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

Three-dimensional magnetic structure of a sunspot: comparison of the photosphere and upper chromosphere

We investigate the magnetic field of a sunspot in the upper chromosphere and compare it to the field's photospheric properties. We observed the main leading sunspot of the active region NOAA 11124 on two days with the Tenrife Infrared Polarimeter-2 (TIP-2) mounted at the German Vacuum Tower Telescope (VTT). Through inversion of Stokes spectra of the He I triplet at 1083.0 nm, we obtained the magnetic field vector of the upper chromosphere. For comparison with the photosphere we applied height-depended inversions of the Si I 1082.71 nm and Ca I 1083.34 nm lines. We found that the umbral magnetic field strength in the upper chromosphere is lower by a factor of 1.30-1.65 compared to the photosphere. The magnetic field strength of the umbra decreases from the photosphere towards the upper chromosphere by an average rate of 0.5-0.9 G km$^{-1}$. The difference in the magnetic field strength between both atmospheric layers steadily decreases from the sunspot center to the outer boundary of the sunspot, with the field (in particular its horizontal component) being stronger in the chromopshere outside the spot, suggestive of a magnetic canopy. The sunspot displays a twist that on average is similar in the two layers. However, the differential twist between photosphere and chromosphere increases rapidly towards the outer penumbral boundary. The magnetic field vector is more horizontal with respect to the solar surface by roughly 5-20$^\circ$ in the photosphere compared to the upper chromosphere. Above a lightbridge, the chromospheric magnetic field is equally strong as that in the umbra, whereas the lightbridge's field is weaker than its surroundings in the photosphere by roughly 1 kG. This suggests a cusp-like magnetic field structure above the lightbridge.Comment: 12 pages, 15 figures, accepted for publication in A&

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

Structure of sunspot penumbral filaments: a remarkable uniformity of properties

The sunspot penumbra comprises numerous thin, radially elongated filaments that are central for heat transport within the penumbra, but whose structure is still not clear. To investigate the fine-scale structure of these filaments, we perform a depth-dependent inversion of spectropolarimetric data of a sunspot very close to solar disk center obtained by Hinode (SOT/SP). We have used a recently developed spatially coupled 2D inversion scheme which allows us to analyze the fine structure of individual penumbral filaments up to the diffraction limit of the telescope. Filaments of different sizes in all parts of penumbra display very similar magnetic field strengths, inclinations and velocity patterns. The similarities allowed us to average all these filaments and to extract the physical properties common to all of them. This average filament shows upflows associated with an upward pointing field at its inner, umbral end and along its axis, downflows along the lateral edge and strong downflows in the outer end associated with a nearly vertical, strong and downward pointing field. The upflowing plasma is significantly hotter than the downflowing plasma. The hot, tear-shaped head of the averaged filament can be associated with a penumbral grain. The central part of the filament shows nearly horizontal fields with strengths of ~1kG. The field above the filament converges, whereas a diverging trend is seen in the deepest layers near the head of the filament. We put forward a unified observational picture of a sunspot penumbral filament. It is consistent with such a filament being a magneto-convective cell, in line with recent MHD simulations. The uniformity of its properties over the penumbra sets constraints on penumbral models and simulations. The complex and inhomogeneous structure of the filament provides a natural explanation for a number of long-running controversies in the literature.Comment: 19 pages; 12 figures; accepted for publication in A&

Solar-Cycle Variation of quiet-Sun Magnetism and Surface Gravity Oscillation Mode

The origin of the quiet Sun magnetism is under debate. Investigating the solar cycle variation observationally in more detail can give us clues about how to resolve the controversies. We investigate the solar cycle variation of the most magnetically quiet regions and their surface gravity oscillation ($f$-) mode integrated energy ($E_f$). We use 12 years of HMI data and apply a stringent selection criteria, based on spatial and temporal quietness, to avoid any influence of active regions (ARs). We develop an automated high-throughput pipeline to go through all available magnetogram data and to compute $E_f$ for the selected quiet regions. We observe a clear solar cycle dependence of the magnetic field strength in the most quiet regions containing several supergranular cells. For patch sizes smaller than a supergranular cell, no significant cycle dependence is detected. The $E_f$ at the supergranular scale is not constant over time. During the late ascending phase of Cycle 24 (SC24, 2011-2012), it is roughly constant, but starts diminishing in 2013, as the maximum of SC24 is approached. This trend continues until mid-2017, when hints of strengthening at higher southern latitudes are seen. Slow strengthening continues, stronger at higher latitudes than at the equatorial regions, but $E_f$ never returns back to the values seen in 2011-2012. Also, the strengthening trend continues past the solar minimum, to the years when SC25 is already clearly ascending. Hence the $E_f$ behavior is not in phase with the solar cycle. The anticorrelation of $E_f$ with the solar cycle in gross terms is expected, but the phase shift of several years indicates a connection to the poloidal large-scale magnetic field component rather than the toroidal one. Calibrating AR signals with the QS $E_f$ does not reveal significant enhancement of the $f$-mode prior to AR emergence.Comment: 10 pages, 11 figures, submitted to Astronomy & Astrophysic

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&

Magnetic fields inferred by Solar Orbiter: A comparison between SO/PHI-HRT and SDO/HMI

Context. The High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager on board the Solar Orbiter spacecraft (SO/PHI) and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both infer the photospheric magnetic field from polarised light images. SO/PHI is the first magnetograph to move out of the Sun–Earth line and will provide unprecedented access to the Sun’s poles. This provides excellent opportunities for new research wherein the magnetic field maps from both instruments are used simultaneously. Aims. We aim to compare the magnetic field maps from these two instruments and discuss any possible differences between them. Methods. We used data from both instruments obtained during Solar Orbiter’s inferior conjunction on 7 March 2022. The HRT data were additionally treated for geometric distortion and degraded to the same resolution as HMI. The HMI data were re-projected to correct for the 3° separation between the two observatories. Results. SO/PHI-HRT and HMI produce remarkably similar line-of-sight magnetograms, with a slope coefficient of 0.97, an offset below 1 G, and a Pearson correlation coefficient of 0.97. However, SO/PHI-HRT infers weaker line-of-sight fields for the strongest fields. As for the vector magnetic field, SO/PHI-HRT was compared to both the 720-second and 90-second HMI vector magnetic field: SO/PHI-HRT has a closer alignment with the 90-second HMI vector. In the weak signal regime (< 600 G), SO/PHI-HRT measures stronger and more horizontal fields than HMI, very likely due to the greater noise in the SO/PHI-HRT data. In the strong field regime (≳600 G), HRT infers lower field strengths but with similar inclinations (a slope of 0.92) and azimuths (a slope of 1.02). The slope values are from the comparison with the HMI 90-second vector. Possible reasons for the differences found between SO/PHI-HRT and HMI magnetic field parameters are discussed.Sección Deptal. de Óptica (Óptica)Fac. de Óptica y OptometríaTRUEBMWi - Bundesministerium für Wirtschaft und Energie (Alemania)AEI/MCIN/10.13039/501100011033Ministerio de ciencia e innovación de EspañaInstituto Astrofísico de Andalucía (España)Agencia Estatal de Investigación (España)Fondo Europeo de Desarrollo Regional (Fondos FEDER)Centre national d'études spatiales (CNES) (Francia)CSIC (Centro Superior de Investigaciones Científicas) (España)pu

Observations of Running Waves in a Sunspot Chromosphere

Abstract. Spectropolarimetric time series data of the primary spot of active region NOAA 9448 were obtained in the Si I 10827˚A line and the He I10830˚A multiplet with the Tenerife Infrared Polarimeter. Throughout the time series the spectrograph slit was fixed over a region covering umbra, a light bridge, penumbra, and quiet sun. We present speeds of running penumbral waves in the chromosphere, their relation to both photospheric and chromospheric umbral oscillations, and their dependence on the magnetic field topology. 1