Quiet Solar Photosphere Research Articles

Exploring Magnetic Loops and Serpentine Fields in the Quiet Sun with the GRIS-IFU

Synthetic observations produced from radiative magnetohydrodynamic simulations have predicted that higher polarization fractions in the quiet solar photosphere would be revealed by increasing the total integration time of observations at GREGOR resolutions. We present recently acquired disk center observations of the Fe i 15648.5 Å line obtained with the GREGOR telescope equipped with the GRIS-IFU during excellent seeing conditions, showing exceptionally high polarization fractions. Our observations reveal an internetwork region with a majority (>60%) of magnetized pixels displaying a clear transverse component of the magnetic field. This result is in stark contrast to previous disk center GRIS-IFU observations in this spectral line, which had predominantly vertical magnetic fields in the deep photosphere. At the same time, the median magnetic field strength is weaker than previous GRIS-IFU observations, indicating that the larger fraction of polarization signals cannot be explained by a more active target. We use the Stokes Inversion based on Response functions (SIR) code to analyze the data, performing over 45 million inversions, and interrogate the impact of two conflicting approaches to the treatment of noise on the retrieval of the magnetic inclination and azimuth. We present several case studies of the zoo of magnetic features present in these data, including small-scale magnetic loops that seem to be embedded in a sea of magnetism, and serpentine fields, focusing on regions where full-vector spectropolarimetry has been achieved. We also present a new open-source Python 3 analysis tool, SIR Explorer, which we use to examine the dynamics of these small-scale magnetic features.

Constraining the magnetic vector in the quiet solar photosphere and the impact of instrumental degradation

Context. With the advent of next generation high resolution telescopes, our understanding of how the magnetic field is organized in the internetwork (IN) photosphere is likely to advance significantly. Aims. We aim to evaluate the extent to which we can retrieve accurate information about the magnetic vector in the IN photosphere using inversion techniques. Methods. We use a snapshot produced from high resolution three-dimensional magnetohydrodynamic (MHD) simulations and employ the Stokes Inversions based on Response functions (SIR) code to produce synthetic observables in the same near infrared spectral window as observed by the GREGOR Infrared Spectrograph (GRIS), which contains the highly magnetically sensitive photospheric Fe I line pair at 15 648.52 Å and 15 652.87 Å. We then use a parallelized wrapper to SIR to perform nearly 14 million inversions of the synthetic spectra to test how well the ‘true’ MHD atmospheric parameters can be constrained statistically. Finally, we degrade the synthetic Stokes vector spectrally and spatially to GREGOR resolutions and examine how this influences real observations, considering the impact of stray light, spatial resolution and signal-to-noise (S/N) in particular. Results. We find that the depth-averaged parameters can be recovered by the inversions of the undegraded profiles, and by adding simple gradients to magnetic field strength, inclination, and line of sight velocity we show that an improvement in the χ2 value is achieved. We also evaluate the extent to which we can constrain these parameters at various optical depths, with the kinematic and thermodynamic parameters sensitive deeper in the atmosphere than the magnetic parameters. We find the S/N and spatial resolution both play a significant role in determining how the degraded atmosphere appears. At the same time, we find that the magnetic and kinematic parameters are invariant upon inclusion of an unpolarized stray light. We compare our results to recent IN observations obtained by GREGOR. We studied a linear polarization feature which resembles those recently observed by GRIS in terms of appearing as ‘loop-like’ structures and exhibiting very similar magnetic flux density. Thus, we demonstrate that realistic MHD simulations are capable of showing close agreement with real observations, and the symbiosis between them and observations continues to prove essential. We finally discuss the considerations that must be made for DKIST-era observations.

Can Small-scale Magnetic Fields Be the Major Cause for the Near-surface Effect of the Solar p-mode Frequencies?

Abstract Small-scale magnetic fields are not only the fundamental element of the solar magnetism but also closely related to the structure of the solar atmosphere. The observations have shown that there is a ubiquitous tangled small-scale magnetic field with a strength of 60–130 G in the canopy-forming layer of the quiet solar photosphere. On the other hand, the multidimensional MHD simulations show that the convective overshooting expels the magnetic field to form the magnetic canopies at a height of about 500 km in the upper photosphere. However, the distribution of such small-scale “canopies” in the solar photosphere cannot be rigorously constrained by either observations or numerical simulations. Based on stellar standard models, we identify that these magnetic canopies can act as a global magnetic arch splicing layer, and we find that the reflections of the solar p-mode oscillations at this magnetic arch splicing layer result in significant improvement on the discrepancy between the observed and calculated p-mode frequencies. The location of the magnetic arch splicing layer is determined at a height of about 630 km, and the inferred strength of the magnetic field is about 90 G. These features of the magnetic arch splicing layer derived independently in the present study are quantitatively in agreement with the presence of small-scale magnetic canopies such as those obtained by the observations and 3D MHD simulations.

The Impact of Limited Time Resolution on the Forward-scattering Polarization in the Solar Sr I 4607 Å Line

Abstract Theoretical investigations predicted that high spatiotemporal resolution observations in the Sr i 4607 Å line must show a conspicuous scattering polarization pattern at the solar disk center, which encodes information on the unresolved magnetism of the intergranular photospheric plasma. Here we present a study of the impact of limited time resolution on the observability of such forward-scattering (disk-center) polarization signals. Our investigation is based on three-dimensional radiative transfer calculations in a time-dependent magnetoconvection model of the quiet solar photosphere, taking into account anisotropic radiation pumping and the Hanle effect. This type of radiative transfer simulation is computationally costly, which is why the time variation had not been investigated before for this spectral line. We compare our theoretical results with recent disk-center filter polarimetric observations in the Sr i 4607 Å line, showing that there is good agreement in the polarization patterns. We also show what we can expect to observe with the Visible Spectro-Polarimeter at the upcoming Daniel K. Inouye Solar Telescope.

Magnetic Energy Balance in the Quiet Sun on Supergranular Spatial and Temporal Scales

Abstract Small-scale magnetic fields are ubiquitous in the quiet solar photosphere and may store and transfer huge amounts of energy to the upper atmospheric layers. For this reason, it is fundamental to constrain the energetics of the quiet Sun. By taking advantage of a 24 hr long magnetogram time series acquired by the Hinode mission without interruption, we computed, for the first time, the average rate of change of magnetic energy density on supergranular spatial and temporal scales. We found that the regions where this quantity is positive correspond with the longest magnetic field decorrelation times, with the latter being consistent with the timescales of magnetic energy density variation. This suggests that, on average, the energy provided by photospheric electric and magnetic fields and current density is effective in sustaining the magnetic fields in the network.

A new spectroscopic method for measuring the temperature gradient in the solar photosphere

Context. The contribution of quiet-Sun regions to the solar irradiance variability is currently unclear. Certain solar-cycle variations of the quiet-Sun’s physical structure, such as the temperature gradient, might affect the irradiance. Accurate measurements of this quantity over the course of the activity cycle would improve our understanding of long-term irradiance variations. Aims. In a previous work, we introduced and successfully tested a new spectroscopic method for measuring the photospheric temperature gradient directly on a geometric scale in the case of non-magnetic regions. In this paper, we generalize this method for moderately magnetized regions that may be encountered in the quiet solar photosphere. Methods. To simulate spectroscopic observations, we used synthetic Stokes profiles I and V of the magnetic FeI 630.15 nm line and intensity profiles of the non-magnetic FeI 709 nm line computed from realistic three-dimensional magneto-hydrodynamical simulations of the photospheric granulation and line radiative transfer under local thermodynamical equilibrium conditions. We then obtained maps at different levels in the line-wings by convolution with the instrumental point spread function (PSF) under various conditions of atmospheric turbulence – with and without correction by an adaptive optics (AO) system. The PSF were obtained with the PAOLA software and the AO performance is inspired by the system that will be operating on the Daniel K. Inouye Solar Telescope. Results. We considered different conditions of atmospheric turbulence and photospheric regions with different mean magnetic strengths of 100 G and 200 G. As in non-magnetic cases studied in our previous work, the image correction by the AO system is mandatory for obtaining accurate measurements of the temperature gradient. We show that the non-magnetic line at 709 nm may be safely used in all the cases we have investigated. However, the intensity profile of the magnetic-sensitive line is broadened by the Zeeman effect, which would bias our temperature-gradient measurement. We thus implemented a correction procedure of the line profile for this magnetic broadening in the case of weakly magnetized regions. In doing so, we remarked that in the weak-field regime, the right- and left-hand (I + V and I − V) components have similar shapes, however, they are shifted in opposite directions due to the Zeeman effect. We thus reconstructed the intensity profile by shifting back the I + V and I − V profiles and by adding the re-centered profiles. The measurement then proceeds as in the non-magnetic case. We find that this correction procedure is efficient in regions where the mean magnetic strength is smaller or on the order of 100 G. Conclusions. The new method we implement here may be used to measure the temperature gradient in the quiet Sun from ground-based telescopes equipped with an efficient AO system. We stress that we derive the gradient on a geometrical scale and not on an optical-depth scale as we would do with other standard methods. This allows us to avoid any confusion due to the effect of temperature variations on the continuum opacity in the solar photosphere.

Velocity Field Diagnostics of the Quiet Sun Using the Lambda-Meter Method: Si I 1082.7 nm Line

The validity of the lambda-meter method for determining the quiet Sun velocity field using the Si I 1082.7 nm line is investigated. To this end, the intensity profiles of this line were calculated for the solar disk center by means of NLTE simulations in a three-dimensional model atmosphere describing the small-scale magnetic activity in the quiet solar photosphere. The velocity field recovered using the lambda-meter method from theoretical NLTE profiles of the Si I 1082.7 nm line was compared with the velocity field from the model atmosphere. The influence of atmospheric and instrumental effects on the results is considered. These effects are atmospheric turbulence and light diffraction by telescope aperture, such as VTT, GREGOR, and EST/DKIST. It is shown that, in the case of observations of the Si I 1082.7 nm line on large-diameter telescopes like GREGOR and EST/DKIST with a spatial resolution substantially better than 0.27″, the lambda-meter method provides reliable values of the velocity field for the lower and upper solar photosphere. For the middle photosphere, the correlation between the inferred and the real velocities is worse, particularly when using the smaller diameter telescopes like VTT. Under a poor spatial resolution exceeding 2″, information about the velocity field can be obtained only for the uppermost photospheric layers. For this case, the lambda-meter velocities turn out to be noticeably smaller than the real values.

The diagnostic potential of the weak field approximation for investigating the quiet Sun magnetism: the Si I 10 827 Å line

Aims. We aim to investigate the validity of the weak field approximation (WFA) for determining magnetic fields in quiet regions of the solar photosphere using the polarization caused by the Zeeman effect in the Si I10 827 Å line.Methods. We solved the NLTE line formation problem by means of multilevel radiative transfer calculations in a three-dimensional (3D) snapshot model taken from a state-of-the-art magneto-convection simulation of the small-scale magnetic activity in the quiet solar photosphere. The 3D model used is characterized by a surface mean magnetic field strength of about 170 G. The calculated Stokes profiles were degraded because of the atmospheric turbulence of Earth and light diffraction by the telescope aperture. We apply the WFA to the StokesI,Q,U,Vprofiles calculated for different seeing conditions and for the apertures of the VTT, GREGOR, EST and DKIST telescopes. We compare the inferred longitudinal and transverse components of the magnetic field with the original vertical and horizontal fields of the 3D model.Results. We find that with a spatial resolution significantly better than 0.5″ the surface maps of the magnetic field inferred from the Stokes profiles of the Si I10 827 Å line applying the WFA are close to the magnetic field of the model on the corrugated surface, corresponding to line optical depth unity at Δλ ≈ 0.1 Å for a disk-center line of sight. The correlation between them is relatively high, except that the inferred longitudinal and transverse components of the magnetic field turn out to be lower than in the 3D model.Conclusions. The use of the WFA for interpreting high-spatial-resolution spectropolarimetric observations of the Si I10 827 Å line obtained with telescopes like GREGOR, EST, and DKIST allows the longitudinal and transverse components of the magnetic field to be retrieved with reasonable precision over the whole quiet solar photosphere, the result being worse for telescopes of lower aperture.

Three-lobed near-infrared Stokes V profiles in the quiet Sun

Context. The 1.5-m GREGOR solar telescope can resolve structures as small as 0.4′′ at near-infrared wavelengths on the Sun. At this spatial resolution the polarized solar spectrum shows complex patterns, such as large horizontal and/or vertical variations of the physical parameters in the solar photosphere. Aims. We investigate a region of the quiet solar photosphere exhibiting three-lobed Stokes V profiles in the Fe I spectral line at 15 648 Å. The data were acquired with the GRIS spectropolarimeter attached to the GREGOR telescope. We aim at investigating the thermal, kinematic and magnetic properties of the atmosphere responsible for these measured complex signals. Methods. The SIR inversion code is employed to retrieve the physical parameters of the lower solar photosphere from the observed polarization signals. We follow two different approaches. On the one hand, we consider that the multi-lobe circular polarization signals are only produced by the line-of-sight variation of the physical parameters. We therefore invert the data assuming a single atmospheric component that occupies the entire resolution element in the horizontal plane and where the physical parameters vary with optical depth τ (i.e., line-of-sight). On the other hand, we consider that the multi-lobe circular polarization signals are produced not by the optical depth variations of the physical parameters but instead by their horizontal variations. Here we invert the data assuming that the resolution element is occupied by two different atmospheric components where the kinematic and magnetic properties are constant along the line-of-sight. Results. Both approaches reveal some common features about the topology responsible for the observed three-lobed Stokes V signals: both a strong (>1000 Gauss) and a very weak (<10 Gauss) magnetic field with opposite polarities and harboring flows directed in opposite directions must co-exist (either vertically or horizontally interlaced) within the resolution element. Conclusions.

Reconnection brightenings in the quiet solar photosphere

We describe a new quiet-Sun phenomenon which we call "Quiet-Sun Ellerman-like Brightenings" (QSEB). QSEBs are similar to Ellerman bombs (EB) in some respects but differ significantly in others. EBs are transient brightenings of the wings of the Balmer H-alpha line that mark strong-field photospheric reconnection in complex active regions. QSEBs are similar but smaller and less intense Balmer-wing brightenings that occur in quiet areas away from active regions. In the H-alpha wing we measure typical lengths of less than 0.5 arcsec, widths of 0.21 arcsec, and lifetimes of less than a minute. We discovered them using high-quality H-alpha imaging spectrometry from the Swedish 1-m Solar Telescope (SST) and show that in lesser-quality data they cannot be distinguished from more ubiquitous facular brightenings, nor in the ultraviolet diagnostics currently available from space platforms. We add evidence from concurrent SST spectropolarimetry that QSEBs also mark photospheric reconnection events, but in quiet regions on the solar surface.

MARKOV PROPERTIES OF THE MAGNETIC FIELD IN THE QUIET SOLAR PHOTOSPHERE

ABSTRACT The observed magnetic field on the solar surface is characterized by a very complex spatial and temporal behavior. Although feature-tracking algorithms have allowed us to deepen our understanding of this behavior, subjectivity plays an important role in the identification and tracking of such features. In this paper, we study the temporal stochasticity of the magnetic field on the solar surface without relying on either the concept of magnetic feature or on the subjective assumptions about their identification and interaction. The analysis is applied to observations of the magnetic field of the quiet solar photosphere carried out with the Imaging Magnetograph eXperiment (IMaX) instrument on board the stratospheric balloon, Sunrise. We show that the joint probability distribution functions of the longitudinal ( ) and transverse ( ) components of the magnetic field, as well as of the magnetic pressure ( ), verify the necessary and sufficient condition for the Markov chains. Therefore, we establish that the magnetic field as seen by IMaX with a resolution of 0.″15–0.″18 and 33 s cadence, which can be considered as a memoryless temporal fluctuating quantity.

Impact of surface dynamo magnetic fields on the solar abundance of the CNO elements

Most studies of the solar metallicity, based on abundance determinations of the CNO elements, ignore the fact that the quiet solar photosphere is significantly magnetized by a small-scale magnetic field with a mean field strength of ~100 G. Here we quantify how this significant magnetization affects determinations of the abundances of these chemical elements. To this end, we used two three-dimensional models of the solar photosphere taken from a magneto-convection simulation with small-scale dynamo action, one virtually unmagnetized, and the other characterized by a mean field strength of 160 G in the low photosphere. We performed local thermodynamic equilibrium spectral synthesis for a large set of C i, N i, and O i lines to derive abundance corrections. We included the magnetic broadening of the lines (direct effect) and the magnetically induced changes of the photospheric temperature stratification (indirect effect). We find that these small-scale dynamo magnetic fields only negligibly affect the determination of the solar abundances of carbon, nitrogen, and oxygen.

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.

The impact of surface dynamo magnetic fields on the solar iron abundance

Most chemical abundance determinations ignore that the solar photosphere is significantly magnetized by the ubiquitous presence of a small-scale magnetic field. A recent investigation has suggested that there should be a significant impact on the derived iron abundance, owing to the magnetically induced changes on the photospheric temperature and density structure (indirect effect). The three-dimensional (3D) photospheric models used in that investigation have non-zero net magnetic flux values and stem from magnetoconvection simulations without small-scale dynamo action. Here we address the same problem by instead using 3D models of the quiet solar photosphere that result from a state-of-the-art magneto-convection simulation with small-scale dynamo action, where the net magnetic flux is zero. One of these 3D models has negligible magnetization, while the other is characterized by a mean field strength of 160 Gauss in the low photosphere. With such 3D models we carried out spectral synthesis for a large set of Fe i lines to derive abundance corrections, taking the above-mentioned indirect effect and the Zeeman broadening of the intensity profiles (direct effect) into account. We conclude that if the magnetism of the quiet solar photosphere is mainly produced by a small-scale dynamo, then its impact on the determination of the solar iron abundance is negligible.

The impact of surface dynamo magnetic fields on the chemical abundance determination

AbstractThe solar abundances of Fe and of the CNO elements play an important role in addressing a number of important issues such as the formation, structure, and evolution of the Sun and the solar system, the origin of the chemical elements, and the evolution of stars and galaxies. Despite the large number of papers published on this issue, debates about the solar abundances of these elements continue. The aim of the present investigation is to quantify the impact of photospheric magnetic fields on the determination of the solar chemical abundances. To this end, we used two 3D snapshot models of the quiet solar photosphere with a different magnetization taken from recent magneto-convection simulations with small-scale dynamo action. Using such 3D models we have carried out spectral synthesis for a large set of Fei, Ci, Ni, and Oi lines, in order to derive abundance corrections caused by the magnetic, Zeeman broadening of the intensity profiles and the magnetically induced changes of the photospheric temperature structure. We find that if the magnetism of the quiet solar photosphere is mainly produced by a small-scale dynamo, then its impact on the determination of the abundances of iron, carbon, nitrogen and oxygen is negligible.

Spatial variations of Stokes profiles of magnetoactive lines Fe I

Solutions of the polarized radiative transfer problem were obtained within the 3D MHD model of the quiet solar atmosphere. Spatial variations of the Stokes profile parameters caused by the granulation structure and small-scale magnetic fields in the quiet solar photosphere for neutral iron magnetoactive lines are studied. The modulation effect of Stokes V profile parameters (amplitude and area) by the granulation structure of the solar photosphere is revealed. This effect is significant mainly in intergranules, in which the modulation depth reaches 50%. The correlation of Stokes profile parameters with small-scale solar granulation magnetic fields is investigated. It is shown that it is possible to construct calibration relationships that provide the correlation coefficient of 0.98 in diagnostics of small-scale magnetic fields using Stokes profile parameters of Fe I lines λ 525.02 and λ 524.71 nm.

NONLINEAR FORCE-FREE FIELD MODELING OF THE SOLAR MAGNETIC CARPET AND COMPARISON WITHSDO/HMI ANDSUNRISE/IMAX OBSERVATIONS

In the quiet solar photosphere, the mixed polarity fields form a magnetic carpet, which continuously evolves due to dynamical interaction between the convective motions and magnetic field. This interplay is a viable source to heat the solar atmosphere. In this work, we used the line-of-sight (LOS) magnetograms obtained from the Helioseismic and Magnetic Imager (HMI) on the \textit{Solar Dynamics Observatory} (\textit{SDO}), and the Imaging Magnetograph eXperiment (IMaX) instrument on the \textit{Sunrise} balloon-borne observatory, as time dependent lower boundary conditions, to study the evolution of the coronal magnetic field. We use a magneto-frictional relaxation method, including hyperdiffusion, to produce time series of three-dimensional (3D) nonlinear force-free fields from a sequence of photospheric LOS magnetograms. Vertical flows are added up to a height of 0.7 Mm in the modeling to simulate the non-force-freeness at the photosphere-chromosphere layers. Among the derived quantities, we study the spatial and temporal variations of the energy dissipation rate, and energy flux. Our results show that the energy deposited in the solar atmosphere is concentrated within 2 Mm of the photosphere and there is not sufficient energy flux at the base of the corona to cover radiative and conductive losses. Possible reasons and implications are discussed. Better observational constraints of the magnetic field in the chromosphere are crucial to understand the role of the magnetic carpet in coronal heating.

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.

Effect of small-scale magnetic fields on magnetically sensitive Fe I λ 525.02 and λ 1564.85 nm line profiles in the quiet solar photosphere

An integrated effect of small-scale magnetic fields on online absorption coefficient is analytically estimated. The formation of magnetically sensitive Fe I lines under the conditions of undisturbed solar photosphere in the presence of small-scale magnetic fields is studied. It is shown that these fields can broaden the wings of magnetically sensitive lines.

Hinode SOT/SP and SoHO/MDI quiet Sun magnetic field. Implications of their differences on the extrapolated chromospheric field and the height of the magnetic canopy

Aims. We explore the differences in the measurement of the magnetic field of the quiet solar photosphere provided by the Michelson Doppler Imager (MDI) onboard SoHO and the SpectroPolarimeter (SOT/SP) onboard Hinode and the ensuing implications for the extrapolated chromospheric magnetic field and the determination of the location of the magnetic canopy. Methods. We employ potential field extrapolation to reconstruct the chromospheric magnetic field using the magnetic field of the photosphere provided by the two instruments. We also calculate the plasma-β parameter using the VAL C model atmosphere of the quiet Sun to determine the height of the magnetic canopy. Results. MDI underestimates the magnetic field of the quiet Sun sometimes by a factor of five, which leads to an overestimation of the height of the magnetic canopy by up to ∼550km. Although the overall magnetic field configuration does not differ significantly when calculated with either MDI or SOT/SP, the data of the latter lead to lower and more extended canopies. The difference in the resolution of the two instruments does not seem to affect the chromospheric magnetic field higher than 1000km. Conclusions. The height of the magnetic canopy is an important parameter to consider when investigating wave propagation and the oscillatory properties of the quiet Sun regions in the network and internetwork. The canopy height’s derivation depends very much on the sensitivity of the instruments used to measure the photospheric magnetic field. Consequently precise measurements of the photospheric magnetic field are crucial to accurately reconstruct the chromospheric magnetic field and to distinguish between the various wave modes.