parameters and the corresponding Stokes profiles. A number of specialized artificial neural networks, are used to model the functional relation between the model atmosphere, magnetic field strength, field inclination, and field azimuth, on one hand and the individual components (I,Q,U,V) of the Stokes profiles, on the other hand. We performed an extensive statistical evaluation and show that our new approach yields accurate local as well as disk-integrated Stokes profiles over a wide range of atmospheric conditions. The mean rms errors for the Stokes I and V profiles are well below 0.2% compared to the exact numerical solution. Errors for Stokes Q and U are in the range of 1%. Our approach does not only offer an accurate approximation to the LTE polarized radiative transfer it, moreover, accelerates the synthesis by a factor of more than 1000.Comment: A&A, in pres

Aspects of noncommutative Lorentzian geometry for globally hyperbolic spacetimes

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almost-everywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwards, using a $C^*$-algebra approach, the spacetime causal structure and the Lorentzian distance are generalized into noncommutative structures giving rise to a Lorentzian version of part of Connes' noncommutative geometry. The generalized noncommutative spacetime consists of a direct set of Hilbert spaces and a related class of $C^*$-algebras of operators. In each algebra a convex cone made of self-adjoint elements is selected which generalizes the class of causal functions. The generalized events, called {\em loci}, are realized as the elements of the inductive limit of the spaces of the algebraic states on the $C^*$-algebras. A partial-ordering relation between pairs of loci generalizes the causal order relation in spacetime. A generalized Lorentz distance of loci is defined by means of a class of densely-defined operators which play the r\^ole of a Lorentzian metric. Specializing back the formalism to the usual globally hyperbolic spacetime, it is found that compactly-supported probability measures give rise to a non-pointwise extension of the concept of events.Comment: 43 pages, structure of the paper changed and presentation strongly improved, references added, minor typos corrected, title changed, accepted for publication in Reviews in Mathematical Physic

Centrifugation and capillarity integrated into a multiple analyte whole blood analyser

A unique clinical chemistry analyser is described which processes 90 μl of whole blood (fingerstick or venous) into multiple aliquots of diluted plasma and reports the results of 12 tests in 14 min. To perform a panel of tests, the operator applies the unmetered sample directly into a single use, 8 cm diameter plastic rotor which contains the required liquid diluent and dry reagents. Using centrifugal and capillary forces, the rotor meters the required amount of blood, separates the red cells, meters the plasma, meters the diluent, mixes the fluids, distributes the fluid to the reaction cuvettes and mixes the reagents and the diluted plasma in the cuvettes. The instrument monitors the reagent reactions simultaneously using nine wavelengths, calculates the results from the absorbance data, and reports the results

PCA detection and denoising of Zeeman signatures in stellar polarised spectra

Our main objective is to develop a denoising strategy to increase the signal to noise ratio of individual spectral lines of stellar spectropolarimetric observations. We use a multivariate statistics technique called Principal Component Analysis. The cross-product matrix of the observations is diagonalized to obtain the eigenvectors in which the original observations can be developed. This basis is such that the first eigenvectors contain the greatest variance. Assuming that the noise is uncorrelated a denoising is possible by reconstructing the data with a truncated basis. We propose a method to identify the number of eigenvectors for an efficient noise filtering. Numerical simulations are used to demonstrate that an important increase of the signal to noise ratio per spectral line is possible using PCA denoising techniques. It can be also applied for detection of magnetic fields in stellar atmospheres. We analyze the relation between PCA and commonly used well-known techniques like line addition and least-squares deconvolution. Moreover, PCA is very robust and easy to compute.Comment: accepted to be published in A&