We aim at demonstrating the capabilities of a newly developed method for determining electric currents in the solar photosphere. We employ three-dimensional radiative magneto-hydrodynamic (MHD) ...simulations to produce synthetic Stokes profiles in several spectral lines with a spatial resolution similar to what the newly operational 4-meter Daniel K. Inouye Solar Telescope (DKIST) solar telescope should achieve. We apply a newly developed inversion method of the polarized radiative transfer equation with magneto-hydrostatic (MHS) constraints to infer the magnetic field vector in the three-dimensional Cartesian domain, \(\mathbf{B}(x,y,z),\) from the synthetic Stokes profiles. We then apply Ampere's law to determine the electric currents, \({\bf j}\), from the inferred magnetic field, \(\mathbf{B}(x,y,z),\) and compare the results with the electric currents present in the original MHD simulation. We show that the method employed here is able to attain reasonable reliability (close to 50 % of the cases are within a factor of two, and this increases to 60 %-70 % for pixels with \(B\ge300\) G) in the inference of electric currents for low atmospheric heights (optical depths at 500 nm \(\tau_{5}\in\)1,0.1) regardless of whether a small or large number of spectral lines are inverted. Above these photospheric layers, the method's accuracy strongly deteriorates as magnetic fields become weaker and as the MHS approximation becomes less accurate. We also find that the inferred electric currents have a floor value that is related to low-magnetized plasma, where the uncertainty in the magnetic field inference prevents a sufficiently accurate determination of the spatial derivatives. We present a method that allows the inference of the three components of the electric current vector at deep atmospheric layers (photospheric layers) from spectropolarimetric observations.
Inversion techniques applied to the radiative transfer equation for polarized light are capable of inferring the physical parameters in the solar atmosphere (temperature \(T\), magnetic field \({\bf ...B}\), and line-of-sight velocity \(v_{\rm los}\)) from observations of the Stokes vector (i.e., spectropolarimetric observations) in spectral lines. Inferences are usually performed in the \((x,y,\tau_c)\) domain, where \(\tau_c\) refers to the optical-depth scale. Generally, their determination in the \((x,y,z)\) volume is not possible due to the lack of a reliable estimation of the gas pressure, particularly in regions of the solar surface harboring strong magnetic fields. We aim to develop a new inversion code capable of reliably inferring the physical parameters in the \((x,y,z)\) domain. We combine, in a self-consistent way, an inverse solver for the radiative transfer equation (Firtez-DZ) with a solver for the magneto-hydrostatic (MHS) equilibrium, which derives realistic values of the gas pressure by taking the magnetic pressure and tension into account. We test the correct behavior of the newly developed code with spectropolarimetric observations of two sunspots recorded with the spectropolarimeter (SP) instrument on board the Hinode spacecraft, and we show how the physical parameters are inferred in the \((x,y,z)\) domain, with the Wilson depression of the sunspots arising as a natural consequence of the force balance. In particular, our approach significantly improves upon previous determinations that were based on semiempirical models. Our results open the door for the possibility of calculating reliable electric currents in three dimensions, \({\bf j}(x,y,z)\), in the solar photosphere. Further consistency checks would include a comparison with other methods that have recently been proposed and which achieve similar goals.
In this work, we study the accuracy that can be achieved when inferring the atmospheric information from realistic numerical magneto-hydrodynamic simulations that reproduce the spatial resolution we ...will obtain with future observations made by the 4m class telescopes DKIST and EST. We first study multiple inversion configurations using the SIR code and the Fe I transitions at 630 nm until we obtain minor differences between the input and the inferred atmosphere in a wide range of heights. Also, we examine how the inversion accuracy depends on the noise level of the Stokes profiles. The results indicate that when the majority of the inverted pixels come from strongly magnetised areas, there are almost no restrictions in terms of the noise, obtaining good results for noise amplitudes up to 1\(\times10^{-3}\) of \(I_c\). At the same time, the situation is different for observations where the dominant magnetic structures are weak, and noise restraints are more demanding. Moreover, we find that the accuracy of the fits is almost the same as that obtained without noise when the noise levels are on the order of 1\(\times10^{-4}\)of \(I_c\). We, therefore, advise aiming for noise values on the order of or lower than 5\(\times10^{-4}\) of \(I_c\) if observers seek reliable interpretations of the results for the magnetic field vector reliably. We expect those noise levels to be achievable by next-generation 4m class telescopes thanks to an optimised polarisation calibration and the large collecting area of the primary mirror.
We analyse the temporal evolution of the inclination component of the magnetic field vector for the penumbral area of 25 isolated sunspots. Compared to previous works, the use of data from the HMI ...instrument aboard the SDO observatory facilitates the study of very long time series (\(\approx\)1 week), compared to previous works, with a good spatial and temporal resolution. We used the wavelet technique and we found some filamentary-shaped events with large wavelet power. Their distribution of periods is broad, ranging from the lower limit for this study of 48 minutes up to 63 hours. An interesting property of these events is that they do not appear homogeneously all around the penumbra but they seem to concentrate at particular locations. The cross-comparison of these wavelet maps with AIA data shows that the regions where these events appear are visually related to the coronal loops that connect the outer penumbra to one or more neighbouring opposite polarity flux patches.
Inversion codes for the polarized radiative transfer equation can be used to infer the temperature \(T\), line-of-sight velocity \(v_{\rm los}\), and magnetic field \(\rm{\bf B}\) as a function of ...the continuum optical-depth \(\tau_{\rm c}\). However, they do not directly provide the gas pressure \(P_{\rm g}\) or density \(\rho\). In order to obtain these latter parameters, inversion codes rely instead on the assumption of hydrostatic equilibrium (HE) in addition to the equation of state (EOS). Unfortunately, the assumption of HE is rather unrealistic across magnetic field lines. This is because the role of the Lorentz force, among other factors, is neglected. This translates into an inaccurate conversion from optical depth \(\tau_{\rm c}\) to geometrical height \(z\). We aim at improving this conversion via the application of magneto-hydrostatic (MHS) equilibrium instead of HE. We develop a method to solve the momentum equation under MHS equilibrium (i.e., taking the Lorentz force into account) in three dimensions. The method is based on the solution of a Poisson-like equation. Considering the gas pressure \(P_{\rm g}\) and density \(\rho\) from three-dimensional magneto-hydrodynamic (MHD) simulations of sunspots as a benchmark, we compare the results from the application of HE and MHS equilibrium. We find that HE retrieves the gas pressure and density within an order of magnitude of the MHD values in only about 47 \% of the domain. This translates into an error of about \(160-200\) km in the determination of the \(z-\tau_{\rm c}\) conversion. On the other hand, the application of MHS equilibrium allows determination of \(P_{\rm g}\) and \(\rho\) within an order of magnitude in 84 \% of the domain. In this latter case, the \(z-\tau_{\rm c}\) conversion is obtained with an accuracy of \(30-70\) km.
We present a numerical code that solves the forward and inverse problem of the polarized radiative transfer equation in geometrical scale under the Zeeman regime. The code is fully parallelized, ...making it able to easily handle large observational and simulated datasets. We checked the reliability of the forward and inverse modules through different examples. In particular, we show that even when properly inferring various physical parameters (temperature, magnetic field components, and line-of-sight velocity) in optical depth, their reliability in height-scale depends on the accuracy with which the gas-pressure or density are known. The code is made publicly available as a tool to solve the radiative transfer equation and perform the inverse solution treating each pixel independently. An important feature of this code, that will be exploited in the future, is that working in geometrical-scale allows for the direct calculation of spatial derivatives, which are usually required in order to estimate the gas pressure and/or density via the momentum equation in a three-dimensional volume, in particular the three-dimensional Lorenz force.
Context. The solar magnetic field is responsible for all aspects of solar activity. Thus, emergence of magnetic flux at the surface is the first manifestation of the ensuing solar activity. Aims. ...Combining high-resolution and synoptic observations aims to provide a comprehensive description of flux emergence at photospheric level and of the growth process that eventually leads to a mature active region. Methods. The small active region NOAA 12118 emerged on 2014 July 17 and was observed one day later with the 1.5-m GREGOR solar telescope on 2014 July 18. High-resolution time-series of blue continuum and G-band images acquired in the blue imaging channel (BIC) of the GREGOR Fabry-Pérot Interferometer (GFPI) were complemented by synoptic line-of-sight magnetograms and continuum images obtained with the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Horizontal proper motions and horizontal plasma velocities were computed with local correlation tracking (LCT) and the differential affine velocity estimator (DAVE), respectively. Morphological image processing was employed to measure the photometric and magnetic area, magnetic flux, and the separation profile of the emerging flux region during its evolution. Results. The computed growth rates for photometric area, magnetic area, and magnetic flux are about twice as high as the respective decay rates. The space-time diagram using HMI magnetograms of five days provides a comprehensive view of growth and decay. It traces a leaf-like structure, which is determined by the initial separation of the two polarities, a rapid expansion phase, a time when the spread stalls, and a period when the region slowly shrinks again. The separation rate of 0.26 km s-1 is highest in the initial stage, and it decreases when the separation comes to a halt. Horizontal plasma velocities computed at four evolutionary stages indicate a changing pattern of inflows. In LCT maps we find persistent flow patterns such as outward motions in the outer part of the two major pores, a diverging feature near the trailing pore marking the site of upwelling plasma and flux emergence, and low velocities in the interior of dark pores. We detected many elongated rapidly expanding granules between the two major polarities, with dimensions twice as large as the normal granules.
Regardless of the physical origin of stellar magnetic fields - fossil or dynamo induced - an inclination angle between the magnetic and rotation axes is very often observed. Absence of observational ...evidence in this direction in the solar case has led to generally assume that its global magnetic field and rotation axes are well aligned. We present the detection of a monthly periodic signal of the photospheric solar magnetic field at all latitudes, and especially near the poles, revealing that the main axis of the Sun's magnetic field is not aligned with the surface rotation axis. This result reinforces the view of our Sun as a common intermediate-mass star. Furthermore this detection challenges and imposes a strong observational constraint to modern solar dynamo theories.
We study the polar magnetism near an activity maximum when these regions change their polarity, from which it is expected that its magnetism should be less affected by the global field. To fully ...characterise the magnetic field vector, we use deep full Stokes polarimetric observations of the 15648.5 Å and 15652.8 Å FeI lines. We observe the north pole as well as a quiet region at disc centre to compare their field distributions. In order to calibrate the projection effects, we observe an additional quiet region at the east limb. We find that the two limb datasets share similar magnetic field vector distributions. This means that close to a maximum, the poles look like typical limb, quiet-Sun regions. However, the magnetic field distributions at the limbs are different from the distribution inferred at disc centre. At the limbs, we infer a new population of magnetic fields with relatively strong intensities (\(\sim\)600-\(\sim\)800 G), inclined by 30 deg with respect to the line of sight, and with an azimuth aligned with the solar disc radial direction. We propose that this new population at the limbs is due to the observation of unresolved magnetic loops as seen close to the limb. These loops have typical granular sizes as measured in the disc centre. At the limbs, where the spatial resolution decreases, we observe them spatially unresolved, which explains the new population of magnetic fields that is inferred. This is the first (indirect) evidence of small-scale magnetic loops outside the disc centre and would imply that these small-scale structures are ubiquitous on the entire solar surface. This result has profound implications for the energetics not only of the photosphere, but also of the outer layers since these loops have been reported to reach the chromosphere and the low corona.
We study the dynamics of plasma along the legs of an arch filament system (AFS) from the chromosphere to the photosphere, observed with high-cadence spectroscopic data from two ground-based solar ...telescopes: the GREGOR telescope (Tenerife) using the GREGOR Infrarred Spectrograph (GRIS) in the He I 10830 Å range and the Swedish Solar Telescope (La Palma) using the CRisp Imaging Spectro-Polarimeter to observe the Ca II 8542 Å and Fe I 6173 Å spectral lines. The temporal evolution of the draining of the plasma was followed along the legs of a single arch filament from the chromosphere to the photosphere. The average Doppler velocities inferred at the upper chromosphere from the He I 10830 Å triplet reach velocities up to 20-24~km~s\(^{-1}\), in the lower chromosphere and upper photosphere the Doppler velocities reach up to 11~km~s\(^{-1}\) and 1.5~km~s\(^{-1}\) in the case of the Ca II 8542 Å and Si I 10827 Å spectral lines, respectively. The evolution of the Doppler velocities at different layers of the solar atmosphere (chromosphere and upper photosphere) shows that they follow the same LOS velocity pattern, which confirm the observational evidence that the plasma drains towards the photosphere as proposed in models of AFSs. The Doppler velocity maps inferred from the lower photospheric Ca I 10839 Å or Fe I 6173 Å spectral lines do not show the same LOS velocity pattern. Thus, there is no evidence that the plasma reaches the lower photosphere. The observations and the nonlinear force-free field extrapolations demonstrate that the magnetic field loops of the AFS rise with time. We found flow asymmetries at different footpoints of the AFS. The NLFFF values of the magnetic field strength give us a clue to explain these flow asymmetries.
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