Stokes polarimetry of the Zeeman and Hanle effects

Transcription

1 33 Stokes polarimetry of the Zeeman and Hanle effects Jan O. Stenflo I Abstract Magnetic fields are responsible for almost all variability in the Universe on intermediate time scales. The information on the magnetic fields is encoded in the polarization of the radiation from the Sun and stars through the Zeeman and Hanle effects. Stokes polarimetry is the observational tool that gives us access to this information and allows us to determine the structure and evolution of the fields. Space-based observations are needed for two main reasons: (1) To allow high and stable angular resolution over a large field of view. (2) To get access to the vacuum ultraviolet (VUV), which contains information on the magnetic fields in the corona and the chromosphere-corona transition region. VUV polarimetry has considerable potential but has been much neglected in the past. Dimensionality and trade-offs in information space From scalar to 4-vector measurements Spectro-polarimetry enhances the dimensionality of information space from a scalar problem (radiance) in the case of ordinary spectrometry to a 4-D (polarization vector) problem. The different components of the Stokes vector (which we will define later, see Page 545) carry different and complementary types of information that are not contained in the intensity spectrum, in particular information on magnetic fields in the radiating medium. Trade-offs in parameter space For the design of observing programmes it is helpful to consider another 4- D parameter space, namely that spanned by the angular, spectral, and temporal resolutions, together with the radiometric and polarimetric accuracies. These four parameters cannot be optimized simultaneously, even with the largest conceivable telescopes; trade-offs are always needed (cf., Stenflo 2001). The radiance of a star does not depend on its distance, only on its effective temperature. Therefore the I Institute of Astronomy, ETH Zurich, CH-8093 Zurich, Switzerland 543

2 Stokes polarimetry of the Zeeman and Hanle effects proximity of the Sun does not help much when we study resolution elements close to the telescope diffraction limit; we quickly run out of photons. In Stokes polarimetry it has become possible to eliminate systematic effects such that the polarimetric accuracy is only constrained by the quantum limit of the photon Poisson statistics, down to levels of in the degree of polarization (Stenflo 2004a). For a precision of 10 5 we need to collect photo-electrons in the detector, or, when accounting for all the efficiencies and optical transmissions of the telescope system, of the order of photons per resolution element. This has routinely been achieved in combination with high spectral resolution, but at the expense of the angular and temporal resolutions. In most solar magnetic field work priority has been given to angular resolution at the expense of polarimetric precision. Then the temporal resolution has to be sufficiently high, since smaller structures evolve faster, and the integration time should not be longer than the evolutionary time scale. To resolve 100 km on the Sun (0.14 ) the integration time should be shorter than 10 s, the approximate time it takes for a sound wave to cross the resolution element. The photon flux then limits the relative polarization accuracy in resolved spectral lines to at best 0.1%. This is fully sufficient for most applications of the longitudinal Zeeman effect (lineof-sight magnetograms in the form of circular-polarization maps), but it is marginal for the transverse Zeeman effect and insufficient for the Hanle effect. Physical origins of polarization Polarization is associated with broken symmetries. The spatial symmetry may be broken by the presence of a magnetic field. This is the origin of the Zeeman effect. The symmetry can also be broken by anisotropic scattering. The presence of magnetic fields then leads to polarization phenomena that are covered by the term Hanle effect. By Zeeman-effect polarization we generally refer to polarization effects that are not dependent on coherent scattering processes. The Zeeman and Hanle effects are sensitive to magnetic fields in very different parameter ranges and therefore provide mutually highly complementary diagnostic information. While the Zeeman effect has been applied in astrophysical contexts for a century, since Hale used it to discover magnetic fields in sunspots (Hale 1908), applications of the Hanle effect are still in their infancy. Stokes vector imaging Why the Stokes formalism is needed The polarization of an electromagnetic wave is determined by the oscillations of the two orthogonal electric vectors E x and E y in an x-y coordinate system in a plane transverse to the wave propagation. E x and E y can be combined into a complex 2-vector, the Jones vector, which is characterized by four parameters (two amplitudes and two phases). A Jones vector however always represents light that is fully elliptically polarized. It is incapable of describing partially polarized radiation, i.e., a natural beam of light.

3 545 F F F F unpolarized o o 0 45 right-handed circular polarization Figure 33.1: Idealized polarizing filters used in the operational definition of the Stokes parameters. Each wave train or photon is always fully elliptically polarized. Partial polarization is produced by the process of incoherent superposition of an ensemble of wave packets with arbitrary phase relations. To properly describe the polarization state of such an ensemble we need the Stokes formalism (cf., Stenflo 1994). The most convenient way of defining the Stokes vector I, which consists of the four Stokes parameters I, Q, U, V, or S k, k = 0, 1, 2, 3, i.e., S 0 I I = S 1 S 2 Q U, (33.1) V S 3 is in terms of the four idealized filters F k shown in Figure F 0 represents empty space, F 1 and F 2 transmit linear polarization with the electric vector at position angles 0 and 45, respectively, while F 3 transmits right-handed circular polarization. Let I k be the radiance of the beam behind each filter. Then I k = 1 2 (S 0 + S k ). (33.2) The physical meaning of the Stokes parameters S k can be understood as follows: If we replace filters F k with ones that transmit the orthogonal polarization state, then Q, U, and V change sign. From this it follows that Stokes I represents the intensity, Stokes Q the intensity difference between horizontal and vertical linear polarization, Stokes U the intensity difference between linear polarizations at +45 and 45, Stokes V the intensity difference between right- and left-handed circular polarizations. In the Stokes formalism the effects of a medium can be described in terms of a 4 4 matrix, the Mueller matrix, which operates on the incoming Stokes vector to produce the output Stokes vector. The medium can be a stellar atmosphere, telescope optics, a train of polarization optics (modulators, wave plates, polarizers), or all of this combined. It can be treated as a black box described by a single Mueller matrix M. If the ith component inside the black box has Mueller matrix M i, then the total matrix is formed by matrix multiplications: M = M n M n 1... M 2 M 1. (33.3)

4 Stokes polarimetry of the Zeeman and Hanle effects The ordering of the matrices is essential, from right to left when following the direction of the light beam. Calibration is done by inserting known polarizers in front of the system (cf., Stenflo 1994). Polarization modulation and demodulation To measure polarization we need to form differences between orthogonal polarization states. Beam splitters may be used to record the orthogonal states simultaneously on different portions of a detector. This is not convenient for simultaneous recording of all of the four Stokes parameters, moreover the different pixel sensitivities in the different parts of the detector (the gain table) limit the polarization accuracy. High-precision vector polarimetry therefore uses temporal modulation of the various polarization states. In ground-based observations one needs to modulate faster than the atmospheric seeing fluctuations ( > 1 khz), but this requirement can be much relaxed in space-based observations. Mechanical modulation (rotating retarder plate) may introduce beam wobble and influence of optical inhomogeneities. Better precision is achieved with electro-optical modulation, which can be done with piezoelastic modulators (PEM), or with nematic or ferro-electric liquid crystals. PEMs have the great advantage that basically any optical material may be used, like lithium fluoride, which has good transmittance in the vacuum ultraviolet. The main disadvantage is the high, sinusoidal modulation frequency (typically 50 khz), which may not be changed, since PEMs are resonant devices. The compatibility problem that this causes when PEMs are used in combination with the slow read-out of large CCD detectors has been elegantly solved with the ZIMPOL (Zurich Imaging Polarimeter) technology (Povel 1995, 2001; Gandorfer et al 2005), which in the future might become superseded by CMOS technology. For space applications the use of rotating wave plates or nematic liquid crystals in the visible, and rotating wave plates in the vacuum ultraviolet, may be the appropriate solution. Instrumental polarization Since the telescope optics are generally polarizing they corrupt the Stokes vector that we want to determine. Therefore the optics for the polarization analysis (the modulation package, preceded by the polarization calibration optics) should be placed as early as possible in the optical train. The part of the telescope that is in front of the polarization calibration optics should produce as little polarization as possible. This is the case if this part of the optical system is axially symmetric. If significant instrumental polarization is unavoidable in the telescope design, then it is much more manageable if it is constant in time. Although instrumental polarization may in principle be calibrated, modelled, and removed in the data reduction, large instrumental polarization should be optically compensated for as much as possible to avoid nasty effects of detector non-linearities, which generate spurious polarization signals that are next to impossible to calibrate or model.

5 547 Figure 33.2: Line-of-sight component of the magnetic field recorded by the Hinode satellite on 13 December 2006 during a proton flare. Bright and dark areas represent magnetic fields directed towards and away from the observer. Hinode is a Japanese mission developed, launched and operated by ISAS/JAXA, in partnership with NAOJ, NASA and STFC (UK). Additional operational support is provided by ESA and NSC (Norway). Spectral and spatial information space Polarimetry may be combined with any system for spectral selection. The data cube consists of the two spatial coordinates on the Sun, x and y, and the wavelength coordinate λ. Since the detector is a 2-D device, scanning is needed to cover a 3-D portion of the data cube. With (stigmatic) spectrographs one gets images in (x, λ) space for each given y, and then needs to stepwise scan in y to build up an image of the Sun. With narrow-band filters one gets (x, y) images for each given λ, and needs to stepwise tune the filter in λ to build up line-profile information. One interesting alternative that combines these two features is the solar chromatograph (Stenflo 1973b), which gives monochromatic (x, y) images, but such that the wavelength λ varies linearly with y. Therefore line profile information is simultaneously present in each image, although it is convolved with the spatial coordinate. This solution is based on the concept of subtractive double dispersion and has so far only been systematically implemented in the MSDP instrument of the French THEMIS telescope on Tenerife (Mein 2002). Advantages of observations above Earth s atmosphere Space-based Stokes vector polarimetry has two main advantages: (1) It gives superior and stable angular resolution over a large field of view. (2) It gives access to the extraterrestrial/vacuum ultraviolet (VUV) part of the spectrum. The stable

6 Stokes polarimetry of the Zeeman and Hanle effects angular resolution is needed to explore the evolution of the small-scale magnetic fields, to understand magneto-convection, dynamo processes and the underlying mechanisms of solar and stellar activity. Access to the VUV is needed to explore the magnetic fields in the solar transition region and corona. This is of profound importance for understanding the dynamics and the heating processes of the outer solar atmosphere, which ultimately control the space weather and terrestrial effects. At the time of writing the highest angular resolution in solar observations is still achieved from the ground thanks to the application of adaptive optics: the images from the Swedish Solar Telescope SST on La Palma reach the diffraction limit of 0.1 for the 1m telescope. Adaptive-optics correction, however, only works over a small field of view, which in future may be improved upon by more complex multi-conjugate adaptive optics systems (Berkefeld et al 2001). The quality of the adaptive-optics correction improves when the atmospheric seeing is better, but since the seeing is almost always highly variable on time scales of minutes or less, it is next to impossible to obtain evolutionary sequences that can compete with space-based observations. In contrast, the spacecraft Hinode achieves an angular resolution of 0.2 over the whole large field of view (cf., Figure 33.2), and the resolution remains the same over the course of the mission, thus allowing evolutionary sequences of extraordinary quality and length (Kosugi et al 2007). For observations in the visible, space-based instruments of modest spatial resolution still have great advantages. An example is the Michelson Doppler Imager (MDI) on the SOHO spacecraft (Scherrer et al 1995; Title 2010). In spite of its relatively low spatial resolution of 4 it has been of tremendous value, since it has given us a continuous time series that covers more than one solar activity cycle with high-quality full-disk magnetograms that all have the same resolution. Zeeman-effect observations Magnetic-field evolution Although the magnetic-field evolution occurs on all scales, the key to the understanding of solar magnetism, basic dynamo processes, and the underlying mechanisms of stellar activity may be found in the smallest scales. Some of the most fundamental still unanswered questions concern the emergence, decay, and removal of the photospheric magnetic flux. All the emerged magnetic flux has to be removed on the solar-cycle time scale and be in statistical equilibrium with the emergence rate, otherwise the photosphere would quickly get choked with undisposed magnetic flux. We know that as we go from active regions to ephemeral regions and still smaller scales, the emergence rate increases dramatically, but we do not know how one can get rid of the flux at such tremendous rates. We need to determine the relative contributions of the following three alternative removal mechanisms: (i) Cancellation of opposite polarities (reconnection). (ii) Flux retraction (reprocessing in the convection zone). (iii) Flux expulsion (and the role of coronal mass ejections). In spite of decades of hard work we still know practically nothing about the relative roles of these processes.

7 549 Figure 33.3: Illustration of the fractal-like pattern of quiet-sun magnetic fields. The rectangular area covered by the left map (from Kitt Peak) is about 15% of the area of the solar disk, while the map to the right (from the Swedish La Palma telescope) covers an area that is 100 times smaller. The white and black areas correspond to magnetic flux of positive and negative polarities, separated by grey voids of seemingly no flux. Analysis of Hanle-effect observations (cf., Page 550) of atomic and molecular lines have shown that these grey regions are actually not voids at all, but are teeming with turbulent magnetic fields that carry a significant magnetic energy density. Since these turbulent fields are tangled with mixed polarities on very small scales, they are invisible to observations of the Zeeman effect, but they are revealed by observing the Hanle effect (Stenflo 2004b). Small-scale structuring Observations with improved angular resolution in combination with indirect diagnostics have shown that the magnetic structuring extends from the global scales towards the diffusion scales far beyond the telescope resolution. There is a remarkable degree of self-similarity over the various scales, suggesting a fractal-like nature (cf., Figure 33.3). The scales that we are beginning to resolve (the dimensions of the photon mean free path and the pressure scale height) are of critical importance for a physical understanding of the scale spectrum of magneto-convection. Since however the structuring continues far into the unresolved domain, we always need to complement the direct, resolved observations with indirect techniques to extract statistical information about the unresolved structures, like the line-ratio method (Stenflo 1973a). These indirect methods are now being extended through applications of the Hanle effect.

8 Stokes polarimetry of the Zeeman and Hanle effects Figure 33.4: Trajectory of a damped classical oscillator, illustrating the Hanle-effect depolarization and rotation of the plane of polarization when the magnetic field is oriented along the line of sight. The three diagrams represent different values of the field strength, which increases from left to right. Hanle-effect observations Classical and quantum descriptions of the Hanle effect In contrast to the Zeeman-effect polarization the Hanle effect is a coherency phenomenon that only occurs in coherent scattering processes. Magnetic fields remove the degeneracy of the radiatively excited and coherently superposed magnetic substates and thereby cause partial decoherence that leaves a signature in the polarization of the scattered radiation. In a classical description the damped dipole oscillations that are induced by the incident radiation precess in the presence of a magnetic field, as pictured in Figure In the illustrated case it is assumed that vertical oscillations are induced by the excitation process, and that we observe the emitted radiation along the magnetic field direction. The trajectory of the damped oscillator forms a rosette pattern that becomes more isotropic when the field is stronger. The emitted polarization is obtained from the Fourier transform of the rosette pattern. In the absence of magnetic fields the scattered radiation would be linearly polarized in the vertical direction (in the illustrated case), but as the field strength is increased, the plane of polarization rotates, and the amount of polarization is reduced. If the classical equation for the dipole oscillation is decomposed in the three Cartesian coordinate equations, the component equations are coupled to each other due to the v B term of the Lorentz force. If we however decompose in terms of complex spherical vectors, the component equations decouple (cf., Stenflo 1994). These three components correspond to the m = 0, ±1 transitions (the π and σ components) in the quantum-mechanical picture. Since they oscillate with slightly different frequencies due to the Larmor precession (which is the source of the Zee-

9 551 man splitting), the damped oscillators gradually get out of phase, which leads to partial decoherence depending on the strength of the magnetic field. Observational signatures of the Hanle effect The Hanle effect leaves its imprints in the linear polarization. Its two main signatures are depolarization and rotation of the plane of polarization when the scattering geometry resembles 90 scattering. Figure 33.5 shows an example of the qualitatively different signatures of the Hanle and Zeeman effects. The Hanle effect also occurs in forward scattering, where it generates linear polarization in the presence of transverse magnetic fields (Trujillo Bueno 2001). Preconditions for the Hanle effect to be observable at all are (i) that coherent scattering plays a significant role in the formation of the spectral line, and (ii) that the scattering polarization has observable amplitude. Condition (i) favours strong resonance lines, which anyway dominate the spectrum from the chromospherecorona transition region. Condition (ii) requires that the incident radiation field of the scattering process is significantly anisotropic. In the vacuum ultraviolet the radiance contrasts of the solar structures are much larger than in the visible, which implies that the local anisotropies of the radiation field are large. The expected local fluctuations of the scattering polarization are therefore expected to be large as well. In the visible the contrasts are much smaller, with the consequence that the anisotropy due to the limb darkening becomes more important than the local radiance fluctuations. This global anisotropy determines the polarization scale of the Second Solar Spectrum (Stenflo and Keller 1997), the highly-structured spectrum in linear polarization that is exclusively due to coherent scattering. Due to the scattering geometry when limb darkening is the source of the anisotropy, the polarization amplitude increases monotonically as we approach the limb. Therefore, in the visible part of the spectrum, the best conditions for the observability of the Hanle effect are found in a zone near (but inside) the solar limb, or in prominences above the limb. The situation is somewhat different in the vacuum ultraviolet, since the anisotropies are more local than global. Therefore the observability should be less restricted to a limb zone. For structures that are rather high above the solar surface the global anisotropy would however dominate, if the total illumination from the underlying solar disk occupies a solid angle that is significantly smaller than a half sphere (2π). Complementarity of the Zeeman and Hanle effects While the Zeeman-effect polarization becomes measurable when the Zeeman splitting is comparable to the Doppler width of the spectral line used, the sensitivity range for the Hanle effect is where the Zeeman splitting is comparable to the damping width or inverse life time of the excited atomic or molecular state. Since the damping width is typically two orders of magnitude smaller than the Doppler width, the Hanle effect is sensitive to correspondingly weaker fields. This makes it particularly suited for diagnostics of magnetic fields in the transition region and corona, where the fields are relatively weak due to the rapid expansion with height of the many strong, photospheric flux concentrations. In addition, since the Zeeman

10 Stokes polarimetry of the Zeeman and Hanle effects Sr I 4607 Å, a photospheric line Ca I 4227 Å, a chromospheric line Figure 33.5: Examples of Hanle-effect signatures in Stokes spectra (the intensity I and the three fractional polarizations Q/I, U/I, and V/I) recorded with groundbased instrumentation, illustrating the difference between the Hanle and Zeeman effects. The photospheric Sri 4607Å line and the chromospheric Cai 4227Å line exhibit strong linear polarization due to coherent scattering, which in the presence of magnetic fields gets modified by the Hanle effect (seen as spatial variations of Q/I and U/I along the slit). The surrounding spectral lines display the usual transverse Zeeman effect in the linear polarization (Stokes Q/I and U/I), and the longitudinal Zeeman effect in the circular polarization (Stokes V/I). The recordings were made with the Zurich Imaging Polarimeter (ZIMPOL) at the McMath-Pierce facility (Kitt Peak). splitting scales with λ 2, the signatures of the Zeeman effect are tiny in the vacuum ultraviolet. Another fundamental area where the Zeeman and Hanle effects are highly complementary concerns the spatially unresolved domain of magneto-convection. The Zeeman effect is blind to spatially unresolved turbulent fields with zero net magnetic flux, in contrast to the Hanle effect that has different symmetry properties (the sign of the Hanle depolarization is independent of field polarity). Observational strategy and interpretational issues The Hanle-effect signatures depend on the anisotropies of the radiation field, on the scattering geometry, and on optical-depth effects in the medium, in addition to the magnetic field. To disentangle these effects it helps to apply a strategy of using combinations of spectral lines that are affected similarly by the non-magnetic

11 553 factors, but which differ in their magnetic sensitivities (in analogy with the lineratio technique for Zeeman-effect observations). A further problem is that the Hanle effect in principle delivers only two observables (amount of depolarization and rotation of the plane of polarization), while the magnetic field vector has three spatial components. For a unique interpretation one therefore needs additional observational or modelling constraints. The longitudinal Zeeman effect has the great advantage that it allows circular polarization maps to be directly interpreted as maps of the line-of-sight component of the magnetic flux density. In contrast, the magnetic-field information that is carried by the Hanle-effect signatures is rather convolved with other factors in a way that prevents magnetic maps from being extracted without additional information. Still, the Hanle effect provides information about parameter domains that are not accessible by other means, but which are needed for understanding the fundamental physical processes on the Sun. Stokes polarimetry in the vacuum ultraviolet Advantages of the VUV region The VUV and X-ray regions of the solar spectrum are full of resonance lines that are formed in the chromosphere-corona transition region or above. Observations in such lines allow us to diagnose the physics of the outer solar atmosphere where the coronal heating takes place, the solar wind is driven, and the space weather is generated. Crude information on coronal magnetic fields can be obtained with radio-astronomical techniques, forbidden-line scattering polarization in the visible, and (more recently) by recordings of the longitudinal Zeeman effect of forbidden coronal lines in the near infrared. Spectro-polarimetry in the vacuum ultraviolet remains a promising but largely unexploited area with considerable potential. The VUV region down to about 1050Å is of special interest, since transmission optics like lithium fluoride can be used throughout this range, which makes it feasible to apply retarders and modulators for complete Stokes polarimetry. At shorter wavelengths one may still determine the linear polarization by using the partially polarizing properties of oblique reflections, but circular polarization appears to be out of reach. This may however not be such a serious limitation, since the Hanle effect has its signatures in the linear polarization, while the circular polarization is a property of the Zeeman effect. Due to its λ 2 dependence the Zeeman effect will be ineffective at short wavelengths. In the VUV its observability will mainly be limited to sunspots. Since the Hanle effect is sensitive to considerably weaker fields than the Zeeman effect, we expect that it will play the leading diagnostic role in the VUV and below. Coronal magnetic fields have field strengths in the Hanle sensitivity range for allowed line transitions. All the allowed coronal and transition-region lines are in the EUV or soft X-ray region, which can only be accessed from space. The Hanle effect can also be used to diagnose the expanding envelopes of hot stars, but also here the relevant spectral lines are in the VUV, inaccessible from ground. Since magnetic fields play a key role for the physics of stellar transition

12 Stokes polarimetry of the Zeeman and Hanle effects Figure 33.6: Optical scheme of the first space-based spectro-polarimeter for the recording of scattering polarization in the vacuum ultraviolet (Stenflo et al 1976). It was flown on Intercosmos 16 in regions, coronae, and stellar winds, we need space-based observations of the Hanle effect to diagnose these domains. Choice of polarization optics Very little has been done in the area of VUV polarimetry, it still represents almost virgin territory. For the detection of linear polarization one needs to make a trade-off between polarization efficiency and transmission. Thus Brewster-angle reflection on uncoated dielectric surfaces gives complete polarization, but the reflectivity is generally low. Coated reflective surfaces give good throughput and varying degree of polarization, depending on the choice of coating. A good choice is to use 60 reflection (near the Brewster angle) on a gold-coated mirror, which gives a degree of polarization of about 70%. In contrast, an aluminium-coated mirror gives about 5% polarization or less. Magnesium fluoride (MgF 2 ) is birefringent and may be used as a retarder down to 1150Å. It can also be used as the material for a polarizing Wollaston beam splitter. A rotating MgF 2 retarder plate was used by the UVSP instrument (Woodgate et al 1980) on the SMM satellite to record the circular polarization due to the Zeeman effect in the Civ Å line above a sunspot (Henze et al 1982), and to record the scattering polarization across the Mgii k and h lines near the solar limb (Henze and Stenflo 1987). The first attempt to record scattering polarization in the VUV was made in 1976 with a Swedish-built spectro-polarimeter on the Soviet satellite Intercosmos 16 (Stenflo et al 1976, 1980). As shown in Figure 33.6, most of the polarization

13 555 analysis took place already at the first, oblique plane mirror, which was divided in two halves, one coated with gold, the other with aluminium. The beams from the two halves were sent to two different photomultipliers. The ratio between the signals from the two detectors could be normalized to unity at the unpolarized disk centre and would then differ from unity if other parts of the solar disk were polarized. Gratings produce partial linear polarization and may therefore serve the role of polarization analyzer. This brings polarimetric capabilities to instruments that have not been specifically designed for polarimetry. Not only the UVSP instrument on SMM but also SUMER on SOHO made use of this property. In the case of SUMER the rotation of the whole SOHO spacecraft was used to detect the linear O vi 1032 Å line polarization in the corona, through modulation of the signal with spacecraft roll angle (Hassler et al 1997; Raouafi et al 1999). For future instruments it should be possible to develop piezoelastic modulators from lithium fluoride (LiF). Thereby one should be able to design a polarimetric system that could record the full Stokes vector down to a wavelength of 1050Å. Solar and non-solar opportunities While Stokes polarimetry in the VUV remains a seriously neglected area in the planning of space missions, a few concrete projects are in an advanced stage. Thus polarimetric instrumentation has been planned to be used in the ASCE mission (Gardner et al 2003; Romoli et al 2003) to follow up on the initial results from the SOHO mission in the coronal EUV lines. The linear polarization in these lines carries information on the acceleration of the solar wind through the Doppler dimming effect (Fineschi 2001) as well as on coronal magnetic fields through the Hanle effect. Another mission, developed for launch as a sounding rocket payload, is the Solar Ultraviolet Magnetograph Investigation (SUMI, West et al 2000), which plans to measure magnetic fields in the solar transition region by recording the polarization caused by the Zeeman effect in the Civ Å and Å lines and in the Mgii k and h lines at 2795Å and 2803Å. In the area of stellar physics the astronomy department at the University of Wisconsin in Madison has taken the lead in applying EUV scattering polarization and the Hanle effect to constrain the geometry, dynamics, and magnetic fields in hot, expanding stellar envelopes with P Cygni type spectral lines (Cassinelli and Nordsieck 2001; Ignace et al 2004). For this purpose they have developed a sounding rocket payload, the Far-Ultraviolet SpectroPolarimeter (FUSP) for high-precision spectro-polarimetry in the range 1050 Å to 1500 Å. The polarization analysis is done with a stressed lithium fluoride rotating wave plate, which is followed by a diamond Brewster-angle mirror (Nordsieck et al 2003). Bibliography Berkefeld T, Soltau D, von der Lühe O (2006) Multi-conjugate solar adaptive optics with the VTT and GREGOR. Proc SPIE :1 9

14 Stokes polarimetry of the Zeeman and Hanle effects Cassinelli JP, Nordsieck KH, Ignace R (2001) Determination of magnetic fields in the winds from hot stars using the Hanle effect. ASP Conf Ser 248: Fineschi S (2001) Space-based instrumentation for magnetic field studies of solar and stellar atmospheres. Astron Soc Pacific Conf Ser 248: Gandorfer AM, Povel HP, Steiner P (plus six authors) (2005) Solar polarimetry in the near UV with the Zurich Imaging Polarimeter ZIMPOL II. Astron Astrophys 422: Gardner LD, Kohl JL, Daigneau PS (plus eight authors) (2003) The Advanced Spectroscopic and Coronagraphic Explorer: science payload design concept. Proc SPIE 4843:1 7 Hale GE (1908) On the probable existence of a magnetic field in Sun-spots. Astrophys J 28: Hassler DM, Lemaire P, Longval Y (1997) Polarization sensitivity of the SUMER instrument on SOHO. Appl Opt 36: Henze W, Stenflo JO (1987) Polarimetry in the Mg II H and K lines. Sol Phys 111: Henze W Jr, Tandberg-Hanssen E, Hagyard MJ (plus seven authors) (1982) Observations of the longitudinal magnetic field in the transition region and photosphere of a sunspot. Sol Phys 81: Ignace R, Nordsieck KH, Cassinelli JP (2004) The Hanle effect as a diagnostic of magnetic fields in stellar envelopes. IV. Application to polarized P Cygni wind lines. Astrophys J 609: Kosugi T, Matsuzaki K, Sakao T (plus twenty-two authors) (2007) The Hinode (Solar-B) mission: An overview. Sol Phys 243:3 17 Mein P (2002) The MSDP of THEMIS: Capabilities, first results and prospects. Astron Astrophys 381: Nordsieck KH, Jaehnig KP, Burgh EB (plus three authors) (2003) Instrumentation for high-resolution spectropolarimetry in the visible and far-ultraviolet. Proc SPIE 4843: Povel H (1995) Imaging Stokes polarimetry with piezoelastic modulators and charge-coupled-device image sensors. Opt Eng 34: Povel H (2001) Ground-based instrumentation for solar magnetic field studies, with special emphasis on the Zurich Imaging Polarimeters. Astron Soc Pacific Conf Ser 248: Raouafi N-E, Lemaire P, Sahal-Bréchot S (1999) Detection of the O VI nm line polarization by the SUMER spectrometer on the SOHO spacecraft. Astron Astrophys 345: Romoli M, Fineschi S, Uslenghi M (plus seven authors) (2003) The ASCE EUV polarimeter. Mem Soc Astron Italiana 74: Scherrer PH, Bogart, RS, Bush RI (plus ten authors) (1995) The Solar Oscillations Investigation Michelson Doppler Imager. Sol Phys 162: Stenflo JO (1973a) Magnetic-field structure of the photospheric network. Sol Phys 32:41 63 Stenflo JO (1973b) Solar chromatograph. Appl Opt 12: Stenflo JO (1994) Solar Magnetic Fields Polarized Radiation Diagnostics. Kluwer, Dordrecht, 385 pp

15 557 Stenflo JO (2001) Limitations and opportunities for the diagnostics of solar and stellar magnetic fields. Astron Soc Pacific Conf Ser 248: Stenflo JO (2004a) The new world of scattering physics seen by high-precision imaging polarimetry. Rev Mod Astron 17: Stenflo JO (2004b) Hidden magnetism. Nature 430: Stenflo JO, Keller CU (1997) The second solar spectrum. A new window for diagnostics of the Sun. Astron Astrophys 321: Stenflo JO, Holzreuter R (2003) Distribution of magnetic fields at scales beyond the spatial resolution limit. Astron Soc Pacific Conf Ser 286: Stenflo JO, Biverot H, Stenmark L (1976) Ultraviolet polarimeter to record resonance-line polarization in the solar spectrum around nm. Appl Opt 15: Stenflo JO, Dravins D, Wihlborg N (plus five authors) (1980) Search for spectral line polarization in the solar vacuum ultraviolet. Sol Phys 66:13 19 Title AM (2010) Michelson interferometers. ISSI SR-009: Trujillo Bueno J (2001) Atomic polarization and the Hanle effect. Astron Soc Pacific Conf Ser 236: West EA, Porter JG, Davis JM (plus four authors) (2000) Overview of the solar Ultraviolet Magnetograph Investigation. Proc SPIE 4139: Woodgate BE, Brandt JC, Kalet MW (plus seven authors) (1980) The Ultraviolet Spectrometer and Polarimeter on the Solar Maximum Mission. Sol Phys 65:73 90