Partial frequency redistribution of polarized radiation

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

Evolution of Magnetic fields in Bok Globules?

We study the influence and structure of the magnetic field in the early phases of low-mass star formation using polarization maps of Bok globules at a wavelength of 850 μm, obtained with the Submillimeter Common-User Bolometer Array (SCUBA) at the James Clerk Maxwell Telescope (JCMT). We discuss observations of the following sources: CB 26—a small globule with a nearly dispersed dense core and a young and large circumstellar disk, CB 54—a large globule with a massive dense core and a deeply embedded young stellar cluster, and B 335, CB 230, and CB 244—three nearby, relatively isolated small globules with low-mass protostellar cores. We find strongly aligned polarization vectors in the case of CB 26, B 335, and CB 230, whereas the vector orientations in the case of CB 54 and CB 244 are more or less randomly distributed. The degree of polarization, amounting to several percent, was found to decrease toward the center in each source. Assuming dichroic emission by aligned non-spherical grains as the polarization mechanism, where the magnetic field plays a role in the alignment process, we derive magnetic field strengths and structures from the observed polarization patterns. We compare the magnetic field topology with the morphology and outflow directions of the globules. In the Class 0 sources B 335, CB 230, and CB 244, the magnetic field is oriented almost perpendicular to the ouflow direction. In contrast, the inclination between outflow axis and magnetic field direction is much more moderate (36°) in the more evolved Class I source CB26.     

Polarization of radiation from a strongly magnetized accretion disk: The asymptotic spectral distribution

We calculate the polarization of the radiation from an optically thick accretion disk with a vertical averaged magnetic field. The polarization arises from the scattering of light by free electrons in a magnetized disk plasma. The Faraday rotation of the polarization plane during the propagation of a photon in a medium with a magnetic field is considered as the main effect. We discuss various models of optically thick accretion disks with a vertical averaged magnetic field. Our main goal is to derive simple asymptotic formulas for the polarization of radiation in the case where the Faraday rotation angle Ψ ≫ 1 at the Thomson optical depth τ = 1. The results of our calculations allow the magnetic field strength in the region of the marginally stable orbit near a black hole to be estimated from polarimetric observations, including X-ray observations expected in the future. Since the polarization spectrum of the radiation strongly depends on the accretion disk model, a realistic physical model of the accretion disk can be determined from data on the polarization of its radiation.     

Magnetic fields of active galactic nuclei and quasars with regions of polarized broad Hα lines

Estimates of magnetic fields for a number of active galactic nuclei are presented. These estimates are based on the observed polarization degrees and position angles of broad Hα lines and in the nearby continuum and on asymptotic analytical formulas for the Stokes parameters of the radiation emerging from a magnetized accretion disk (the Milne problem in a magnetized atmosphere). The characteristic observed feature of the wavelength dependence of the polarization degree inside the line—a minimum at the center and a fast increase of the position angle from one wing to another—can be explained by the superposition of resonance emission from two or more clouds located in the right (Keplerian velocity directed away from the observer) and left (Keplerian velocity directed toward the observer) parts of the orbit in the rotating magnetized accretion disk. The main component in our mechanism is the azimuthal magnetic field in the disk. The presence of a magnetic field perpendicular to the disk plane (which is usually weaker than the azimuthal field) results in the asymmetry of the distribution of the polarization degree and position angle inside the line. The inferred magnetic field strengths at the galactocentric distances where broad lines are emitted can be used to estimate the magnetic fields in the region of the centermost stable orbit and at the horizon of the central black hole, using the power-law dependence of the magnetic field strength corresponding to the standard model of the accretion disk.     

Infrared polarimetry of the southern massive star-forming region G333.6−0.2

We present     spectropolarimetry, and 12- and 2-μm imaging polarimetry of the southern massive star-forming region G333.6−0.2. Spectro-polarimetry measurements show that the polarization observed towards the nebula contains a mixture of both absorptive and emissive polarizations. Model fitting to the spectra indicates that the temperature of the mid-infrared emitting dust grains is generally ∼200 K and the optical depth of the absorbing dust at 9.7 μm is ∼1.5. Fits are also made to the polarimetry spectra, which show a reasonably constant peak absorptive polarization (∼3.4 per cent at 43°) across the face of the H  ii region. This absorptive polarization position angle is consistent with that found by the 2-μm imaging polarimetry     and is most likely due to the Galactic magnetic field local to G333.6−0.2. When the absorptive polarization is subtracted from the 12-μm polarization image, the emissive polarization pattern that is intrinsic to the star-forming region is revealed. A probable magnetic field configuration implied by the intrinsic polarization suggests star formation initially influenced by the Galactic magnetic field which is eventually perturbed by the star formation process.     

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

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

An interpretation of the broad-band circular polarization of sunspots

The broad-band circular polarization of sunspots is discussed on the basis of the observations made in the Okayama Astrophysical Observatory. The observation with the spectrograph proves that it is the integrated polarization of spectral lines in the observed spectral range. A velocity gradient in the line-of-sight can produce this integrated polarization due to the differential saturation between Zeeman components of magnetically sensitive lines. The observed degree of polarization and its spatial distribution in sunspots is explained when we introduce a differentially twisted magnetic field in addition to the velocity gradient. The differential twist has the azimuth rotation of the magnetic field along the line-of-sight and generates the circular polarization from the linear polarization due to the magneto-optical effect. The required azimuth rotation is reasonable and amounts at most to 30°. The required velocity gradient is compatible with the line asymmetry and its spatial distribution observed in sunspots. The observed polarity rule leads to the conclusion that the sunspot magnetic field has the differential twist with the right-handed azimuth rotation relative to the direction of the main magnetic field, without regard to the magnetic polarity and to the solar cycle. The twist itself is left-handed under the photosphere, when the sunspot is assumed to be a unwinding emerging magnetic field.     

Comparison of two methods for determining the magnetic fields near black holes

We compare two methods for estimating the magnetic field near a black hole—based on a statistical formula that relates the magnetic field on the horizon of the black hole to its mass and on a direct magnetic field determination from optical polarimetric observations. An optically thick magnetized accretion disk is usually formed around the black hole in active galactic nuclei. The linear polarization of the radiation emerging from the disk is related to the local magnetic field and the polarization in Milne’s classical problem. The magnetic field in the region from where the radiation with the observed wavelength comes can be estimated by measuring this polarization. On the other hand, this field can be estimated from the above statistical formula if the field near the black hole is extrapolated into the accretion disk using a standard power law. Comparison of the magnetic field obtained from the observed polarization with the extrapolated field can serve to estimate the accuracy of the latter and the exponent in the adopted extrapolation law. As an example, we compare these two methods for the source NGC 4258.     

Magnetic field of solar prominences: The procedure of radio observations

The first successful radio astronomical results of measurements of the magnetic field of solar prominences are presented. The accuracy of polarization and magnetic field observations is 3 · · 10⁻⁴ and 2 G, respectively. The observations were made by the 22-meter radio telescope of the Crimean Astrophysical Observatory at wavelengths of 8 and 13.5 mm. It has been found that the value of the magnetic fields coincides with the optical one (from 7 to 30 G), but the image of radio polarization differs from the intensity.     

Theoretical study of the Fraunhofer lines polarization: The case of Ca i 4227

The measurements by Brückner (1963) of the Ca i 4227 polarization at the Sun's limb provides us with a test for the theory of line polarization. Computations are developed taking into account: (a) the transfer polarization, due to the anisotropy of radiation field; (b) the depolarizing collisions acting in the wings. The magnetic field is not taken into account and the theory is not valid in the Doppler core. In the wings a very good fit is obtained, using appropriate source-functions fitting the observed profiles at the center of the disk, and from center to limb.     

Parsec-scale polarization of the jet in quasar 4C 71.07

Very long-baseline interferometry (VLBI) observations of the quasar 4C 71.07 (0836+710) at frequencies of 5 and 8.4 GHz at two epochs are used to investigate apparent misalignments between the magnetic field and jet direction found in this source. The observed polarization angles are not consistent with Faraday rotation of synchrotron radiation from an aligned magnetic field. Internal Faraday rotation in a uniform spherical source is also ruled out by the observations, and while the misalignments could result from internal Faraday rotation in a non-uniform source, no strong signatures of this effect were found. The jet shows two distinct kinks at which the ridge-line changes direction and then reverts to its original direction. The magnetic field in these regions is parallel to the jet, and remains so as the jet bends. It seems likely that the largest remaining misalignment is associated with another such kink that is unresolved by these observations. The percentage polarization decreases near the bright knots, consistent with enhancement in brightness by compressions in the plane normal to the jet axis. The inferred rotation measure is low (100 rad m⁻²) throughout the jet, as for other quasars. However near the core, the polarization position angles suggest a rotation measure that appears to be uncharacteristically low by comparison with other quasars.     

Model of polarization state of compressional surface MHD waves in the low-altitude cusp

Examination of thermal plasma data obtained by low-altitude satellite measurements indicates that the intersection of the cusp in the dayside magnetosphere with the topside ionosphere creates a distinct plasma geometry at low altitudes. This region consists of one or two plasma discontinuities with steep boundaries. As a result of the plasma structuring in the cusp which commonly takes place in the winter hemisphere, the propagation of compressional surface MHD waves is supported. This point is illustrated by an analysis of the polarization state of compressional surface MHD waves propagating along a plasma layer with thickness a and ambient magnetic field B₀ parallel to the interfaces. The results obtained are applicable to the case of a single interface, which is derived in the limit a → ∞. In the general case the polarization of the compressional surface MHD waves in the plane transverse to the magnetic field B₀ is elliptical. This feature of the polarization state of the compressional surface modes does not follow from the former analysis by Edwin and Roberts (1982, Solar Phys. 76, 239) for a magnetic slab, because the disturbance components parallel to the interfaces and perpendicular to the magnetic field B₀ have not been examined. Although the absence of these components does not prove to be essential for deriving the exact dispersion equation for arbitrary wave directions of the surface modes, they must be included when considering polarization states. The surface mode polarization in the plasma layer changes its sense three times: at interfaces X = 0 and X = a and in the middle plane X = a/2. For the symmetrical (sausage) mode the wave disturbance component b_n transverse (normal) to the interfaces becomes zero in the middle plane; for the asymmetrical (kink) mode, the component b_t parallel to the interfaces and transverse to the ambient magnetic field is zeroed in the same plane. For a moving observer such as a satellite the polarization patterns which might be recorded change, depending on the velocity of the observer and the angles at which the layered cusp is traversed. An essential feature in the polarization of the compressional surface MHD modes is the presence of jumps in the magnetic disturbance component b_t at the interfaces. These jumps disappear only for propagation along the ambient magnetic field. In this particular case the component b_t vanishes and then the surface modes are undistinguishable from the body modes.     

Milestones in the Observations of Cosmic Magnetic Fields

Magnetic fields are observed everywhere in the universe. In this review, we concentrate on the observational aspects of the magnetic fields of Galactic and extragalactic objects. Readers can follow the milestones in the observations of cosmic magnetic fields obtained from the most important tracers of magnetic fields, namely, the star-light polarization, the Zeeman effect, the rotation measures (RMs, hereafter) of extragalactic radio sources, the pulsar RMs, radio polarization observations, as well as the newly implemented sub-mm and mm polarization capabilities. The magnetic field of the Galaxy was first discovered in 1949 by optical polarization observations. The local magnetic fields within one or two kpc have been well delineated by starlight polarization data. The polarization observations of diffuse Galactic radio background emission in 1962 confirmed unequivocally the existence of a Galactic magnetic field. The bulk of the present information about the magnetic fields in the Galaxy comes from anal     

Polarization of hard X-rays from solar flares

The polarization of hard solar X-radiation (> 10 keV) is calculated on the assumption that electrons get a non-isotropic velocity distribution in the initial phase of a flare. The brems-strahlung generated by nonthermal electrons spiralling around magnetic field lines with discrete pitch angles is considerably polarized if observed at approximately right angles to the magnetic field. In the energy range from 10 to 50 keV the degree of polarization is not strongly dependent on the photon energy. For pitch-angle distributions of the form sin² and cos², the polarization has opposite signs; it decreases appreciably at high photon energies. The observation of X-ray polarization will be useful in deducing the physical conditions in flares.     

First detection of polarization of the submillimeter diffuse Galactic dust emission by Archeops

We present the first determination of the Galactic polarized emission at 353 GHz by Archeops. The data were taken during the Arctic night of February 7, 2002 after the balloon-borne instrument was launched by CNES from the Swedish Esrange base near Kiruna. In addition to the 143 and 217 GHz frequency bands dedicated to CMB studies, Archeops had one 545 GHz and six 353 GHz bolometers mounted in three polarization sensitive pairs that were used for Galactic foreground studies. We present maps of the I,Q,U Stokes parameters over 17% of the sky and with a 13 arcmin resolution at 353 GHz (850 μm). They show a significant Galactic large scale polarized emission coherent on the longitude ranges [100°,120°] and [180°,200°] with a degree of polarization at the level of 4–5%, in agreement with expectations from starlight polarization measurements. Some regions in the Galactic plane (Gem OB1, Cassiopeia) show an even stronger degree of polarization in the range 10–20%. Those findings provide strong evidence for a powerful grain alignment mechanism throughout the interstellar medium and a coherent magnetic field coplanar to the Galactic plane. This magnetic field pervades even some dense clouds. Extrapolated to high Galactic latitude, these results indicate that interstellar dust polarized emission is the major foreground for PLANCK-HFI CMB polarization measurement.     

Wave-particle interactions in the ulf range: GEOS-1 and -2 results

Electromagnetic waves in the frequency range 0.2–11 Hz have been detected onboard the GEOS-1 and -2 satellites. The purpose of this paper is to report on these observations. The three orthogonal magnetic sensors allow us to determine the polarization of the waves. Two kinds of waves are commonly observed, which can easily be distinguished by their polarization.

(1) Waves with a magnetic field aligned with the DC magnetic field. These events often present a typical harmonic structure. The fundamental—which is not always observed—is often in the neighbourhood of the proton gyrofrequency F_H+. These waves are generally observed above F_H+. We will show that these emissions can be interpreted as magnetosonic waves destabilized by energetic protons (E 15 keV) with a ringlike distribution function.

(2) Waves with a magnetic field in a plane perpendicular to the DC magnetic field. These emissions are identified as Ion Cyclotron Waves (ICW's). These waves can, under certain conditions, propagate along the line of force of the magnetic field and reach the ground. They can be identified with the well-known Pcl oscillations, which generally have a clear periodic structure. In contrast these periodic structures are seldom observed onboard the satellites. At the geostationary orbit, these emissions exist in limited frequency domains, which are well organized by the helium gyrofrequency F_He+.     

Spatial dispersion of Faraday rotation and its connexion with mode coupling

It is shown that the lack of linear polarization in the microwave radiation of solar bursts (reported in a earlier paper) may be explained by spatial dispersion of Faraday rotation. The maximum source diameter s without noticeable destruction of linear polarization is determined by the electron density and the magnetic field strength in the volume, where the linear polarization is generated. In the case where linear polarization is produced by the radiation source, s is smaller than only 20 km. In the other case where linear polarization is produced by mode coupling in a quasi-transverse magnetic field in the corona, the s-values are found to range from 10 to 6000 km, which is still much smaller than the generally adopted sizes of microwave burst sources. The second case has been investigated for several models of magnetic fields.     

Coronal emission line polarization

A discussion of a program for the computation of coronal emission line polarization is presented. The starting point is a general formulation of the scattering function for magnetic dipole transitions between any two total angular momentum levels, J J, J ± 1. Illustration of the behavior of the scattering function for different transitions is given. The integration of the scattering function over the solar disk and along the line of sight accounting for arbitrary distribution of magnetic fields as well as an inhomogeneous temperature and density structure of the corona is considered next.Sample results are presented for the numerical computation of the angle of maximum polarization and the degree of maximum polarization to be expected from idealized magnetic field configurations such as radial and dipole. A computation is included for a realistic field configuration predicted to exist at the time of the 1966 eclipse. The magnetic field input to the scattering calculation is based upon the potential field extension of photospheric magnetic fields. It is the purpose of the sample calculations to demonstrate how the measurement of emission polarization measurements can be interpreted in terms of the direction of coronal magnetic fields. Factors which lend ambiguity to such interpreations are clearly illustrated from the examples. These include the Hanle-effect depolarization and the depolarization at the Van Vleck angle.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Polarization fields produced by winds in the equatorial F-region

Neutral air winds blowing across the magnetic field cause a slow transverse drift of the positive ions, perpendicular to both the winds and the magnetic field. This drift sets up an electric polarization field which can only be neutralized by currents flowing along magnetic field lines and through the E-layer. But at night the E-layer conductivity may be too small to close this circuit, so that polarization fields build up in the F-layer, causing the plasma to drift with the wind. This polarization effect may influence the behaviour of the nighttime equatorial F-layer and contribute to ‘superrotation’ of the atmosphere.