Observations of Faraday rotation for extragalactic sources probe magnetic fields both inside and outside the Milky Way. Building on our earlier estimate of the Galactic contribution, we set out to estimate the extragalactic contributions. We discuss the problems involved; in particular, we point out that taking the difference between the observed values and the Galactic foreground reconstruction is not a good estimate for the extragalactic contributions. We point out a degeneracy between the contributions to the observed values due to extragalactic magnetic fields and observational noise and comment on the dangers of over-interpreting an estimate without taking into account its uncertainty information. To overcome these difficulties, we develop an extended reconstruction algorithm based on the assumption that the observational uncertainties are accurately described for a subset of the data, which can overcome the degeneracy with the extragalactic contributions. We present a probabilistic derivation of the algorithm and demonstrate its performance using a simulation, yielding a high quality reconstruction of the Galactic Faraday rotation foreground, a precise estimate of the typical extragalactic contribution, and a well-defined probabilistic description of the extragalactic contribution for each data point. We then apply this reconstruction technique to a catalog of Faraday rotation observations for extragalactic sources. The analysis is done for several different scenarios, for which we consider the error bars of different subsets of the data to accurately describe the observational uncertainties. By comparing the results, we argue that a split that singles out only data near the Galactic poles is the most robust approach. We find that the dispersion of extragalactic contributions to observed Faraday depths is most likely lower than 7 rad/m 2 , in agreement with earlier results, and that the extragalactic contribution to an individual data point is poorly constrained by the data in most cases.

We examine the proposal that the dispersion measures (DMs) and Faraday rotation measures (RMs) of extragalactic linearly polarized fast radio bursts (FRBs) can be used to probe the intergalactic magnetic field (IGMF) in filaments of galaxies. The DM through the cosmic web is dominated by contributions from the warmhot intergalactic medium (WHIM) in filaments and from the gas in voids. On the other hand, RM is induced mostly by the hot medium in galaxy clusters, and only a fraction of it is produced in the WHIM. We show that if one excludes FRBs whose sightlines pass through galaxy clusters, the line of sight (LOS) strength of the IGMF in filaments, B , is approximately (, where C is a known constant. Here, the redshift of the FRB is not required to be known; f DM is the fraction of total DM due to the WHIM, while á + ñ z 1 is the redshift of interevening gas weighted by the WHIM gas density, both of which can be evaluated for a given cosmology model solely from the DM of an FRB. Using data on structure formation simulations and a model IGMF, we show thatclosely reproduces the density-weighted LOS strength of the IGMF in filaments of the large-scale structure.

We investigate the Faraday rotation measure (RM) due to the intergalactic magnetic field (IGMF) through the cosmic web up to cosmological distances, using a model IGMF based on turbulence dynamo in the large-scale structure of the universe. By stacking the IGMF and gas density data up to redshift z = 5 and taking account of the redshift distribution of polarized background radio sources against which the RM is measured, we simulate the sky map of the RM. The contribution from galaxy clusters is subtracted from the map, based on several different criteria of X-ray brightness and temperature. Our findings are as follows. The distribution of RM for radio sources of different redshifts shows that the root-mean-square (rms) value increases with redshift and saturates for z 1. The saturated value is RM rms ≈ several rad m −2 . The probability distribution function of |RM| follows the lognormal distribution. The power spectrum has a broad plateau over the angular scale of ∼ 1 − 0.1 • with a peak around ∼ 0.15 • . The second-order structure function has a flat profile in the angular separation of 0.2 • . Our results could provide useful insights for surveys to explore the IGMF with the Square Kilometer Array (SKA) and upcoming SKA pathfinders.Subject headings: intergalactic medium -large-scale structure of universemagnetic fields -polarization

Faraday rotation measures (RMs) and more general Faraday structures are key parameters for studying cosmic magnetism and also are sensitive probes of faint ionized thermal gas. There is a need to define what derived quantities are required for various scientific studies, and then to address the challenges in determining Faraday structures. A wide variety of algorithms have been proposed to reconstruct these structures. In preparation for the Polarization Sky Survey of the Universe's Magnetism (POSSUM) to be conducted with the Australian Square Kilometre Array Pathfinder (ASKAP) and the ongoing Galactic Arecibo L-band Feeds Array Continuum Transit Survey (GALFACTS), we run a Faraday structure determination data challenge to benchmark the currently available algorithms including Faraday synthesis (previously called RM synthesis in the literature), wavelet, compressive sampling and QU -fitting. The input models include sources with one Faraday thin component, two Faraday thin components and one Faraday thick component. The frequency set is similar to POS-SUM/GALFACTS with a 300-MHz bandwidth from 1.1 to 1.4 GHz. We define three figures of merit motivated by the underlying science: a) an average RM weighted by polarized intensity, RM wtd , b) the separation ∆φ of two Faraday components and c) the reduced chi-squared χ 2 r . Based on the current test data of signal to noise ratio of about 32, we find that: (1) When only one Faraday thin component is present, most methods perform as expected, with occasional failures where two components are incorrectly found; (2) For two Faraday thin components, QU -fitting routines perform the best, with errors close to the theoretical ones for RM wtd , but with significantly higher errors for ∆φ. All other methods including standard Faraday synthesis frequently identify only one component when ∆φ is below or near the width of the Faraday point spread function; (3) No methods, as currently implemented, work well for Faraday thick components due to the narrow bandwidth; (4) There exist combinations of two Faraday components which produce a large range of acceptable fits and hence large uncertainties in the derived single RMs; in these cases, different RMs lead to the same Q, U behavior, so no method can recover a unique input model. Further exploration of all these issues is required before upcoming surveys will be able to provide reliable results on Faraday structures.

We report on the results of a Suzaku observation of the plasma in the filament located between the two massive clusters of galaxies Abell 399 and Abell 401. Abell 399 (z=0.0724) and Abell 401 (z=0.0737) are expected to be in the initial phase of a cluster merger. In the region between the two clusters, we find a clear enhancement in the temperature of the filament plasma from 4 keV (expected value from a typical cluster temperature profile) to kT∼6.5 keV. Our analysis also shows that filament plasma is present out to a radial distance of 15 ′ (1.3 Mpc) from a line connecting the two clusters. The temperature profile is characterized by an almost flat radial shape with kT∼6-7 keV within 10 ′ or ∼0.8 Mpc. Across r=8 ′ from the axis, the temperature of the filament plasma shows a drop from 6.3 keV to 5.1 keV, indicating the presence of a shock front. The Mach number based on the temperature drop is estimated to be M ∼1.3. We also successfully determined the abundance profile up to 15 ′ (1.3 Mpc), showing an almost constant value (Z=0.3 solar) at the cluster outskirt. We estimated the Compton y-parameter to be ∼14.5±1.3 × 10 −6 , which is in agreement with Planck's results (14-17×10 −6 on the filament). The line of sight depth of the filament is l∼1.1 Mpc, indicating that the geometry of filament is likely a pancake shape rather than cylindrical. The total mass of the filamentary structure is ∼7.7×10 13 M ⊙ . We discuss a possible interpretation of the drop of X-ray emission at the rim of the filament, which was pushed out by the merging activity and formed by the accretion flow induced by the gravitational force of the filament.

We investigate a non-equilibrium ionization state and an electron–ion two-temperature structure of the intracluster medium (ICM) in merging galaxy clusters using a series of $N$-body and hydrodynamic simulations. Mergers with various sets of mass ratios and impact parameters are systematically investigated, and it is found that, in most cases, ICM significantly departs from the ionization equilibrium state at the shock layers with a Mach number of $\sim $1.5–2.0 in the outskirts of the clusters, and the shock layers with a Mach number of $\sim $2–4 in front of the ICM cores. Accordingly, the intensity ratio between FeXXV and FeXXVI K$\alpha$ line emissions is significantly altered from that in the ionization equilibrium state. If the effect of the two-temperature structure of ICM is incorporated, the electron temperature is $\sim $10%–20% and $\sim $30%–50% lower than the mean temperature of ICM at the shock layers in the outskirts and in front of the ICM cores, respectively, and the deviation from the ionization equilibrium state becomes larger. We also address the dependence of the intensity ratio on the viewing angle with respect to the merging plane.

Studying the nature and origin of the intergalactic magnetic field (IGMF) is an outstanding problem of cosmology. Measuring Faraday rotation would be a promising method to explore the IGMF in the large-scale structure (LSS) of the universe. We investigated the Faraday rotation measure (RM) due to the IGMF in filaments of galaxies using simulations for cosmological structure formation. We employed a model IGMF based on turbulence dynamo in the LSS of the universe; it has an average strength of B ∼ 10 nG and a coherence length of several × 100 h −1 kpc in filaments. With the coherence length smaller than path length, the inducement of RM would be a random walk process, and we found that the resultant RM is dominantly contributed by the density peak along line of sight. The rms of RM through filaments at the present universe was predicted to be ∼ 1 rad m −2 . In addition, we predicted that the probability distribution function of |RM| through filaments follows the log-normal distribution, and the power spectrum of RM in the local universe peaks at a scale of ∼ 1 h −1 Mpc. Our prediction of RM could be tested with future instruments.Subject headings: intergalactic medium -large-scale structure of universemagnetic fields -polarization

Rotation measure (RM) grids of extragalactic radio sources have been widely used for studying cosmic magnetism. But their potential for exploring the intergalactic magnetic field (IGMF) in filaments of galaxies is unclear, since other Faraday-rotation media such as the radio source itself, intervening galaxies, and the interstellar medium of our Galaxy are all significant contributors. We study statistical techniques for discriminating the Faraday rotation of filaments from other sources of Faraday rotation in future large-scale surveys of radio polarization. We consider a 30 • × 30 • field-of-view toward the south Galactic pole, while varying the number of sources detected in both present and future observations. We select sources located at high redshifts and toward which depolarization and optical absorption systems are not observed, so as to reduce the RM contributions from the sources and intervening galaxies. It is found that a high-pass filter can satisfactorily reduce the RM contribution from the Galaxy, since the angular scale of this component toward high Galactic latitudes would be much larger than that expected for the IGMF. Present observations do not yet provide a sufficient source density to be able to estimate the RM of filaments. However, from the proposed approach with forthcoming surveys, we predict significant residuals of RM that should be ascribable to filaments. The predicted structure of the IGMF down to scales of 0.1 • should be observable with data from the SKA, if we achieve selections of sources toward which sightlines do not contain intervening galaxies and RM errors are less than a few rad m −2 . Subject headings: intergalactic medium -large-scale structure of universe -magnetic fields -polarization -ISM: magnetic fields