E. Khomenko

Quiet-Sun inter-network magnetic fields observed in the infrared

This paper presents the results of an investigation of the quiet Suns magnetic field based on high-resolution infrared spectropolarimetric observations obtained with the Tenerife Infrared Polarimeter (TIP) at the German VTT of the Observatorio del Teide. We observed two very quiet regions at disc centre. The seeing was exceptionally good during both observing runs, being excellent during one of them. In both cases the network was intentionally avoided to the extent possible, to focus the analysis on the characteristics of the weak polarization signals of the inter-network regions. We find that the Stokes V profile of Fe  15648 A line in almost 50% of the pixels and Stokes Q and/or U in 20% of the pixels have a signal above 10 −3 (in units of continuum intensity Ic), which is significantly above the noise level of 2−3 × 10 −4 . This implies that we detect fluxes as low as 2 × 10 15 Mx/px. We find evidence that we have detected most of the net flux that is in principle detectable at 1 �� resolution with the Zeeman effect. The observed linear polarization resulting from the transverse Zeeman effect indicates that the magnetic fields have a broad range of inclinations, although most of the pixels show polarization signatures which imply an inclination of about 20 ◦ . Nearly 30% of the selected V-profiles have irregular shapes with 3 or more lobes, suggesting mixed polarities with different LOS velocity within the resolution element. The profiles are classified using a single value decomposition approach. The spatial distribution of the magnetic signal shows that profiles of different classes (having different velocities, splitting, asymmetries) are clustered together and form patches, close to the spatial resolution in size. Most of the field is found to be located in intergranular lanes. The statistical properties of the mainly inter-network field sampled by these observations are presented, showing that most of the observed fields are weak with relatively few kG features. The field strength distribution peaks at 350 G and has a FWHM of 300 G. Other parameters, such as profile asymmetries, filling factors and line-of-sight velocities are also determined and discussed.

Channeling 5 Minute Photospheric Oscillations into the Solar Outer Atmosphere through Small-Scale Vertical Magnetic Flux Tubes

We report two-dimensional MHD simulations which demonstrate that photospheric 5 minute oscillations can leak into the chromosphere inside small-scale vertical magnetic flux tubes. The results of our numerical experiments are compatible with those inferred from simultaneous spectropolarimetric observations of the photosphere and chromosphere obtained with the Tenerife Infrared Polarimeter (TIP) at 10830 A. We conclude that the efficiency of energy exchange by radiation in the solar photosphere can lead to a significant reduction of the cutoff frequency and may allow for the propagation of the 5 minute waves vertically into the chromosphere.

Nonlinear Numerical Simulations of Magneto-Acoustic Wave Propagation in Small-Scale Flux Tubes

We present results of nonlinear, two-dimensional, numerical simulations of magneto-acoustic wave propagation in the photosphere and chromosphere of small-scale flux tubes with internal structure. Waves with realistic periods of three to five minutes are studied, after horizontal and vertical oscillatory perturbations are applied to the equilibrium model. Spurious reflections of shock waves from the upper boundary are minimized by a special boundary condition. This has allowed us to increase the duration of the simulations and to make it long enough to perform a statistical analysis of oscillations. The simulations show that deep horizontal motions of the flux tube generate a slow (magnetic) mode and a surface mode. These modes are efficiently transformed into a slow (acoustic) mode in the vA<cS atmosphere. The slow (acoustic) mode propagates vertically along the field lines, forms shocks, and remains always within the flux tube. It might effectively deposit the energy of the driver into the chromosphere. When the driver oscillates with a high frequency, above the cutoff, nonlinear wave propagation occurs with the same dominant driver period at all heights. At low frequencies, below the cutoff, the dominant period of oscillations changes with height from that of the driver in the photosphere to its first harmonic (half period) in the chromosphere. Depending on the period and on the type of the driver, different shock patterns are observed.

Multi-layer Study of Wave Propagation in Sunspots

We analyze the propagation of waves in sunspots from the photosphere to the chromosphere using time series of co-spatial Ca II H intensity spectra (including its line blends) and polarimetric spectra of Si I 10827 and the He I 10830 multiplet. From the Doppler shifts of these lines we retrieve the variation of the velocity along the line-of-sight at several heights. Phase spectra are used to obtain the relation between the oscillatory signals. Our analysis reveals standing waves at frequencies lower than 4 mHz and a continuous propagation of waves at higher frequencies, which steepen into shocks in the chromosphere when approaching the formation height of the Ca II H core. The observed non-linearities are weaker in Ca II H than in He I lines. Our analysis suggests that the Ca II H core forms at a lower height than the He I 10830 line: a time delay of about 20 s is measured between the Doppler signal detected at both wavelengths. We fit a model of linear slow magnetoacoustic wave propagation in a stratified atmosphere with radiative losses according to Newtons cooling law to the phase spectra and derive the difference in the formation height of the spectral lines. We show that the linear model describes well the wave propagation up to the formation height of Ca II H, where non-linearities start to become very important.

MAGNETO-ACOUSTIC WAVES IN SUNSPOTS: FIRST RESULTS FROM A NEW THREE-DIMENSIONAL NONLINEAR MAGNETOHYDRODYNAMIC CODE

Waves observed in the photosphere and chromosphere of sunspots show complex dynamics and spatial patterns. The interpretation of high-resolution sunspot wave observations requires modeling of three-dimensional (3D) nonlinear wave propagation and mode transformation in the sunspot upper layers in realistic spot model atmospheres. Here, we present the first results of such modeling. We have developed a 3D nonlinear numerical code specially designed to calculate the response of magnetic structures in equilibrium to an arbitrary perturbation. The code solves the 3D nonlinear MHD equations for perturbations; it is stabilized by hyper-diffusivity terms and is fully parallelized. The robustness of the code is demonstrated by a number of standard tests. We analyze several simulations of a sunspot perturbed by pulses of different periods at a subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of 3 and 5 minutes. We present a detailed description of the 3D mode transformation in a non-trivial sunspot-like magnetic field configuration, including the conversion between fast and slow magneto-acoustic waves and the Alfven wave, by calculation of the wave energy fluxes. Our main findings are as follows: (1) the conversion from acoustic to the Alfven mode is only observed if the driving pulse is located out of the sunspot axis, but this conversion is energetically inefficient; (2) as a consequence of the cutoff effects and refraction of the fast magneto-acoustic mode, the energy of the evanescent waves with periods around 5 minutes remains almost completely below the level β = 1; (3) waves with frequencies above the cutoff propagate field aligned to the chromosphere and their power becomes dominating over that of evanescent 5 minute oscillations, in agreement with observations.

MAGNETOHYDROSTATIC SUNSPOT MODELS FROM DEEP SUBPHOTOSPHERIC TO CHROMOSPHERIC LAYERS

In order to understand the influence of magnetic fields on the propagation properties of waves, as derived from different local helioseismology techniques, forward modeling of waves is required. Such calculations need a model in magnetohydrostatic equilibrium as an initial atmosphere through which to propagate oscillations. We provide a method to construct such a model in equilibrium for a wide range of parameters, for use in simulations of artificial helioseismologic data. The method combines the advantages of self-similar solutions and current-distributed models. A set of models is developed by numerical integration of magnetohydrostatic equations from the subphotospheric to chromospheric layers.

THEORETICAL MODELING OF PROPAGATION OF MAGNETOACOUSTIC WAVES IN MAGNETIC REGIONS BELOW SUNSPOTS

We use two-dimensional numerical simulations and eikonal approximation to study properties of magnetohydrodynamic (MHD) waves traveling below the solar surface through the magnetic structure of sunspots. We consider a series of magnetostatic models of sunspots of different magnetic field strengths, from 10 Mm below the photosphere to the low chromosphere. The purpose of these studies is to quantify the effect of the magnetic field on local helioseismology measurements by modeling waves excited by subphotospheric sources. Time-distance propagation diagrams and wave travel times are calculated for models of various field strengths and compared to the nonmagnetic case. The results clearly indicate that the observed time-distance helioseismology signals in sunspot regions correspond to fast MHD waves. The slow MHD waves form a distinctly different pattern in the time-distance diagram, which has not been detected in observations. The numerical results are in good agreement with the solution in the short-wavelength (eikonal) approximation, providing its validation. The frequency dependence of the travel times is in good qualitative agreement with observations.

Solar Fe abundance and magnetic fields - Towards a consistent reference metallicity

Aims. We investigate the impact on Fe abundance determination of including magnetic flux in series of 3D radiationmagnetohydrodynamics (MHD) simulations of solar convection, which we used to synthesize spectral intensity profiles corresponding to disc centre. Methods. Ad ifferential approach is used to quantify the changes in theoretical equivalent width of a set of 28 iron spectral lines spanning a wide range in wavelength, excitation potential, oscillator strength, Lande factor, and formation height. The lines were computed in local thermodynamic equilibrium (LTE) using the spectral synthesis code LILIA. We used input magnetoconvection snapshots covering 50 min of solar evolution and belonging to series having an average vertical magnetic flux density of � Bvert� = 0, 50, 100, and 200 G. For the relevant calculations we used the Copenhagen Stagger code. Results. The presence of magnetic fields causes both a direct (Zeeman-broadening) effect on spectral lines with non-zero Lande factor and an indirect effect on temperature-sensitive lines via a change in the photospheric T − τ stratification. The corresponding correction in the estimated atomic abundance ranges from a few hundredths of a dex up to |Δlog � (Fe)� |∼ 0.15 dex, depending on the spectral line and on the amount of average magnetic flux within the range of values we considered. The Zeeman-broadening effect gains relatively more importance in the IR. The largest modification to previous solar abundance determinations based on visible spectral lines is instead due to the indirect effect, i.e., the line-weakening caused by a warmer stratification as seen on an optical depth scale. Our results indicate that the average solar iron abundance obtained when using magnetoconvection models can be ∼0.03–0.11 dex higher than when using the simpler hydrodynamics (HD) convection approach. Conclusions. We demonstrate that accounting for magnetic flux is important in state-of-the-art solar photospheric abundance determinations based on 3D convection simulations.

Fluid description of multi-component solar partially ionized plasma

We derive self-consistent formalism for the description of multi-component partially ionized solar plasma, by means of the coupled equations for the charged and neutral components for an arbitrary number of chemical species, and the radiation field. All approximations and assumptions are carefully considered. Generalized Ohms law is derived for the single-fluid and two-fluid formalism. Our approach is analytical with some order-of-magnitude support calculations. After general equations are developed we particularize to some frequently considered cases as for the interaction of matter and radiation.

Rayleigh-Taylor instability in prominences from numerical simulations including partial ionization effects

We study the Rayleigh-Taylor instability (RTI) at a prominence-corona transition region in a non-linear regime. Our aim is to understand how the presence of neutral atoms in the prominence plasma influences the instability growth rate, and the evolution of velocity, magnetic field vector and thermodynamic parameters of turbulent drops. We perform 2.5D numerical simulations of the instability initiated by a multi-mode perturbation at the corona-prominence interface using a single-fluid MHD approach including a generalized Ohms law. The initial equilibrium configuration is purely hydrostatic and contains a homogeneous horizontal magnetic field forming an angle with the direction in which the plasma is perturbed. We analyze simulations with two different orientations of the magnetic field. For each field orientation we compare two simulations, one for the pure MHD case, and one including the ambipolar diffusion in the Ohms law (AD case). Other than that, both simulations for each field orientation are identical. The numerical results in the initial stage of the instability are compared with the analytical linear calculations. We find that the configuration is always unstable in the AD case. The growth rate of the small-scale modes in the non-linear regime is up to 50% larger in the AD case than in the purely MHD case and the average velocities of flows are a few percent larger. Significant drift momenta are found at the interface between the coronal and the prominence material at all stages of the instability, produced by the faster downward motion of the neutral component with respect to the ionized component. The differences in temperature of the bubbles between the ideal and non-ideal case are also significant, reaching 30%. There is an asymmetry between large rising bubbles and small-scale down flowing fingers, favoring the detection of upward velocities in observations.