arXiv subjects

T. A. Carroll

Publications and source records attributed to T. A. Carroll.

43 records · Page 3Linked to original sources

arXiv2008

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.

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arXiv2008

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.

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arXiv2008

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.

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arXiv2008

Zeeman-Doppler Imaging of Late-Type Stars -- The Surface Magnetic Field of II Peg

Late-type stars in general possess complicated magnetic surface fields which makes their detection and in particular their modeling and reconstruction challenging. In this work we present a new Zeeman-Doppler imaging code which is especially designed for the application to late-type stars. This code uses a new multi-line cross-correlation technique by means of a principal component analysis to extract and enhance the quality of individual polarized line profiles. It implements the full polarized radiative transfer equation and uses an inversion strategy that can incorporate prior knowledge based on solar analogies. Moreover, our code utilizes a new regularization scheme which is based on local maximum entropy to allow a more appropriate reproduction of complex surface fields as those expected for late-type stars. In a first application we present Zeeman-Doppler images of II Pegasi which reveal a surprisingly large scale surface structure with one predominant (unipolar) magnetic longitude which is mainly radially oriented.

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arXiv2007

The Meso-Structured Magnetic Atmosphere -- A Stochastic Polarized Radiative Transfer Approach

We present a general radiative transfer model which allows the Zeeman diagnostics of complex and unresolved solar magnetic fields. Present modeling techniques still rely to a large extent on a-priori assumptions about the geometry of the underlying magnetic field. In an effort to obtain a more flexible and unbiased approach we pursue a rigorous statistical description of the underlying atmosphere. Based on a Markov random field model the atmospheric structures are characterized in terms of probability densities and spatial correlations. This approach allows us to derive a stochastic transport equation for polarized light valid in a regime with an arbitrary fluctuating magnetic field on finite scales. One of the key ingredients of the derived stochastic transfer equation is the correlation length which provides an additional degree of freedom to the transport equation and can be used as a diagnostic parameter to estimate the characteristic length scale of the underlying magnetic field. It is shown that the stochastic transfer equation represents a natural extension of the (polarized) line formation under the micro- and macroturbulent assumption and contains both approaches as limiting cases. In particular, we show how in an inhomogeneous atmosphere asymmetric Stokes profiles develop and that the correlation length directly controls the degree of asymmetry and net circular polarization (NCP). In a number of simple numerical model calculations we demonstrate the importance of a finite correlation length for the polarized line formation and its impact on the resulting Stokes line profiles.

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arXiv2007

Stokes Profile Inversion in Meso-Structured Magnetic Atmospheres

Based on the Meso-Structured Magnetic Atmosphere (MESMA) approximation, recently introduced by Carroll & Kopf (2007), we present first results of an inversion of spectropolarimetric observations obtained from solar internetwork regions. To cope with the inherent complexity of the mostly unresolved magnetic field in the solar photosphere the MESMA approach provides a statistical description of the underlying atmosphere in terms of a random Markov field. This statistical model allows us to derive a stochastic transfer equation for polarized light. The stochastic transfer equation explicitly accounts for the spatial correlation -- the characteristic length scale -- of the underlying magnetic and non-magnetic structures. We use this new diagnostic parameter in an inversion approach to demonstrate that the magnetic flux structures in the solar internetwork possess a finite correlation length which is not compatible with the classical flux tube picture.

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arXiv2007

The Characteristic Length Scale of the Magnetic Fluctuation in a Sunspot Penumbra: A Stochastic Polarized Radiative Transfer Approach

The characteristic size of penumbral structures are still below the current resolution limit of modern solar telescopes. Though we have seen a significant progress in theoretical work over the last decades no tight constraints can be placed on the size of penumbral structures in order to favor models with relatively large and thick magnetic flux elements, just at or below the current resolution limit, or on the other hand, clusters of optically thin micro-structures. Based on a macroscopic 2-component inversion and the approach of polarized radiative transfer in stochastic media, we have estimated the characteristic length scale of the magnetic fluctuation in a sunspot penumbra from observed Stokes spectra. The results yield a coherent picture for the entire magnetic neutral line of the penumbra and indicate that the magnetic fluctuations have a typical length scale between 30 km and 70 km.

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