The high- and low-frequency descriptions of the pre-decoupling plasma are deduced from the Vlasov-Landau treatment generalized to curved space-times and in the presence of the relativistic fluctuations of the geometry. It is demonstrated that the interplay between one-fluid and two-fluid treatments is mandatory for a complete and reliable calculation of the polarization observables. The Einstein-Boltzmann hierarchy is generalized to handle the dispersive propagation of the electromagnetic disturbances in the pre-decoupling plasma. Given the improved physical and numerical framework, the polarization observables are computed within the magnetized $Λ$CDM paradigm (m$Λ$CDM). In particular, the Faraday-induced B-mode is consistently estimated by taking into account the effects of the magnetic fields on the initial conditions of the Boltzmann hierarchy, on the dynamical equations and on the dispersion relations. The complete calculations of the angular power spectra constitutes the first step for the derivation of magnetized maps of the CMB temperature and polarization which are here obtained for the first time and within the minimal m$Λ$CDM model. The obtained results set the ground for direct experimental scrutiny of large-scale magnetism via the low and high frequency instruments of the Planck explorer satellite.
We study the effect of Faraday rotation due to a homogeneous magnetic field on the polarization of the cosmic microwave background (CMB). Scalar fluctuations give rise only to parity-even E-type polarization of the CMB. However in the presence of a magnetic field, a non-vanishing parity-odd B-type polarization component is produced through Faraday rotation. We derive the exact solution for the E and B modes generated by scalar perturbations including the Faraday rotation effect of a uniform magnetic field, and evaluate their cross-correlations with temperature anisotropies. We compute the angu…
The S-Z effect and Faraday rotation from halos are examined over a wide mass range, an including gas condensation and magnetic field evolution. Contributions to the CMB angular power spectrum are evaluated for galaxy clusters, galaxy groups and galaxies. Smaller mass halos are found to play a more important role than massive halos for the B-mode polarisation associated with the S-Z CMB anisotropies. The B-modes from Faraday rotation dominate the secondary B-modes caused by gravitational lensing at l > 3000. Measurement of B-mode polarisation in combination with the S-Z power spectrum can poten…
A simple introduction to physics of CMBR polarization and the Faraday rotation of the latter in cosmic magnetic field is presented. The content of the lecture is the following: 1. Description of polarization of photons. 2. Polarization field of CMBR. 3. Faraday effect. 4. Cosmic magnetic fields. 5. Faraday rotation of CMBR polarization.
A magnetic field, coherent over the horizon size at the decoupling and strong enough to rotate the polarization plane of the CMBR, can be generated from the electromagnetic vacuum fluctuations amplified by the space-time evolution of the dilaton coupling. The possible relevance of this result for superstring inspired cosmological models is discussed. Particular attention will be paid to the connection between Faraday rotation signals and stochastic gravity-wave backgrounds.
We present a diagnostic test of possible Galactic contamination of cosmic microwave background sky maps designed to provide an independent check on the methods used to compile these maps. The method involves a non-parametric measurement of cross-correlation between the Faraday rotation measure (RM) of extragalactic sources and the measured microwave signal at the same angular position. We argue that statistical properties of the observed distribution of rotation measures are consistent with a Galactic origin, an argument reinforced by a direct measurement of cross-correlation between dust, fre…
We examine the rotation of the plane of polarization for linearly polarized light rays by the weak gravitational field of an isolated physical system. Based on the rotation of inertial frames, we review the general integral expression for the net rotation. We apply this formula, analogue to the usual electromagnetic Faraday effect, to some interesting astrophysical systems: uniformly shifting mass monopoles and a spinning external shell.
The observed magnetic field of microgauss strength in clusters of galaxies should induce the Faraday rotation effect on the linearly polarized cosmic microwave background (CMB) radiation when the CMB radiation propagates through a cluster at low redshift. Employing the Press-Schechter prescription for the cluster abundance under the cold dark matter (CDM) scenario and a plausible isothermal $β$-model for the gas distribution, we compute angular power spectra of the CMB polarization fields including the Faraday rotation mixing effect under the simple assumption of uniform magnetic field configu…
Measurements of the Faraday rotation of the cosmic microwave background radiation (CMBR) polarization could provide evidence for the existence of primordial magnetic fields. The Faraday rotation could also allow the study of some properties of these fields. In this paper, we calculate the angular dependence of the Faraday rotation correlator for different assumptions about the spectral index and correlation length of the magnetic field. We show that the helical part of the magnetic field does not make any contribution to the correlator. We stress the importance of the angular resolution of the…
A joint action of depth and bandwidth depolarization in the interstellar medium is considered using a model of N homogeneous synchrotron layers with Faraday rotation. The bandwidth depolarization can be used in multifrequency polarimetric observations of Galactic diffuse synchrotron radio emission to investigate the interstellar ionized medium and magnetic field in the direction to the Faraday-thick objects of known distances.
A primordial cosmological magnetic field induces Faraday rotation of the cosmic microwave background polarization. This rotation produces a curl-type polarization component even when the unrotated polarization possesses only gradient-type polarization, as expected from scalar density perturbations. We compute the angular power spectrum of curl-type polarization arising from small Faraday rotation due to a weak stochastic primordial magnetic field with a power-law power spectrum. The induced polarization power spectrum peaks at arcminute angular scales. Faraday rotation is one of the few cosmol…
A Faraday rotation experiment can set limits on the magnetic moment of a electrically-neutral, dark-matter particle, and the limits increase in stringency as the candidate-particle mass decreases. Consequently, if we assume the dark-matter particle to be a thermal relic, our most stringent constraints emerge at the keV mass scale. We discuss how such an experiment could be realized and determine the limits on the magnetic moment as a function of mass which follow given demonstrated experimental capacities.
We study the propagation of gravitational waves in a collisionless plasma with an external magnetic field parallel to the direction of propagation. Due to resonant interaction with the plasma particles the gravitational wave experiences cyclotron damping or growth, the latter case being possible if the distribution function for any of the particle species deviates from thermodynamical equilibrium. Furthermore, we examine how the damping and dispersion depends on temperature and on the ratio between the cyclotron- and gravitational wave frequency. The presence of the magnetic field leads to dif…
We present the results of multi-frequency polarization VLA observations of radio sources from the complete sample of northern, radio-bright BL Lac objects compiled by H. Kuhr and G. Schmidt. These were used to determine the integrated rotation measures of 18 objects, 15 of which had never been measured previously, which hindered analysis of the intrinsic polarization properties of objects in the complete sample. These measurements make it possible to correct the observed orientations of the linear polarizations of these sources for the effect of Faraday rotation. The most probable origin for F…
Equipartition magnetic fields can dramatically affect the polarization of radiation emerging from accretion disk 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 polari…
A primordial magnetic field in the early universe will cause Faraday rotation of the linear polarization of the cosmic microwave background generated via Compton scattering at the surface of last scattering. This rotation induces a non-zero parity-odd (B-mode) polarization component. The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data puts an upper limit on the magnitude of the B-polarization power spectrum; assuming that the B-polarization signal is totally due to the Faraday rotation effect, the upper limits on the comoving amplitude of a primordial stochastic magnetic field range fr…
We present a sequence of 12 monthly polarimetric 15, 22, and 43 GHz VLBA observations of the radio galaxy 3C 120 revealing a systematic presence of gradients in Faraday rotation and degree of polarization across and along the jet. The degree of polarization increases with distance from the core and toward the jet edges, and has an asymmetric profile in which the northern side of the jet is more highly polarized. The Faraday rotation measure is also stratified across the jet width, with larger values for the southern side. We find a localized region of high Faraday rotation measure superposed o…
We revisit the polarisation induced by Faraday rotation when Cosmic Microwave Background photons traverse magnetised plasma. We compute the secondary B-mode angular power spectrum from Faraday rotation due to magnetic fields in galaxies and galaxy clusters with masses ranging from $10^{11}$ to $10^{16.5} M_\odot$. We investigate its dependence on the electron and the magnetic field profiles. Namely, we consider both the beta-profile of electron density as well as an electron density distribution based on the Navarro-Frenk-White dark matter profile. We model the magnetic field structure in gala…
We confirm the reality of a reversal of the sign of the Faraday Rotation Measure in the Galactic plane in Cygnus (Lazio et al, 1990), possibly associated with the Cygnus OB1 association. The rotation measure changes by several hundred rad/m$^2$ over an angular scale of $2-5^{\circ}$. We show that a simple model of an expanding plasma shell with an enhanced density and magnetic field, consistent with observations of H$α$ emission in this part of sky, and physically associated with a superbubble of the Cygnus OB1 association, can account for the magnitude and angular scale of this feature.
Our modelling of FR I radio jets as decelerating, relativistic flows allows us to derive their orientations accurately. We present images of Faraday rotation for two of these these objects (3C 31 and NGC 315) and show that the fluctuations of rotation measure (RM) are larger in the fainter (receding) jets, as expected if the rotation occurs in the hot galaxy/group halos. The gas density is much lower in NGC 315 and the RM fluctuations are only just detectable.
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 co…
We propose a new method to calculate Faraday rotation measure maps from multi-frequency polarisation angle data. In order to solve the so called n-pi ambiguity problem which arises from the observationally ambiguity of the polarisation angle which is only determined up to additions of +-n*pi, where n is an integer, we suggest using a global scheme. Instead of solving the n-pi ambiguity for each data point independently, our algorithm, which we chose to call "Pacman" (Polarisation Angle Correcting rotation Measure ANalysis), solves the n-pi ambiguity for a high signal-to-noise region ``democrat…
Very long baseline interferometric observations of the radio galaxy 3C 120 show a systematic presence of gradients in Faraday rotation and degree of polarization across and along the jet. These are revealed by the passage of multiple superluminal components throughout the jet as they move out from the core in a sequence of 12 monthly polarimetric observations taken with the VLBA at 15, 22, and 43 GHz. The degree of polarization has an asymmetric profile in which the northern side of the jet is more highly polarized. The Faraday rotation measure is also stratified across the jet width, with lar…
The existence of a primordial magnetic field at the last scattering surface may induce a measurable Faraday rotation in the polarization of the cosmic microwave background. We calculate the magnitude of this effect by evolving the radiative transfer equations for the microwave background polarization through the epoch of last scatter, in the presence of a magnetic field. For a primordial field amplitude corresponding to a present value of $10^{-9}{\rm G}$ (which would account for the observed galactic field if it were frozen in the pre-galactic plasma), we find a rotation angle of around $1^\c…
Using high frequency (12-22 GHz) VLBA observations we confirm the existence of a Faraday rotation measure gradient of ~ 500 rad/m^2/mas transverse to the jet axis in the quasar 3C 273. The gradient is seen in two epochs spaced roughly six months apart. This stable transverse rotation measure gradient is expected if a helical magnetic field wraps around the jet. The overall order to the magnetic field in the inner projected 40 parsecs is consistent with a helical field. However, we find an unexpected increase in fractional polarization along the edges of the source, contrary to expectations. Th…
Faraday rotation measurements of polarized extragalactic sources probe the Galactic magnetized, ionized interstellar medium. Rotation measures of these sources behind the inner Galactic plane are used to explore characteristics of the structure in the spiral arms and in interarm regions. Structure in the spiral arms has a characteristic outer scale of a few parsecs only, whereas interarm regions typically show structure up to scales of hundreds of parsecs. The data indicate that in the spiral arms, the random component of the magnetic field dominates over the regular field, but in the interarm…
We are developing a new approach to investigate cluster magnetic field strengths and structures. It is based on the comparison of simulated Rotation Measure and radio halo images, obtained from 3-dimensional multi-scale cluster magnetic fields models, with observations. This approach is applied to A2255 in which wide diffuse radio emissions and Rotation Measure images show the evidence of cluster magnetic fields on both large and small scales.
Multifrequency polarimetry with the VLBA confirms the previously reported time-varying Faraday rotation measure (RM) in the quasar 3C-279. Variability in the RM and electric vector position angle (EVPA) of the jet component (C4) is seen making it an unreliable absolute EVPA calibrator. 3C-273 is also shown to vary its RM structure on 1.5 year time-scales. Variation in the RM properties of quasars may result from a Faraday screen which changes on time-scales of a few years, or from the motion of jet components which sample spatial variations in the screen. A new component emerging from the core…
Different ray paths through a turbulent plasma can produce stochastic Faraday rotation leading to depolarization of any linearly polarized component. Simple theory predicts that the average values of the Stokes parameters decay according to $<Q>$, $<U>\propto\exp(-δ_l)$, with $δ_l\proptoλ^4$. It is pointed out that a definitive test for such depolarization is provided by the fact that $<Q^2+U^2>$ remains constant while $<Q>^2+< U>^2$ decreases $\propto\exp(-2δ_l)$. The averages to which this effect, called polarization covariance, should apply are discussed; it should apply to spatial averages…
Results from a survey of the parsec scale Faraday rotation measure properties for 40 quasars, radio galaxies and BL Lac objects are presented. Core rotation measures for quasars vary from approximately 500 to several thousand radians per meter squared. Quasar jets have rotation measures which are typically 500 radians per meter squared or less. The cores and jets of the BL Lac objects have rotation measures similar to those found in quasar jets. The jets of radio galaxies exhibit a range of rotation measures from a few hundred radians per meter squared to almost 10,000 radians per meter square…
We have measured the Faraday rotation toward a large sample of polarized radio sources behind the Large Magellanic Cloud (LMC), to determine the structure of this galaxy's magnetic field. The magnetic field of the LMC consists of a coherent axisymmetric spiral of field strength ~1 microgauss. Strong fluctuations in the magnetic field are also seen, on small (<0.5 parsecs) and large (~100 parsecs) scales. The significant bursts of recent star formation and supernova activity in the LMC argue against standard dynamo theory, adding to the growing evidence for rapid field amplification in galaxies…
