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Inferences of the magnetic field in the solar atmosphere by means of spectropolarimetric inversions (i.e., Stokes inversion codes) yield magnetic fields that are non-solenoidal($\nabla\cdot{\bf B} \ne 0$). Because of this, results obtained by such methods are sometimes put into question. We aim to develop and implement a new technique that can retrieve magnetic fields that are simultaneously consistent with observed polarization signals and with the null divergence condition. The method used in this work strictly imposes $\nabla\cdot{\bf B}=0$ by determining the vertical component of the magnetic field ($B_{\rm z}$) from the horizontal ones ($B_{\rm x},B_{\rm y}$). We implement this solenoidal inversion into the FIRTEZ Stokes inversion code and apply it to spectropolarimetric observations of a sunspot observed with the Hinode/SP instrument. We show that the solenoidal inversion retrieves a vertical component of the magnetic field that is consistent with the vertical component of the magnetic field inferred from the non-solenoidal one. We demonstrate that the solenoidal inversion is capable of a better overall fitting to the observed Stokes vector than the non-solenoidal inversion. In fact, the solenoidal magnetic field fits Stokes $V$ worse, but this is compensated by a better fit to Stokes $I$. We find a direct correlation between the worsening in the fit to the circular polarization profiles by the solenoidal inversion and the deviations in the inferred $B_{\rm z}$ with respect to the non-solenoidal inversion. These results support the idea that common Stokes inversion techniques fail to reproduce $\nabla\cdot{\bf B}=0$ mainly as a consequence of the uncertainties in the determination of the individual components of the magnetic field., Comment: 10 pages, 10 figures, accepted for publication in Astronomy & Astrophysics

The importance of the quiet-Sun magnetism is that it is always there to a greater or lesser extent, being a constant provider of energy, independently of the solar cycle phase. The open questions about the quiet-Sun magnetism include those related to its origin. Most people claim that the local dynamo action is the mechanism that causes it. This fact would imply that the quiet-Sun magnetism is nearly the same at any location over the solar surface and at any time. Many works claim that the quiet Sun does not have any variation at all, although a few of them raise doubt on this claim and find mild evidence of a cyclic variation in the the quiet-Sun magnetism. In this work, we detect clear variations in the internetwork magnetism both with latitude and solar cycle. In terms of latitude, we find an increase in the averaged magnetic fields toward the solar poles. We also find long-term variations in the averaged magnetic field at the disk center and solar poles, and both variations are almost anticorrelated. These findings do not support the idea that the local dynamo action is the unique factory of the quiet-Sun magnetism., Comment: 8 pages, 4 figures, 1 table

This paper describes an adaptation of the Optimal Localized Averaging (OLA) inversion technique, originally developed for geo- and helioseismological applications, to the interpretation of solar spectroscopic data. It focuses on inverting the thermodynamical properties of the solar atmosphere assuming that the atmosphere and radiation field are in Local Thermodynamic Equilibrium (LTE). We leave inversions for magnetic field and non-LTE inversions for future work. The advantage with the OLA method is that it computes solutions that are optimally resolved (in depth) with minimal cross-talk error between variables. Additionally, the method allows for direct assessment of the vertical resolution of the inverted solutions. The primary challenges faced when adapting the method to spectroscopic inversions originate with the possible large amplitude differences between the atmospheric model used to initiate the inversion and the underlying atmosphere it aims to recover, necessitating the development of an iterative scheme. Here we describe the iterative OLA method we have developed for both single and multi-variable inversions and demonstrate its performance on simulated data and synthesized spectra. We note that when carrying out multi-variable inversions, employing response function amplification factors can address the inherent spectral-sensitivity bias that makes it hard to invert for less spectrally-sensitive variables. The OLA method can, in most cases, reliably invert as well as or better than the frequently employed Stokes Inversion based on Response functions (SIR) scheme, however some difficulties remain. In particular, the method struggles to recover large-scale offsets in the atmospheric stratification. We propose future strategies to improve this aspect., Comment: 18 pages, 9 figures. Submitted to ApJ

The suitability of solar pores as magnetic wave guides has been a key topic of discussion in recent years. Here we present observational evidence of propagating magnetohydrodynamic wave activity in a group of five photospheric solar pores. Employing data obtained by the Facility Infrared Spectropolarimeter at the Dunn Solar Telescope, oscillations with periods on the order of 5 minutes were detected at varying atmospheric heights by examining Si I 10827 \r{A} line bisector velocities. Spectropolarimetric inversions, coupled with the spatially resolved root mean square bisector velocities, allowed the wave energy fluxes to be estimated as a function of atmospheric height for each pore. We find propagating magnetoacoustic sausage mode waves with energy fluxes on the order of 30 kW/m$^{2}$ at an atmospheric height of 100 km, dropping to approximately 2 kW/m$^{2}$ at an atmospheric height of around 500 km. The cross-sectional structuring of the energy fluxes reveals the presence of both body- and surface-mode sausage waves. Examination of the energy flux decay with atmospheric height provides an estimate of the damping length, found to have an average value across all 5 pores of $L_d \approx 268$km, similar to the photospheric density scale height. We find the damping lengths are longer for body mode waves, suggesting that surface mode sausage oscillations are able to more readily dissipate their embedded wave energies. This work verifies the suitability of solar pores to act as efficient conduits when guiding magnetoacoustic wave energy upwards into the outer solar atmosphere., Comment: 20 pages, 9 figures, Accepted for publication in PHILOS T R SOC A

Photospheric vortex flows are thought to play a key role in the evolution of magnetic fields. Recent studies show that these swirling motions are ubiquitous in the solar surface convection and occur in a wide range of temporal and spatial scales. Their interplay with magnetic fields is poorly characterized, however. We study the relation between a persistent photospheric vortex flow and the evolution of a network magnetic element at a supergranular vertex. We used long-duration sequences of continuum intensity images acquired with Hinode and the local correlation-tracking method to derive the horizontal photospheric flows. Supergranular cells are detected as large-scale divergence structures in the flow maps. At their vertices, and cospatial with network magnetic elements, the velocity flows converge on a central point. One of these converging flows is observed as a vortex during the whole 24 h time series. It consists of three consecutive vortices that appear nearly at the same location. At their core, a network magnetic element is also detected. Its evolution is strongly correlated to that of the vortices. The magnetic feature is concentrated and evacuated when it is caught by the vortices and is weakened and fragmented after the whirls disappear. This evolutionary behavior supports the picture presented previously, where a small flux tube becomes stable when it is surrounded by a vortex flow., Comment: 6 pages, 3 figures, accepted for publication in A&A

Since the early 1970s, inversion techniques have become the most useful tool for inferring the magnetic, dynamic, and thermodynamic properties of the solar atmosphere. The intrinsic model dependence makes it necessary to formulate specific means that include the physics in a properly quantitative way. The core of this physics lies in the radiative transfer equation (RTE), where the properties of the atmosphere are assumed to be known while the unknowns are the four Stokes profiles. The solution of the (differential) RTE is known as the direct or forward problem. From an observational point of view, the problem is rather the opposite: the data are made up of the observed Stokes profiles and the unknowns are the solar physical quantities. Inverting the RTE is therefore mandatory. Indeed, the formal solution of this equation can be considered an integral equation. The solution of such an integral equation is called the inverse problem. Inversion techniques are automated codes aimed at solving the inverse problem. The foundations of inversion techniques are critically revisited with an emphasis on making explicit the many assumptions underlying each of them. An incremental complexity procedure is advised for the implementation in practice. Coarse details of the profiles or coarsely sam- pled profiles should be reproduced first with simple model atmospheres (with, for example, a few physical quantities that are constant with optical depth). If the Stokes profiles are well sampled and differences between synthetic and observed ones are greater than the noise, then the inversion should proceed by using more complex models (that is, models where physical quantities vary with depth or, eventually, with more than one component). Significant im- provements are expected as well from the use of new inversion techniques that take the spatial degradation by the instruments into account., Comment: Invited review accepted for publication in Living Reviews in Solar Physics. 84 pages, 30 figures

We analyze spectropolarimetric data taken with the Hinode spacecraft in quiet solar regions at the disk center. Distorted redshifted Stokes $V$ profiles are found showing a characteristic evolution that always follows the same sequence of phases. We have studied the statistical properties of these events using spectropolarimetric data from Hinode/SP. We also examined the upper photosphere and the low chromosphere using Mg i b2 and Ca ii h data from Hinode. Finally, we have applied the SIRGAUSS inversion code to the polarimetric data in order to infer the atmospheric stratification of the physical parameters. We have also obtained these physical parameters taking into account dynamical terms in the equation of motion. The Stokes V profiles display a bump that evolves in four different time steps, and the total process lasts 108 seconds. The Stokes I shows a strongly bent red wing and the continuum signal exhibits a bright point inside an intergranular lane. This bright point is correlated with a strong redshift in the Mg i b2 line and a bright feature in Ca ii h images. The model obtained from the inversion of the Stokes profiles is hotter than the average quiet-Sun model, with a vertical magnetic field configuration and field strengths in the range of kG values. It also presents a LOS velocity stratification with a Gaussian perturbation whose center is moving to deeper layers with time. We have examined a particular type of event that can be described as a plasmoid of hot plasma that is moving downward from the top of the photosphere, placed over intergranular lanes and always related to strong magnetic field concentrations. We argue that the origin of this plasmoid could be a magnetic reconnection that is taking place in the chromosphere., Comment: 18 pages, 14 figures

The aim of this work is the determination of the twist, writhe, and self magnetic helicity of penumbral filaments located in an inner Sunspot penumbra. To this extent, we inverted data taken with the spectropolarimeter (SP) aboard Hinode with the SIR (Stokes Inversion based on Response function) code. For the construction of a 3D geometrical model we applied a genetic algorithm minimizing the divergence of the magnetic field vector and the net magnetohydrodynamic force, consequently a force-free solution would be reached if possible. We estimated two proxies to the magnetic helicity frequently used in literature: the force-free parameter and the current helicity term. We show that both proxies are only qualitative indicators of the local twist as the magnetic field in the area under study significantly departures from a force-free configuration. The local twist shows significant values only at the borders of bright penumbral filaments with opposite signs on each side. These locations are precisely correlated to large electric currents. The average twist (and writhe) of penumbral structures is very small. The spines (dark filaments in the background) show a nearly zero writhe. The writhe per unit length of the intraspines diminishes with increasing length of the tube axes. Thus, the axes of tubes related to intraspines are less wrung when the tubes are more horizontal. As the writhe of the spines is very small, we can conclude that the writhe reaches only significant values when the tube includes the border of a intraspine., Comment: 7 pages, 4 figures; Astrophysical Journal, in press

Spectra of late-type stars are usually analyzed with static model atmospheres in local thermodynamic equilibrium (LTE) and a homogeneous plane-parallel or spherically symmetric geometry. The energy balance requires particular attention, as two elements which are particularly difficult to model play an important role: line blanketing and convection. Inversion techniques are able to bypass the difficulties of a detailed description of the energy balance. Assuming that the atmosphere is in hydrostatic equilibrium and LTE, it is possible to constrain its structure from spectroscopic observations. Among the most serious approximations still implicit in the method is a static and homogeneous geometry. In this paper, we take advantage of a realistic three-dimensional radiative hydrodynamical simulation of the solar surface to check the systematic errors incurred by an inversion assuming a plane-parallel horizontally-homogeneous atmosphere. The thermal structure recovered resembles the spatial and time average of the three-dimensional atmosphere. Furthermore, the abundances retrieved are typically within 10% (0.04 dex) of the abundances used to construct the simulation. The application to a fairly complete dataset from the solar spectrum provides further confidence in previous analyses of the solar composition. There is only a narrow range of one-dimensional thermal structures able to fit the absorption lines in the spectrum of the Sun. With our carefully selected dataset, random errors are about a factor of two smaller than systematic errors. A small number of strong metal lines can provide very reliable results. We foresee no major difficulty in applying the technique to other similar stars, and obtaining similar accuracies, using spectra with a resolving power about 50,000 and a signal-to-noise ratio as low as 30., Comment: 65 pages, figures included; uses aastex; to appear in The Astrophysical Journal

An inversion technique to recover LTE one-dimensional model photospheres for late-type stars, which was previously applied to the Sun (Allende Prieto et al. 1998), is now employed to reconstruct, semi-empirically, the photospheres of cooler dwarfs: the metal-poor Gmb1830 and the active star of solar-metallicity Eps Eri. The model atmospheres we find reproduce satisfactorily all the considered weak-to-moderate neutral lines of metals, satisfying in detail the excitation equilibrium of iron, the wings of strong lines, and the slope of the optical continuum. The retrieved models show a slightly steeper temperature gradient than flux-constant model atmospheres in the layers where log tau <= -0.5. We argue that these differences should reflect missing ingredients in the flux-constant models and point to granular-like inhomogeneities as the best candidate. The iron ionization equilibrium is well satisfied by the model for Gmb1830, but not for Eps Eri, for which a discrepancy of 0.2 dex between the logarithmic iron abundance derived from neutral and singly ionized lines may signal departures from LTE. The chemical abundances of calcium, titanium, chromium, and iron derived with the empirical models from neutral lines do not differ much from previous analyses based on flux-constant atmospheric structures., Comment: 27 pages, AASTEX; 9 Figures (12 PostScript files); to be published in The Astrophysical Journal

An inversion technique has been developed to recover LTE one-dimensional model photospheres for late-type stars from very high resolution, high signal-to-noise stellar line profiles. It is successfully applied to the Sun by using a set of clean Ti I, Ca I, Cr I, and Fe I normalized line profiles with accurate transition probabilities and taking advantage of the well understood collisional enhancement of the wings of the Ca I line at 6162 A. Line and continuum center-to-limb variations, continuum flux, and wings of strong metal lines are synthesized by means of the model obtained and are compared with solar observations, as well as with predictions from other well known theoretical and empirical solar models, showing the reliability of the inversion procedure. The prospects for and limitations of the application of this method to other late-type stars are discussed., Comment: 28 pages, 8 figures; uses aasms4; accepted for publication in ApJ