Linear and Circular Polarization Properties of Jets

I discuss the transfer of polarized synchrotron radiation in relativistic jets. I argue that the main mechanism responsible for the circular polarization properties of compact synchrotron sources is likely to be Faraday conversion and that, contrary to common expectation, a significant rate of Faraday rotation does not necessarily imply strong depolarization. The long-term persistence of the sign of circular polarization, observed in some sources, is most likely due to a small net magnetic flux generated in the central engine, carried along the jet axis and superimposed on a highly turbulent magnetic field. I show that the mean levels of circular and linear polarizations depend on the number of field reversals along the line of sight and that the gradient in Faraday rotation across turbulent regions can lead to`correlation depolarization'. The model is potentially applicable to a wide range of synchrotron sources. In particular, I demonstrate how the model can naturally explain the excess of circular over linear polarization in the Galactic Center (SgrA^*) and the low-luminosity AGN M81^*.     

Elemental abundance analyses with DAO spectrograms — XVIII. The double-lined spectroscopic binary 46 Draconis

Equipartition magnetic fields can dramatically affect the polarization of radiation emerging from accretion disc atmospheres in active galactic nuclei. We extend our previous work on this subject by exploring the interaction between Faraday rotation and absorption opacity in local, plane-parallel atmospheres with parameters appropriate for accretion discs. Faraday rotation in pure scattering atmospheres acts to depolarize the radiation field by rotating the polarization planes of photons after last scattering. Absorption opacity in an unmagnetized atmosphere can increase or decrease the polarization compared to the pure scattering case, depending on the thermal source function gradient. Combining both Faraday rotation and absorption opacity, we find the following results. If absorption opacity is much larger than scattering opacity throughout the atmosphere, then Faraday rotation generally has only a small effect on the emerging polarization because of the small electron column density along a photon mean free path. However, if the absorption opacity is not too large and it acts alone to increase the polarization, then the effects of Faraday rotation can be enhanced over those in a pure scattering atmosphere. Finally, while Faraday rotation often depolarizes the radiation field, it can in some cases increase the polarization when the thermal source function does not rise too steeply with optical depth. We confirm the correctness of the analytic calculation by Silant'ev of the high magnetic field limit of the pure scattering atmosphere, which we incorrectly disputed in our previous paper.     

Probing the Circular Polarization of Relativistic Jets on VLBI Scales

High resolution studies of circular polarization allow us see where it arises in a jet, study its local fractional level and spectrum, and compare these results to local measures of linear polarization and Faraday rotation. Here we not only review past results from Very Long Baseline Array (VLBA) circular polarization studies, but we also present preliminary new results on two quasars. In the core of PKS 0607–157, we find strong circular polarization at 8 GHz and much weaker levels at 15 GHz. Combined with the linear polarization data, we favor a simple model where the circular is produced by Faraday conversion driven by a small amount of Faradayrotation. In the core of 3C 345, we find strong circular polarization at 15 GHz in a component with distinct linear polarization. This core component is optically thick at 8 GHz, where we detect no circular polarization. With opposite trends in frequency for PKS 0607–157 and 3C 345, it seems clear that local conditions in a jet can have a strong effect on circular polarization and need to be taken into account when studying inhomogeneous objects with multi-frequency observations.     

The equation of polarization transfer in an inhomogeneous magnetized plasma

Recently we have derived the equation of polarization transfer in an inhomogeneous magnetized plasma in the case where absorption is so weak that the characteristic modes can be considered to be orthogonal. We extend this investigation to the study of polarization transfer in a plasma where the characteristic polarizations need not be orthogonal. We obtain explicit expressions for the Faraday rotation tensor, the absorption tensor, the mode-coupling tensor and the tensor describing the explicit spatial variation of characteristic polarizations due to plasma inhomogeneity.     

Theoretical Models for Producing Circularly Polarized Radiation in Extragalactic Radio Sources

We discuss the production of circular polarization in compact radio sources both by the intrinsic mechanism and by Faraday conversion. We pay particular attention to the magnetic field structure, considering partially ordered fields and Laing sheets, and distinguishing between uniform and unidirectional fields. (The latter can be constrained by flux conservation arguments.) In most cases, Faraday conversion is the more important mechanism. Conversion operates on Stokes U, which can be generated by internal Faraday rotation, or by magnetic field fluctuations, which can therefore produce circular polarization even in a pure pair plasma. We also show that the spectrum of circular polarization in an inhomogeneous jet can be quite different from that in a uniform source, being flat or even inverted.     

Circular Polarization and Magnetic Fields in Jet Models

The detection of circular polarization in compact synchrotron sources provides new insights into magnetic field configurations and the low-energy population of electrons in relativistic jets. Conversion of linear to circular polarization can be stimulated by Faraday rotation or turbulence in the source itself. A detailed model for the properties of the radio emission of Sgr A^* in the galactic center is presented.     

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.     

The polarization of optical radiation from the magnetic white dwarfs

It is pointed out that, because of the large Faraday rotation an outlet of linear polarization from the photosphere of a white dwarf is hampered. In accordance with this fact it is proposed to distinguish two types of magnetic white dwarfs. The first type (its representative is Grw 70°8247) has a linear polarization which is comparable in magnitude with the circular one. Polarization of radiation from the white dwarfs of the first type cannot arise in the photosphere. It arises in the corona of the star either as a result of cyclotron emission of hot electrons (T～10⁶ K) or as a result of scattering of slightly polarized emission from the photosphere in the corona. For the first type dwarfs such magnetic fields are required thatω _B ω_opt, i.e.B(1?3)×10⁸G. The white dwarfs of the second type (its representative is G 99-37) have their linear polarization much smaller than the circular one. Polarization of these white dwarfs can arise as a result of the transfer of radiation in the nonisothermal photosphere. Magnetic fields required for the second type can be much smaller:B cos γ=(1?10)×10⁶ G. It is shown that the photospheric model allows to obtain the quantitative accordance of the theory with all the observational data for G 99-37 and is not in accordance with the data for Grw 70°8247, at the same time the model with cyclotron emission from the corona explains the magnitude of both linear and circular polarization and their wavelength dependence for Grw 70°8247.     

Measurements of Faraday Rotation Through the Solar Corona During the 2009 Solar Minimum with the MESSENGER Spacecraft

Measurements of Faraday rotation through the solar corona were collected using the radio beacon aboard the MESSENGER spacecraft during the longest solar minimum in a century. As MESSENGER entered superior conjunction, the plane of polarization of its radio signal was observed to rotate as it traversed the circularly birefringent plasma of the Sun’s atmosphere. On time scales of less than three hours, these uncalibrated plane of polarization observations of Faraday rotation can be used to investigate the dynamic processes in the solar plasma, such as magnetohydrodynamic (MHD) waves and coronal mass ejections (CMEs). Here we describe the MESSENGER Faraday rotation experiment, the data processing conducted to obtain the plane of polarization, and the estimation of error.     

The appearance of polarization in radiation from hot stars due to the faraday rotation effect as a possible method of determining stellar magnetic fields

The effect of Faraday rotation is shown to lead to the appearance of linear polarization of stellar radiation scattered in an optically-thin circumstellar electron-magnetized shell, even in the case when the shell is spherical. The spectral dependence of the polarization degree is evaluated for scattering in (i) a spherically-symmetric magnetized shell with a power-law radial dependence of the electron density, and (ii) a non-spherical ellipsoidal uniform envelope. The position of maximum in the polarization spectrum permits us to determine the magnetic field magnitude on a star surface. If the rotational and magnetic axes do not coincide, the periodic variability of the polarization will be observed with the period of stellar rotation. Some Be-stars, such as Cas, 48 Lib, EW Lac, Aqr, HD 45677, X Per, are proposed as candidates to be investigated for magnetic fields, as well as some stars of the T Tau-type. This method may be also applied to supernovae shells.     

Circular polarization in pulsar integrated profiles

We present a systematic study of the circular polarization in pulsar integrated profiles, based on published polarization data. For core components, we find no significant correlation between the sense change of circular polarization and the sense of linear position-angle variation. Circular polarization is not restricted to core components and, in some cases, reversals of circular polarization sense are observed across the conal emission. In conal double profiles, the sense of circular polarization is found to be correlated with the sense of position-angle variation. Pulsars with a high degree of linear polarization often have one hand of circular polarization across the whole profile. For most pulsars, the sign of circular polarization is the same at 50-cm and 20-cm wavelengths, and the degree of polarization is similar, albeit with a wide scatter. However, at least two cases of frequency-dependent sign reversals are known. This diverse behaviour may require more than one mechanism to generate circular polarization.     

On the observation of linear polarization of solar microwave bursts

It is known that mode coupling may occur in quasi-transverse magnetic field regions of the solar corona, which produces linear polarization at microwave frequencies. A microwave polarimeter measuring all 4 Stokes parameters at 8.918 GHz simultaneously at three different highfrequency bandwidths (40 kHz, 400 kHz and 5 MHz) has been developed in order to observe the linear component and its Faraday rotation. The respective minimum detectable changes of the Stokes parameters I, Q, U and V are 9, 3 and 1 solar flux unit at an integration time of 1 s. For burst intensities greater than 300 solar flux units, the minimum detectable degree of linear and circular polarization is 1 %–3 %, depending on the bandwidth. Observations of 68 bursts showed that most of the bursts were circularly polarized. No linear polarization could be found within the limits of accuracy of our polarimeter. Two possible explanations for this result are discussed. The possibility of mode coupling however cannot be excluded from these first observations.     

Radio continuum and H I observations of the supernova remnant G296.8–00.3

We present Australia Telescope Compact Array (ATCA) observations of the supernova remnant (SNR) G296.8–00.3. A 1.3-GHz continuum image shows the remnant to have a complex multi-shelled appearance, with an unusual rectangular strip running through its centre. H I absorption yields a kinematic distance to the remnant of 9.6 ± 0.6 kpc, from which we estimate an age in the range (2–10) × 10³ yr. The ATCA's continuum mode allows a measurement of the Faraday rotation across the band, from which we derive a mean rotation measure towards the SNR of 430 rad m⁻². We consider possible explanations for the morphology of G296.8–00.3, and conclude that either it has a biannular structure, as might be produced through interaction with an asymmetric progenitor wind, or its appearance is caused by the effects of the surrounding interstellar medium.   We argue that the adjacent pulsar J1157–6224 is at a similar distance to the SNR, but that a physical association is highly unlikely. The pulsar is the only detectable source in the field in circular polarization, suggesting a method for finding pulsars during aperture synthesis.     

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.     

Effects of Faraday rotation observed in filter magnetograph data

In this paper we analyze the effects of Faraday rotation on the azimuth of a transverse magnetic field as determined from the linear polarization in the inverse Zeeman effect. Observations of a simple sunspot were obtained with the Marshall Space Flight Center's vector magnetograph over the wavelength interval of 170 mÅ redward of line center of the Fe i 5250.22 Å spectral line to 170 mÅ to the blue, in steps of 10 mÅ. These data were analyzed to produce the variation of the azimuth as a function of wavelength at each pixel over the field of view of the sunspot. At selected locations in the sunspot, curves of the observed variation of azimuth with wavelength were compared with model calculations for the azimuth at each wavelength as derived from the inverse Zeeman effect modified by Faraday rotation. From these comparisons we derived the maximum amount of rotation as functions of both the magnitude and inclination of the sunspot's field. These results show that Faraday rotation of the azimuth will be a significant problem in observations taken near the center of a spectral line for fields as low as 1200 G and inclinations of the field in the range 20–80 deg. Conversely, they show that measurements taken in the wing of a spectral line are relatively free of the effects of Faraday rotation.     

Circular Polarization Observed in Interplanetary Type III Radio Storms

We report the detection and analysis of circular polarization in solar type III radio storms at hectometric-to-kilometric wavelengths. We find that a small (usually less than 5%), but statistically significant, degree of circular polarization is present in all interplanetary type III radio storms below 1 MHz. The sense of the polarization, which is right-hand circular for some storms and left-hand circular for others, is maintained for the entire duration of the type III storm (usually many days). For a given storm, the degree of circular polarization peaks near central meridian crossing of the associated active region. At a given time, the degree of circular polarization is found to generally vary as the logarithm of the observing frequency. The radiation characteristics, including the polarization, for one interplanetary type III storm exhibits an unusual 1.6 hour oscillation. Based on the standard plasma emission theory of type III radiation, we discuss the implications of these observations for the magnitude and radial dependence of the solar magnetic field above active regions on the Sun.     

On spectral dependence of polarization of asteroids

From the analysis of all of the data available on the spectral dependence of polarization of light reflected by asteroids, it has been shown that the slope of the spectral dependence of polarization of asteroids changes its sign, when moving from the negative branch of the phase curve of polarization to the positive one. This effect also manifests itself in the spectral behavior of polarization of the Moon and, probably, in the polarization of the other atmosphereless bodies. From the analysis of a population of asteroids of different types, a weak correlation between the spectral slopes of the polarization degree and the albedo has been found.     

The Sunyaev–Zel'dovich effect and Faraday rotation contributions of galaxy groups to the CMB angular power spectrum

The Sunyaev–Zel'dovich (SZ) effect and the Faraday rotation from haloes are examined over a wide mass range, including gas condensation and magnetic field evolution. Contributions to the cosmic microwave background (CMB) angular power spectrum are evaluated for galaxy clusters, galaxy groups and galaxies. Smaller mass haloes are found to play a more important role than massive haloes for the B -mode polarization associated with the SZ CMB anisotropies. The B modes from the Faraday rotation dominate the secondary B modes caused by gravitational lensing at  ℓ > 3000  . Measurement of B -mode polarization in combination with the SZ power spectrum can potentially provide important constraints on intracluster magnetic field and gas evolution at early epochs.     

Magnetic field and radius of the innermost stable circular orbit near super‐massive black holes in active galactic nuclei

Magnetic fields in an accretion disk around the central black hole can modify the size of the innermost stable circular orbit (ISCO) and can produce a difference to the classical Novikov‐Thorne radius. We estimated the ISCO magnetic field strength from the polarimetric observations of the accretion‐disk radiation. This estimate is obtained taking into account the effect of the Faraday rotation of the polarization plane at the distance of the mean free path of photons between successive electron scattering events. We present the new method for estimating the ISCO radius in the accretion disk, i.e. in the nearest vicinity of a central black hole. Our estimates confirmed the Frolov, Shoom & Tzounis (2014) and Ranea‐Sandoval & Garcia (2015) conclusion that the magnetic field in the accretion disk decreases the size of the innermost stable circular orbit. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.