Using the infrared iron lines to probe solar subsurface convection

Studying the properties of the solar convection using high-resolution spectropolarimetry began in the early 90's with the focus on observations in the visible wavelength regions. Its extension to the infrared (IR) remains largely unexplored. The IR iron lines around 15600\,$\rm{\AA}$, most commonly known for their high magnetic sensitivity, also have a non-zero response to line-of-sight velocity below $\log (\tau)=0.0$. In this paper we aim to tap this potential to explore the possibility of using them to measure sub-surface convective velocities. By assuming a snapshot of a three-dimensional magnetohydrodynamic simulation to represent the quiet Sun, we investigate how well the iron IR lines can reproduce the LOS velocity in the cube and up to what depth. We use the recently developed spectropolarimetric inversion code SNAPI and discuss the optimal node placements for the retrieval of reliable results from these spectral lines. We find that the IR iron lines can measure the convective velocities down to $\log (\tau)=0.5$, below the photosphere, not only at original resolution of the cube but also when degraded with a reasonable spectral and spatial PSF and stray light. Meanwhile, the commonly used Fe~{\sc i} 6300\,\AA{} line pair performs significantly worse. Our investigation reveals that the IR iron lines can probe the subsurface convection in the solar photosphere. This paper is a first step towards exploiting this diagnostic potential.Comment: 11 pages, Accepted for publication in Astronomy and Astrophysic

Using Realistic MHD Simulations for Modeling and Interpretation of Quiet-Sun Observations with the Solar Dynamics Observatory Helioseismic and Magnetic Imager

The solar atmosphere is extremely dynamic, and many important phenomena develop on small scales that are unresolved in observations with the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO). For correct calibration and interpretation of the observations, it is very important to investigate the effects of small-scale structures and dynamics on the HMI observables, such as Doppler shift, continuum intensity, spectral line depth, and width. We use 3D radiative hydrodynamics simulations of the upper turbulent convective layer and the atmosphere of the Sun, and a spectro-polarimetric radiative transfer code to study observational characteristics of the Fe I 6173A line observed by HMI in quiet-Sun regions. We use the modeling results to investigate the sensitivity of the line Doppler shift to plasma velocity, and also sensitivities of the line parameters to plasma temperature and density, and determine effective line formation heights for observations of solar regions located at different distances from the disc center. These estimates are important for the interpretation of helioseismology measurements. In addition, we consider various center-to-limb effects, such as convective blue-shift, variations of helioseismic travel-times, and the 'concave' Sun effect, and show that the simulations can qualitatively reproduce the observed phenomena, indicating that these effects are related to a complex interaction of the solar dynamics and radiative transfer.Comment: 21 pages, 10 figures, accepted for publication in Ap

Measurements of Photospheric and Chromospheric Magnetic Fields

The Sun is replete with magnetic fields, with sunspots, pores and plage regions being their most prominent representatives on the solar surface. But even far away from these active regions, magnetic fields are ubiquitous. To a large extent, their importance for the thermodynamics in the solar photosphere is determined by the total magnetic flux. Whereas in low-flux quiet Sun regions, magnetic structures are shuffled around by the motion of granules, the high-flux areas like sunspots or pores effectively suppress convection, leading to a temperature decrease of up to 3000 K. The importance of magnetic fields to the conditions in higher atmospheric layers, the chromosphere and corona, is indisputable. Magnetic fields in both active and quiet regions are the main coupling agent between the outer layers of the solar atmosphere, and are therefore not only involved in the structuring of these layers, but also for the transport of energy from the solar surface through the corona to the interplanetary space. Consequently, inference of magnetic fields in the photosphere, and especially in the chromosphere, is crucial to deepen our understanding not only for solar phenomena such as chromospheric and coronal heating, flares or coronal mass ejections, but also for fundamental physical topics like dynamo theory or atomic physics. In this review, we present an overview of significant advances during the last decades in measurement techniques, analysis methods, and the availability of observatories, together with some selected results. We discuss the problems of determining magnetic fields at smallest spatial scales, connected with increasing demands on polarimetric sensitivity and temporal resolution, and highlight some promising future developments for their solution.Comment: Accepted for publication in "Space Science Reviews"; 42 pages, 16 figure

Measuring the Wilson depression of sunspots using the divergence-free condition of the magnetic field vector

Context: The Wilson depression is the difference in geometric height of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Aims: We aim at developing a robust method for deriving the Wilson depression that only requires the information about the magnetic field that is accessible from spectropolarimetry, and that does not rely on assumptions on the geometry of sunspots or on their magnetic field. Methods: Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We focus on large spatial scales only in order to reduce the number of free parameters. Results: We test the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we apply the method to Hinode observations of a sunspot. The derived Wilson depression (about 600 km) is consistent with results typically obtained from the Wilson effect. We also find that the Wilson depression obtained from using horizontal force balance gives 110 - 180 km smaller Wilson depressions than both, what we find and what we deduce directly from the simulations. This suggests that the magnetic pressure and the magnetic curvature force contribute to the Wilson depression by a similar amount.Comment: 12 pages, 8 figures. Accepted for publication in Astronomy & Astrophysic

Vigorous convection in a sunspot granular light bridge

Light bridges are the most prominent manifestation of convection in sunspots. The brightest representatives are granular light bridges composed of features that appear to be similar to granules. An in-depth study of the convective motions, temperature stratification, and magnetic field vector in and around light bridge granules is presented with the aim of identifying similarities and differences to typical quiet-Sun granules. Spectropolarimetric data from the Hinode Solar Optical Telescope were analyzed using a spatially coupled inversion technique to retrieve the stratified atmospheric parameters of light bridge and quiet-Sun granules. Central hot upflows surrounded by cooler fast downflows reaching 10 km/s clearly establish the convective nature of the light bridge granules. The inner part of these granules in the near surface layers is field free and is covered by a cusp-like magnetic field configuration. We observe hints of field reversals at the location of the fast downflows. The quiet-Sun granules in the vicinity of the sunspot are covered by a low-lying canopy field extending radially outward from the spot. The similarities between quiet-Sun and light bridge granules point to the deep anchoring of granular light bridges in the underlying convection zone. The fast, supersonic downflows are most likely a result of a combination of invigorated convection in the light bridge granule due to radiative cooling into the neighboring umbra and the fact that we sample deeper layers, since the downflows are immediately adjacent to the slanted walls of the Wilson depression.Comment: 10 pages, 11 figure

Evershed and counter-Evershed flows in sunspot MHD simulations

There have been a few reports in the literature of counter-Evershed flows observed in well developed sunspot penumbrae, i.e. flows directed towards the umbra along penumbral filaments. Here we investigate the driving forces of such counter-Evershed flows in a radiative magnetohydrodynamic simulation of a sunspot and compare them with the forces acting on the normal Evershed flow. The simulation covers a timespan of 100 solar hours and generates an Evershed outflow exceeding 8 km s$^{-1}$ in the penumbra along radially aligned filaments where the magnetic field is almost horizontal. Additionally, the simulation produces a fast counter-Evershed flow (i.e., an inflow near $\tau = 1$) in some regions within the penumbra, reaching peak flow speeds of $\sim$12 km s$^{-1}$. The counter-Evershed flows are transient and typically last a few hours before they turn into outflows again. By using the kinetic energy equation and evaluating its various terms in the simulation box, we found that the Evershed flow occurs due to overturning convection in a strongly inclined magnetic field while the counter-Evershed flows can be well described as siphon flows.Comment: Paper accepted for publication in The Astrophysical Journa

The Height of Chromospheric Loops in an Emerging Flux Region

Context. The chromospheric layer observable with the He I 10830 {\AA} triplet is strongly warped. The analysis of the magnetic morphology of this layer therefore requires a reliable technique to determine the height at which the He I absorption takes place. Aims. The He I absorption signature connecting two pores of opposite polarity in an emerging flux region is investigated. This signature is suggestive of a loop system connecting the two pores. We aim to show that limits can be set on the height of this chromospheric loop system. Methods. The increasing anisotropy in the illumination of a thin, magnetic structure intensifies the linear polarization signal observed in the He I triplet with height. This signal is altered by the Hanle effect. We apply an inversion technique incorporating the joint action of the Hanle and Zeeman effects, with the absorption layer height being one of the free parameters. Results. The observed linear polarization signal can be explained only if the loop apex is higher than \approx5 Mm. Best agreement with the observations is achieved for a height of 6.3 Mm. Conclusions. The strength of the linear polarization signal in the loop apex is inconsistent with the assumption of a He I absorption layer at a constant height level. The determined height supports the earlier conclusion that dark He 10830 {\AA} filaments in emerging flux regions trace emerging loops.Comment: 7 pages, 4 figure

Quiet Sun magnetic fields observed by Hinode: Support for a local dynamo

The Hinode mission has revealed copious amounts of horizontal flux covering the quiet Sun. Local dynamo action has been proposed to explain the presence of this flux. We sought to test whether the quiet Sun flux detected by Hinode is due to a local or the global dynamo by studying long-term variations in the polarisation signals detectable at the disc centre of the quiet Sun between November 2006 and May 2012, with particular emphasis on weak signals in the internetwork. The investigation focusses on line-integrated circular polarisation V_tot and linear polarisation LP_tot profiles obtained from the Fe I 6302.5 \AA absorption line in Hinode SOT/SP. Both circular and linear polarisation signals show no overall variation in the fraction of selected pixels from 2006 until 2012. There is also no variation in the magnetic flux in this interval of time. The probability density functions (PDF) of the line-of-sight magnetic flux can be fitted with a power law from 1.17 x 10^17 Mx to 8.53 x 10^18 Mx with index \alpha=-1.82 \pm 0.02 in 2007. The variation of \alpha 's across all years does not exceed a significance of 1\sigma. Linearly polarised features are also fitted with a power law, with index \alpha=-2.60 \pm 0.06 in 2007. Indices derived from linear polarisation PDFs of other years also show no significant variation. Our results show that the ubiquitous horizontal polarisation on the edges of bright granules seen by Hinode are invariant during the minimum of cycle 23. This supports the notion that the weak circular and linear polarisation is primarily caused by an independent local dynamo

Vertical magnetic field gradient in the photospheric layers of sunspots

We investigate the vertical gradient of the magnetic field of sunspots in the photospheric layer. Independent observations were obtained with the SOT/SP onboard the Hinode spacecraft and with the TIP-2 mounted at the VTT. We apply state-of-the-art inversion techniques to both data sets to retrieve the magnetic field and the corresponding vertical gradient. In the sunspot penumbrae we detected patches of negative vertical gradients of the magnetic field strength, i.e.,the magnetic field strength decreases with optical depth in the photosphere. The negative gradient patches are located in the inner and partly in the middle penumbrae in both data sets. From the SOT/SP observations, we found that the negative gradient patches are restricted mainly to the deep photospheric layers and are concentrated near the edges of the penumbral filaments. MHD simulations also show negative gradients in the inner penumbrae, also at the locations of filaments. Both in the observations and simulation negative gradients of the magnetic field vs. optical depth dominate at some radial distances in the penumbra. The negative gradient with respect to optical depth in the inner penumbrae persists even after averaging in the azimuthal direction, both in the observations and, to a lesser extent, also in MHD simulations. We interpret the observed localized presence of the negative vertical gradient of the magnetic field strength in the observations as a consequence of stronger field from spines expanding with height and closing above the weaker field inter-spines. The presence of the negative gradients with respect to optical depth after azimuthal averaging can be explained by two different mechanisms: the high corrugation of equal optical depth surfaces and the cancellation of polarized signal due to the presence of unresolved opposite polarity patches in the deeper layers of the penumbra.Comment: 17 pages, 25 figures, accepted for publication in A&

Milne-Eddington inversions of the He I 10830 {\AA} Stokes profiles: Influence of the Paschen-Back effect

The Paschen-Back effect influences the Zeeman sublevels of the He I multiplet at 10830 {\AA}, leading to changes in strength and in position of the Zeeman components of these lines. We illustrate the relevance of this effect using synthetic Stokes profiles of the He I 10830 {\AA} multiplet lines and investigate its influence on the inversion of polarimetric data. We invert data obtained with the Tenerife Infrared Polarimeter (TIP) at the German Vacuum Tower Telescope (VTT). We compare the results of inversions based on synthetic profiles calculated with and without the Paschen-Back effect being included. We find that when taking into account the incomplete Paschen-Back effect, on average 16% higher field strength values are obtained. We also show that this effect is not the main cause for the area asymmetry exhibited by many He I 10830 Stokes V-profiles. This points to the importance of velocity and magnetic field gradients over the formation height range of these lines.Comment: Accepted for publication in A&A on Jun 12th 200