Effect of interstellar density fluctuations on signal dispersion measure

The effect of electron number density fluctuations in the interstellar medium on signals from pulsars is studied in terms of the frequency dependent signal dispersion. It is shown that if the density fluctuations are representative of long wavelength (1100 pc) [or large scale length (1100 pc)] disturbances in the interstellar gas, then the observed signal dispersion is not a measure of the integral of the electron number density in the line of sight. Evidence has been presented elsewhere for believing that such long wavelength disturbances should exist in the interstellar gas, so this result indicated that some care must be exercised in the interpretation of signal dispersion measurements from pulsars.     

Rotation measure variations for 20 millisecond pulsars

We report on variations in the mean position angle of the 20 millisecond pulsars being observed as part of the Parkes Pulsar Timing Array (PPTA) project. It is found that the observed variations are dominated by changes in the Faraday rotation occurring in the Earth??s ionosphere. Two ionospheric models are used to correct for the ionospheric contribution and it is found that one based on the International Reference Ionosphere gave the best results. Little or no significant long-term variation in interstellar RM was found with limits typically about 0.1 rad?m^?2?yr^?1 in absolute value. In a few cases, apparently significant RM variations over timescales of a few 100 days or more were seen. These are unlikely to be due to localised magnetised regions crossing the line of sight since the implied magnetic fields are too high. Most probably they are statistical fluctuations due to random spatial and temporal variations in the interstellar electron density and magnetic field along the line of sight.     

The Magnetic Field of the Solar Corona from Pulsar Observations

We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation resulting from propagation of the polarised emission from a number of pulsars through the magnetic field of the solar corona. This method yields independent measures of the integrated electron density, via dispersion of the pulsed signal and the magnetic field, via the amount of Faraday rotation. In principle this allows the determination of the integrated magnetic field through the solar corona along many lines of sight without any assumptions regarding the electron density distribution. We present a detection of an increase in the rotation measure of the pulsar J1801-2304 of approximately 170 rad m² at an elongation of 0.96° from the centre of the solar disc. This corresponds to a lower limit of the magnetic field strength along this line of sight of >41.8 nT. The lack of precision in the integrated electron density measurement restricts this result to a limit, but application of coronal plasma models can further constrain this to approximately 0.5 μT, along a path passing 2.7 solar radii from the solar limb, which is consistent with predictions obtained using extensions to the source surface models published by the Wilcox Solar Observatory.     

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.     

The termination of the solar wind

It has previously been suggested that the solar wind might terminate at distances of 5 AU to 20 AU from the Sun, and that the solar wind might be drastically slowed down by charge exchange and photoionization of interstellar hydrogen atoms which approach the Sun. However, recent satellite measurements of resonantly scattered Lyman alpha radiation, together with pulsar dispersion and Faraday rotation measures, imply very small values for the interstellar hydrogen density (0.05 cm⁻³) and magnetic field strength (3 μG). As a result, the solar wind is not expected to be slowed down by more than about 30% inside the termination distance, which is expected to be about 100 AU.     

Faraday rotation and signal dispersion: The geometrical optics approximation,an exact solution,and first order smoothing theory

We critically discuss the three approximations which have been employed to estimate the influence of interstellar fluctuations in both electron density and magnetic field on Faraday rotation measure and signal dispersion measure in the radio band. We demonstrate that: (i) the geometrical optics approximation employed by Ginzburg and Eruhimov (1971) relies on the unproven assertion thatall ray paths are essentially the same as the geometrical distance between source and observer; (ii) the exact solution is physically meaningless; (iii) the purported proof of Ginzburg and Eruhimov that earlier work by Lerche is in error, is itself in error and also self-contradictory; (iv) the first order smoothing theory employed earlier by Lerche gives the exact correction to the phase of the ordered field provided only that theirreducible part of a three-point correlation function is negligible.Receipt delayed by postal strike in Great Britain.     

Fluctuations in the interplanetary plasma

Spacecraft based observations of fluctuations in the interplanetary magnetic field and solar wind speed yield dominant spatial scales of the order 10⁶ km, and negligible structure below about 500 km. Earth based observations of the angular broadening and scintillation of cosmic radio sources have been interpreted in terms of electron density scales of order a few hundred km. It is suggested that for scales below a few hundred km, there exists an enhanced level of small scale density fluctuations not accompanied by comparable magnetic variations. This proposal is shown to be consistent with radio observations, the contribution of the much larger electron density irregularities being quite negligible. A physical mechanism that might account for the small scale fluctuations is described.     

Nonhelical mean‐field dynamos in a sheared turbulence

Mechanisms of nonhelical large‐scale dynamos (shear‐current dynamo and effect of homogeneous kinetic helicity fluctuations with zero mean) in a homogeneous turbulence with large‐scale shear are discussed. We have found that the shearcurrent dynamo can act even in random flows with small Reynolds numbers. However, in this case mean‐field dynamo requires small magnetic Prandtl numbers (i.e., when Pm < Pm^cr < 1). The threshold in the magnetic Prandtl number, Pm^cr = 0.24, is determined using second order correlation approximation (or first‐order smoothing approximation) for a background random flow with a scale‐dependent viscous correlation time τ_c = (νk 2)^–1 (where ν is the kinematic viscosity of the fluid and k is the wave number). For turbulent flows with large Reynolds numbers shear‐current dynamo occurs for arbitrary magnetic Prandtl numbers. This dynamo effect represents a very generic mechanism for generating large‐scale magnetic fields in a broad class of astrophysical turbulent systems with large‐scale shear. On the other hand, mean‐field dynamo due to homogeneous kinetic helicity fluctuations alone in a sheared turbulence is not realistic for a broad class of astrophysical systems because it requires a very specific random forcing of kinetic helicity fluctuations that contains, e.g., low‐frequency oscillations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Zur Struktur der interstellaren Materie bei Zeta Persei

The region around ξ Persei is qualified for an extended investigation of the interstellar matter in a limited volume because of its position in the Galaxy and the high brightness of ξ Persei. The basis for this analysis were spectra of high dispersion, 21 cm line profiles, photoelectric UBV measurements, measurements of star light polarization, and a photographic three colour photometry. The total numbers of absorbers per cm² for Ca II and Na I were evaluated by the dublet ratio method. The adaption of observations to models for the distribution of the interstellar gas yielded the abundances of Ca and Na. Ca is deficient by about a factor 150. The total number of H I atoms per cm² followed from a gaussian analysis of 21 cm lines. The results of the analysis can be best described by a model consisting of a dense H I layer with a density of 20 to 140 cm⁻³ situated 10 to 30 pc in front of ξ Persei. The interstellar reddening is not uniform in this region; the extension of this cloud in the line of sight is about 100 pc. The structure analysis of reddening provided micro-scales of 0.4 and 4.5 pc for the fluctuations in density of interstellar absorbing matter. On the assumption that the interstellar dust consists of silicate grains the density ratio between interstellar gas and dust amounts to nearly 35. The total mass of the interstellar matter in the analysed region is ≤ 1100 z.dstR;⊙. The direction and strength of the magnetic field were estimated from the star light polarization; according to that the field strength is about 8 · 10⁻⁶G. It is likely that the interstellar matter around ξ Persei is connected with the evolution of the association II Persei.     

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.     

Magnetic Field in Selected Directions of the Galaxy, Direction of the Spiral Arm of Sagittarius

Faraday rotation data on 40 pulsars are used in a detailed study of the magnetic field and its fluctuations in the direction of the spiral arm of Sagittarius. These results mostly agree with standard models for the galactic magnetic field. A magnetic field on the order of 3.2 G is directed from galactic longitude l ₀=55° (toward the sun). However, an asymmetry has been found in the degrees of rotation relative to a plane lying in the southern hemisphere parallel to the galactic plane and at a distance of 50-60 pc from it. All the pulsars with measures of dispersion greater than 30 pc·cm^-3 and lying to the north of this plane have positive measures of rotation which increase linearly with distance, while the pulsars lying to the south of this plane have unusually absolutely low negative measures of rotation. We propose that the spiral arm of Sagittarius lies entirely to the north of this plane, while the negative measures of rotation of the pulsars below this plane are caused by the magnetic field of the halo of the southern hemisphere of the galaxy. The magnetic field in the arm of Sagittarius is regular to a great extent and its fluctuating component is roughly half the regular component.     

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.     

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)     

Axisymmetry vs. nonaxisymmetry of a Taylor‐Couette flow with azimuthal magnetic fields

The instability of a supercritical Taylor‐Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm = 1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current‐induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m = 1 are excited even without rotation for large enough Hartmann numbers (“Tayler instability”). For slow rotation their growth rates scale with the Alfvén frequency of the magnetic field but for fast rotation they scale with the rotation rate of the inner cylinder. In the nonlinear regime the ratio of the energy of the magnetic m = 1 modes and the toroidal background field is very low for the non‐rotating Tayler instability but it strongly grows if differential rotation is present. For super‐Alfv´enic rotation the energies in the m = 1 modes of flow and field do not depend on the molecular viscosity, they are almost in equipartition and contain only 1.5 % of the centrifugal energy of the inner cylinder. The geometry of the excited magnetic field pattern is strictly nonaxisymmetric for slow rotation but it is of the mixed‐mode type for fast rotation – contrary to the situation which has been observed at the surface of Ap stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The environment of Hercules A

We have made VLA radio total intensity and polarisation observations in the A, B and C configurations at 1665, 1435, 1365 and 1295 MHz and in the B, C and D configurations at 8465 and 8415 MHz to study the environment of the powerful radio galaxy Hercules A. We have also made ROSAT PSPC and HRI X-ray observations to study the intracluster gas in the Hercules A cluster. We have mapped the Faraday rotation field with high resolution (1.′′42.5 h⁻¹₁₀₀ kpc for q₀=0), and combined this with the X-ray data on the gas distribution in order to map the magnetic field of the cluster. We have found that Hercules A exhibits a strong Laing-Garrington effect: the western side of the radio emission is more depolarised than the eastern side. The X-ray observations have revealed an extended X-ray emission elongated along the radio galaxy axis and a weak nuclear component. The Hercules A cluster is a cooling flow cluster, which appears isothermal at large radii. Comparing the Faraday dispersion profile with the X-ray estimated density profile, we found that the magnetic field is decreasing with radius and we have estimated a central value of 3B₀ (μG) 9. The estimated core electron density of n₀6.6×10³ m⁻³ reveals a dense environment in which Hercules A is situated.     

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.     

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.