Quiet Sun Photosphere Research Articles

One-dimensional, geometrically stratified semi-empirical models of the quiet-Sun photosphere and lower chromosphere

One-dimensional, semi-empirical models of the solar atmosphere are widely employed in numerous contexts within solar physics, ranging from the determination of element abundances and atomic parameters to studies of the solar irradiance and from Stokes inversions to coronal extrapolations. These models provide the physical parameters (i.e. temperature, gas pressure, etc.) in the solar atmosphere as a function of the continuum optical depth $ c $. The transformation to the geometrical $z$ scale (i.e. vertical coordinate) is provided via vertical hydrostatic equilibrium. Our aim is to provide updated, one-dimensional, semi-empirical models of the solar atmosphere as a function of $z,$ but employing the more general case of three-dimensional magneto-hydrostatic equilibrium (MHS) instead of vertical hydrostatic equilibrium (HE). We employed a recently developed Stokes inversion code that, along with non-local thermodynamic equilibrium effects, considers MHS instead of HE. This code is applied to spatially and temporally resolved spectropolarimetric observations of the quiet Sun obtained with the CRISP instrument attached to the Swedish Solar Telescope. We provide average models for granules, intergranules, dark magnetic elements, and overall quiet-Sun as a function of both $ c $ and $z$ from the photosphere to the lower chromosphere. We demonstrate that, in these quiet-Sun models, the effect of considering MHS instead of HE is negligible. However, employing MHS increases the consistency of the inversion results before averaging. We surmise that in regions with stronger magnetic fields (i.e. pores, sunspots, network) the benefits of employing the magneto-hydrostatic approximation will be much more palpable.

Quantifying Poynting Flux in the Quiet Sun Photosphere

Poynting flux is the flux of magnetic energy, which is responsible for chromospheric and coronal heating in the solar atmosphere. It is defined as a cross product of the electric and magnetic fields, and in ideal MHD conditions it can be expressed in terms of the magnetic field and plasma velocity. Poynting flux has been computed for active regions and plages, but estimating it in the quiet Sun (QS) remains challenging due to resolution effects and polarimetric noise. However, with the upcoming DKIST capabilities, such estimations will become more feasible than ever before. Here, we study QS Poynting flux in SUNRISE/IMaX observations and MURaM simulations. We explore two methods for inferring transverse velocities from observations—FLCT and a neural network–based method DeepVel—and show DeepVel to be the more suitable method in the context of small-scale QS flows. We investigate the effect of azimuthal ambiguity on Poynting flux estimates, and we describe a new method for azimuth disambiguation. Finally, we use two methods for obtaining the electric field. The first method relies on an idealized Ohm’s law, whereas the second is a state-of-the-art inductive electric field inversion method PDFI_SS. We compare the resulting Poynting flux values with theoretical estimates for chromospheric and coronal energy losses and find that some of the Poynting flux estimates are sufficient to match the losses. Using MURaM simulations, we show that photospheric Poynting fluxes vary significantly with optical depth, and that there is an observational bias that results in underestimated Poynting fluxes due to an unaccounted shear term contribution.

Quantifying Properties of Photospheric Magnetic Cancellations in the Quiet Sun Internetwork

We analyzed spectropolarimetric data from the Swedish 1 m Solar Telescope to investigate the physical properties of small-scale magnetic cancellations in the quiet Sun photosphere. Specifically, we looked at the full Stokes polarization profiles along the Fe i 557.6 nm and of the Fe i 630.1 nm lines measured by the CRisp Imaging SpectroPolarimeter to study the temporal evolution of the line-of-sight magnetic field during 42.5 minutes of quiet Sun evolution. From this magnetogram sequence, we visually identified 38 cancellation events. We then used the Yet Another Feature Tracking Algorithm to characterize the physical properties of these magnetic cancellations. We found on average 1.6 × 1016 Mx of magnetic flux canceled in each event with an average cancellation rate of 3.8 × 1014 Mx s−1. The derived canceled flux is associated with strong downflows, with an average speed of V LOS ≈ 1.1 km s−1. Our results show that the average lifetime of each event is 9.2 minutes with an average of 44.8% of initial magnetic flux being canceled. Our estimates of magnetic fluxes provide a lower limit since studied magnetic cancellation events have magnetic field values that are very close to the instrument noise level. We observed no horizontal magnetic fields at the cancellation sites and therefore cannot conclude whether the events are associated with structures that could cause magnetic reconnection.

Linear Polarization Features in the Quiet-Sun Photosphere: Structure and Dynamics

We present detailed characteristics of linear polarization features (LPFs) in the quiet-Sun photosphere from high-resolution observations obtained with Sunrise/IMaX. We explore differently treated data with various noise levels in linear polarization signals, from which structure and dynamics of the LPFs are studied. Physical properties of the detected LPFs are also obtained from the results of Stokes inversions. The number of LPFs and their sizes and polarization signals are found to be strongly dependent on the noise level and on the spatial resolution. While the linear polarization with a signal-to-noise ratio geq4.5 covers about 26% of the entire area in the least noisy data in our study (with a noise level of 1.7times10^{-4} in the unit of Stokes I continuum), the detected (spatially resolved) LPFs cover about 10% of the area at any given time, with an occurrence rate on the order of 8times10^{-3}mbox{ s}^{-1} arcsec−2. The LPFs were found to be short lived (in the range of 30 – 300 s), relatively small structures (radii of approx0.1 – 1.5 arcsec), highly inclined, posing hG fields, and they move with an average horizontal speed of 1.2 km s−1. The LPFs were observed (almost) equally on both upflow and downflow regions, with an intensity contrast always larger than that of the average quiet Sun.

Structure of the solar photosphere studied from the radiation hydrodynamics code ANTARES

The ANTARES radiation hydrodynamics code is capable of simulating the solar granulation in detail unequaled by direct observation. We introduce a state-of-the-art numerical tool to the solar physics community and demonstrate its applicability to model the solar granulation. The code is based on the weighted essentially non-oscillatory finite volume method and by its implementation of local mesh refinement is also capable of simulating turbulent fluids. While the ANTARES code already provides promising insights into small-scale dynamical processes occurring in the quiet-Sun photosphere, it will soon be capable of modeling the latter in the scope of radiation magnetohydrodynamics. In this first preliminary study we focus on the vertical photospheric stratification by examining a 3-D model photosphere with an evolution time much larger than the dynamical timescales of the solar granulation and of particular large horizontal extent corresponding to 25''times25'' on the solar surface to smooth out horizontal spatial inhomogeneities separately for up- and downflows. The highly resolved Cartesian grid thereby covers sim4~mbox{Mm} of the upper convection zone and the adjacent photosphere. Correlation analysis, both local and two-point, provides a suitable means to probe the photospheric structure and thereby to identify several layers of characteristic dynamics: The thermal convection zone is found to reach some ten kilometers above the solar surface, while convectively overshooting gas penetrates even higher into the low photosphere. An approx145~mbox{km} wide transition layer separates the convective from the oscillatory layers in the higher photosphere.

Milne‐Eddington inversion for unresolved magnetic structures in the quiet Sun photosphere

AbstractThis paper is first devoted to present our method for modeling unresolved magnetic structures in the Milne‐Eddington inversion of spectropolarimetric data. The related definitions and other approaches and different used inversion algorithms are recalled for comparison. In a second part, we apply our method to quiet Sun data outside active regions. We obtain the quiet Sun photospheric magnetic field as composed of unresolved opening and connected magnetic flux tubes, which form a loop carpet of field lines. We then analyze the spatial correlation, which we also observed for the magnetic field vector, in terms of flux tube diameter, distance, and field strength. We find that different observations with the Zurich imaging polarimeter and THEMIS polarimeter mounted on the THEMIS telescope give very close results, and we add results also very close derived from HINODE/Solar Optical Telescope/spectropolarimeter observations analyzed with the same method. We obtain a mean flux tube diameter of 30 km, a mean flux tube distance of 230 km, and a mean flux tube magnetic field of 1.3 kG.

On the Generation of Hydrodynamic Shocks by Mixed Beams and Occurrence of Sunquakes in Flares

Observations of solar flares with sunquakes by space- and ground-based instruments reveal essentially different dynamics of seismic events in different flares. Some sunquakes are found to be closely associated with the locations of hard X-ray (HXR) and white-light (WL) emission, while others are located outside either of them. In this article we investigate possible sources causing a seismic response in a form of hydrodynamic shocks produced by the injection of mixed (electron plus proton) beams, discuss the velocities of these shocks, and the depths where they deposit the bulk of their energy and momentum. The simulation of hydrodynamic shocks in flaring atmospheres induced by electron-rich and proton-rich beams reveals that the linear depth of the shock termination is shifted beneath the level of the quiet solar photosphere on a distance from 200 to 5000 km. The parameters of these atmospheric hydrodynamic shocks are used as initial condition for another hydrodynamic model developed for acoustic-wave propagation in the solar interior (Zharkov, Mon. Not. Roy. Astron. Soc. 431, 3414, 2013). The model reveals that the depth of energy and momentum deposition by the atmospheric shocks strongly affects the propagation velocity of the acoustic-wave packet in the interior. The locations of the first bounces from the photosphere of acoustic waves generated in the vicinity of a flare are seen as ripples on the solar surface, or sunquakes. Mixed proton-dominated beams are found to produce a strong supersonic shock at depths 200 – 300 km under the level of the quiet-Sun photosphere and in this way produce well-observable acoustic waves, while electron-dominated beams create a slightly supersonic shock propagating down to 5000 km under the photosphere. This shock can only generate acoustic waves at the top layers beneath the photosphere since the shock velocity very quickly drops below the local sound speed. The distance \(\Delta\) of the first bounce of the generated acoustic waves is discussed in relation to the minimal phase velocities of wave packets defined by the acoustic cutoff frequency and the parameters of atmospheric shock termination beneath the photosphere.

MAGNETIC UPFLOW EVENTS IN THE QUIET-SUN PHOTOSPHERE. I. OBSERVATIONS

Rapid magnetic upflows in the quiet-Sun photosphere were recently uncovered from both SUNRISE/IMaX and Hinode/SOT observations. Here, we study magnetic upflow events (MUEs) from high-quality, high- (spatial, temporal, and spectral) resolution, and full Stokes observations in four photospheric magnetically sensitive Fe I lines centered at 525.021, 617.334, 630.151, and 630.250 nm acquired with the Swedish Solar Telescope (SST)/CRISP. We detect MUEs by subtracting in-line Stokes V signals from those in far blue wing whose signal-to-noise ratio (S/N) >= 7. We find a larger number of MUEs at any given time (0.02 per square arcsec), larger by one to two orders of magnitude, than previously reported. The MUEs appear to fall into four classes presenting different shapes of Stokes V profiles with (I) asymmetric double lobes, (II) single lobes, (III) double-humped (two same-polarity lobes), and (IV) three lobes (an extra blue-shifted bump in addition to double-lobes), of which less than half are single-lobed. We also find that MUEs are almost equally distributed in network and internetwork areas and they appear in the interior or at the edge of granules in both regions. Distributions of physical properties, except that of horizontal velocity, of the MUEs (namely, Stokes V signal, size, line-of-sight velocity, and lifetime) are almost identical for the different spectral lines in our data. A bisector analysis of our spectrally resolved observations shows that these events host modest upflows and do not show direct indication of the presence of supersonic upflows reported earlier. Our findings reveal that numbers, types (classes), and properties determined for MUEs can strongly depend on the detection techniques used and the properties of the employed data, namely, S/Ns, resolutions, and wavelengths.

Pair separation of magnetic elements in the quiet Sun

The dynamic properties of the quiet Sun photosphere can be investigated by analyzing the pair dispersion of small-scale magnetic fields (i.e., magnetic elements). By using $25$ hr-long Hinode magnetograms at high spatial resolution ($0".3$), we tracked $68,490$ magnetic element pairs within a supergranular cell near the disk center. The computed pair separation spectrum, calculated on the whole set of particle pairs independently of their initial separation, points out what is known as a super-diffusive regime with spectral index $\gamma=1.55\pm0.05$, in agreement with the most recent literature, but extended to unprecedented spatial and temporal scales (from granular to supergranular). Furthermore, for the first time, we investigated here the spectrum of the mean square displacement of pairs of magnetic elements, depending on their initial separation $r_0$. We found that there is a typical initial distance above (below) which the pair separation is faster (slower) than the average. A possible physical interpretation of such a typical spatial scale is also provided.

The ion–atom absorption processes as one of the factors of the influence on the sunspot opacity

As a continuation of the previous investigations of the symmetric and strongly non-symmetric ion-atom absorption processes in the far UV region within the models of the quiet Sun photosphere, these processes are studied here within a model of the sunspot. Here we mean the absorption processes in the H$(1s)$+H$^{+}$ and H$(1s)+X^{+}$ collisions and the processes of the photo-dissociation of the H$_{2}^{+}$ and H$X^{+}$ molecular ions, where $X$ is one of the metal atoms: $X=$Na, Ca, Mg, Si and Al. Obtained results show that the influence of the considered ion-atom absorption processes on the opacity of sunspots in the considered spectral region (110 nm $\lesssim \lambda \lesssim$ 230 nm) is not less and in some parts even larger than the influence of the referent electron-atom processes. In such a way, it is shown that the considered ion-atom absorption processes should be included \emph{ab initio} in the corresponding models of sunspots of solar-type and near solar-type stars. Apart of that, the spectral characteristics of the considered non-symmetric ion-atom absorption processes (including here the case $X$ = Li), which can be used in some further applications, have been determined and presented within this work.

SOLAR MAGNETIC TRACKING. IV. THE DEATH OF MAGNETIC FEATURES

The removal of magnetic flux from the quiet-sun photosphere is important for maintaining the statistical steady-state of the magnetic field there, for determining the magnetic flux budget of the Sun, and for estimating the rate of energy injected into the upper solar atmosphere. Magnetic feature death is a measurable proxy for the removal of detectable flux. We used the SWAMIS feature tracking code to understand how nearly 20000 detected magnetic features die in an hour-long sequence of Hinode/SOT/NFI magnetograms of a region of quiet Sun. Of the feature deaths that remove visible magnetic flux from the photosphere, the vast majority do so by a process that merely disperses the previously-detected flux so that it is too small and too weak to be detected. The behavior of the ensemble average of these dispersals is not consistent with a model of simple planar diffusion, suggesting that the dispersal is constrained by the evolving photospheric velocity field. We introduce the concept of the partial lifetime of magnetic features, and show that the partial lifetime due to Cancellation of magnetic flux, 22 h, is 3 times slower than previous measurements of the flux turnover time. This indicates that prior feature-based estimates of the flux replacement time may be too short, in contrast with the tendency for this quantity to decrease as resolution and instrumentation have improved. This suggests that dispersal of flux to smaller scales is more important for the replacement of magnetic fields in the quiet Sun than observed bipolar cancellation. We conclude that processes on spatial scales smaller than those visible to Hinode dominate the processes of flux emergence and cancellation, and therefore also the quantity of magnetic flux that threads the photosphere.

Empirical determination of the temperature stratification in the photosphere of the quiet Sun

Context. Detailed realistic 3D simulations of the photosphere of the Sun are now available, but 1D models of the average quiet-Sun photosphere are still widely used, in particular for spectro-polarimetric inversions. Aims. Here we present an empirical determination of the average radiation temperature variations as a function of the geometrical height above the continuum formation level in the solar photosphere.Methods. We used high resolution spectroscopic scans in the 630 nm Fe i line pair at varying heliocentric angles along the north-south polar axis of the Sun, made with SOT onboard Hinode. Implementing a new method for image reconstruction, we obtained images of the photospheric granulation at constant continuum opacity levels, from the upper photosphere seen at line centers to the low photosphere. The Fourier cross-spectra of images at different opacity levels were computed, and we derived the formation depths of images without referring to any atmospheric model, by measuring the slope of the cross-spectrum phase. Results. A modified Milne-Eddington model for the line formation was tested by comparing it with the average line-intensity profiles observed at solar disk center. It yields consistent results for the FeI 630.2 nm line, whereas the FeI line at 630.1 nm is not well reproduced by the model. We ascribe this discrepancy to non-LTE effects in the line formation processes. The average image intensities at the different FeI 630.2 nm levels were used to determine the depth-variation of the temperature for an average 1D model of the quiet photosphere. We compared our empirical temperature model with the widely used FALC model. Both models agree well for the temperature variations with the continuum optical depth. But in the low photosphere, the temperature gradient we measure with respect to the geometrical height is significantly softer than in Model C. We argue that some of the assumptions used to solve the pseudohydrostatic equilibrium in semi-empirical models are probably at fault. We also derived empirical values for the 630 nm continuum absorption coefficient as a function of the geometrical height in the low photosphere. Finally, we were able to measure the altitude of the base of the granulation contrast inversion layer, which is found at about 130 km above the base of the photosphere, in agreement with 3D MHD simulations.

THE STORAGE AND DISSIPATION OF MAGNETIC ENERGY IN THE QUIET SUN CORONA DETERMINED FROM SDO /HMI MAGNETOGRAMS

In recent years, higher cadence, higher resolution observations have revealed the quiet-Sun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the small-scale coronal magnetic field exhibits similar complexity. For the first time, the quiet-Sun coronal magnetic field is continuously evolved through a series of non-potential, quasi-static equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain small-scale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex small-scale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona.

Spectropolarimetric diagnostics of unresolved magnetic fields in the quiet solar photosphere

AbstractA few years before the Hinode space telescope was launched, an investigation based on the Hanle effect in atomic and molecular lines indicated that the bulk of the quiet solar photosphere is significantly magnetized, due to the ubiquitous presence of an unresolved magnetic field with an average strength 〈B〉, ≈ 130 G. It was pointed out also that this “hidden” field must be much stronger in the intergranular regions of solar surface convection than in the granular regions, and it was suggested that this unresolved magnetic field could perhaps provide the clue for understanding how the outer solar atmosphere is energized. In fact, the ensuing magnetic energy density is so significant that the energy flux estimated using the typical value of 1 km/s for the convective velocity (thinking in rising magnetic loops) or the Alfvén speed (thinking in Alfvén waves generated by magnetic reconnection) turns out to be substantially larger than that required to balance the chromospheric energy losses. Here we present a brief review of the research that led to such conclusions, with emphasis on a new three-dimensional radiative transfer investigation aimed at determining the magnetization of the quiet Sun photosphere from the Hanle effect in the Sr I 4607 Å line and the Zeeman effect in Fe I lines.

The quiet-Sun photosphere and chromosphere

The overall structure and the fine structure of the solar photosphere outside active regions are largely understood, except possibly the important roles of a turbulent near-surface dynamo at its bottom, internal gravity waves at its top and small-scale vorticity. Classical one-dimensional static radiation-escape modelling has been replaced by three-dimensional time-dependent magento-hydrodynamic simulations that come closer to reality. The solar chromosphere, in contrast, remains little understood, although its pivotal role in coronal mass and energy loading makes it a principal research area. Its fine structure defines its overall structure, so that hard-to-observe and hard-to-model small-scale dynamical processes are key to understanding. However, both chromospheric observation and chromospheric simulation presently mature towards the required sophistication. Open-field features seem of greater interest than easier-to-see closed-field features.

SPATIAL AND TEMPORAL DISTRIBUTIONS OF TRANSIENT HORIZONTAL MAGNETIC FIELDS WITH DEEP EXPOSURE

We obtained a long exposure vector magnetogram of the quiet Sun photosphere at the disk center with wide FOV of $51" \times 82"$. The observation was performed at Fe I 525.0 nm with the shutter-less mode of the Narrow Band Filter Imager of the Solar Optical Telescope (SOT) on board Hinode satellite. We summed the linear polarization ($LP$) maps taken with time cadence of 60 seconds for 2 hours to obtain a map with as long an exposure as possible. The polarization sensitivity would be more than 4.6 (21.2 in exposure time) times the standard observation with the SOT spectro-polarimeter. The $LP$ map shows a cellular structure with a typical scale of $5" - 10"$. We find that the enhanced $LP$ signals essentially consist of the isolated sporadic transient horizontal magnetic fields (THMFs) with life time of 1-10 min, and are not contributed by long-duration weak horizontal magnetic fields. The cellular structure coincides in position with the negative divergence of the horizontal flow field, i.e., mesogranular boundaries with downflows. Azimuth distribution appears to be random for the scale size of the mesogranules. Some pixels have two separate appearances of THMFs, and the measured time intervals are consistent with the random appearance. THMFs tend to appear at the mesogranular boundaries, but appear randomly in time. We discuss the origin of THMFs based on these observations.

Mesoscale dynamics on the Sun's surface from HINODE observations

Context: Aims: The interactions of velocity scales on the Sun's surface, from granulation to supergranulation are still not understood, nor are their interaction with magnetic fields. We thus aim at giving a better description of dynamics in the mesoscale range which lies between the two scales mentioned above. Methods: We analyse a 48 h high-resolution time sequence of the quiet Sun photosphere at the disk center obtained with the Solar Optical Telescope onboard Hinode. The observations, which have a field of view of 100´´ × 100´´, typically contain four supergranules. We monitor in detail the motion and evolution of granules as well as those of the radial magnetic field. Results: This analysis allows us to better characterize Trees of Fragmenting Granules issued from repeated fragmentation of granules, especially their lifetime statistics. Using floating corks advected by measured velocity fields, we show their crucial role in the advection of the magnetic field and in the build up of the network. Finally, thanks to the long duration of the time series, we estimate that the turbulent diffusion coefficient induced by horizontal motion is approximately 430 km2 s-1. Conclusions: These results demonstrate that the long living families contribute to the formation of the magnetic network and suggest that supergranulation could be an emergent length scale building up as small magnetic elements are advected and concentrated by TFG flows. Our estimate for the magnetic diffusion associated with this horizontal motion might provide a useful input for mean-field dynamo models.

Small-scale magnetic field dynamics on the Sun at high spatial and temporal resolution

Aims. We present examples of the time evolution of phenomena occurring in the quiet Sun photosphere as seen from observations of high spatial and spectral resolution and with a time cadence of 23 s.

The Dependence of Ephemeral Region Emergence on Local Flux Imbalance

We investigate the distribution and evolution of existing and emerging magnetic network elements in the quiet-Sun photosphere. The ephemeral region emergence rate is found to depend primarily on the imbalance of magnetic flux in the area surrounding its emergence location, such that the rate of flux emergence is lower within strongly unipolar regions by at least a factor of 3 relative to flux-balanced quiet Sun. As coronal holes occur over unipolar regions, this also means that ephemeral regions occur less frequently there, but we show that this is an indirect effect-independent of whether the region is located within an open-field coronal hole or a closed-field quiet region. We discuss the implications of this finding for near-photospheric dynamo action and for the coupling between closed coronal and open heliospheric fields.

The Distribution of Quiet Sun Magnetic Field Strengths from 0 to 1800 G

The quiet-Sun photospheric plasma has a variety of magnetic field strengths going from zero to 1800 G. The empirical characterization of these field strengths requires a probability density function (PDF), i.e., a function P(B) describing the fraction of quiet Sun occupied by each field strength B. We show how to combine magnetic field strength measurements based on the Zeeman effect and the Hanle effect to estimate an unbiased P(B). The application of the method to real observations renders a set of possible PDFs, which outline the general characteristics of the quiet-Sun magnetic fields. Their most probable field strength differs from zero. The magnetic energy density is a significant fraction of the kinetic energy of the granular motions at the base of the photosphere (larger than 15% or larger than 2 × 103 ergs cm-3). The unsigned flux density (or mean magnetic field strength) has to be between 130 and 190 G. A significant part of the unsigned flux (between 10% and 50%) and of the magnetic energy (between 45% and 85%) are provided by the field strengths larger than 500 G, which, however, occupy only a small fraction of the surface (between 1% and 10%). The fraction of kG fields in the quiet Sun is even smaller, but they are important for a number of reasons. The kG fields still trace a significant fraction of the total magnetic energy, they reach the high photosphere, and they appear in unpolarized light images. The quiet-Sun photosphere has far more unsigned magnetic flux and magnetic energy than the active regions and the network combined.