Unresolved Magnetic Field Research Articles

The polarization angle in the wings of Ca I 4227: A new observable for diagnosing unresolved photospheric magnetic fields

Context. When observed in quiet regions close to the solar limb, many strong resonance lines show conspicuous linear polarization signals, produced by scattering processes (i.e., scattering polarization), with extended wing lobes. Recent studies indicate that, contrary to what was previously believed, the wing lobes are sensitive to the presence of relatively weak longitudinal magnetic fields through magneto-optical (MO) effects. Aims. We theoretically investigate the sensitivity of the scattering polarization wings of the Ca I 4227 Å line to the MO effects, and we explore its diagnostic potential for inferring information on the longitudinal component of the photospheric magnetic field. Methods. We calculate the intensity and polarization profiles of the Ca I 4227 Å line by numerically solving the problem of the generation and transfer of polarized radiation under non-local thermodynamic equilibrium conditions in one-dimensional semi-empirical models of the solar atmosphere, taking into account the joint action of the Hanle, Zeeman, and MO effects. We consider volume-filling magnetic fields as well as magnetic fields occupying a fraction of the resolution element. Results. In contrast to the circular polarization signals produced by the Zeeman effect, we find that the linear polarization angle in the scattering polarization wings of Ca I 4227 presents a clear sensitivity, through MO effects, not only to the flux of the photospheric magnetic field, but also to the fraction of the resolution element that the magnetic field occupies. Conclusions. We identify the linear polarization angle in the wings of strong resonance lines as a valuable observable for diagnosing unresolved magnetic fields. Used in combination with observables that encode information on the magnetic flux and other properties of the observed atmospheric region (e.g., temperature and density), it can provide constraints on the filling factor of the magnetic field.

ПОРІВНЯННЯ РІЗНИХ МЕТОДІВ ВИМІРЮВАННЯ МАГНІТНИХ ПОЛІВ У СОНЯЧНИХ СПАЛАХАХ

We present a comparison of possibilities of three methods of magnetic field measurements using the Zeeman effect, namely, method of ”center of gravity”, splitting of Stokes V peaks and analysis of bisectors of I ± V profiles. We note that first method gives very averaged data in form of effective magnetic field Beff which presents the lower limit of local magnetic field in spatially unresolved structures. Splitting of Stokes V peaks DlV can present local magnetic field B, but only in a case when this splitting exceeds considerably the splitting of peaks of the Stokes I gradient dI/dl. Analysis of bisectors of I ± V profiles presents simple method for rapid diagnostics of magnetic field inhomogeneity. In particular, in case of really weak and homogeneous magnetic field, bisectors of I + V and I – V profiles should be parallel to each other. If these bisectors are non-parallel having some extrema, this could be an evidence of hidden presence of strong spatially unresolved magnetic field. Last method is very subtle but needs careful accounting of instrumental effects in line profiles. In this paper, we present also new data related to magnetic fields in limb solar flare of 14 July 2005. Spectral observations of this flare were carried out with the Echelle spectrograph of the Horizontal Solar Telescope of the Astronomical Observatory of Taras Shevchenko National University of Kyiv. In order to measure the magnetic fields in this flare, I ± V profiles of Нa line were studied. It was found that effective magnetic field Вeff in the flare reached 850 ± 100 G on height 16 Mm. However, the spectral evidences to yet stronger local fields of 104 – 105 G range were found. In particular, for several places of the flare, a weak circular polarization of opposite signs was found in line wings on distances of 1.8-2.2 Å from line center. If this polarization to interpret as manifestations of the Zeeman effect, the corresponding magnetic field is » 85–100 kG.

ВИМІРЮВАННЯ ПРОСТОРОВО НЕРОЗДІЛЬНИХ МАГНІТНИХ ПОЛІВ ЗМІШАНОЇ ПОЛЯРНОСТІ ЗА СПОСТЕРЕЖЕННЯМИ ЕФЕКТУ ЗЕЄМАНА В СОНЯЧНОМУ ФАКЕЛІ

It is shown that it is quite possible to measure spatially unresolved magnetic fields of mixed polarity by the Zeeman effect if their intensity exceeds 150-200 G. This means that one can interconnect the ranges of the registration of these fields based on the Hanle and Zeeman effects. This thesis is illustrated by the results of calculations of the half-width of the Stokes profile I for the FeI 5247.1 and 5250.2 lines. Parameter I is sensitive to the presence of magnetic fields, regardless of whether they have the same magnetic polarity within the input aperture of the instrument, or the opposite one. According to the calculations, if the accuracy of the measurement of the half-width ratio of these two lines is increased to 0.5 %, then it is possible to measure the magnetic fields from 70-100 G. On the basis of the proposed method, an estimate of the intensity of the magnetic fields of mixed polarity in a solar faculae in the tail part of the active region NOAA 1809 was made, which on the day of observations, August 6, 2013, was located not far from the Sun’s disc center. The Echelle Zeeman-spectrogram of this region was obtained on the Horizontal Solar Telescope of Astronomical Observatory of Taras Shevchenko National University of Kyiv. The magnetic field in the faculae was measured in two ways: by shift of of the “center of gravity”of the profiles of the FeI 5247.1 and FeI 5250.2 Ǻ lines in the I + V i I – V spectra and also by the half-width ratio of the profiles I of these lines. The first method allows to measure the effective magnetic field Beff, which turned out to be 280 G by FeI 5250.2 and 360 G by FeI 5247.1. The corresponding ratio Beff (5247.1) / Beff (5250.2) ≈ 1.3 indicates the existence of the sub-telescopic flux tubes with kilogauss fields. However, the ratio of the half-width of the Stokes I profiles of these two lines is 1.08, which corresponds to the magnetic field ± 650 G, if magnetic field is purely longitudinal. Based on the analysis of these data as well as the results of other studies, one can conclude that in the investigated faculae there were probably three magnetic field field components: the fluxtubes with kG field Bfluxtube, the areas of background field Bbackgr of regular magnetic polarity, and the areas of subtelescopic fields Bmixpol of mixed magnetic polarity. In absolute value the magnetic flux of tangled mixed-polarity field exceeds the flux of entire regular field with the intensities of Bfluxtube and Bbackgr at least 2-fold.

Spectral manifestations of extremely strong magnetic fields in the sunspot umbra

Fine peculiarities of the Zeeman effect in two big sunspots of October 29, 2003, and October 25, 2014, are analyzed. In order to search spectral evidences of very strong spatially unresolved magnetic fields, the Stokes I±V and V profiles of the FeI 6301.5 and 6302.5Å lines are studied in detail. Confirmed are two effects discovered earlier by Lozitsky (2016): (a) non-parallelism of bisectors in the FeI 6301.5 line at a distance of about ±250mÅ from the line center and (b) the existence of weak secondary peaks in Stokes V of the FeI 6302.5 line placed at a distance of, on the average, ±375mÅ from the line center. Close correlation (r=0.77±0.06) was found between (a) and (b) effects indicating the reality of very strong (≈8kG) unresolved magnetic fields. For the first sunspot, the presence of the abovementioned 8-kG fields is traced along 12Mm of the sunspot umbra. The filling factor is 0.2–0.3 here, and the relative Doppler velocities (without Evershed’s effect) are from −1.7 to −3.1km/s (plasma lifting). Similar parameters were also obtained for the second sunspot.

Investigation of Spatially Unresolved Magnetic Field Outside Sunspots Using Hinode/SOT Observations

AbstractThe structure of photospheric magnetic fields outside sunspots is investigated in three active regions using Hinode/Solar Optical Telescope(SOT) observations. We analyze Zeeman effect in FeI 6301.5 and FeI 6302.5 lines and determine the observed magnetic field value Beff for each of them. We find that the line ratio Beff(6301)/Beff(6302) is close to 1.3 in the range Beff < 0.2 kG, and close to 1.0 for 0.8 kG < Beff < 1.2 kG. We find that the observed magnetic field is formed by flux tubes with the magnetic field strengths 1.3 − 2.3 kG even in places with weak observed magnetic field fluxes. We also estimate the diameters of smallest magnetic flux tubes to be 15 − 20 km.

Indications of 8-kilogauss magnetic field existence in the sunspot umbra

We present magnetic field diagnostics in two big sunspot of different magnetic polarity observed on 18 May 2002 and 29 October 2003. In these sunspots, according to visual measurements, magnetic field strength in Fe I 5250.2Ǻ line was about 3500 gauss. The existence of stronger fields follows from the detailed study of fine spectral effects in I±V and V profiles of Fe I 6301.5 and 6302.5Ǻ lines, such as: (a) non-parallelism of bisectors in Fe I 6301.5 line related to distance about ±250mǺ from the line center, and (b) weak secondary Stokes V peaks on distance, on the average, ±375mǺ from the Fe I 6302.5Ǻ center. Consequently, we argue that these peculiarities indicate to the fact that spatially unresolved magnetic fields exist in the sunspot umbra, their strength being about 8kG. In small structures with such very strong fields magnetic polarity was the same as in the background field of the sunspot umbra, and Doppler velocity is about −1.9km/s (lifting of plasma).

Stochastic forecasting of the geomagnetic field from the COV-OBS.x1 geomagnetic field model, and candidate models for IGRF-12

We present the geomagnetic field model COV-OBS.x1, covering 1840 to 2020, from which have been derived candidate models for the IGRF-12. Towards the most recent epochs, it is primarily constrained by first differences of observatory annual means and measurements from the Oersted, Champ, and Swarm satellite missions. Stochastic information derived from the temporal spectra of geomagnetic series is used to construct the a priori model covariance matrix that complements the constraint brought by the data. This approach makes it possible the use of a posteriori model errors, for instance, to measure the ‘observations’ uncertainties in data assimilation schemes for the study of the outer core dynamics. We also present and illustrate a stochastic algorithm designed to forecast the geomagnetic field. The radial field at the outer core surface is advected by core motions governed by an auto-regressive process of order 1. This particular choice is motivated by the slope observed for the power spectral density of geomagnetic series. Accounting for time-correlated model errors (subgrid processes associated with the unresolved magnetic field) is made possible thanks to the use of an augmented state ensemble Kalman filter algorithm. We show that the envelope of forecasts includes the observed secular variation of the geomagnetic field over 5-year intervals, even in the case of rapid changes. In a purpose of testing hypotheses about the core dynamics, this prototype method could be implemented to build the ‘state zero’ of the ability to forecast the geomagnetic field, by measuring what can be predicted when no deterministic physics is incorporated into the dynamical model.

Small-scale magnetic field diagnostics in solar flares using bisectors of I ± V profiles

In the present study, spatially unresolved magnetic fields in solar flares are investigated by analyzing the fine structure of Zeeman splitting in two FeI lines. Namely, we consider bisector splitting of I±V Stokes profiles in 5123.7 and 5233Ǻ lines. The analysis of bisector splitting functions (BSF) of the 5233Ǻ line averaged over 12 solar flares of different classes, from C5 to X1.4, reveals two distinct peaks, around Δλ=80–110mǺ and 170–200mǺ. Such peculiarities indicate the unacceptability of weak field approximation for FeI 5233 line and need interpretation in the framework of inhomogeneous models with strong magnetic field components. Consequently, we argue that the named two peaks can reflect the existence of two discrete modes of subtelescopic magnetic fields with strengths about 6 and 12kG in photospheric layers.

A meta-analysis of the magnetic line broadening in the solar atmosphere

A multi-line Bayesian analysis of the Zeeman broadening in the solar atmosphere is presented. A hierarchical probabilistic model, based on the simple but realistic Milne-Eddington approximation to the solution of the radiative transfer equation, is used to explain the data in the optical and near infrared. Our method makes use of the full line profiles of a more than 500 spectral lines from 4000 $\AA$ to 1.8 $\mu$m. Although the problem suffers from a strong degeneracy between the magnetic broadening and any other remaining broadening mechanism, the hierarchical model allows to isolate the magnetic contribution with reliability. We obtain the cumulative distribution function for the field strength and use it to put reliable upper limits to the unresolved magnetic field strength in the solar atmosphere. The field is below 160-180 G with 90% probability.

EFFECTS OF UNRESOLVED MAGNETIC FIELD ON Fe I 617.3 AND 630.2 nm LINE SHAPES

The contribution of the quiet Sun to solar irradiance variability, due either to changes of the solar effective temperature or to the presence of unresolved magnetic field, is still poorly understood. In this study we investigate spectral line diagnostics that are sensitive to both temperature variations and the presence of small scale unresolved magnetic features in these areas of the solar atmosphere. Specifically we study the dependence on the magnetic flux density of three parameters describing the shape of two magnetically sensitive FeI lines, at 630.2 nm and 617.3 nm, namely the line core intensity (IC), full width at half maximum (FWHM), and the equivalent width (EQW). To this aim we analyze observations of active region NOAA 11172, acquired with IBIS at the Dunn Solar Telescope, as well as results from numerical synthesis. Our results show that IC is sensitive to both temperature and magnetic flux density variations, FWHM is mostly affected by magnetic field changes, and EQW is mostly sensitive to temperature. Variations of a few percent of the measured line parameters are found in observational data that was spatially degraded to represent quiet-Sun, disk-centre, medium resolution observations. It is therefore possible to disentangle magnetic from pure thermodynamic effects by comparison of temporal variations of the EQW and the FWHM of either the two FeI lines.

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.

POLARIMETRIC DIAGNOSTICS OF UNRESOLVED CHROMOSPHERIC MAGNETIC FIELDS

For about a decade, spectro-polarimetry of HeI 10830 has been applied to the magnetic diagnostics of the solar chromosphere. This resonance line is very versatile, as it is visible both on disk and in off-limb structures, and it has a good sensitivity to both the weak-field Hanle effect and the strong-field Zeeman effect. Recent observations of an active-region filament showed that the linear polarization was dominated by the transverse Zeeman effect, with very little or no hint of scattering polarization. This is surprising, since the HeI levels should be significantly polarized in a conventional scattering scenario. To explain the observed level of atomic depolarization by collisional or radiative processes, one must invoke plasma densities larger by several orders of magnitude than currently known values for prominences. We show that such depolarization can be explained quite naturally by the presence of an unresolved, highly entangled magnetic field, which averages to give the ordered field inferred from spectro-polarimetric data, over the typical temporal and spatial scales of the observations. We present a modeling of the polarized HeI 10830 in this scenario, and discuss its implications for the magnetic diagnostics of prominences and spicules, and for the general study of unresolved magnetic field distributions in the solar atmosphere.

Observational evidences for multi-component magnetic field structure in solar flares

Two solar flares of 25 July 1981 and 5 November 2004 of importance 2N and M4.1/1B, respectively, were investigated using observational data obtained with the Echelle spectrograph of the Kyiv University Astronomical Observatory. Stokes I and V profiles of the FeI lines 5233, 5247.1, 5250.2, 5250.6, 5576.1 and of CrI 5247.6 A have been analyzed. We found several evidences for the existence of spatially unresolved magnetic field structures with kG strengths. In particular, the values of the measured average longitudinal field B ∥ depend on the Lande factors g of the lines: in general, B ∥ increases with increasing factor g. Analogously, the observed line ratio B ∥(5250.2)/B ∥(5247.1) is increasing with increasing distance Δλ from the line center. The observed Stokes V profiles show some deviations from that of an assumed homogeneous field, presented by the Stokes I gradient, dI/dλ. A comparison with the non-split line FeI 5576.1 A shows that some of these deviations are real and indicate the presence of subtelescopic magnetic elements with discrete field strengths of several kG. The lines with large Lande factors have considerable broadenings of the Stokes I profiles, indicating a strong background magnetic field of mixed polarity. On the basis of all these data we conclude that a four-component magnetic field structure is a possible explanation. The field strengths are about ±1.05 kG in the background field, and 1.3−1.5, 3.9−4.0, and 7.4−7.8 kG at level of middle photosphere (h ≈ 300 km) in the spatially unresolved, small-scale magnetic elements.

Concerning the Existence of a "Turbulent" Magnetic Field in the Quiet Sun

We report on the a 5F-y 5Fo multiplet of Ti I and its interest for the study of turbulent magnetic fields in the quiet solar photosphere. In particular, we argue that the sizable scattering polarization signal of the 4536 A line (whose lower and upper levels have Lande factors equal to zero), relative to the rest of the lines in the multiplet, gives direct evidence for the existence of a ubiquitous, unresolved magnetic field. We cannot determine precisely the strength of the magnetic field, but its very existence is evidenced by the differential Hanle effect technique that this Ti I multiplet provides.

Center-to-limb variation of scattering polarization in molecular solar lines: Observations and modeling

We present center-to-limb measurements of the scattering polarization observed in molecular lines of C 2 and MgH in the spectral range between 515.7 and 516.1 nm, together with a radiative transfer model for the formation of these lines. The observations were performed in July 2000 with THEMIS inside the south polar limb. We were able to measure the polarization at distances between 1 arcsec and 50 arcsec from the solar limb. The lines appear as very weak absorption features in the intensity spectrum but their linear polarization clearly dominates in the polarization spectrum. We introduce here a simple radiative transfer model which allows to interpret the observed center-to-limb variations of both the intensity and linear polarization. The basic assumption is that molecular lines are formed higher in the photosphere than the continuous photospheric radiation. Molecules are thus illuminated by the polarized continuum photospheric radiation field. We account for a possible Hanle eect due to weak unresolved magnetic fields but we neglect depolarizing collisions. The model depends on four parameters which are determined by fitting both the intensity and polarization in 9 molecular lines of the observed spectral domain. Making use of the dierential Hanle eect in the dierent lines of C2 we show that the C2 lines are aected by the Hanle eect due to a weak unresolved magnetic field. Its mean strength is on the order of 15 Gauss in the upper photosphere and increases to values on the order of 50 Gauss at larger depths. These results are in good agreement with those derived previously (Faurobert et al. 2001) from the linear polarization of the SrI 460.7 nm line which was observed simultaneously. Such a weak field has almost no eect on the MgH lines.

Observation of He I 10830 dark points : Li Hui, Fan Zhong-yu & You Jian-qi Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210009

We present magnetic field diagnostics in two big sunspot of different magnetic polarity observed on 18 May 2002 and 29 October 2003. In these sunspots, according to visual measurements, magnetic field strength in Fe I 5250.2 Ǻ line was about 3500 gauss. The existence of stronger fields follows from the detailed study of fine spectral effects in I ± V and V profiles of Fe I 6301.5 and 6302.5 Ǻ lines, such as: (a) non-parallelism of bisectors in Fe I 6301.5 line related to distance about ±250 mǺ from the line center, and (b) weak secondary Stokes V peaks on distance, on the average, ±375 mǺ from the Fe I 6302.5 Ǻ center. Consequently, we argue that these peculiarities indicate to the fact that spatially unresolved magnetic fields exist in the sunspot umbra, their strength being about 8 kG. In small structures with such very strong fields magnetic polarity was the same as in the background field of the sunspot umbra, and Doppler velocity is about −1.9 km/s (lifting of plasma).

Measurements of magnetic fields and the analysis of stokes profiles

Recent advances in polarimetry allowing the recording of polarized line profiles with high spectral resolution and signal-to-noise ratio over large portions of the solar spectrum offer rich new diagnostic possibilities. Thus we can now in a systematic way build models of the height variation of the magnetic field, temperature, density, and mass motions in the spatially unresolved subarcsecond magnetic structures. The analysis of the Stokes spectra also allows us to build a foundation for proper diagnostics of vector magnetic fields, a goal that cannot be achieved before the intrinsic properties of the spatially unresolved magnetic fields have been determined. Another new diagnostic tool is the Hanle effect. A recent exploratory survey of coherence effects through the recording of the linear polarization with high spectral resolution throughout the whole visible solar spectrum aims at establishing a foundation for the exploitation of the Hanle effect on the solar disk.