Stokes II — A new polarimeter for solar observations

A Stokes polarimeter has been built at the High Altitude Observatory to obtain line profiles in both linear and circular polarization in solar spectral lines. These measurements are interpreted using the theory of radiative transfer in the presence of a magnetic field to obtain vector magnetic fields on the solar disk and using the theory of resonance scattering and the Hanle effect to obtain vector magnetic fields in prominences. The polarimeter operates on the Sacramento Peak Observatory 40 cm coronagraph. It is an extensively modified and improved version of an earlier instrument.Polarization modulation is achieved by two KD^*P Pockels cells at the coronagraph prime focus and demodulation is by a microprocessor. The instrument control and data handling is done by a minicomputer. Silicon photodiode 128 element line array detectors have replaced the two photomultipliers used on the earlier instrument. This gives a speed increase of a factor of 50.A polarization scrambler provides a chop to a reference beam of unpolarized light by time scrambling the polarization of the solar beam. This device improves sensitivity to polarizations less than 0.01%. The polarization measurements are photon noise limited in most cases. This noise is 0.1% for a typical three second observation which is about one gauss on the longitudinal field and 10 gauss on the transverse field.The National Center for Atmospheric Research is sponsored by The National Science Foundation.     

Predictions on the application of the Hanle effect to map the surface magnetic field of Jupiter

In this paper we evaluate the possibility of detecting, for the first time, the surface magnetic field of Jupiter (∼1 bar level) by observing the change of linear polarization induced by the Hanle effect on the H Lyman-alpha (Lyα) emission line of the planet. We find that, indeed, the Hanle effect, which results from the interaction between a local magnetic field and the atomic polarization induced by absorption of anisotropic radiation, is sensitive to relatively weak values of the strength of the magnetic fields expected on planets. First, we show that for the Lyα emission backscattered by atomic H in the presence of a magnetic field, the Hanle effect is polarizing. This new result is in total contrast to the depolarizing effect predicted and observed for emission lines scattered at right angles in solar prominences. Additionally, to estimate the polarization rate for the case of Jupiter, we have considered three magnetic field models: a dipole field for reference, an O₄ based model [Connerney, J.E.P., 1981. The magnetic field of Jupiter—A generalized inverse approach. J. Geophys. Res. 86, 7679-7693], and finally, an O₆ based model [Khurana, K.K., 1997. Euler potential models of Jupiter's magnetospheric field. J. Geophys. Res. 102, 11295-11306]. In all models, we show that for the jovian backscattered Lyα line, the Hanle effect does enhance the Lyα linear polarization; the polarization rate may exceed 2% at specific regions of the jovian disc, making detection possible either remotely or from an orbiter around Jupiter. In general, depending on the instrumental sensitivity and the observing strategy used, we show that accurate mapping of the linear polarization rate at the planetary surface (thermosphere) or off-disc (corona) may provide a rather accurate estimate of the jovian total magnetic field strength on large area scales.     

Polarized light,magnetographs, and solar magnetic fields

Analysis of the effects of polarization in lines used in longitudinal (Babcock) and transverse (Severny) magnetographs shows that previous straightforward analyses of observations may lead to spurious results. Measures of the longitudinal magnetic-field strengths in prominences and in the chromosphere have been underestimated by more than 10% whenever the measured field has been less than 10 gauss. Transverse magnetograph results are subject to resonance polarization effects that may dominate the magnetic signal. The panchromatic transverse magnetograph results discussed by Dollfus and Leroy are based solely on curve of growth polarization interpretations. Again, except within a few degrees of the center of the disk, resonance polarization effects can dominate, and radically change, the interpretations of the observations.     

The determination of vector magnetic fields in prominences from the observations of the Stokes profiles in the D3 line of helium

A method is presented to measure the magnetic field vector in prominences by means of the polarimetric observations in the D₃ line of He obtained with the High Altitude Observatory Stokes polarimeter. The characteristics of the observed Stokes profiles are discussed. The theory of the Hanle effect is reformulated in the representation of the irreducible tensors of the density matrix, and is generalized to derive the circular polarization profiles across the spectral line in terms of the intensity and direction of the prominence magnetic field. The circular polarization profile so deduced can be employed to obtain useful information which adds to that carried by the linear polarization observations. A non-linear least-squares algorithm is proposed to derive the measurement of the magnetic field from the observations, and a consistency check is suggested to test the adequacy of the theoretical model to describe the physics of the He I atomic excitation in prominences.On leave from: Astrophysical Observatory of Arcetri, Largo E. Fermi, 5, 50125 Firenze, Italy.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Measurements of the magnetic field in solar prominences with a spectrally scanning magnetograph

We describe observations with a new magnetograph capable of recording the whole profile of emission lines in prominences. Two recordings are used simultaneously to study the Zeeman effect in circularly polarized light. The spectral scan is produced by the action of piezo ceramics of a Perot-Fabry inter ferometer combined with a narrow band interference filter.The instrument is calibrated using 100% circularly polarized light and an emission line produced in Laboratory conditions in a simulated longitudinal magnetic field. The magnetograph was attached to the large coronagraph (Ø 53 cm) of Kislovodsk to give a series of measurements of the H line of several quiescent and active prominences. The observed values of the longitudinal component of the magnetic field are between: -25 G + 13 G with a noise level at ±2 G for a corresponding resolution of 8 arc sec.Effects produced by the instrumental polarization are discussed.S.A.S. Institut d'Astrophysique du CNRS, 98bis, Bd Arago, F 75014 Paris.     

Partial frequency redistribution of polarized radiation

Resonance polarization, which is created by the scattering of an anisotropic radiation field in regions of zero or weak magnetic fields, is strongly dependent on the frequency redistribution taking place during the scatterings. Here we discuss the frequency redistribution matrix relevant to resonance lines, concentrating on linear polarization. First we analyze in detail the redistribution matrix in a zero magnetic field given by the theory of Omont, Smith and Cooper (1972), revisited by Domke and Hubeny (1988). We explain that the linear polarization maxima which may appear in the wings of the Stokes Q profiles of strong resonances lines such as the Ca I 4227 Å line are coherent frequency redistribution effects. Various approximate forms of the frequency redistribution matrix are also examined. For resonance polarization in a weak magnetic field, we suggest a new expression for the redistribution matrix which can be used at all line frequencies, and is consistent with the condition that the Hanle effect acts only in the line core.     

Polarization of the sodium D lines in prominences

The expected polarization of the sodium D lines from solar prominences is computed as a function of the local magnetic field vector. To this aim, the formulation of the Hanle effect in terms of the statistical tensors developed by Landi Degl'Innocenti (1982) is employed, with minor changes connected to hyperfine structure. The sodium atoms are described in the incomplete Paschen-Back regime so that the validity of the results is not limited to weak magnetic fields. The polarization diagrams obtained are discussed and compared with the corresponding diagrams for the helium D₃ line.     

Diagnostics with the Hanle effect

The Hanle effect has been extensively used for the determination of the magnetic field strength and direction in solar prominences. Here we address the problem of the diagnostics of weak magnetic fields in the solar photosphere and chromosphere by means of their Hanle effect in some selected absorption lines. As this is a relatively new area we will focus on the diagnostic methods and summarize some results that relate to the presence of a weak, turbulent magnetic field in the photosphere and to the chromospheric magnetic canopy. Finally we will outline some directions for future work.     

Comparative Analysis of Prominence Magnetic Field Measurements: Differences in Results Between Zeeman and Hanle Measurements

Results of magnetic field measurements in prominences using the Zeeman and Hanle methods are discussed critically. By considering an example of three prominences, for which magnetic field data from both methods are available, the discrepancies between the methods are demonstrated. The authors believe that the existing Hanle method does not reflect adequately the actual reality. To overcome the discrepancies calls for comparative analysis of prominence magnetic field measurements by both methods.     

The Hanle effect and the diagnostics of turbulent magnetic fields in the solar atmosphere

The theory of the Hanle effect is used to interpret the linear polarization measured in a number of spectral lines on the solar disk near the heliographic north and south poles, in search for a turbulent magnetic field in the solar atmosphere. The Hanle depolarization is separated from a number of other effects, including collisional depolarization and scattering geometry. Although the main aim of the paper is to elucidate the physics of the Hanle effect as applied to the Sun, our results indicate the existence of hidden or turbulent magnetic flux near the temperature minimum of the solar atmosphere, with a field strength between 10 and 100 G. This field is hidden in the sense that it is not seen in measurements of the longitudinal Zeeman effect (solar magnetograms). It carries more total magnetic flux than the kG network fields.     

The line-ratio method applied to vectormagnetographic measurements

Since solar magnetic fields are inhomogeneous, the averaging of Stokes parameter I within the entrance slit of the magnetograph is different from averaging Stokes Q₀ and V, because the former contains also light from non-magnetic, while the latter only contain light from magnetic regions. If the magnetographic calibration functions are calculated for homogeneous magnetic fields, errors arise, when they are used to reduce measurements of inhomogeneous fields. Therefore, we propose to use the line-ratio method to transform magnetographic measurements into the parameters of the magnetic vector field. The Q ratios and the V ratios of two carefully selected lines are free from errors of this kind. This is also the case for the Q ratios in line core and line wings in single-line magnetographs. An iterative method is presented to calculate the magnetic field parameters using the corresponding new calibration functions. An important advantage is, that the influence of scattered light in sunspots is also eliminated in a good approximation and the filling factor in plages can be estimated. This method is now used to determine magnetic vector fields in plages and sunspots of active regions with a new double-vector magnetograph.     

Measurement of the prominences magnetic field

A new type of magnetograph has been built capable to measure weak magnetic fields in the chromosphere and corona. Measurements of magnetic field in two prominences are demonstrated as examples.     

Vector magnetic fields in prominences

Observations of linear polarization in two resolved components of HeI D₃ are interpreted using the Hanle effect to determine vector magnetic fields in thirteen prominences. As in all vector magnetic field measurements, there is a two-fold ambiguity in field direction that is symmetric to a 180° rotation about the line-of-sight. The polar angles of the fields show a pronounced preference to be close to 90° from the local solar radius, i.e., the field direction is close to horizontal. Azimuth angles show internal consistency from point to point in a given prominences, but because of the rotational symmetry, the fields may be interpreted, in most cases, as crossing the prominence either in the same sense as the underlying photospheric fields or in the opposite sense. An exceptionally well observed large prominence of approximately planar geometry exhibits no measurable change in the vector magnetic field either with height or with location along the prominence axis. A second well observed large prominence overlying a sharply curved magnetic neutral line, when interpreted assuming that the prominence field has the same sense as the photospheric field, shows a rotation in the azimuth angle of the field relative to the observer by about 150° and relative to the local plane of the prominence by about 65°. In the alternative interpretation in which the prominence field has the opposite sense of the photospheric field, the field still rotates by 150° relative to the observer but remains essentially constant with respect to the plane of the prominence. This prominence erupted shortly after the extended observations. One good quality observation during the course of the eruption gives a vector field fully consistent with the pre-eruption field in the same segment of the prominence.     

Aspects of the zero level problem of solar magnetographs

The zero level problem of solar magnetographs is particularly important for observations of large-scale magnetic fields on the Sun. Experiments conducted at the STOP telescope of the Sayan observatory show that, in addition to adjustment errors of the polarization analyzer and the spectrograph focusing, spurious signals of the magnetograph are caused by polarization effects in optical components preceding the polarization analyzer and aberration errors of the spectrograph.     

Circular Polarization in a Solar Filament

Integrating 26 624 pairs of video frames, the authors have mapped the circular polarization in an active-region filament against the solar disk by using a traditional magnetograph working at the Hβ line. This filament, offset the disk center, appeared at the boundary of three decayed active regions. It was quiet and away from any strong enhanced network. The mapped circular polarization in the filament has an average polarization degree of 1.1×10⁻³ with a measurement precision of 4×10⁻⁴. The mapping of circular polarization in a filament may provide a supplementary diagnosis of the filament magnetic field, in addition to the mapping of linear polarization via the Hanle effect. However, the interpretation of the circular polarization requires treatment of the full quantum problem of Zeeman and non-Zeeman effects of Stokes line profiles.     

The Hanle effect of the coronal Lα line of hydrogen: Theoretical investigation

This paper is devoted to a computation of the effect of a magnetic field on the linear polarization of the coronal L line of hydrogen. Recent works (Gabriel et al., 1971) have shown that the linear polarization of this line is due to resonant scattering of the incident chromospheric L line. The Hanle effect is the modification of this linear polarization, due to the magnetic field. After having briefly recalled the main features of this effect and the conditions of the coronal L line formation, we present the theoretical formalism to be used for Hanle effect computations. The effect of the hyperfine structure of the line is included. Then the results of our computations are given in terms of linear polarization as a function of the magnetic field. We get that the effect of the hyperfine structure on these results is negligible, although this is not evident a priori. When the hyperfine structure is neglected, the line structure is simplified and the Hanle effect can be expressed with analytical formulae, which we give in the last part of this paper. After integration along the line of sight, these formulae could be used for magnetic field determination in the solar corona from measurements of the linear polarization of the L line.     

A paradox in measuring the magnetic field of the Sun

Significant discrepancies are often observed among the values of the mean magnetic field (MMF) of the Sun as a star observed by various instruments using various spectral lines. This is conventionally attributed to the measurement errors and “saturation” of a solar magnetograph in fine-structure photospheric elements with a strong magnetic field. Measurements of the longitudinal MMF performed in 1968–2006 at six observatories are compared in this paper. It is shown that the degree of discrepancy (slopes b of linear regression lines) varies significantly over the phase of the 11-year cycle. This gives rise to a paradox: the magnetograph calibration is affected by the state of the Sun itself. The proposed explanation is based on quantum properties of light, namely, nonlocality and “coupling” of photons whose polarization at the telescope-spectrograph output is determined by spacious parts of the solar disk. In this case, the degree of coupling, or “identity,” of photons depends on the field distribution in the photosphere and the instrument design (as Bohr said, “the instrument inevitably affects the result”). The “puzzling” values of slope b are readily explained by the dependence of the coupling on the solar-cycle phase. The very statistical nature of light makes discrepancies unavoidable and requires the simple averaging of data to obtain the best approximation of the actual MMF. A 39-year time series of the MMF absolute value is presented, which is indicative of significant variations in the magnitude of the solar magnetic field with a cycle period of 10.5(7) yr.     

Magnetograph measurements with temperature-sensitive lines

Certain discrepancies between theoretical and empirical calibrations of magnetograph response are resolved by recognizing the existence of line profile changes in magnetic regions. Many of the photospheric lines commonly used for magnetic field measurements weaken greatly in magnetic regions outside of sunspots. Unless due account is made of the line profile change, the magnetograph measurements underestimate magnetic flux and field strengths.The 5250.2 Å line is especially sensitive to weakening in magnetic regions. Measurements made with this line underestimate the true field by a factor ranging from about two on the linear portion of the profile to five near the line core.Kitt Peak National Observatory Contribution No. 500.Operated by the Association of Universities for Research in Astronomy Inc., under contract with the National Science Foundation.     

Vector magnetic fields in prominences

A preliminary discussion is presented of measurements of the polarization of the He i D₃ multiplet in a quiescent prominence, observed with a wavelength-scanning Stokes polarimeter. For a series of 43 observations in the same prominence, the linear polarization of the major component of D₃ lies primarily in the range 1 to 2% and of the wing component, the range 2 to 5%; the polarization vector angle lies primarily in the range 10–25° for the major component, and 25–35° for the other component. From a more limited data set, the polarization of both components is found to first increase as a function of height in the prominence, and then to decrease; the polarization angles of the major component vary in a random-like way with height, while the wing component shows a systematic change. The amount of polarization and the angle of polarization are governed by the Hanle effect. The collective effect of the group of lines at the peak of D₃ evidently has a different sensitivity to the Hanle effect than does the wing component, thus yielding at least four independent measurements - two polarizations and two angles. With some redundancy, the vector magnetic field can then be established using the detailed theory of the Hanle effect. Since the wing component of D₃ is a simple triplet, an initial estimate of the magnetic field strength and its horizontal orientation, 0, relative to the line of sight, is simply obtained. Examples of such calculations are presented.The National Center for Atmospheric Research is sponsored by the National Science Foundation.Operated by the Association of Universities for Research in Astronomy, Inc. under contract AST 78-17292 with the National Science Foundation.     

Complete determination of the magnetic field vector and of the electron density in 14 prominences from linear polarizaton measurements in the HeI D3 and Hα lines

The present paper is devoted to the interpretation of linear polarization data obtained in 14 quiescent prominences with the Pic-du-Midi coronagraph-polarimeter by J. L. Leroy, in the two lines Hei D₃ andH quasi-simultaneously. The linear polarization of the lines is due to scattering of the anisotropic photospheric radiation, modified by the Hanle effect due to the local magnetic field. The interpretation of the polarization data in the two lines is able to provide the 3 components of the magnetic field vector, and one extra parameter, namely the electron density, because the linear polarization of H is also sensitive to the depolarizing effect of collisions with the electrons and protons of the medium. Moreover, by using two lines with different optical thicknesses, namely Hei D₃, which is optically thin, and H, which is optically thick ( = 1), it is possible to solve the fundamental ambiguity, each line providing two field vector solutions that are symmetrical in direction with respect to the line of sight in the case of the optically thin line, and which have a different symmetry in the case of the optically thick line.It is then possible to determine without ambiguity the polarity of the prominence magnetic field with respect to that of the photospheric field: 12 prominences are found to be Inverse polarity prominences, whereas 2 prominences are found to be Normal polarity prominences. It must be noticed that in 12 of the 14 cases, the line-of-sight component of the magnetic field vector has a Normal polarity (to the extent that the notion of polarity of a vector component is meaningful; no polarity can be derived in the 2 remaining cases); this may explain the controversy between the results obtained with methods based on the Hanle effect with results obtained through the Zeeman effect. A dip of the magnetic field lines across the prominence has been assumed, to which the optically thick H line is sensitive, and the optically thin Hei D₃ line is insensitive.For the Inverse prominences, the average field strength is 7.5±1.2 G, the average angle,, between the field vector and the prominence long axis is 36° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 29° ± 20°, and the average electron density is 2.1 × 10¹⁰ ± 0.7 × 10¹⁰ cm^–3. For the Normal prominences, the average field strength is 13.2±2.0 G, the average angle,, between the field vector and the prominence long axis is 53° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 0° ± 20° (horizontal field), and the average electron density is 8.7 × 10⁹ ± 3.0 × 10⁹ cm^–3.