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.     

Is the Long-Term Persistency of Circular Polarisation due to the Constant Helicity of the Magnetic Fields in Rotating Quasar Engines?

Many compact radio sources like quasars, blazars, radio galaxies, and micro-quasars emit circular polarisation (CP) with surprising temporal persistent handedness. We propose that the CP is caused by Faraday conversion (FC) of linear polarisation (LP) synchrotron light which propagates along a line-of-sight (LOS) through helical magnetic fields. Jet outflows from radio galaxies should have the required magnetic helicity in the emission region due to the magnetic torque of the accretion disc. Also advection dominated accretion flow (ADAF)should contain magnetic fields with the same helicity. However, a jetregion seems to be the more plausible origin of CP. The proposed scenario requires Faraday rotation (FR) to be insignificant in the emission region. The proposed mechanism works in electron-positron(e^±) as well as electron-proton (e/p) plasma. In the latter case, the emission region should consist of individual flux tubes with independent polarities in order to suppress too strong FR– as it was already proposed for FR based CP generation models. The predominant CP is expected to mostly counter-rotate (rotation is measured here in sky-projection) with respect to the central engine in all cases (jet or ADAF, e^± or e/p plasma) and therefore allows to measure the sense of rotation of quasar engines. The engine of SgrA^* is expected – in this scenario – to rotate clockwise and therefore counter-Galactic, as do the young hot stars in its vicinity, which are thought to feed SgrA^* by their winds. Generally, sources with Stokes-V<0 (V>0) are expected to rotate clockwise(counter-clockwise).     

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.     

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.     

On the degree of circular polarization of synchrotron radiation

Formulas describing synchrotron radiation are extended to include the effect of the presence of an ambient medium and the effect of reabsorption and Faraday rotation on the degree of circular polarization. Results are: (1) The onset of Razin-Tsytovich suppression has no significant effect on the degree of circular polarization. (2) The onset of self-absorption in a source subject to weak Faraday rotation (negligible Faraday rotation in an absorption length) causes the degree of circular polarization to reverse its sign and to decrease (by between one half and one quarter for typical parameters) in magnitude. (3) As in (2) but for strong Faraday rotation (many rotations of the plane of polarization in an absorption length) the degree of circular polarization also reverses its sign and becomes slightly smaller in magnitude than for weak Faraday rotation.The transfer equation including the effects of the polarization is discussed in detail.     

Solution of the Milne Problem for a Magnetized Atmosphere

The Milne problem is solved numerically for a magnetized semi-infinite electron atmosphere in the case where the magnetic field is directed along the normal to the medium. The calculated angular distribution, degree of linear polarization, and positional angle of inclination of the plane of polarization of the emerging radiation are given in tables for a number of values of the Faraday rotation parameter and for degrees of intrinsic optical absorption, q=0, 0.2, and 0.4. It is assumed that the magnetic field B10⁶ G, so that scattering in the optical range is purely Thomson scattering.     

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.     

Observations of magnetic fields in the Milky Way and in nearby galaxies with a Square Kilometre Array

The role of magnetic fields in the dynamical evolution of galaxies and of the interstellar medium (ISM) is not well understood, mainly because such fields are difficult to directly observe. Radio astronomy provides the best tools to measure magnetic fields: synchrotron radiation traces fields illuminated by cosmic-ray electrons, while Faraday rotation and Zeeman splitting allow us to detect fields in all kinds of astronomical plasmas, from lowest to highest densities. Here, we describe how fundamental new advances in studying magnetic fields, both in our own Milky Way and in other nearby galaxies, can be made through observations with the proposed Square Kilometre Array. Underpinning much of what we propose is an all-sky survey of Faraday rotation, in which we will accumulate tens of millions of rotation measure measurements toward background radio sources. This will provide a unique database for studying magnetic fields in individual Galactic supernova remnants and Hii regions, for characterizing the overall magnetic geometry of our Galaxy’s disk and halo, and for understanding the structure and evolution of magnetic fields in galaxies. Also of considerable interest will be the mapping of diffuse polarized emission from the Milky Way in many narrow bands over a wide frequency range. This will allow us to carry out Faraday tomography of the Galaxy, yielding a high-resolution three-dimensional picture of the magnetic field within a few kpc of the Sun, and allowing us to understand its coupling to the other components of the ISM. Finally, direct synchrotron imaging of a large number of nearby galaxies, combined with Faraday rotation data, will allow us to determine the magnetic field structure in these sources, and to test both the dynamo and primordial field theories for field origin and amplification.     

Modeling the total and polarized emission in evolving galaxies: “Spotty” magnetic structures

Future radio observations with the Square Kilometre Array (SKA) and its precursors will be sensitive to trace spiral galaxies and their magnetic field configurations up to redshift z ≈ 3. We suggest an evolutionary model for the magnetic configuration in star‐forming disk galaxies and simulate the magnetic field distribution, the total and polarized synchrotron emission, and the Faraday rotation measures for disk galaxies at z ≲ 3. Since details of dynamo action in young galaxies are quite uncertain, we model the dynamo action heuristically relying only on well‐established ideas of the form and evolution of magnetic fields produced by the mean‐field dynamo in a thin disk. We assume a small‐scale seed field which is then amplified by the small‐scale turbulent dynamo up to energy equipartition with kinetic energy of turbulence. The large‐scale galactic dynamo starts from seed fields of 100 pc and an averaged regular field strength of 0.02 μG, which then evolves to a “spotty” magnetic field configuration in about 0.8 Gyr with scales of about one kpc and an averaged regular field strength of 0.6 μG. The evolution of these magnetic spots is simulated under the influence of star formation, dynamo action, stretching by differential rotation of the disk, and turbulent diffusion. The evolution of the regular magnetic field in a disk of a spiral galaxy, as well as the expected total intensity, linear polarization and Faraday rotation are simulated in the rest frame of a galaxy at 5GHz and 150 MHz and in the rest frame of the observer at 150 MHz. We present the corresponding maps for several epochs after disk formation. Dynamo theory predicts the generation of large‐scale coherent field patterns (“modes”). The timescale of this process is comparable to that of the galaxy age. Many galaxies are expected not to host fully coherent fields at the present epoch, especially those which suffered from major mergers or interactions with other galaxies. A comparison of our predictions with existing observations of spiral galaxies is given and discussed (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Coronal magnetic fields from faraday rotation observations

In the first part of this communication we briefly summarize the results of the first observation of linear polarization in the microwave emission above a solar active region obtained with the Westerbork Synthesis Radio Telescope, taking advantage of the very narrow bandwidths of a multi-channel spectral line receiver. The intensity of the Stokes parameterU, measured at several points close to the line of zero circular polarization, showed a clear sinusoidal trend as a function of ², in accordance to what is expected from Faraday rotation (Alissandrakis and Chiuderi Drago, 1994). Combining the measured period of the Faraday rotation with the observed deplacement of the depolarization line with respect to the photospheric neutral line, the height above the photosphere of the depolarization point and the value of the electron density and the magnetic field at this point are computed. Although the calculations are done in the very simplified assumptions of a bipolar magnetic field and of a density following hydrostatic equilibrium, they represent the first estimate of the coronal magnetic field in an active region, far from sunspots.Presented at the CESRA-Workshop on Coronal Magnetic Energy Release at Caputh near Potsdam in May 1994.     

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.     

The depolarization properties of powerful extragalactic radio sources as a function of cosmic epoch

We use the observed polarization properties of a sample of 26 powerful radio galaxies and radio-loud quasars to constrain the conditions in the Faraday screens local to the sources. We adopt the cosmological redshift, low-frequency radio luminosity and physical size of the large-scale radio structures as our 'fundamental' parameters. We find no correlation of the radio spectral index with any of the fundamental parameters. The observed rotation measure is also independent of these parameters, suggesting that most of the Faraday rotation occurs in the Galactic foreground. The difference between the rotation measures of the two lobes of an individual source, as well as the dispersion of the rotation measure, shows significant correlations with the source redshift, but not with the radio luminosity or source size. This is evidence that the small-scale structure observed in the rotation measure is caused by a Faraday screen local to the sources. The observed asymmetries between the lobes of our sources show no significant trends with each other or other source properties. Finally, we show that the commonly used model for the depolarization of synchrotron radio emission by foreground Faraday screens is inconsistent with our observations. We apply alternative models to our data and show that they require a strong increase of the dispersion of the rotation measure inside the Faraday screens with cosmological redshift. Correcting our observations with these models for redshift effects, we find a strong correlation of the depolarization measure with redshift and a significantly weaker correlation with radio luminosity. We do not find any (anti-)correlation of depolarization measure with source size. All our results are consistent with a decrease in the order of the magnetic field structure of the Faraday screen local to the sources for increasing cosmological redshift.     

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.     

The circular polarization of sources of synchrotron radiation

The degree of circular polarizationp _c is calculated for two models of a source of synchrotron radiation:

1. A source with an inhomogeneous magnetic field and isotropic angular distribution of the electrons with respect to the magnetic field;
2. A source with a homogeneous magnetic field and anisotropic angular distribution of the electrons in which the anisotropy of angular distribution substantially increases with the electron energy.

The first model can be used to describe extended radio-sources; and the second, to describe compact radio-sources. For those sources, whose observed polarization properties correspond to the first model, we obtain an integral equation which connects the observed distribution of the sources with the extent of their linear and circular polarization (p _l andp _c ) and the unknown distribution of the sources over the strengthB and the degree of homogeneity ?=(B ₀/B)² of the magnetic field;B ₀ is a homogenous field,B ₀?B. A solution of the integral equation obtained is found for a particular case. This solution makes it possible to determine the distribution of different types of sources over ? if the distribution of these sources in the extent of linear polarization is known. The formulae obtained make it possible to indicate which sources with a known degree of linear polarization should be expected to exhibit highest circular polarization. In the discussion of the first model the question is raised as to the information one can get about the magnetic field by using observations of both linear and circular polarization for a separate source, and for a number of sources. It is shown that the determination of the most probable values ofB and ? in a separate source based on the known values ofp _l andp _c for the source, is possible only if one knows the distribution overB and ? of the sources of the type to which the source in question belongs. The observational data now available make it possible to find the distribution of the sources only over ?. Since the distribution overB and ? is at present unknown, even a very strong upper limit forp _c in the case of a separate source does not enable us to give an exact upper limit for the strength of the magnetic field in this source. In the first model the upper limit for the magnetic field can be obtained only if the upper limit ofp _c is known for a certain number of sourcesN, withN?1. This limit allows for much stronger fields than are usually admitted. This last fact should be taken into consideration when one deals with the results of observations of circular polarization in sources with strong magnetic fields. The first model presents some difficulties when we compare it with observations of some compact sources. The second model can explain why one observes in these sources a violation of the lawp _c ～v ^?1/2 and a change of sign inp _c when the frequency of the observationsv changes.     

A detection of the Faraday rotation by the solar vector magnetograph

The Faraday rotation in the sunspot atmosphere is statistically detected by examining directions of the linear polarization obtained with the vector magnetograph of the Okayama Astrophysical Observatory. It is very effective near the spectral line center and the azimuth of the linear polarization deviates greatly from the magnetic field azimuth. In the case of the iron line, 5250 Å, the magnetic field azimuth will be obtained with an accuracy better than 15°, if observed in the line wing from 27 to 80 mÅ relative to the line center.     

A moving Type IV radio burst and its relation to the coronal magnetic field

A moving Type IV burst, observed with the Culgoora radioheliograph on 1970 April 29, moved out to about 3 R and attained high circular polarization before fading. The appearance of the moving Type IV source suggests an isolated, self-contained, synchrotron emitting plasmoid. Magnetic field maps of the corona derived from photospheric observations indicate that the plasmoid moved almost radially outward from the flare region along open field lines. To explain the observed source structure and high unipolar polarization, we suggest that a ring of electric current was ejected from the low corona and guided by coronal magnetic field lines; the radio emission was synchrotron radiation generated by mildly-relativistic electrons trapped in the poloidal magnetic field of the ring current.Part of the research reported here was carried out while the author was at the Division of Radiophysics, C.S.I.R.O., Sydney, Australia.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Galactic Diffuse Polarized Emission

Diffuse polarized emission by synchrotron is a key tool to investigate magnetic fields in the Milky Way, particularly the ordered component of the large scale structure. Key observables are the synchrotron emission itself and the RM is by Faraday rotation. In this paper the main properties of the radio polarized diffuse emission and its use to investigate magnetic fields will be reviewed along with our current understanding of the galactic magnetic field and the data sets available. We will then focus on the future perspective discussing RM-synthesis – the new powerful instrument devised to unlock the information encoded in such an emission – and the surveys currently in progress like S-PASS and GMIMS.     

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.     

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.