E. Landi Degl'Innocenti

Polarization in spectral lines

A unifying theoretical approach is presented to derive from the general principles of Quantum Electrodynamics both the radiative transfer equations for polarized radiation and the statistical equilibrium equations for an atomic system interacting with a polarized radiation field. The radiation field is described by means of Stokes parameters while the atomic system is described in terms of its density-matrix operator. The non-diagonal terms of the density matrix are fully accounted for so that this formalism can be suitably employed to describe a wide variety of physical phenomena like resonance scattering, the Hanle effect and the Zeeman effect, either in optically thin or optically thick atmospheres, together with all the possible intermediate situations.The general formulae derived in the first sections of the paper are subsequently particularized introducing the dipole approximation in the relevant matrix elements describing the interaction between the atomic system and the radiation field. The final equations assume a quite compact expression by the introduction of suitable spherical tensors connected with the components of the polarization unit vectors associated with each direction of the radiation field. The general expressions and the main properties of these tensors are discussed in the Appendix.

Magneto-optical effects and the determination of vector magnetic fields from stokes profiles

The analysis procedure proposed by Auer et al. (1977) for deducing magnetic field vectors from Stokes profiles has been tested to investigate the influence of magneto-optical effects on the deduced field parameters. The quality of the fit between synthetic profiles generated with the inclusion of magneto-optical effects and the profiles returned by the inversion routine is also investigated. The results show that magneto-optical effects should be included in the inversion routine especially to increase the accuracy of the deduced, azimuth of the magnetic field.

UNNOFIT inversion of spectro-polarimetric maps observed with THEMIS

This paper presents the inversion of a spectro-polarimetric scan (240 arcsec×340 arcsec) of an active region and a filament, obtained with THEMIS, on December 7, 2003, in the two Fe I lines at 6302.5 A and 6301.5 A. The inversion was applied to each line separately, using the UNNOFIT code of tet{b13 La84}, improved by the introduction of a magnetic filling factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, are derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved. The tests run with UNNOFIT show that the magnetic field strength, B, and the magnetic filling factor, α, cannot be separately recovered by the inversion of Fe I 6302.5 A, but that their product, α B, which is the local average magnetic field, is recovered. The magnetic flux is only its longitudinal component. Our results also reveal two distinct regimes, corresponding to two different ranges of local average magnetic field strength as inferred from Fe I 6302.5 A: a) The network, having a field inclined of about 20°-30° from the vertical in Fe I 6302.5 A (more spreaded, but non-horizontal in Fe I 6301.5 A), with a homogeneous azimuth. In this zone, the local average field strength in Fe I 6302.5 A is larger than 45 G. b) The internetwork, where the field is turbulent (with a horizontal trend, more spreaded at lower altitudes), and with local average field strength in Fe I 6302.5 A smaller than 45 G. The two lines gives coherent results, in particular in magnetic field azimuth. From this we conclude that the turbulence of the internetwork field is of solar origin. This work has been presented in detail by tet{b13 Bo06}.

The Hanle and Zeeman Effects in Solar Spicules: A Novel Diagnostic Window on Chromospheric Magnetism

A large set of high precision full-Stokes spectropolarimetric observations of the He-D3 line in spicules has been recorded with the ZIMPOL polarimeter at the Gregory-Coude Telescope in Locarno. The observational technique allow us to obtain measurements free from seeing induced spurious effects. The instrumental polarization is well under control and taken into account in the data analysis. The observed Stokes profiles are interpreted according to the quantum theory of the Hanle and Zeeman effects with the aim of obtaining information on the magnetic field vector. To this end, we make use of a suitable Stokes inversion technique. The results are presented giving emphasis on a few particularly interesting measurements which show clearly the operation of the Hanle and Zeeman effects in solar chromospheric spicules.

On the solution of the radiative transfer equations for polarized radiation

A general formalism is presented to obtain an analytical solution of the radiative transfer equations for polarized radiation when the absorption Mueller matrix for the Stokes parameters is constant along the ray-path. The formalism is then applied to find an analytical approximation of the Stokes parameters profiles for a typical chromospheric line having an optical-depth dependence of the source function of the form S(τ) = (ɛ + δ)1/2(1 + ɛ)1/2.

On the diagnostic of magnetic fields in sunspots through the interpretation of stokes parameters profiles

The inversion routine proposed by Aueret al. (1977), for the determination of vector magnetic fields from Stokes profiles, has been generalized to include magneto-optical and damping effects. Synthetic profiles have then been generated from a sunspot model atmosphere accounting for the depth variation of the relevant physical parameters such as the magnetic field amplitude, inclination angle, etc...., each variation being considered one at a time. Alfvén waves and magnetic inhomogeneities over the field of view have also been considered. These synthetic profiles have been presented to the inversion routine. The results of the fits show that the magnetic field amplitude and direction are always recovered with good accuracy when these quantities are constant in the model atmosphere, and, in those cases where te magnetic field vector is supposed to vary monotonically with optical depth, the values recovered are always intermediate between the values corresponding to the top and bottom of the atmosphere. Moreover, we found that the differences between synthetic and best-fit profiles are able to characterize, in many cases, the particular physical situation considered.

Interpretation of second solar spectrum observations of the Sr I 4607 Å line in a quiet region: Turbulent magnetic field strength determination

This paper presents and interprets some observations of the limb polarization of Sr  4607 A obtained with the spec- tropolarimeter of the French-Italian telescope THEMIS in quiet regions close to the solar North Pole on 2002 December 7-9. The linear polarization was measured for a series of limb distances ranging from 4 to 160 arcsec, corresponding to heights of optical depth unity in the line core ranging from about 330 to 220 km, respectively, above the τ5000 = 1 level. To increase the polarimetric sensitivity, the data were averaged along the spectrograph slit (one arcmin long) set parallel to the solar limb. Since the data show no rotation of the linear polarization direction with respect to the limb direction, the observed depolarization is ascribed to the Hanle effect of a turbulent weak magnetic field, the zero-field polarization being derived from a model. The in- terpretation is performed by means of an algorithm which describes the process of line formation in terms of the atomic density matrix formalism, the solar atmosphere being described by an empirical, plane-parallel model. The collisional rates entering the model (inelastic collisions with electrons, elastic depolarizing collisions with neutral hydrogen), have been computed by applying fast semi-classical methods having a typical accuracy of the order of 20% or better (see Derouich 2004), leading to 6% inaccuracy on the magnetic field strength determination. We assume a unimodal distribution for the intensity of the turbulent field. The computed intensity profile has been adjusted to the observed one in both depth and width, by varying both micro- turbulent and macroturbulent velocities. The best adjustment is obtained for respectively 1.87 km s −1 (micro) and 1.78 km s −1 (macro). The evaluation of the magnetic depolarization leads then to the average value of 46 Gauss for the turbulent magnetic field strength, with a gradient of −0.12 Gauss/km. Our results are in very good agreement with the value of 60 Gauss determined at large µ, in the volume-filling field case, by Trujillo Bueno et al. (2004, Nature, 430, 326), using a 3D magneto-convective simulation. This validates our method.

A qualitative interpretation of the second solar spectrum of Ce ll

This is a theoretical investigation on the formation of the linearly polarized line spectrum of ionized cerium in the sun. We calculate the scattering line polarization pattern emergent from a plane-parallel layer of Ce ii atoms illuminated from below by the photospheric radiation field, taking into account the differential pumping induced in the various magnetic sublevels by the anisotropic radiation field. We find that the line polarization pattern calculated with this simple model is in good qualitative agreement with reported observations. Interestingly, the agreement improves when some amount of atomic level depolarization is considered. We find that the best fit to the observations corresponds to the situation where the ground and metastable levels are depolarized to about one fifth of the corresponding value obtained in the absence of any depolarizing mechanism. One possibility to have this situation is that the depolarizing rate value of elastic collisions is exactly D = 106 s−1, which is rather unlikely. Therefore, we interpret that fact as due to the presence of a turbulent magnetic field in the limit of saturated Hanle effect for the lower-levels. For this turbulent magnetic field we obtain a lower limit of 0.8 Gauss and an upper limit of 200–300 Gauss.

Solar magnetism eXplorer (SolmeX)

The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona—that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200 m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. SolmeX integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations.

FREQUENCY REDISTRIBUTION FUNCTION FOR THE POLARIZED TWO-TERM ATOM*

We present a generalized frequency redistribution function for the polarized two-term atom in an arbitrary magnetic field. This result is derived within a new formulation of the quantum problem of coherent scattering of polarized radiation by atoms in the collisionless regime. The general theory, which is based on a diagrammatic treatment of the atom-photon interaction, is still a work in progress. However, the results anticipated here are relevant enough for the study of the magnetism of the solar chromosphere and of interest for astrophysics in general.