Astronomy and Astrophysics Review manuscript No.(will be inserted by the editor)

Jan O. Stenflo

Stokes polarimetry of theZeeman and Hanle effects

Received: date

Abstract Magnetic fields are responsible for almost all variability in theUniverse on intermediate time scales. The information on the magnetic fieldsis encoded in the polarization of the radiation from the Sun and stars throughthe Zeeman and Hanle effects. Stokes polarimetry is the observational toolthat gives us access to this information and allows us to determine the struc-ture and evolution of the fields. Space-based observations are needed for twomain reasons: (1) To allow high and stable angular resolution over a large fieldof view. (2) To get access to the vacuum ultraviolet (VUV), which contains in-formation on the magnetic fields in the corona and the chromosphere-coronatransition region. VUV polarimetry has considerable potential but has beenmuch neglected in the past.

Keywords Polarimetry · Zeeman effect · Hanle effect · Sun · Magneticfields

1 Dimensionality and trade-offs in information space

1.1 From scalar to 4-vector measurements

Spectro-polarimetry enhances the dimensionality of information space froma 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 on page 3) carry different and complementary typesof information that is not contained in the spectral radiance, in particularinformation on magnetic fields in the radiating medium.

J.O. StenfloInstitute of Astronomy, ETH Zurich, HIT J, CH-8093 Zurich, SwitzerlandTel.: +41-44-6323804Fax: +41-44-6321205E-mail: stenflo@astro.phys.ethz.ch

2 Jan O. Stenflo

1.2 Trade-offs in parameter space

For the design of observing programs it is helpful to consider another 4-Dparameter space, namely that spanned by the angular, spectral, and temporalresolutions together with the radiometric and polarimetric accuracy. Thesefour parameters cannot be optimized simultaneously, even with the largestconceivable telescopes, but trade-offs are always needed (cf., Stenflo 2001).The radiance of a star does not depend on its distance, only on its effectivetemperature. Therefore the proximity of the Sun does not help much when westudy resolution elements close to the telescope diffraction limit, we quicklyrun out of photons.

In Stokes polarimetry it has become possible to eliminate systematic ef-fects such that the polarimetric accuracy is only constrained by the quantumlimit of the photon Poisson statistics, down to levels of 5×10−6 in the degreeof polarization (Stenflo 2004a). For a precision of 10−5 we need to collect 1010

photo-electrons in the detector, or, when accounting for all the efficienciesand optical transmissions of the telescope system, on the order of 1012 pho-tons per resolution element. This has routinely been achieved in combinationwith high spectral resolution, but at the expense of the angular and temporalresolutions.

In most solar magnetic field work priority has been given to angular reso-lution at the expense of polarimetric precision. Then the temporal resolutionhas to be sufficiently high, since smaller structures evolve faster, and theintegration time should not be longer than the evolutionary time scale. Toresolve 100km on the Sun (0.14′′) the integration time should be shorter than10 s, the approximate time it takes for a sound wave to cross the resolutionelement. The photon flux then limits the relative polarization accuracy inresolved spectral lines to at best 0.1%. This is fully sufficient for most ap-plications of the longitudinal Zeeman effect (line-of-sight magnetograms inthe form of circular-polarization maps), but it is marginal for the transverseZeeman effect and insufficient for the Hanle effect.

1.3 Physical origins of polarization

Polarization is associated with broken symmetries. The spatial symmetrymay be broken by the presence of a magnetic field. This is the origin of theZeeman effect. The symmetry can also be broken by anisotropic scattering.The modification of such scattering polarization by magnetic fields leads topolarization phenomena that are covered by the term “Hanle effect”. ByZeeman-effect polarization we generally refer to the polarization effects thatare not dependent on coherent scattering processes.

The Zeeman and Hanle effects are sensitive to magnetic fields in verydifferent parameter ranges and therefore provide mutually highly comple-mentary diagnostic information. While the Zeeman effect has been appliedin astrophysical contexts for a century, since Hale used it to discover mag-netic fields in sunspots (Hale 1908), applications of the Hanle effect are stillin their infancy.

Stokes polarimetry of the Zeeman and Hanle effects 3

right-handedcircular polarization

450unpolarized o o

F F F F0 1 2 3

Fig. 1 Idealized polarizing filters used in the operational definition of the Stokesparameters.

2 Stokes vector imaging

2.1 Why the Stokes formalism is needed

The polarization of an electromagnetic wave is determined by the oscilla-tions of the two orthogonal electric vectors Ex and Ey in an x-y coordinatesystem in a plane transverse to the wave propagation. Ex and Ey can becombined into a complex 2-vector, the Jones vector, which is characterizedby four parameters (two amplitudes and two phases). A Jones vector howeveralways represents light that is 100% elliptically polarized. It is incapable ofdescribing partially polarized radiation, i.e., a natural beam of light.

Each wave train or photon is always fully elliptically polarized. Partialpolarization is produced by the process of incoherent superposition of anensemble of wave packets with arbitrary phase relations. To properly describethe 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 consistsof the four Stokes parameters I , Q, U , V , or Sk, k = 0, 1, 2, 3, i.e.,

I =

S0

S1

S2

S3

≡

IQUV

, (1)

is in terms of the four idealized filters Fk shown in Figure 1. F0 representsempty space, F1 and F2 transmit linear polarization with the electric vectorat position angles 0 and 45◦, respectively, while F3 transmits right-handedcircular polarization. Let Ik be the radiance of the beam behind each filter.Then

Ik =1

2(S0 + Sk) . (2)

The physical meaning of the Stokes parameters Sk can be understood asfollows: If we replace filters Fk with ones that transmit the orthogonal po-larization state, then Q, U , and V change sign. From this it follows thatStokes I represents the intensity, Stokes Q the intensity difference betweenhorizontal and vertical linear polarization, Stokes U the intensity differencebetween linear polarizations at + and −45◦, Stokes V the intensity differencebetween right- and left-handed circular polarizations.

4 Jan O. Stenflo

In the Stokes formalism the effects of a medium can be described in termsof a 4×4 matrix, the Mueller matrix, which operates on the incoming Stokesvector to produce the output Stokes vector. The medium can be a stellaratmosphere, telescope optics, a train of polarization optics (modulators, waveplates, 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 Mi, then the total matrix is formed bymatrix multiplications:

M = MnMn−1 . . .M2M1 . (3)

The ordering of the matrices is essential, from right to left when following thedirection of the light beam. Calibration is done by inserting known polarizersin front of the system (cf., Stenflo 1994).

2.2 Polarization modulation and demodulation

To measure polarization we need to form differences between orthogonal po-larization states. Beam splitters may be used to record the orthogonal statessimultaneously on different portions of a detector. This is not convenientfor simultaneous recording of all of the four Stokes parameters, moreoverthe different pixel sensitivities in the different parts of the detector (thegain table) limit the polarization accuracy. High-precision vector polarime-try therefore uses temporal modulation of the various polarization states. Inground-based observations one needs to modulate faster than the atmosphericseeing fluctuations ( ∼> 1 kHz), but this requirement can be much relaxed inspace-based observations. Mechanical modulation (rotating retarder plate)may introduce beam wobble and influence of optical inhomogeneities. Bet-ter precision is achieved with electro-optical modulation, which can be donewith piezoelastic modulators (PEM), or with nematic or ferro-electric liquidcrystals. PEMs have the great advantage that basically any optical materialmay be used, like lithium fluoride, which has good transmittance in the vac-uum ultraviolet. The main disadvantage is the high, sinusoidal modulationfrequency (typically 50 kHz), which may not be changed, since PEMs are res-onant devices. The compatibility problem that this causes when PEMs areused in combination with the slow read-out of large CCD detectors has beenelegantly solved with the ZIMPOL (Zurich Imaging Polarimeter) technology(Povel 1995, 2001; Gandorfer et al 2005), which in the future might becomesuperseded by CMOS technology. Simpler but still acceptable solutions forspace applications would be to use rotating wave plates or nematic liquidcrystals in the visible, and rotating wave plates in the vacuum ultraviolet.

2.3 Instrumental polarization

Since the telescope optics is generally polarizing it corrupts the Stokes vectorthat we want to determine. Therefore the optics for the polarization analy-sis (the modulation package, preceded by the polarization calibration optics)

Stokes polarimetry of the Zeeman and Hanle effects 5

should be placed as early as possible in the optical train. The part of thetelescope that is in front of the polarization calibration optics should pro-duce as little polarization as possible. This is the case if this part of theoptical system is axially symmetric. If significant instrumental polarizationis unavoidable in the telescope design, then it is much more manageable if itis constant in time. Although instrumental polarization may in principle becalibrated, modeled, and removed in the data reduction, large instrumentalpolarization should be optically compensated for as much as possible to avoidnasty effects of detector non-linearities, which generate spurios polarizationsignals that are next to impossible to calibrate or model.

2.4 Spectral and spatial information space

Polarimetry may be combined with any system for spectral selection. Thedata cube consists of the two spatial coordinates on the Sun, x and y, andthe wavelength coordinate λ. Since the detector is a 2-D device, scanning isneeded to cover a 3-D portion of the data cube. With (stigmatic) spectro-graphs one gets images in (x, λ) space for each given y, and then needs tostepwise scan in y to build up an image of the Sun. With narrow-band filtersone gets (x, y) images for each given λ, and needs to stepwise tune the filterin λ to build up line-profile information.

One interesting alternative that combines these two features is the solarchromatograph (Stenflo 1973b), which gives monochromatic (x, y) images,but such that the wavelength λ varies linearly with y. Therefore line profileinformation is simultaneously present in each image, although it is convolvedwith the spatial coordinate. This solution is based on the concept of subtrac-tive double dispersion and has so far only been systematically implementedin the MSDP instrument of the French THEMIS telescope on Tenerife (Mein2002).

2.5 Advantages of observations above Earth’s atmosphere

Space-based Stokes vector polarimetry has two main advantages: (1) It givessuperior and stable angular resolution over a large field of view. (2) It givesaccess to the extraterrestrial/vacuum ultraviolet (VUV) part of the spectrum.The stable angular resolution is needed to explore the evolution of the small-scale magnetic fields, to understand magneto-convection, dynamo processesand the underlying mechanisms of solar and stellar activity. Access to theVUV is needed to explore the magnetic fields in the solar transition regionand corona. This is of profound importance for understanding the dynamicsand the heating processes of the outer solar atmosphere, which ultimatelycontrol the space weather and terrestrial effects.

The highest angular resolution in solar observations is still achieved fromground thanks to the application of adaptive optics, as demonstrated by theimages from the Swedish Solar Telescope SST on La Palma, which reach thediffraction limit of 0.1′′ for the 1m telescope. Adaptive-optics correction how-ever only works over a small field of view, which in future may be improved

6 Jan O. Stenflo

Fig. 2 Line-of-sight component of the magnetic field recorded by the Hinode satel-lite on 13 December 2006 during a proton flare. Bright and dark areas representmagnetic fields directed towards and away from the observer. Hinode is a Japanesemission developed, launched and operated by ISAS/JAXA, in partnership withNAOJ, NASA and STFC (UK). Additional operational support is provided byESA and NSC (Norway).

upon by more complex multi-conjugate adaptive optics systems (Berkefeldet al 2001). The quality of the adaptive-optics correction improves when theatmospheric seeing is better, and since the seeing is almost always highlyvariable on time scales of minutes or less, it is next to impossible to obtainevolutionary sequences that can compete with space-based observations. Incontrast the spacecraft Hinode achieves an angular resolution of 0.2′′ overthe whole large field of view (cf., Figure 2), and the resolution remains thesame over the course of the mission, thus allowing evolutionary sequences ofextraordinary quality and length (Kosugi et al 2007).

Even for observations in the visible, space-based instruments of modestspatial resolution have great advantages. An example is the Michelson Dopp-ler Imager (MDI) on the SOHO spacecraft (Scherrer et al 1995; Title 2008).In spite of its relatively low spatial resolution of 4′′ it has been of tremendousvalue, since it has given us a continuous time series that covers more thanone solar activity cycle with high-quality full-disk magnetograms that allhave the same resolution.

3 Zeeman-effect observations

3.1 Magnetic field evolution

Although the magnetic-field evolution occurs on all scales, the key to the un-derstanding of solar magnetism, basic dynamo processes, and the underlyingmechanisms of stellar activity may be found in the smallest scales. Some of

Stokes polarimetry of the Zeeman and Hanle effects 7

Fig. 3 Illustration of the fractal-like pattern of quiet-Sun magnetic fields. Therectangular area covered by the left map (from Kitt Peak) is about 15 % of the areaof 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 correspondto magnetic flux of positive and negative polarities, separated by grey voids ofseemingly no flux. Analysis of Hanle-effect observations (cf., page 8) of atomic andmolecular lines have shown that these grey regions are actually no voids at all, butare teeming with turbulent magnetic fields that carry a significant magnetic energydensity. Since these turbulent fields are tangled with mixed polarities on very smallscales, they are invisible to observations of the Zeeman effect, but they get revealedby observing the Hanle effect (Stenflo 2004b).

the most fundamental still unanswered questions concern the emergence, de-cay, and removal of the photospheric magnetic flux. All the emerged magneticflux has to be removed on the solar cycle time scale and be in statistical equi-librium with the emergence rate, otherwise the photosphere would quicklyget choked with undisposed magnetic flux. We know that as we go from ac-tive regions to ephemeral regions and still smaller scales, the emergence rateincreases dramatically, but we do not know how one can get rid of the flux atsuch tremendous rates. We need to determine the relative contributions of thefollowing three alternative removal mechanisms: (i) Cancellation of oppositepolarities (reconnection). (ii) Flux retraction (reprocessing in the convectionzone). (iii) Flux expulsion (and the role of coronal mass ejections). In spiteof decades of hard work we still know practically nothing about the relativeroles of these processes.

3.2 Small-scale structuring

Observations with improved angular resolution in combination with indirectdiagnostics have shown that the magnetic structuring extends from the globalscales towards the diffusion scales far beyond the telescope resolution. Thereis a remarkable degree of self-similarity over the various scales, suggesting afractal-like nature (cf., Figure 3). The scales that we are beginning to resolve(the dimensions of the photon mean free path and the pressure scale height)

8 Jan O. Stenflo

Fig. 4 Trajectory of a damped classical oscillator, illustrating the Hanle effectdepolarization and rotation of the plane of polarization when the magnetic field isoriented along the line of sight. The three diagrams represent different values ofthe field strength, which increases from left to right.

are of critical importance for a physical understanding of the scale spectrumof magneto-convection. Since however the structuring continues far into theunresolved domain, we always need to complement the direct, resolved ob-servations with indirect techniques to extract statistical information aboutthe unresolved structures, like the line-ratio method (Stenflo 1973a). Theseindirect methods are now being extended through applications of the Hanleeffect.

4 Hanle-effect observations

4.1 Classical and quantum descriptions of the Hanle effect

In contrast to the Zeeman-effect polarization the Hanle effect is a coherencyphenomenon that only occurs in coherent scattering processes. Magneticfields remove the degeneracy of the radiatively excited and coherently super-posed magnetic substates and thereby cause partial decoherence that leavesa signature in the polarization of the scattered radiation.

In a classical description the damped dipole oscillations that are inducedby the incident radiation precess in the presence of a magnetic field, as pic-tured in Figure 4. In the illustrated case it is assumed that vertical oscilla-tions are induced by the excitation process, and that we observe the emittedradiation along the magnetic field direction. The trajectory of the dampedoscillator forms a rosette pattern that becomes more isotropic when the fieldis stronger. The emitted polarization is obtained from the Fourier transformof the rosette pattern. In the absence of magnetic fields the scattered radi-ation would be linearly polarized in the vertical direction (in the illustratedcase), but as the field strength is increased, the plane of polarization getsrotated, and the amount of polarization is reduced.

Stokes polarimetry of the Zeeman and Hanle effects 9

If the classical equation for the dipole oscillation is decomposed in thethree Cartesian coordinate equations, the component equations are coupledto each other due to the v×B term of the Lorentz force. If we however decom-pose in terms of complex spherical vectors, the component equations decouple(cf. Stenflo 1994). These three components correspond to the ∆m = 0,±1transitions (the π and σ components) in the quantum-mechanical picture.Since they oscillate with slightly different frequencies due to the Larmor pre-cession (which is the source of the Zeeman splitting), the damped oscillatorsgradually get out of phase, which leads to partial decoherence depending onthe strength of the magnetic field.

4.2 Observational signatures of the Hanle effect

The Hanle effect leaves its imprints in the linear polarization. Its two mainsignatures are depolarization and rotation of the plane of polarization whenthe scattering geometry resembles 90◦ scattering. Figure 5 shows an exampleof the qualitatively different signatures of the Hanle and Zeeman effects.The Hanle effect also occurs in forward scattering, where it generates linearpolarization in the presence of transverse magnetic fields (Trujillo Bueno2001).

A precondition for the Hanle effect to be observable at all is (i) that co-herent scattering plays a significant role in the formation of the spectral line,and (ii) that the scattering polarization has observable amplitude. Condition(i) favors strong resonance lines, which anyways dominate the spectrum fromthe chromosphere-corona transition region. Condition (ii) requires that theincident radiation field of the scattering process is significantly anisotropic.In the vacuum ultraviolet the intensity contrasts of the solar structures aremuch larger than in the visible, which implies that the local anisotropies ofthe radiation field are large. The expected local fluctuations of the scatter-ing polarization are therefore expected to be large as well. In the visible thecontrasts are much smaller, with the consequence that the anisotropy due tothe limb darkening becomes more important than the local intensity fluctua-tions. This global anisotropy determines the polarization scale of the “SecondSolar Spectrum” (Stenflo and Keller 1997), the highly structured spectrumin linear polarization that is exclusively due to coherent scattering.

Due to the scattering geometry when limb darkening is the source ofthe anisotropy, the polarization amplitude increases monotonically as we ap-proach the limb. Therefore, in the visible part of the spectrum, the bestconditions 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 situationis somewhat different in the vacuum ultraviolet, since the anisotropies aremore local than global. Therefore the observability should be less restrictedto a limb zone. For structures that are rather high above the solar surfacethe global anisotropy would however dominate, if the total illumination fromthe underlying solar disk occupies a solid angle that is significantly smallerthan a half sphere (2π sr).

10 Jan O. Stenflo

�� ����������� ����� �������� �������������� ������ ���������

Fig. 5 Examples of Hanle-effect signatures in Stokes spectra (the radiance I andthe three fractional polarizations Q/I, U/I, and V/I) recorded with ground-basedinstrumentation, illustrating the difference between the Hanle and Zeeman effects.The photospheric Sr i 4607 A line and the chromospheric Ca i 4227 A line exhibitstrong linear polarization due to coherent scattering, which in the presence of mag-netic fields gets modified by the Hanle effect (seen as spatial variations of Q/Iand U/I along the slit). The surrounding spectral lines display the usual transverseZeeman effect in the linear polarization (Stokes Q/I and U/I), and the longitudinalZeeman effect in the circular polarization (Stokes V/I). The recordings were madewith the Zurich Imaging Polarimeter (ZIMPOL) at the McMath-Pierce facility(Kitt Peak).

4.3 Complementarity of the Zeeman and Hanle effects

While the Zeeman-effect polarization becomes measurable when the Zeemansplitting is comparable to the Doppler width of the spectral line used, thesensitivity range for the Hanle effect is where the Zeeman splitting is com-parable to the damping width or inverse life time of the excited atomic ormolecular state. Since the damping width is typically two orders of magnitudesmaller than the Doppler width, the Hanle effect is sensitive to correspond-ingly weaker fields. This makes it particularly suited for diagnostics of mag-netic fields in the transition region and corona, where the fields are relativelyweak due to the rapid expansion with height of the many strong, photosphericflux concentrations. In addition, since the Zeeman splitting scales with λ2,the signatures of the Zeeman effect are tiny in the vacuum ultraviolet.

Another fundamental area where the Zeeman and Hanle effects are highlycomplementary concerns the spatially unresolved domain of magneto-convec-

Stokes polarimetry of the Zeeman and Hanle effects 11

tion. The Zeeman effect is blind to spatially unresolved turbulent fields withzero net magnetic flux, in contrast to the Hanle effect that has differentsymmetry properties (the “sign” of the Hanle depolarization is independentof field polarity).

4.4 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, inaddition to the magnetic field. To disentangle these effects it helps to applya strategy of using combinations of spectral lines that are affected similarlyby the non-magnetic factors, but which differ in their magnetic sensitivities(in analogy with the line-ratio technique for Zeeman effect observations). Afurther problem is that the Hanle effect in principle delivers only two observ-ables (amount of depolarization and rotation of the plane of polarization),while the magnetic field vector has three spatial components. For a uniqueinterpretation one therefore needs additional observational or modelling con-straints.

The longitudinal Zeeman effect has the great advantage that it allowscircular polarization maps to be directly interpreted as maps of the line-of-sight component of the magnetic flux density. In contrast, the magnetic-fieldinformation that is carried by the Hanle-effect signatures is rather convolvedwith other factors in a way that prevents magnetic maps to be extractedwithout additional information. Still the Hanle effect provides informationabout parameter domains that are not accessible by other means, but whichare needed for understanding the fundamental physical processes on the Sun.

5 Stokes polarimetry in the vacuum ultraviolet

5.1 Advantages of the VUV region

The VUV and X-ray regions of the solar spectrum are full of resonance linesthat are formed in the chromosphere-corona transition region or above. Ob-servations in such lines allow us to diagnose the physics of the outer solar at-mosphere where the coronal heating takes place, the solar wind is driven, andthe space weather is generated. Crude information on coronal magnetic fieldscan be obtained with radio astronomical techniques, forbidden-line scatteringpolarization in the visible, and (more recently) by recordings of the longitu-dinal Zeeman effect of forbidden coronal lines in the near infrared. Spectro-polarimetry in the vacuum ultraviolet remains a promising but largely unex-ploited area with considerable potential.

The VUV region down to about 1050 A is of special interest, since trans-mission optics like lithium fluoride can be used throughout this range, whichmakes it feasible to apply retarders and modulators for complete Stokes po-larimetry. At still shorter wavelengths one may still determine the linearpolarization by using the partially polarizing properties of oblique reflec-tions, but circular polarization appears to be out of reach. This may however

12 Jan O. Stenflo

not be such a serious limitation, since the Hanle effect has its signatures inthe linear polarization, while the circular polarization is a property of theZeeman effect.

Due to its λ2 dependence the Zeeman effect will be ineffective at shortwavelengths. In the VUV its observability will mainly be limited to sunspots.Since the Hanle effect is sensitive to considerably weaker fields than theZeeman effect, we expect that it will play the leading diagnostic role in theVUV and below. Coronal magnetic fields have field strengths in the Hanlesensitivity range for allowed line transitions. All the allowed coronal andtransition-region lines are in the EUV or soft X-ray region, which can onlybe accessed from space.

The Hanle effect can also be used to diagnose the expanding envelopesof hot stars, but also here the relevant spectral lines are in the VUV, inac-cessible from ground. Since magnetic fields play a key role for the physicsof stellar transition regions, coronae, and stellar winds, we need space-basedobservations of the Hanle effect to diagnose these domains.

5.2 Choice of polarization optics

Very little has been done in the area of VUV polarimetry, it still representsalmost virgin territory. For the detection of linear polarization one needsto make a trade-off between polarization efficiency and transmission. ThusBrewster-angle reflection on uncoated dielectric surfaces gives complete po-larization, but the reflectivity is generally low. Coated reflective surfaces givegood throughput and varying degree of polarization, depending on the choiceof 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 aluminum-coated mirror gives about 5% or less.

Magnesium fluoride (MgF2) is birefringent and may be used as a retarderdown to 1150 A. It can also be used as the material for a polarizing Wollas-ton beam splitter. A rotating MgF2 retarder plate was used by the UVSPinstrument (Woodgate et al 1980) on the Solar Maximum Mission (SMM)satellite to record the circular polarization due to the Zeeman effect in theC iv 1548.2 A line above a sunspot (Henze et al 1982), and to record the scat-tering polarization across the Mg ii k and h lines near the solar limb (Henzeand Stenflo 1987).

The first attempt to record scattering polarization in the VUV was madein 1976 with a Swedish-built spectro-polarimeter on the Soviet satellite In-tercosmos 16 (Stenflo et al 1976, 1980). As shown in Figure 6, most of the po-larization analysis took place already at the first, oblique plane mirror, whichwas divided in two halves, one coated with gold, the other with aluminum.The beams from the two halves were sent to two different photomultipliers.The ratio between the signals from the two detectors could be normalizedto unity at the unpolarized disk center and would then differ from unity ifother parts of the solar disk were polarized.

Gratings produce partial linear polarization and may therefore serve therole as polarization analyzer. This brings polarimetric capabilities to instru-ments that have not been specifically designed for polarimetry. Not only the

Stokes polarimetry of the Zeeman and Hanle effects 13

Fig. 6 Optical scheme of the first space-based spectro-polarimeter for the recordingof scattering polarization in the vacuum ultraviolet (Stenflo et al 1976). It was flownon Intercosmos 16 in 1976.

UVSP instrument on SMM but also SUMER on SOHO made use of thisproperty. In the case of SUMER the rotation of the whole SOHO spacecraftwas used to detect the linear Ovi 1032 A line polarization in the coronathrough the modulation of the signal with spacecraft roll angle (Hassler etal 1987; Raouafi et al 1999).

For future instruments it should be possible to develop piezoelastic mod-ulators from lithium fluoride (LiF). Thereby one should be able to designa polarimetric system that could record the full Stokes vector down to awavelength of 1050 A.

5.3 Solar and non-solar opportunities

While Stokes polarimetry in the VUV remains a seriously neglected area inthe planning of space missions, a few concrete projects are in an advancedstage. Thus polarimetric instrumentation has been planned to be used in theAdvanced Spectroscopic and Coronagraphic Explorer (ASCE) mission (Gard-ner et al 2003; Romoli et al 2003) to follow up on the initial results fromthe SOHO mission in the coronal EUV lines. The linear polarization in theselines carries information on the acceleration of the solar wind through theDoppler dimming effect (Fineschi 2001) as well as on coronal magnetic fieldsthrough the Hanle effect.

14 Jan O. Stenflo

Another mission, scheduled for launch as a sounding rocket payload in2008, is the Solar Ultraviolet Magnetograph Investigation (SUMI) (West etal 2000), which plans to measure magnetic fields in the solar transition regionby recording the polarization caused by the Zeeman effect in the C iv 1548.2and 1550.8 A lines and in the Mg ii k and h lines at 2795 and 2803 A.

In the area of stellar physics the astronomy department at the Univer-sity of Wisconsin in Madison has taken the lead in applying EUV scatteringpolarization and the Hanle effect to constrain the geometry, dynamics, andmagnetic fields in hot, expanding stellar envelopes with P Cygni type spec-tral lines (Cassinelli and Nordsieck 2001; Ignace et al 2004). For this purposethey have developed a sounding rocket payload, the Far-Ultraviolet Spec-troPolarimeter (FUSP) for high-precision spectro-polarimetry in the range1050 to 1500 A. The polarization analysis is done with a stressed lithiumfluoride rotating wave plate, which is followed by a diamond Brewster-anglemirror (Nordsieck et al 2003).

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