Observed Faraday Rotation Research Articles

Faraday rotation with a single-nuclear-spin qubit in a high-finesse optical cavity

When an off-resonant light field is coupled with atomic spins, its polarization can rotate depending on the direction of the spins via a Faraday rotation which has been used for monitoring and controlling the atomic spins. We observed Faraday rotation by an angle of more than 10 degrees for a single 1/2 nuclear spin of 171Yb atom in a high-finesse optical cavity. By employing the coupling between the single nuclear spin and a photon, we have also demonstrated that the spin can be projected or weakly measured through the projection of the transmitted single ancillary photon.

A SURVEY OF EXTRAGALACTIC FARADAY ROTATION AT HIGH GALACTIC LATITUDE: THE VERTICAL MAGNETIC FIELD OF THE MILKY WAY TOWARD THE GALACTIC POLES

We present a study of the vertical magnetic field of the Milky Way toward the Galactic poles, determined from observations of Faraday rotation toward more than 1000 polarized extragalactic radio sources at Galactic latitudes |b| ⩾ 77°, using the Westerbork Radio Synthesis Telescope and the Australia Telescope Compact Array. We find median rotation measures (RMs) of 0.0 ± 0.5 rad m−2 and +6.3 ± 0.7 rad m−2 toward the north and south Galactic poles, respectively, demonstrating that there is no coherent vertical magnetic field in the Milky Way at the Sun's position. If this is a global property of the Milky Way's magnetism, then the lack of symmetry across the disk rules out pure dipole or quadrupole geometries for the Galactic magnetic field. The angular fluctuations in RM seen in our data show no preferred scale within the range ≈01 to ≈25°. The observed standard deviation in RM of ∼9 rad m−2 then implies an upper limit of ∼1 μG on the strength of the random magnetic field in the warm ionized medium at high Galactic latitudes.

Polarization Analysis of Microscopic Faraday Rotation of Thin Solid Ferrocene Aggregates

The Faraday rotation angles of ferrocene aggregates formed on a glass plate and a water surface were measured by a pulsed magnetic field Faraday-effect measurement system. The observed Faraday rotation of the aggregates showed a dependency on the incident polarization angle with a period of π/2, in contrast to the case of polarized absorption in the absence of a magnetic field, which gave a period of π. The polarization dependency of the Faraday rotation was analyzed in terms of the products of trigonometric functions with the angle of the transition moment of the ferrocene aggregate, inspired by the equations for the Faraday A and B terms. From the polarization angle dependencies in the presence and absence of pulsed magnetic fields, the differences in angles between the optical transition moment and the magneto-optical transition moment were evaluated, and they suggested that the ferrocene molecules in the aggregate formed on a glass plate were oriented more parallel to the horizontal glass surface than those in the aggregate formed on a water surface.

Joule heating and anomalous resistivity in the solar corona

Abstract. Recent radioastronomical observations of Faraday rotation in the solar corona can be interpreted as evidence for coronal currents, with values as large as 2.5×109 Amperes (Spangler, 2007). These estimates of currents are used to develop a model for Joule heating in the corona. It is assumed that the currents are concentrated in thin current sheets, as suggested by theories of two dimensional magnetohydrodynamic turbulence. The Spitzer result for the resistivity is adopted as a lower limit to the true resistivity. The calculated volumetric heating rate is compared with an independent theoretical estimate by Cranmer et al. (2007). This latter estimate accounts for the dynamic and thermodynamic properties of the corona at a heliocentric distance of several solar radii. Our calculated Joule heating rate is less than the Cranmer et al estimate by at least a factor of 3×105. The currents inferred from the observations of Spangler (2007) are not relevant to coronal heating unless the true resistivity is enormously increased relative to the Spitzer value. However, the same model for turbulent current sheets used to calculate the heating rate also gives an electron drift speed which can be comparable to the electron thermal speed, and larger than the ion acoustic speed. It is therefore possible that the coronal current sheets are unstable to current-driven instabilities which produce high levels of waves, enhance the resistivity and thus the heating rate.

FULL POLARIZATION SPECTRA OF 3C 279

We report the results of parsec-scale, multi-frequency VLBA observations of the core region of 3C 279 in Stokes I, linear polarization, and circular polarization. These full polarization spectra are modeled by radiative transfer simulations to constrain the magnetic field and particle properties of the parsec-scale jet in 3C 279. The polarization properties of the core region, including the amount of linear polarization, the amount and sign of Faraday rotation, and the amount and sign of circular polarization can be explained by a consistent physical picture. The base of the jet is modeled as an inhomogeneous Blandford-Konigl style conical jet dominated by a vector-ordered poloidal magnetic field along the jet axis, and we estimate its net magnetic flux. This poloidal field is responsible for the linear and circular polarization from this inhomogeneous component. Farther down the jet the magnetic field in two homogeneous features is dominated by local shocks and a smaller fraction of vector-ordered poloidal field remains along the jet axis. In this picture, we find the jet to be kinetically dominated by protons with the radiating particles being dominated by electrons at an approximate fraction of >~ 75%. Based on the amounts of Faraday conversion deduced for the homogeneous components, we find a plausible range for the lower cutoff in the relativistic particle energy spectrum to be 5 <~ gamma_l <~ 35. The physical picture described here is not unique if the observed Faraday rotation and depolarization occur in screens external to the jet; however, we find the joint explanation of linear and circular polarization observations from a single set of magnetic fields and particle properties internal to the jet to be compelling evidence for this picture. (Abridged)

Coronal magnetic field analysis with Faraday rotation observations of Alfven waves

Faraday rotation observations of an Alfven wave at 4 solar radii during the January 9, 1983 superior conjunction of the Helios spacecraft were simultaneously obtained in Goldstone, California and Canberra, Australia allowing the measurement of the Alfven wave speed. We find that the T. Hoeksema et al. (1982) potential field source surface model performs better than the M. Paetzold et al. (1987) magnetic field magnitude model for predicting the magnitude of the magnetic field in the region based on the observed Alfven speed. Assuming the Alfven wave is monochromatic, coherent, and radially propagating, we determine the minimum magnetic field fluctuation required to reproduce the observations. We use the minimum magnetic field fluctuation to calculate the minimum Alfven wave energy flux of 6 × 1019 W; this is approximately 20% of the wave energy required to accelerate the solar wind.

High-frequency Faraday rotation observations of the solar corona

This thesis, presented on January 31, 2007 under the supervision of Professor Christopher T. Russell, discusses the solar coronal magnetic field observations that can be obtained using the phenomenon of Faraday rotation. It was defended in the Department of Earth and Space Sciences at the University of California, Los Angeles (595 Charles E. Young, Dr. East, Los Angeles, CA 90095). A resume can be found at http://acs-consulting.com/.

A Global Probe of Cosmic Magnetic Fields to High Redshifts

Faraday rotation (RM) probes of magnetic fields in the universe are sensitive to cosmological and evolutionary effects as $z$ increases beyond $\sim $1 because of the scalings of electron density and magnetic fields, and the growth in the number of expected intersections with galaxy-scale intervenors, $d$N/$dz$. In this new global analysis of an unprecedented large sample of RM's of high latitude quasars extending out to $z\sim $3.7 we find that the distribution of RM broadens with redshift in the 20 $-$ 80 rad m$^{-2}$ range range, despite the (1 +$z$)$^{-2}$ wavelength dilution expected in the observed Faraday rotation. Our results indicate that the Universe becomes increasingly ``Faraday-opaque'' to sources beyond $z \sim$ 2, that is, as $z$ increases progressively fewer sources are found with a ``small'' RM in the observer's frame. This is in contrast to sources at $z \la$1. They suggest that the environments of galaxies were significantly magnetized at high redshifts, with magnetic field strengths that were at least as strong within a few Gyr of the Big Bang as at the current epoch. We separately investigate a simple unevolving toy model in which the RM is produced by MgII absorber systems, and find that it can approximately reproduce the observed trend with redshift. An additional possibility is that the intrinsic RM associated with the radio sources was much higher in the past, and we show that this is not a trivial consequence of the higher radio luminosities of the high redshift sources.

Faraday rotation observations of CMEs

Simultaneous observations obtained by the Solwind coronagraph and Faraday rotation of the Helios radio frequency carrier signal in 1979 showed that CMEs produce characteristic ‘W’ or sigmoid transients in Faraday rotation observations similar to those observed by Pioneer 6 and 9 in 1968 and 1970. We demonstrate that a relaxed flux‐rope model is capable of reproducing these observations. Through fitting the model to the observations, we can obtain information on the flux rope orientation, position, size, velocity, rate of change of rope radius and pitch angle. With electron density measurements, we can also obtain a measure of the magnetic field strength. These fits demonstrate that Faraday rotation observations can provide information on the magnetic field of a CME shortly after it erupts.

Coronal Faraday rotation of occulted radio signals

Faraday rotation (FR) observations of radio sources near solar conjunction yield information on the coronal magnetic field at heliospheric distances not reached by in situ exploration. Measurements of FR yield the rotation measure (RM), a wavelength independent quantity defined as the integral along the raypath of the product of the electron density times the raypath-parallel component of the magnetic field. Independent observations or models of the coronal electron density are required in order to extract information about the magnetic field. The radio sounding sources can be either artificial (spacecraft) or natural, but they must be at least partially linearly polarized. The most extensive campaign of coronal radio sounding polarization measurements using a spacecraft was the Helios Faraday Rotation Experiment, which was conducted over the duration of the Helios 1 (1974–1984) and Helios 2 (1976–1980) missions. Other coronal FR experiments have been carried out using natural continuum sources recently a...

Impact of tangled magnetic fields on fossil radio bubbles

There is growing consensus that feedback from active galactic nuclei (AGN) is the main mechanism responsible for stopping cooling flows in clusters of galaxies. AGN are known to inflate buoyant bubbles that supply mechanical power to the intracluster gas [intracluster medium (ICM)]. High Reynolds number hydrodynamical simulations show that such bubbles get entirely disrupted within 100 Myr, as they rise in cluster atmospheres, which is contrary to observations. This artificial mixing has consequences for models trying to quantify the amount of heating and star formation in cool core clusters of galaxies. It has been suggested that magnetic fields can stabilize bubbles against disruption. We perform magnetohydrodynamical simulations of fossil bubbles in the presence of tangled magnetic fields using the high-order pencil code. We focus on the physically motivated case where thermal pressure dominates over magnetic pressure and consider randomly oriented fields with and without maximum helicity and a case where large-scale external fields drape the bubble. We find that helicity has some stabilizing effect. However, unless the coherence length of magnetic fields exceeds the bubble size, the bubbles are quickly shredded. As observations of Hydra A suggest that length-scale of magnetic fields may be smaller than typical bubble size, this may suggest that other mechanisms, such as viscosity, may be responsible for stabilizing the bubbles. However, since Faraday rotation observations of radio lobes do not constrain large-scale ICM fields well if they are aligned with the bubble surface, the draping case may be a viable alternative solution to the problem. A generic feature found in our simulations is the formation of magnetic wakes where fields are ordered and amplified. We suggest that this effect could prevent evaporation by thermal conduction of cold Hα filaments observed in the Perseus cluster.

Assessing the tilt of the solar magnetic field axis through Faraday rotation observations

Context: Faraday rotation measurements of extragalactic radio sources during coronal occultation allow assessment of both the electron density distribution and the three-dimensional magnetic field topology in the outer solar corona. Aims: We simulate the three-dimensional structure of both the coronal magnetic field and the electron density distribution in order to reproduce the excess Faraday rotation measures (RMs) of the occulted radio sources observed during solar activity minimum. In particular, we infer the tilt of the solar magnetic axis with respect to the rotation axis. Methods: We compare the output of the model with Very Large Array (VLA) radio polarimetric measurements of a sample of extragalactic sources observed in May 1997. Information on the magnetic field geometry can be retrieved by fine-tuning the set of model free parameters that best describe the observations. Results: We find that predicted and observed Faraday rotation measures are in excellent agreement, thus supporting the model. Our best-fitting model yields a tilt angle $\theta_{RB}=3.3^{\circ}$ of the solar magnetic axis with respect to the solar rotation axis around Carrington Rotation 1923. This result is consistent with analogous but independent estimates computed from the expansion coefficients of the photospheric field observed at the Wilcox Solar Observatory (WSO).

Deep 1.4 GHz Very Large Array Observations of the Radio Halo and Relic in Abell 2256

We present deep Very Large Array observations of the merging galaxy cluster A2256. This cluster is known to possess diffuse steep-spectrum radio relic emission in the peripheral regions. Our new observations provide the first detailed image of the central diffuse radio halo emission in this cluster. The radio halo extends over more than 800 kpc in the cluster core, while the relic emission covers a region of ~1125 kpc × 520 kpc. A spectral index map of the radio relic shows a spectral steepening from the northwest toward the southeast edge of the emission, with an average spectral index between 1369 and 1703 MHz of α = -1.2 across the relic. Polarization maps reveal high fractional polarization of up to 45% in the relic region with an average polarization of 20% across the relic region. The observed Faraday rotation measure is consistent with the Galactic estimate, and the dispersion in the rotation measure is small, suggesting that there is very little contribution to the rotation measure of the relic from the intracluster medium. We use these Faraday properties of the relic to argue that it is located on the front side of the cluster.

Observation of Toroidal Magnetic Fields on 100 pc Scales in the Galactic Center

We present new submillimeter polarimetric observations of the Galactic center region, made using the SPARO polarimeter that operates at the South Pole. Compared with previous submillimeter polarimetry of this region, our measurements cover much more sky area, and they imply that the molecular gas in the central few hundred pc is threaded by a large scale toroidal magnetic field. We consider this result together with radio observations that show evidence for poloidal fields in the Galactic center, and with Faraday rotation observations. We compare all of these observations with a magnetodynamic model for the Galactic center.

Faraday rotation as a probe of the physical conditions near relativistic jets

Multi-frequency polarimetry with the VLBA can be used to produce Faraday Rotation Measure (RM) maps of the central parsecs of the hosts of relativistic jets. Quasars and radio galaxies have been shown to have RMs of several 1000 rad m 2. Thus, knowledge of the Faraday Rotation in a source is required to recover the intrinsic magnetic field direction in relativistic jets viewed through a large Faraday depth. As the RM is a measure of the magnetic field weighted by the electron density, estimates of the magnetic field strength and topology can be made in close proximity to the jet. We will present results from a survey of 40 quasars, radio galaxies, and BL Lac objects and discuss their RM properties and the nature of the foreground screen responsible for the observed Faraday Rotation.

First Results from the Submillimeter Polarimeter for Antarctic Remote Observations: Evidence of Large-Scale Toroidal Magnetic Fields in the Galactic Center

We have observed the linear polarization of 450 µm continuum emission from the Galactic center, using a new polarimetric detector system that is operated on a 2 m telescope at the South Pole. The resulting polarization map extends � 170 pc along the Galactic plane and � 30 pc in Galactic latitude, and thus covers a significant fraction of the central molecular zone. Our map shows that this region is permeated by large-scale toroidal magnetic fields. We consider our results together with radio observations that show evidence for poloidal fields in the Galactic center, and with Faraday rotation observations. We compare all of these observations with the predictions of a magnetodynamic model for the Galactic center that was proposed in order to explain the Galactic Center Radio Lobe as a magnetically driven gas outflow. We conclude that the observations are basically consistent with the model.

The Evolution of Magnetic Fields in Galaxy Clusters

Cosmological simulations of magnetic fields in galaxy clusters show that remarkable agreement between simulations and observations of Faraday rotation and radio haloes can be achieved assuming that seed fields of ∼ 10−9 G were present at redshifts ∼ 15−20. The structure of the seed field is irrelevant for the final intracluster field. On average, the field grows exponentially with decreasing cluster redshift, but merger events cause steep transient increases in the field strength. Typical field-reversal scales are of order 50h−1kpc. In most cases, the intracluster fields are dynamically unimportant. Assuming secondary electron models, the average structure of cluster radio haloes can naturally be reproduced.

Ionospheric reconstruction using Faraday rotation data: A new technique

Measurements of total electron content of the ionosphere by recording group delay or differential phase of transionospheric satellite signals have been used for reconstruction of ionospheric profiles. Integrated electron content measurements contain little information of ionospheric height distribution and require precise observations. These measurements are difficult for VHF and higher frequencies and require reasonably sophisticated instruments. Faraday rotation measurements, on the other hand, require relatively simple instruments and were widely used throughout the world. Faraday rotation of HF, VHF, and lower UHF band signals contains an additional term, e.g., a known function of the magnetic field. The functional form depends on the ray path and orientation of the magnetic field and in general is a complex quantity. Since the magnetic field distribution in the Earth's ionosphere is known with very high precision, this information can be used to obtain improved reconstruction of the ionospheric profiles. The magnetic field components have a strong dependence with the height, and this provides additional information regarding the ionospheric height retrieval. We have performed simulations using these techniques, and we present results using both simulated data as well as Faraday rotation data measured from several stations. We compare the sensitivities and reconstruction of ionospheric profiles using group delay and Faraday rotation techniques and demonstrate the improvements with the use of Faraday rotation data. The most difficult (in terms of radio propagation) regions, i.e., those near the equatorial regions, are simulated, and data from several stations, i.e., those near Calcutta, India, as well as those from several stations in Africa, are used. For the first time, we present the results of the reconstruction of the ionosphere using both simulated and observed Faraday rotation data. Large amounts of Faraday rotation data have been acquired during the 1960s and 1970s. These data contain a history of the ionosphere. The present technique would allow retrieval of ionospheric profiles over extended regions and could allow inferences to be drawn regarding the long‐term changes in the ionosphere. The technique can also be incorporated in future satellite beacons, and the combination of group delay and Faraday rotation techniques will allow us to obtain superior reconstructions.

Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd 3+ ions in Y 3Fe 5O 12 garnet are analyzed by using quantum theory. In the spontaneous state, the magneto-optical effects originate mainly from the intra-ionic electric dipole transitions between the 4 f 3 and 4 f 25d states split by the spin-orbit, crystal field, and superexchange interactions. For the excited configuration, the coupling scheme of Yanase is extended to the Nd 3+ ion. The magneto-optical resonance frequencies are mainly determined by the splitting of the 5d states induced by the crystal field. The theoretical results of both Nd magnetization and Faraday rotation are in good agreement with experiments. The observed Faraday rotation is proved to be of the paramagnetic type. Although the value of the magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical study, a new assignment about the transitions associated with this resonance is unambiguously determined. The spin-orbit coupling of the ground configuration has a great influence on both the Faraday rotation and magnetization, but, unlike the theoretical results obtained in some metals and alloys, the relation between the Faraday rotation and the spin-orbit coupling strength is more complex than a linear one. The magnitude of the magneto-optical coefficient increases as the spin-orbit interaction strength of the ground configuration decreases when the strength is not very weak. Finally, the temperature dependence of the magneto-optical coefficient and the effect of the mixing of different ground-term multiplets induced by the crystal field are analyzed.

Faraday Rotation and Models for the Plasma Structure of the Solar Corona

Faraday rotation observations of polarized radiation from natural radio sources are unique among remote diagnostics of the solar corona in that they provide information on the coronal magnetic field. Dual frequency radio polarization measurements yield the rotation measure, a quantity that is proportional to the integral along the line of sight of the product of the electron density and the line-of-sight component of the magnetic field. We made linear polarization observations with the NRAO Very Large Array of 13 polarized radio sources occulted by the solar corona. The observations were made at frequencies of 1465 and 1665 MHz on four days in 1997 May and cover a 20 day period, sampling elongations ranging from about 5 to 14 R☉. The magnitudes of the rotation measures observed range from about 11 to 0 rad m-2. The relatively low values for the rotation measures are due to the solar minimum configuration of the corona at the time of the observations, with the lines of sight to the sources generally not crossing sector boundaries. The largest rotation measure was observed for the extended radio source 3C 79 on 1997 May 11 and corresponds to a case in which the line of sight passed next to the streamer belt at small solar elongations. We have developed a three-dimensional model of the solar corona that is in excellent agreement with the observed rotation measures, as well as being completely consistent with other coronal diagnostics such as coronagraph images. In particular, our observations support the coronal magnetic field model of Patzold et al. (1987); they would be inconsistent with coronal magnetic fields significantly weaker or stronger than this model. The plasma density distribution in the corona is successfully modeled by a dense streamer belt component and a more tenuous coronal hole component. Details of these models are given in § 3 of this paper. The principal disagreement between the model and observations occurs for three lines of sight for which the model predicts nearly zero rotation measure but for which we measure small but significant values of -1 to -2 rad m-2. These lines of sight passed over the solar polar regions. We discuss the possibility that these residual rotation measures are due to static coronal plasma structures, not described by global coronal models, or to very long wavelength coronal Alfven waves. Fluctuations in the rotation measure on timescales of a few hours were observed for some sources and not others. When detected, they were of order 1-2 rad m-2 and occurred on timescales of several hours.