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Quantum Spectropolarimetry and the Sun's Hidden

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Quantum Spectropolarimetry and the Sun's Hidden QUANTUM SPECTROPOLARIMETRY AND THE SUN’S HIDDEN MAGNETISM Javier Trujillo Bueno∗ Instituto de Astrof´ısica de Canarias; 38205 La Laguna; Tenerife; Spain ABSTRACT The dynamic jets that we call spicules. • The magnetic fields that confine the plasma of solar • Solar physicists can now proclaim with confidence that prominences. with the Zeeman effect and the available telescopes we The magnetism of the solar transition region and can see only 1% of the complex magnetism of the Sun. • corona. This is indeed∼regrettable because many of the key prob- lems of solar and stellar physics, such as the magnetic coupling to the outer atmosphere and the coronal heat- Unfortunately, our empirical knowledge of the Sun’s hid- ing, will only be solved after deciphering how signifi- den magnetism is still very primitive, especially concern- cant is the small-scale magnetic activity of the remain- ing the outer solar atmosphere (chromosphere, transition ing 99%. The first part of this paper1 presents a gentle ∼ region and corona). This is very regrettable because many introduction to Quantum Spectropolarimetry, emphasiz- of the physical challenges of solar and stellar physics ing the importance of developing reliable diagnostic tools arise precisely from magnetic processes taking place in that take proper account of the Paschen-Back effect, scat- such outer regions. tering polarization and the Hanle effect. The second part of the article highlights how the application of quantum One option to improve the situation is to work hard to spectropolarimetry to solar physics has the potential to achieve a powerful (European?) ground-based solar fa- revolutionize our empirical understanding of the Sun’s cility optimized for high-resolution spectropolarimetric hidden magnetism. observations. Some relevant efforts are going into this di- rection, but we should also start thinking seriously on the Key words: Solar and Stellar Magnetic Fields, Spec- enormous scientific interest of putting a high-sensitivity tropolarimetry, Level crossings and optical pumping. UV polarimeter in a solar space telescope (Trujillo Bueno et al. 2005b; see also Section 4.4). A second possibility is to try to create our own Sun in the computer, learning as much as possible from radiative magnetohydrodynamic 1. INTRODUCTION numerical experiments. A third option is to give a chance to what I like to call Quantum Spectropolarimetry, that is, the possibility of diagnosing solar and stellar magnetic With the term “the Sun’s hidden magnetism” I would like fields via the interpretation of spectral line polarization to refer to all those solar magnetic fields that with the signals caused by a variety of unfamiliar physical pro- available telescopes remain practically invisible to the cesses, such as optical pumping, the Hanle effect, level- Zeeman effect. The following examples belong to this crossings and anti-level-crossings interferences, etc. Ob- category: viously, all three options should be pursued and cleverly combined to facilitate new advances in solar and stellar magnetism. 99% of the magnetism of the ‘quiet’ solar photo- • sphere.∼ The emphasis of this keynote article is on the application of quantum spectropolarimetry to solar physics. The first The solar chromosphere outside active regions. part of the paper presents a ‘gentle’ introduction to this • emerging field of research, emphasizing the importance ∗Consejo Superior de Investigaciones Cient´ıficas (Spain) of developing diagnostic tools that take proper account 1Invited Review at the 11th European Solar Physics Meeting The Dynamic Sun: Challenges for Theory and Observations (ESA SP-600). of the Zeeman and Paschen-Back effects, scattering po- Leuven (Belgium), 11–16 September 2005, Eds. D. Danesy, S. Poedts, larization and the Hanle effect. Only in this way may A. De Groof & J. Andries. ESA Publications Division. Published on we hope to investigate the strength and topology of stel- CDROM., p. 7.1, December 2005. lar magnetic fields in a parameter domain which ranges from field intensities as low as 1 milligauss to many thou- The important point to remember is that the polarization sands of gauss. The second part of the article shows some signals produced by the Zeeman effect are caused by the recent applications in solar physics with emphasis on the wavelength shifts between the π (∆M = M M = 0) u − l hidden magnetic fields of the photosphere, chromosphere and σb,r (∆M = 1) transitions. Such wavelength shifts and corona. are also the physical± origin of the spectral line polariza- tion induced by the Paschen-Back effect discussed below in Section 2.5, since the only difference with respect to the linear Zeeman effect theory considered here lies in 2. GENERATION OF POLARIZED RADIATION the calculation of the positions and strengths of the vari- ous π and σ components. It is suitable to begin by recalling that the state of polar- ization of a quasi-monochromatic beam of electromag- netic radiation can be conveniently characterized in terms of four quantities that can be measured by furnishing our telescopes with a polarimeter. Such observables are the four Stokes parameters (I, Q, U, V ), which were formu- lated by Sir George Stokes in 1852 and introduced into astrophysics by the Nobel laureate Subrahmanyan Chan- drasekhar in 1946. The Stokes I(λ) profile represents the intensity as a function of wavelength, Stokes Q(λ) the intensity difference between vertical and horizontal linear polarization, Stokes U(λ) the intensity difference between linear polarization at +45◦ and 45◦, while Stokes V (λ) the intensity difference between− right- and left-handed circular polarization (cf. Born & Wolf 1994). Note that the definition of the Stokes Q and U parameters requires first choosing a reference direction for Q > 0 in the plane perpendicular to the direction of propagation. Let us now review the most important mechanisms that induce (and modify) polarization signatures in the spec- tral lines that originate in stellar atmospheres: the Zee- man and Paschen-Back effects, scattering processes and the Hanle effect. 2.1. The Zeeman effect As illustrated in Figure 1, the Zeeman effect requires the presence of a magnetic field which causes the atomic and molecular energy levels to split into different mag- netic sublevels characterized by their magnetic quantum Figure 1. The oscillator model for the Zeeman effect indi- number M (Condon & Shortley 1935). Each level of to- cating the characteristic shapes of the circular and linear tal angular momentum J splits into (2J + 1) sublevels, polarization profiles as generated locally via the emission the splitting being proportional to the level’s Lande´ fac- process. It is important to note that the Stokes V (λ) pro- tor, gJ , and to the magnetic field strength. As a re- file changes its sign for opposite orientations of the mag- sult, a spectral line between a lower level with (Jl, gl) netic field vector, while the Stokes Q(λ) profile reverses and an upper level with (Ju, gu) is composed of several sign when the transverse field component is rotated by individual components whose frequencies are given by 90◦. ± νJuMu = ν + ν (g M g M ), where ν is the fre- JlMl 0 L u u l l 0 quency of the line in the absence− of magnetic fields and The Zeeman effect is most sensitive in circular polar- 6 νL = 1.3996 10 B is the Larmor frequency (with B ization (quantified by the Stokes V parameter), with a the magnetic fi×eld strength expressed in gauss). In par- magnitude that for not too strong fields scales with the ticular, a line transition with Jl = 0 and Ju = 1 has ratio between the Zeeman splitting and the width of the three components (see Fig. 1): one π component cen- spectral line (which is very much larger than the natu- tered at ν0 (or at λ0), one σred component centered at ral width of the atomic levels!), and in such a way that ν g ν (or at λ + g ∆λ ), and one σ compo- the emergent Stokes V (λ) profile changes its sign for op- 0 − u L 0 u B blue nent centered at ν0 + guνL (or at λ0 gu∆λB ), where posite orientations of the magnetic field vector. This so- 13 2 − ∆λB = 4.6686 10− λ0B (with λ0 in A˚ and B in called longitudinal Zeeman effect responds to the line- gauss). × of-sight component of the magnetic field. Accordingly, if we have a perfect cancellation of mixed magnetic polar- ities within the spatio-temporal resolution element of the observation, the measured circular polarization would be exactly zero if the thermodynamic and dynamic proper- ties of the mixed magnetic components are similar. The antisymmetric shape of the Stokes V (λ) profiles illus- trated in Fig. 1 can be easily understood by noting the expression of the Stokes-V component of the emission vector: hν 1 % = N A [φ φ ] cosθ, (1) V 4π u ul 2 red − blue where θ is the angle between the magnetic field vector and the line of sight, Aul the Einstein coefficient for the spontaneous emission process, Nu the number of atoms per unit volume in the upper level of the line transition un- der consideration, while φred and φblue are profiles that result from the superposition of the Voigt functions corre- sponding to each individual component. φ red is displaced to the red side of the central wavelength λ0, and φblue to the blue side. For instance, for the particular case of a line transition with Jl = 0 and Ju = 1, φred is a Voigt profile centered at λ0 + gu∆λB and φblue a Voigt profile centered at λ g ∆λ . 0 − u B Figure 2. Spectropolarimetric observation close to the In contrast, the transverse Zeeman effect responds to the edge of the solar disk with half of the spectrograph slit component of the magnetic field perpendicular to the line crossing a moderately magnetized facular region.
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