Quiet Sun Magnetic Fields Research Articles

Collisional effects in modeling solar polarized lines

Context. Rigorous implementation of the effects of collisions in modeling the formation of the polarized solar lines is of utmost importance in order to realistically analyze the available, highly sensitive solar spectropolarimetric observations. Indeed, even when an observation seems to fit well with theory, one can misinterpret results if important effects due to collisions are not correctly implemented in the modeling process. Aims. We point out inconsistencies in the models adopted to implement the Paschen Back effect together with collisional effects on the solar linear polarization formed by scattering of anisotropic radiation. Because the significance of these inconsistencies increases as polarization becomes increasingly responsive to collisions, we investigate the range of hydrogen densities nH to which the polarization is sensitive. Methods. We used the density matrix formalism in the tensorial irreducible basis, which was developed within the theory of atom-radiation interaction and of atomic collisions. We solved the statistical equilibrium equations for multi-level atoms with hyperfine structure (HFS) in order to evaluate the collisional depolarization of levels of the D1-D2 lines of the K I atom. Results. We find that collisions play a prominent role, particularly at hydrogen densities of between 1013 and 1016 cm−3. Conclusions. So far, analyses of polarized lines formed in the presence of solar magnetic field have incorporated, if at all, collisional rates calculated assuming zero magnetic field. This could be a good approximation in the Hanle regime but not in the Paschen Back regime. For typical quiet Sun magnetic fields, the latter regime could be reached, and level-crossing takes place in several atomic systems. Therefore, one must be careful when using collisional rates calculated in the zero-field case to interpret linear polarization formed in magnetized media.

Mapping the Hidden Magnetic Field of the Quiet Sun

Abstract The Sun is the only star where we can resolve the intricate magnetism that all convective stars harbor. Yet, more than 99% of its visible surface along the solar cycle (the so-called quiet Sun) is filled with a tangled, unresolved magnetism. These “hidden” fields are thought to store enough magnetic energy to play a role in the heating of the Sun’s outer atmosphere, but its field strength is still not constrained. Previous investigations based on the Hanle effect in atomic lines claim a strong magnetization of about 100 G, while the same effect in molecules show a factor of 10 weaker fields. The discrepancy disappears if the magnetic field strength of the hidden field is not homogeneous in the solar surface. In this Letter, we prove using magnetohydrodynamical simulations that it is possible to infer the average field strength of the hidden quiet-Sun magnetic fields using multiline inversions of intensity profiles in the Zeeman regime. Using this technique with 15 spectral lines in the 1.5 μm spectral range, we reveal that the spatial distribution of the hidden field is strongly correlated with convection motions, and that the average magnetization is about 46 G. Reconciling our findings with the Hanle ones is not obvious and will require future work on both sides, since it implies an increase of the field strength with height, something that is physically questionable.

Interaction of Magnetic Fields with a Vortex Tube at Solar Subgranular Scale

Abstract Using high-resolution spectropolarimetric data recorded with the Swedish 1 m Solar Telescope, we have identified several instances of granular lanes traveling into granules. These are believed to be the observational signature of underlying tubes of vortical flow with their axis oriented parallel to the solar surface. Associated with these horizontal vortex tubes, we detect in some cases a significant signal in linear polarization, located at the trailing dark edge of the granular lane. The linear polarization appears at a later stage of the granular lane development, and is flanked by patches of circular polarization. Stokes inversions show that the elongated patch of linear polarization signal arises from the horizontal magnetic field aligned with the granular lane. We analyze snapshots of a magnetohydrodynamic numerical simulation and find cases in which the horizontal vortex tube of the granular lane redistributes and transports the magnetic field to the solar surface causing a polarimetric signature similar to what is observed. We thus witness a mechanism capable of transporting magnetic flux to the solar surface within granules. This mechanism is probably an important component of the small-scale dynamo supposedly acting at the solar surface and generating the quiet-Sun magnetic field.

High-resolution spectroscopy of a surge in an emerging flux region

Aims. The regular pattern of quiet-Sun magnetic fields was disturbed by newly emerging magnetic flux, which led a day later to two homologous surges after renewed flux emergence, affecting all atmospheric layers. Hence, simultaneous observations in different atmospheric heights are needed to understand the interaction of rising flux tubes with the surrounding plasma, in particular by exploiting the important diagnostic capabilities provided by the strong chromospheric Hα line regarding morphology and energetic processes in active regions. Methods. A newly emerged active region NOAA 12722 was observed with the Vacuum Tower Telescope (VTT) at Observatorio del Teide, Tenerife, Spain, on 11 September 2018. High spectral resolution observations using the echelle spectrograph in the chromospheric Hαλ6562.8 Å line were obtained in the early growth phase. Noise-stripped Hα line profiles yield maps of line-core and bisector velocities, which were contrasted with velocities inferred from Cloud Model inversions. A high-resolution imaging system recorded simultaneously broad- and narrowband Hα context images. The Solar Dynamics Observatory provided additional continuum images, line-of-sight (LOS) magnetograms, and UV and extreme UV (EUV) images, which link the different solar atmospheric layers. Results. The active region started as a bipolar region with continuous flux emergence when a new flux system emerged in the leading part during the VTT observations, resulting in two homologous surges. While flux cancellation at the base of the surges provided the energy for ejecting the cool plasma, strong proper motions of the leading pores changed the magnetic field topology making the region susceptible to surging. Despite the surge activity in the leading part, an arch filament system in the trailing part of the old flux remained stable. Thus, stable and violently expelled mass-loaded ascending magnetic structures can coexist in close proximity. Investigating the height dependence of LOS velocities revealed the existence of neighboring strong up- and downflows. However, downflows occur with a time lag. The opacity of the ejected cool plasma decreases with distance from the base of the surge, while the speed of the ejecta increases. The location at which the surge becomes invisible in Hα corresponds to the interface where the surge brightens in He IIλ304 Å. Broad-shouldered and dual-lobed Hα profiles suggests accelerated or decelerated and highly structured LOS plasma flows. Significantly broadened Hα profiles imply significant heating at the base of the surges, which is also supported by bright kernels in UV and EUV images uncovered by swaying motions of dark fibrils at the base of the surges. Conclusions. The interaction of newly emerging flux with pre-existing flux concentrations of a young, diffuse active region provided suitable conditions for two homologous surges. High-resolution spectroscopy revealed broadened and dual-lobed Hα profiles tracing accelerated or decelerated flows of cool plasma along the multi-threaded structure of the surge.

Placing limits on long-term variations in quiet-Sun irradiance and their contribution to total solar irradiance and solar radiative forcing of climate

Recent reconstructions of total solar irradiance (TSI) postulate that quiet-Sun variations could give significant changes to the solar power input to Earth's climate (radiative climate forcings of 0.7-1.1 W m-2 over 1700-2019) arising from changes in quiet-Sun magnetic fields that have not, as yet, been observed. Reconstructions without such changes yield solar forcings that are smaller by a factor of more than 10. We study the quiet-Sun TSI since 1995 for three reasons: (i) this interval shows rapid decay in average solar activity following the grand solar maximum in 1985 (such that activity in 2019 was broadly equivalent to that in 1900); (ii) there is improved consensus between TSI observations; and (iii) it contains the first modelling of TSI that is independent of the observations. Our analysis shows that the most likely upward drift in quiet-Sun radiative forcing since 1700 is between +0.07 and -0.13 W m-2. Hence, we cannot yet discriminate between the quiet-Sun TSI being enhanced or reduced during the Maunder and Dalton sunspot minima, although there is a growing consensus from the combinations of models and observations that it was slightly enhanced. We present reconstructions that add quiet-Sun TSI and its uncertainty to models that reconstruct the effects of sunspots and faculae.

On the Contribution of Quiet-Sun Magnetism to Solar Irradiance Variations: Constraints on Quiet-Sun Variability and Grand-minimum Scenarios

Abstract While the quiet-Sun magnetic field shows only little variation with the solar cycle, long-term variations cannot be completely ruled out from first principles. We investigate the potential effect of quiet-Sun magnetism on spectral solar irradiance through a series of small-scale dynamo simulations with zero vertical flux imbalance ( ) and varying levels of small-scale magnetic field strength, and one weak network case with an additional flux imbalance corresponding to a flux density of G. From these setups, we compute the dependence of the outgoing radiative energy flux on the mean vertical magnetic field strength in the photosphere at a continuum optical depth τ = 1 ( ). We find that a quiet-Sun setup with a mean vertical field strength of G is about 0.6% brighter than a non-magnetic reference case. We find a linear dependence of the outgoing radiative energy flux on the mean field strength with a relative slope of 1.4 × 10−4 G−1. With this sensitivity, only a moderate change of the quiet-Sun field strength by 10% would lead to a total solar irradiance variation comparable to the observed solar cycle variation. While this does provide strong indirect constraints on possible quiet-Sun variations during a regular solar cycle, it also emphasizes that potential variability over longer timescales could make a significant contribution to longer-term solar irradiance variations.

Emergence of small-scale magnetic flux in the quiet Sun

Context. We study the evolution of a small-scale emerging flux region (EFR) in the quiet Sun, from its emergence in the photosphere to its appearance in the corona and its decay. Aims. We track processes and phenomena that take place across all atmospheric layers; we explore their interrelations and compare our findings with those from recent numerical modelling studies. Methods. We used imaging as well as spectral and spectropolarimetric observations from a suite of space-borne and ground-based instruments. Results. The EFR appears in the quiet Sun next to the chromospheric network and shows all morphological characteristics predicted by numerical simulations. The total magnetic flux of the region exhibits distinct evolutionary phases, namely an initial subtle increase, a fast increase with a Co-temporal fast expansion of the region area, a more gradual increase, and a slow decay. During the initial stages, fine-scale G-band and Ca II H bright points coalesce, forming clusters of positive- and negative-polarity in a largely bipolar configuration. During the fast expansion, flux tubes make their way to the chromosphere, pushing aside the ambient magnetic field and producing pressure-driven absorption fronts that are visible as blueshifted chromospheric features. The connectivity of the quiet-Sun network gradually changes and part of the existing network forms new connections with the newly emerged bipole. A few minutes after the bipole has reached its maximum magnetic flux, the bipole brightens in soft X-rays forming a coronal bright point. The coronal emission exhibits episodic brightenings on top of a long smooth increase. These coronal brightenings are also associated with surge-like chromospheric features visible in Hα, which can be attributed to reconnection with adjacent small-scale magnetic fields and the ambient quiet-Sun magnetic field. Conclusions. The emergence of magnetic flux even at the smallest scales can be the driver of a series of energetic phenomena visible at various atmospheric heights and temperature regimes. Multi-wavelength observations reveal a wealth of mechanisms which produce diverse observable effects during the different evolutionary stages of these small-scale structures.

On modelling the kinematics and evolutionary properties of pressure-pulse-driven impulsive solar jets

Abstract. In this paper, we describe the kinematical and evolutionary properties of the impulsive cool jets in the solar atmosphere using numerical simulation by Godunov-type PLUTO code at two different quiet-Sun magnetic field strengths (B=56 gauss and B=112 gauss). These types of chromospheric jets originate due to a pressure pulse, which mimics the after-effects of the localized heating in the lower solar atmosphere. These jets may be responsible for the transport of mass and energy in the localized upper atmosphere (i.e. corona). The detection of the height–time profiles for the jets, which were developed by imposing different pressure pulses, exhibit asymmetric near-parabolic behaviour. This infers that the upward motion of the jet occurs under the influence of pressure perturbation. However, its downward motion is not only governed by the gravitational free fall, but also by the complex plasma motions near its base under the effect of counter-propagating pulses. The maximum height and lifetime of the jets with respect to the strength of the pressure pulse show a linear increasing trend. This suggests that if the extent of the heating and, thus, the pressure perturbations are longer, then more longer chromospheric jets can be triggered from the same location in the chromosphere. For a certain amplitude of pressure pulse, the strong magnetic field configuration (B=112 gauss) leads to more longer jets compared with the weaker field (B=56 gauss). This suggests that the strong magnetic field guides the pressure-pulse-driven jets more efficiency towards the higher corona. In conclusion, our model mimics the properties and evolution of the variety of the cool impulsive jets in the chromosphere (e.g. macrospicules, network jets, isolated repeated cool jets, confined and small surges, and so on.).

Background-Subtracted Solar Activity Maps

We introduce the concept of a Background-subtracted Solar Activity Map (BaSAM) as a new quantitative tool to assess and visualize the temporal variation of the photospheric magnetic field and the UV 160 nm intensity. The method utilizes data of the Solar Dynamics Observatory (SDO) and is applicable to both full-disk observations and regions-of-interest. We illustrate and discuss the potential of BaSAM resorting to datasets representing solar minimum and maximum conditions: (1) Contributions of quiet-Sun magnetic fields, i.e. the network and (decaying) plage, to solar activity can be better determined when their variation is measured with respect to the background given by "deep" magnetograms. (2) Flaring and intermittent brightenings are easily appraised in BaSAMs of the UV intensity. (3) Both magnetic-field and intensity variations demonstrated that the flux system of sunspots is well connected to the surrounding supergranular cells. In addition, producing daily full-disk BaSAMs for the entire mission time of SDO provides a unique tool to analyze solar cycle variations, showing how vigorous or frail are the variations of magnetic-field and intensity features.

Small‐scale dynamos in simulations of stratified turbulent convection

Small‐scale dynamo action is often held responsible for the generation of quiet Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small‐scale dynamos in nonrotating turbulent convection at low magnetic Prandtl numbers. We use high‐resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small‐scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers, such as the Sun. As a function of the magnetic Reynolds number (Rm), the growth rate of the dynamo is consistent with an Rm1/2 scaling. No evidence for a logarithmic increase of the growth rate with Rm is found.

Numerical simulations of quiet Sun magnetic fields seeded by the Biermann battery

The magnetic fields of the quiet Sun cover at any time more than 90\% of its surface and their magnetic energy budget is crucial to explain the thermal structure of the solar atmosphere. One of the possible origins of these fields is due to the action of local dynamo in the upper convection zone of the Sun. Existing simulations of the local solar dynamo require an initial seed field, and sufficiently high spatial resolution, in order to achieve the amplification of the seed field to the observed values in the quiet Sun. Here we report an alternative model of seeding based on the action of the Bierman battery effect. This effect generates a magnetic field due to the local imbalances in electron pressure in the partially ionized solar plasma. We show that the battery effect self-consistently creates from zero an initial seed field of a strength of the order of micro G, and together with dynamo amplification, allows the generation of quiet Sun magnetic fields of a similar strength to those from solar observations.

Millimeter radiation from a 3D model of the solar atmosphere

We use state-of-the-art, three-dimensional non-local thermodynamic equilibrium (non-LTE) radiative magnetohydrodynamic simulations of the quiet solar atmosphere to carry out detailed tests of chromospheric magnetic field diagnostics from free-free radiation at millimeter and submillimeter wavelengths (mm/submm). The vertical component of the magnetic field was deduced from the mm/submm brightness spectra and the degree of circular polarization synthesized at millimeter frequencies. We used the frequency bands observed by the Atacama Large Millimeter/Submillimeter Array (ALMA) as a convenient reference. The magnetic field maps obtained describe the longitudinal magnetic field at the effective formation heights of the relevant wavelengths in the solar chromosphere. The comparison of the deduced and model chromospheric magnetic fields at the spatial resolution of both the model and current observations demonstrates a good correlation, but has a tendency to underestimate the model field. The systematic discrepancy of about 10 percent is probably due to averaging of the restored field over the heights contributing to the radiation, weighted by the strength of the contribution. On the whole, the method of probing the longitudinal component of the magnetic field with free-free emission at mm/submm wavelengths is found to be applicable to measurements of the weak quiet-Sun magnetic fields. However, successful exploitation of this technique requires very accurate measurements of the polarization properties (primary beam and receiver polarization response) of the antennas, which will be the principal factor that determines the level to which chromospheric magnetic fields can be measured. Consequently, high-resolution and high-precision observations of circularly polarized radiation at millimeter wavelengths can be a powerful tool for producing chromospheric longitudinal magnetograms.

Spectropolarimetry of Atomic and Molecular Lines near 4135 nm

New spatially scanned spectropolarimetry sunspot observations are made of photospheric atomic and molecular absorption lines near 4135 nm. The relative splittings among several atomic lines are measured and shown to agree with values calculated with configuration interaction and intermediate coupling. Large splitting is seen in a line identified with Fe i at 4137 nm, showing multiple Stokes V components and an unusual linear polarization. This line will be a sensitive probe of quiet-Sun magnetic fields, with a magnetic sensitivity of 2.5 times higher than that of the well-known 1565 nm Fe i line.

Efficient algorithms for the recognition of topologically conjugate gradient-like diffeomorhisms

It is well known that the topological classification of structurally stable flows on surfaces as well as the topological classification of some multidimensional gradient-like systems can be reduced to a combinatorial problem of distinguishing graphs up to isomorphism. The isomorphism problem of general graphs obviously can be solved by a standard enumeration algorithm. However, an efficient algorithm (i. e., polynomial in the number of vertices) has not yet been developed for it, and the problem has not been proved to be intractable (i. e., NPcomplete). We give polynomial-time algorithms for recognition of the corresponding graphs for two gradient-like systems. Moreover, we present efficient algorithms for determining the orientability and the genus of the ambient surface. This result, in particular, sheds light on the classification of configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field.

DYNAMICS OF MULTI-CORED MAGNETIC STRUCTURES IN THE QUIET SUN

We report on the dynamical interaction of quiet-Sun magnetic fields and granular convection in the solar photosphere as seen by \textsc{Sunrise}. We use high spatial resolution (0\farcs 15--0\farcs 18) and temporal cadence (33 s) spectropolarimetric Imaging Magnetograph eXperiment data, together with simultaneous CN and Ca\,\textsc{ii}\,H filtergrams from \textsc{Sunrise} Filter Imager. We apply the SIR inversion code to the polarimetric data in order to infer the line of sight velocity and vector magnetic field in the photosphere. The analysis reveals bundles of individual flux tubes evolving as a single entity during the entire 23 minute data set. The group shares a common canopy in the upper photospheric layers, while the individual tubes continually intensify, fragment and merge in the same way that chains of bright points in photometric observations have been reported to do. The evolution of the tube cores are driven by the local granular convection flows. They intensify when they are "compressed" by surrounding granules and split when they are "squeezed" between two moving granules. The resulting fragments are usually later regrouped in intergranular lanes by the granular flows. The continual intensification, fragmentation and coalescence of flux results in magnetic field oscillations of the global entity. From the observations we conclude that the magnetic field oscillations first reported by \citet{2011ApJ...730L..37M} correspond to the forcing by granular motions and not to characteristic oscillatory modes of thin flux tubes.

CONSTRAINING THE MASSES AND THE NON-RADIAL DRAG COEFFICIENT OF A SOLAR CORONAL MASS EJECTION

Decades of observations show that CMEs can deflect from a purely radial trajectory yet no consensus exists as to the cause of these deflections. Many of theories attribute the CME deflection to magnetic forces. We developed ForeCAT (Kay et al. 2013, Kay et al. 2015), a model for CME deflections based solely on magnetic forces, neglecting any reconnection effects. Here we compare ForeCAT predictions to the observed deflection of the 2008 December 12 CME and find that ForeCAT can accurately reproduce the observations. Multiple observations show that this CME deflected nearly 30{\deg} in latitude (Byrne et al. 2010, Gui et al. 2011) and 4.4{\deg} in longitude (Gui et al. 2011). From the observations, we are able to constrain all of the ForeCAT input parameters (initial position, radial propagation speed, and expansion) except the CME mass and the drag coefficient that affects the CME motion. By minimizing the reduced chi-squared, $\chi^2_{\nu}$, between the ForeCAT results and the observations we determine an acceptable mass range between 4.5x10$^{14}$ and 1x10$^{15}$ g and the drag coefficient less than 1.4 with a best fit at 7.5x10$^{14}$ g and 0 for the mass and drag coefficient. ForeCAT is sensitive to the magnetic background and we are also able to constrain the rate at which the quiet sun magnetic field falls to be similar or to or fall slightly slower than the Potential Field Source Surface model.

Do the quiet sun magnetic fields vary with the solar cycle?

AbstractThe quiet Sun observed in polarized light exhibits a rich and complex magnetic structuring which is still not fully resolved nor understood. The present work is intended to contribute to the debate about the origin of the quiet sun magnetic fields, in relation or not to the global solar dynamo. We present analysis of center-to-limb polarization measurements obtained with the SOT/SP spectropolarimeter onboard the Hinode satellite outside active regions, in 2007 and 2013, i.e. at a minimum and a maximum of the solar cycle, respectively. We compare the spatial fluctuation Fourier spectra of unsigned circular and linear polarization images after corrections for polarization bias and focus variations between the two data sets. The decay of active regions is clearly a source of magnetic fields in the quiet Sun. It leads to a global increase of the polarization fluctuation power spectrum in 2013 in the network. In the internetwork, we observe no variation of the polarization fluctuation power at mesogranular and granular scales, whereas it increases at sub-granular scales. We interpret these results in the following way. At the mesogranular and granular scales very efficient mechanisms of magnetic field removal are operating in the internetwork, that leads to a dissipation or a concentration of magnetic fields on smaller scales. So the cycle-invariant magnetic signal that we detect at mesogranular and granular scales must be continuously created by a dynamo mechanism which is independent of the solar cycle.

The solar cycle variation of topological structures in the global solar corona

The distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the separatrix surfaces that divide the field into topologically distinct regions, allowing open-field regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections (separators) are important likely energy release sites. This paper investigates, throughout the solar cycle, the nature of coronal magnetic-field topologies that arise under the potential-field source-surface approximation. In particular, we characterise the typical global fields at solar maximum and minimum. Global magnetic fields are extrapolated from observed Kitt Peak and SOLIS synoptic magnetograms, from Carrington rotations 1645 to 2144, using the potential-field source-surface model. Hence, variations in the coronal skeleton are studied over three solar cycles. Key building blocks which make up magnetic fields are identified and classified according to the nature of their separatrix surfaces. The magnetic skeleton reveals that, at solar maximum, the global coronal field involves a multitude of topological structures at all latitudes. Many open-field regions exist originating anywhere on the photosphere. At solar minimum, the coronal topology is heavily influenced by the solar dipole. A strong dipole results in a simple large-scale structure involving just two large polar open-field regions, but, at short radial distances between plus or minus 60 deg latitude, the small-scale topology is complex. If the solar dipole if weak, as in the recent minimum, then the low-latitude quiet-sun magnetic fields may be globally significant enough to create many disconnected open-field regions at low latitudes, in addition to the two polar open-field regions.

Distribution of magnetic fields in the quiet Sun

Context. The distribution of magnetic fields in the atmosphere of the quiet Sun has been extensively studied with various methods, but it is still a matter of debate. Previous analyses mostly rely on the inversion of spectro-polarimetric data and different methods lead to somewhat different results. Aims. Here we do not intend to determine the magnetic field vector, but we use total polarization images as tracers of the magnetic field distribution and we study their cross-correlations with granulation and reversed-granulation images. Methods. We used high-resolution spectro-polarimetric scans obtained in the 630 nm FeI line pair at varying heliocentric angles along the north-south polar axis of the Sun, with the Solar Optical Telescope (SOT) onboard Hinode. We obtain polarization images by summing the total polarization (linear and circular) in each line. We compute the 2D correlation of polarization images and their cross-correlations with images of the granulation observed simultaneously in the line wings and with the reversed granulation observed in the line cores, and we examine their center-to-limb variations. Results. The correlation-widths of polarization images have on the average, the same value (1.3 �� ) as the correlation-width of the granulation, showing that the granular scale is a characteristic scale of the quiet Sun magnetic field distribution. At disk center the cross-correlation between total polarization and the granulation shows a negative peak. Out of disk-center both a negative and a positive peak are detected. The cross-correlation of polarization images with the reversed granulation always shows a positive peak. We assign these cross-correlation signals to the presence of two kinds of magnetized regions spatially separated, one of them is located in the intergranular lanes (anti-correlated with the granulation), the other one lies within the bright granules. For images obtained out of disk center, the correlation and anti-correlation peaks are shifted along the north-south direction and the shifts measured at the same limb-distance in the southern and northern hemispheres have opposite values. A consistent interpretation of these shifts is proposed in terms of a perspective effect arising when two images formed at different heights are observed at an angle. We were able to measure the perspective effect for the magnetic component correlated with the reversed granulation. Its polarization signals observed in the FeI 630.25 nm line and in the 630.15 nm line, are formed respectively 100 km and 150 km below the bright features seen at line centers.

Horizontal or vertical magnetic fields on the quiet Sun

Different analyses of identical Hinode SOT/SP data of quiet-sun magnetic fields have in the past led to contradictory answers to the question of whether the angular distribution of field vectors is preferentially horizontal or vertical. These answers have been obtained by combining the measured circular and linear polarizations in different ways to derive the field inclinations. A problem with these combinations is that the circular and linear polarizations scale with field strength in profoundly different ways. Here, we avoid these problems by using an entirely different approach that is based exclusively on the fundamental symmetry properties of the transverse Zeeman effect for observations away from the disk center without any dependence on the circular polarization. Systematic errors are suppressed by the application of a doubly differential technique with the 5247-5250 \AA\ line pair for observations with the ZIMPOL-2 imaging polarimeter on the French THEMIS telescope on Tenerife. This allows us to determine in a model- and resolution-independent way how the angular distribution of the intranetwork magnetic fields changes from being preferentially vertical in the lower and middle photosphere to become preferentially horizontal in the upper photosphere.