Spectropolarimetric NLTE inversion code SNAPI

Context. Inversion codes are computer programs that fit a model atmosphere to the observed Stokes spectra, thus retrieving the relevant atmospheric parameters. The rising interest in the solar chromosphere, where spectral lines are formed by scattering, requires developing, testing, and comparing new non-local thermal equilibrium (NLTE) inversion codes. Aims. We present a new NLTE inversion code that is based on the analytical computation of the response functions. We named the code SNAPI, which is short for spectropolarimetic NLTE analytically powered inversion. Methods. SNAPI inverts full Stokes spectrum in order to obtain a depth-dependent stratification of the temperature, velocity, and the magnetic field vector. It is based on the so-called node approach, where atmospheric parameters are free to vary in several fixed points in the atmosphere, and are assumed to behave as splines in between. We describe the inversion approach in general and the specific choices we have made in the implementation. Results. We test the performance on one academic problem and on two interesting NLTE examples, the Ca II 8542 and Na I D spectral lines. The code is found to have excellent convergence properties and outperforms a finite-difference based code in this specific implementation by at least a factor of three. We invert synthetic observations of Na lines from a small part of a simulated solar atmosphere and conclude that the Na lines reliably retrieve the magnetic field and velocity in the range −3 < logτ < −0.5.

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STiC: A multiatom non-LTE PRD inversion code for full-Stokes solar observations

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834464 ◽

2019 ◽

Vol 623 ◽

pp. A74 ◽

Cited By ~ 32

Author(s):

J. de la Cruz Rodríguez ◽

J. Leenaarts ◽

S. Danilovic ◽

H. Uitenbroek

Keyword(s):

Grid Point ◽

Model Atmosphere ◽

Field Vector ◽

Oscillatory Behavior ◽

Spectral Lines ◽

Physical Parameters ◽

Solar Chromosphere ◽

Thermodynamical Equilibrium ◽

Partial Redistribution ◽

Regularization Techniques

The inference of the underlying state of the plasma in the solar chromosphere remains extremely challenging because of the nonlocal character of the observed radiation and plasma conditions in this layer. Inversion methods allow us to derive a model atmosphere that can reproduce the observed spectra by undertaking several physical assumptions. The most advanced approaches involve a depth-stratified model atmosphere described by temperature, line-of-sight velocity, turbulent velocity, the three components of the magntic field vector, and gas and electron pressure. The parameters of the radiative transfer equation are computed from a solid ground of physical principles. In order to apply these techniques to spectral lines that sample the chromosphere, nonlocal thermodynamical equilibrium effects must be included in the calculations. We developed a new inversion code STiC (STockholm inversion Code) to study spectral lines that sample the upper chromosphere. The code is based on the RH forward synthesis code, which we modified to make the inversions faster and more stable. For the first time, STiC facilitates the processing of lines from multiple atoms in non-LTE, also including partial redistribution effects (PRD) in angle and frequency of scattered photons. Furthermore, we include a regularization strategy that allows for model atmospheres with a complex depth stratification, without introducing artifacts in the reconstructed physical parameters, which are usually manifested in the form of oscillatory behavior. This approach takes steps toward a node-less inversion, in which the value of the physical parameters at each grid point can be considered a free parameter. In this paper we discuss the implementation of the aforementioned techniques, the description of the model atmosphere, and the optimizations that we applied to the code. We carry out some numerical experiments to show the performance of the code and the regularization techniques that we implemented. We made STiC publicly available to the community.

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Solar image denoising with convolutional neural networks

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936069 ◽

2019 ◽

Vol 629 ◽

pp. A99 ◽

Cited By ~ 3

Author(s):

C. J. Díaz Baso ◽

J. de la Cruz Rodríguez ◽

S. Danilovic

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Spatial Coherence ◽

Principal Component ◽

Real Data ◽

Spectral Lines ◽

Solar Chromosphere ◽

Weak Signals ◽

Statistical Characterization ◽

The Magnetic Field

The topology and dynamics of the solar chromosphere are greatly affected by the presence of magnetic fields. The magnetic field can be inferred by analyzing polarimetric observations of spectral lines. Polarimetric signals induced by chromospheric magnetic fields are, however, particularly weak, and in most cases very close to the detection limit of current instrumentation. Because of this, there are only few observational studies that have successfully reconstructed the three components of the magnetic field vector in the chromosphere. Traditionally, the signal-to-noise ratio of observations has been improved by performing time-averages or spatial averages, but in both cases, some information is lost. More advanced techniques, like principal-component analysis, have also been employed to take advantage of the sparsity of the observations in the spectral direction. In the present study, we use the spatial coherence of the observations to reduce the noise using deep-learning techniques. We designed a neural network that is capable of recovering weak signals under a complex noise corruption (including instrumental artifacts and non-linear post-processing). The training of the network is carried out without a priori knowledge of the clean signals, or an explicit statistical characterization of the noise or other corruption. We only use the same observations as our generative model. The performance of this method is demonstrated on both synthetic experiments and real data. We show examples of the improvement in typical signals obtained in current telescopes such as the Swedish 1 m Solar Telescope. The presented method can recover weak signals equally well no matter what spectral line or spectral sampling is used. It is especially suitable for cases when the wavelength sampling is scarce.

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An optimization principle for computing stationary MHD equilibria with solar wind flow

10.5194/egusphere-egu2020-3029 ◽

2020 ◽

Author(s):

Thomas Wiegelmann ◽

Thomas Neukirch ◽

Dieter Nickeler ◽

Iulia Chifu

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Coronal Magnetic Field ◽

Field Vector ◽

Source Surface ◽

Solar Chromosphere ◽

Wind Flow ◽

Solar Wind Flow ◽

Nonlinear Force ◽

The Magnetic Field

Knowledge about the magnetic field and plasma environment is important for almost all physical processes in the solar atmosphere. Precise measurements of the magnetic field vector are done routinely only in the photosphere, e.g. by SDO/HMI. These measurements are used as boundary condition for modelling the solar chromosphere and corona, whereas some model assumptions have to be made. In the low-plasma-beta corona the Lorentz-force vanishes and the magnetic field is reconstructed with a nonlinear force-free model. In the mixed-beta chromosphere plasma forces have to be taken into account with the help of a magnetostatic model. And finally for modelling the global corona far beyond the source surface the solar wind flow has to be incorporated within a stationary MHD model. To do so, we generalize a nonlinear force-free and magneto-static optimization code by the inclusion of a field aligned compressible plasma flow. Applications are the implementation of the solar wind on global scale. This allows to reconstruct the coronal magnetic field further outwards than with potential field, nonlinear force-free and magneto-static models. This way the model might help in future to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe.

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Inhomogeneity and velocity fields effects on scattering polarization in solar prominences

Proceedings of the International Astronomical Union ◽

10.1017/s1743921315004834 ◽

2014 ◽

Vol 10 (S305) ◽

pp. 238-244

Author(s):

I. Milić ◽

M. Faurobert

Keyword(s):

Magnetic Field ◽

Systematic Errors ◽

Field Vector ◽

Velocity Fields ◽

Spectral Lines ◽

Dimensional Model ◽

Vector Magnetic Field ◽

One Dimensional ◽

Solar Prominences ◽

The Magnetic Field

AbstractOne of the methods for diagnosing vector magnetic fields in solar prominences is the so called “inversion” of observed polarized spectral lines. This inversion usually assumes a fairly simple generative model and in this contribution we aim to study the possible systematic errors that are introduced by this assumption. On two-dimensional toy model of a prominence, we first demonstrate importance of multidimensional radiative transfer and horizontal inhomogeneities. These are able to induce a significant level of polarization in Stokes U, without the need for the magnetic field. We then compute emergent Stokes spectrum from a prominence which is pervaded by the vector magnetic field and use a simple, one-dimensional model to interpret these synthetic observations. We find that inferred values for the magnetic field vector generally differ from the original ones. Most importantly, the magnetic field might seem more inclined than it really is.

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The three-dimensional structure of the magnetic field of a sunspot

Proceedings of the International Astronomical Union ◽

10.1017/s1743921309030488 ◽

2008 ◽

Vol 4 (S259) ◽

pp. 225-226

Author(s):

Horst Balthasar ◽

Peter Gömöry

Keyword(s):

Magnetic Field ◽

Spatial Resolution ◽

Near Infrared ◽

Field Vector ◽

Spectral Lines ◽

Dimensional Structure ◽

Diagnostic Tools ◽

Solar Photosphere ◽

Current Densities ◽

The Magnetic Field

AbstractSpectro-polarimetric observations in several spectral lines allow to determine the height variation of the magnetic field of a small sunspot throughout the solar photosphere. The full Stokes-vector is measured with high spatial resolution. From these data we derive the magnetic field vector. The magnetic field strength decreases with height everywhere in the spot, even in the outer penumbra where some other authors have reported the opposite. The precise value of this decrease depends on the exact position in the spot. Values vary between 0.5 and 2.2 G km−1 when they are determined from an iron and a silicon line in the near infrared. The magnetic field is less inclined in the higher layers where the silicon line is formed. Once the magnetic vector field is known, it is straight forward to determine current densities and helicities. Current densities exhibit a radial structure in the penumbra, although it is still difficult to correlate this with the structure seen in the intensity continuum. In spite of this, current densities have a potential to serve as diagnostic tools to understand the penumbra, at least with the spatial resolution of the upcoming telescopes. The mean infered helicity is negative, as expected for a spot in the northern hemisphere. Nevertheless, there are locations inside the spot with positive helicity.

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Broadband Linear Polarization in Ap Stars

International Astronomical Union Colloquium ◽

10.1017/s0252921100020662 ◽

1993 ◽

Vol 138 ◽

pp. 305-309

Author(s):

Marco Landolfi ◽

Egidio Landi Degl’Innocenti ◽

Maurizio Landi Degl’Innocenti ◽

Jean-Louis Leroy ◽

Stefano Bagnulo

Keyword(s):

Magnetic Field ◽

Circular Polarization ◽

Linear Polarization ◽

Rotation Axis ◽

Spectral Lines ◽

Line Of Sight ◽

Long Time ◽

Rotating Star ◽

Ap Stars ◽

The Magnetic Field

AbstractBroadband linear polarization in the spectra of Ap stars is believed to be due to differential saturation between σ and π Zeeman components in spectral lines. This mechanism has been known for a long time to be the main agent of a similar phenomenon observed in sunspots. Since this phenomenon has been carefully calibrated in the solar case, it can be confidently used to deduce the magnetic field of Ap stars.Given the magnetic configuration of a rotating star, it is possible to deduce the broadband polarization at any phase. Calculations performed for the oblique dipole model show that the resulting polarization diagrams are very sensitive to the values of i (the angle between the rotation axis and the line of sight) and β (the angle between the rotation and magnetic axes). The dependence on i and β is such that the four-fold ambiguity typical of the circular polarization observations ((i,β), (β,i), (π-i,π-β), (π-β,π-i)) can be removed.

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Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834296 ◽

2018 ◽

Vol 620 ◽

pp. A191 ◽

Cited By ~ 5

Author(s):

M. Benko ◽

S. J. González Manrique ◽

H. Balthasar ◽

P. Gömöry ◽

C. Kuckein ◽

...

Keyword(s):

Magnetic Field ◽

Magnetic Flux ◽

Temporal Evolution ◽

Vertical Component ◽

Field Vector ◽

Linear Increase ◽

Vertical Magnetic Field ◽

Magnetic Diffusion ◽

The Magnetic Field ◽

Linear Decay

Context. It has been empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. Aims. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28–September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to prove the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. Methods. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. Results. We find a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the sunspot decay shown, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what is seen in stable sunspots. Conclusions. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field is found for the inner penumbral boundary.

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The magnetic field of β Cep and the Be phenomenon

International Astronomical Union Colloquium ◽

10.1017/s0252921100056074 ◽

2000 ◽

Vol 175 ◽

pp. 324-329 ◽

Cited By ~ 10

Author(s):

H.F. Henrichs ◽

J.A. de Jong ◽

J.-F. Donati ◽

C. Catala ◽

G.A. Wade ◽

...

Keyword(s):

Magnetic Field ◽

Longitudinal Magnetic Field ◽

Rotation Period ◽

Spectral Lines ◽

Be Stars ◽

Full Paper ◽

Rapid Rotation ◽

Rotator Model ◽

Maximum Field ◽

The Magnetic Field

AbstractNew circular spectropolarimetric observations of the B1 IIIe star β Cep (υsini = 25 km s−1) show a sinusoidally varying weak longitudinal magnetic field (~ 200 G peak-to-peak). The period corresponds to the 12 day period in the stellar wind variations observed in ultraviolet spectral lines. Maximum field occurs at maximum emission in the UV wind lines. This gives compelling evidence for a magnetic-rotator model for this star, with an unambiguous rotation period of 12 days.The similarity between the Hα emission phases in β Cep and in Be stars suggests that the origin of the Be phenomenon does not have to be rapid rotation: we propose that in β Cep the velocity to bring material in (Keplerian) orbit is provided by the high corotation velocity at the Alfvén radius (~10 R*), whereas in Be stars this is done by the rapid rotation of the surface. In both cases the cause of the emission phases has still to be found. Weak temporary magnetic fields remain the strongest candidate.A full paper, with results including additional measurements in June and July 1999, will appear in A & A.

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Magnetic fields of rapidly oscillating Ap stars

International Astronomical Union Colloquium ◽

10.1017/s0252921100117099 ◽

1993 ◽

Vol 139 ◽

pp. 132-132

Author(s):

G. Mathys

Keyword(s):

Magnetic Field ◽

High Resolution ◽

Magnetic Fields ◽

Zeeman Effect ◽

Rotation Frequency ◽

Spectral Lines ◽

Driving Mechanism ◽

Line Splitting ◽

Ap Stars ◽

The Magnetic Field

Magnetic field appears to play a major role in the pulsations of rapidly oscillating Ap (roAp) stars. Understanding of the behaviour of these objects thus requires knowledge of their magnetic field. Such knowledge is in particular essential to interpret the modulation of the amplitude of the photometric variations (with a frequency very close to the rotation frequency of the star) and to understand the driving mechanism of the pulsation. Therefore, a systematic programme of study of the magnetic field of roAp stars has been started, of which preliminary (and still very partial) results are presented here.Magnetic fields of Ap stars can be diagnosed from the Zeeman effect that they induced in spectral lines either from the observation of line-splitting in high-resolution unpolarized spectra (which only occurs in favourable circumstances) or from the observation of circular polarization of the lines in medium- to high-resolution spectra.

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Attitude Estimation of Underwater Vehicles Using Field Measurements and Bias Compensation

Sensors ◽

10.3390/s19020330 ◽

2019 ◽

Vol 19 (2) ◽

pp. 330 ◽

Cited By ~ 2

Author(s):

Nak Ko ◽

Seokki Jeong ◽

Suk-seung Hwang ◽

Jae-Young Pyun

Keyword(s):

Magnetic Field ◽

Field Measurement ◽

Field Measurements ◽

Underwater Vehicle ◽

Field Vector ◽

Attitude Estimation ◽

Magnetic Field Measurement ◽

Euler Angles ◽

Measured Field ◽

The Magnetic Field

This paper proposes a method of estimating the attitude of an underwater vehicle. The proposed method uses two field measurements, namely, a gravitational field and a magnetic field represented in terms of vectors in three-dimensional space. In many existing methods that convert the measured field vectors into Euler angles, the yaw accuracy is affected by the uncertainty of the gravitational measurement and by the uncertainty of the magnetic field measurement. Additionally, previous methods have used the magnetic field measurement under the assumption that the magnetic field has only a horizontal component. The proposed method utilizes all field measurement components as they are, without converting them into Euler angles. The bias in the measured magnetic field vector is estimated and compensated to take full advantage of all measured field vector components. Because the proposed method deals with the measured field independently, uncertainties in the measured vectors affect the attitude estimation separately without adding up. The proposed method was tested by conducting navigation experiments with an unmanned underwater vehicle inside test tanks. The results were compared with those obtained by other methods, wherein the Euler angles converted from the measured field vectors were used as measurements.

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