Probing magnetic turbulence by synchrotron polarimetry: statistics and structure of magnetic fields from Stokes correlators

We describe a novel technique for probing the statistical properties of cosmic magnetic fields based on radio polarimetry data. Second-order magnetic field statistics like the power spectrum cannot always distinguish between magnetic fields with essentially different spatial structure. Synchrotron polarimetry naturally allows certain fourth-order magnetic field statistics to be inferred from observational data, which lifts this degeneracy and can thereby help us gain a better picture of the structure of the cosmic fields and test theoretical scenarios describing magnetic turbulence. In this work we show that a fourth-order correlator of specific physical interest, the tension force spectrum, can be recovered from the polarized synchrotron emission data. We develop an estimator for this quantity based on polarized emission observations in the Faraday rotation free frequency regime. We consider two cases: a statistically isotropic field distribution, and a statistically isotropic field superimposed on a weak mean field. In both cases the tension force power spectrum is measurable; in the latter case, the magnetic power spectrum may also be obtainable. The method is exact in the idealized case of a homogeneous relativistic electron distribution that has a power-law energy spectrum with a spectral index of   p = 3  , and assumes statistical isotropy of the turbulent field. We carry out numerical tests of our method using synthetic polarized emission data generated from numerically simulated magnetic fields. We show that the method is valid, that it is not prohibitively sensitive to the value of the electron spectral index p , and that the observed tension force spectrum allows one to distinguish between e.g. a randomly tangled magnetic field (a default assumption in many studies) and a field organized in folded flux sheets or filaments.     

Cluster magnetic fields from galactic outflows

We performed cosmological, magnetohydrodynamical simulations to follow the evolution of magnetic fields in galaxy clusters, exploring the possibility that the origin of the magnetic seed fields is galactic outflows during the starburst phase of galactic evolution. To do this, we coupled a semi-analytical model for magnetized galactic winds as suggested by Bertone, Vogt & Enßlin to our cosmological simulation. We find that the strength and structure of magnetic fields observed in galaxy clusters are well reproduced for a wide range of model parameters for the magnetized, galactic winds and do only weakly depend on the exact magnetic structure within the assumed galactic outflows. Although the evolution of a primordial magnetic seed field shows no significant differences to that of galaxy cluster fields from previous studies, we find that the magnetic field pollution in the diffuse medium within filaments is below the level predicted by scenarios with pure primordial magnetic seed field. We therefore conclude that magnetized galactic outflows and their subsequent evolution within the intracluster medium can fully account for the observed magnetic fields in galaxy clusters. Our findings also suggest that measuring cosmological magnetic fields in low-density environments such as filaments is much more useful than observing cluster magnetic fields to infer their possible origin.     

Dynamics of magnetic flux loops in cooling-flow clusters of galaxies

We study the dynamics of magnetic flux loops embedded in an intracluster medium. In order to perform the calculations semi-analytically we make several simplifying assumptions, which include a treatment of only the two ends of the magnetic flux loops, assuming a simple relation between the density and the magnetic field and neglecting heat conduction. Our results indicate that the existence of a large number of magnetic flux loops can naturally lead to a multiphase intracluster medium. A multiphase intracluster medium is inferred from observations of the mass deposition rate in many cooling-flow clusters. The loops will be observed as 'filaments' having different density and temperature from their surroundings, namely X-ray filaments. X-ray filaments have been discovered in a few cases, although their discovery is controversial. Our model predicts that many such X-ray filaments will be discovered with future high-spatial-resolution X-ray telescopes, such as AXAF .     

The effect of magnetic fields on star cluster formation

We examine the effect of magnetic fields on star cluster formation by performing simulations following the self-gravitating collapse of a turbulent molecular cloud to form stars in ideal magnetohydrodynamics. The collapse of the cloud is computed for global mass-to-flux ratios of  ∞, 20, 10, 5  and 3, i.e. using both weak and strong magnetic fields. Whilst even at very low strengths the magnetic field is able to significantly influence the star formation process, for magnetic fields with plasma  β < 1  the results are substantially different to the hydrodynamic case. In these cases we find large-scale magnetically supported voids imprinted in the cloud structure; anisotropic turbulent motions and column density striations aligned with the magnetic field lines, both of which have recently been observed in the Taurus molecular cloud. We also find strongly suppressed accretion in the magnetized runs, leading to up to a 75 per cent reduction in the amount of mass converted into stars over the course of the calculations and a more quiescent mode of star formation. There is also some indication that the relative formation efficiency of brown dwarfs is lower in the strongly magnetized runs due to a reduction in the importance of protostellar ejections.     

Adiabatic scaling relations of galaxy clusters

The aim of this work is to show that, contrary to popular belief, galaxy clusters are not expected to be self-similar, even when the only energy sources available are gravity and shock-wave heating. In particular, we investigate the scaling relations between mass, luminosity and temperature of galaxy groups and clusters in the absence of radiative processes. Theoretical expectations are derived from a polytropic model of the intracluster medium and compared with the results of high-resolution adiabatic gasdynamical simulations. It is shown that, in addition to the well-known relation between the mass and concentration of the dark matter halo, the effective polytropic index of the gas also varies systematically with cluster mass, and therefore neither the dark matter nor the gas profiles are exactly self-similar. It is remarkable, though, that the effects of concentration and polytropic index tend to cancel each other, leading to scaling relations whose logarithmic slopes roughly match the predictions of the most-basic self-similar models. We provide a phenomenological fit to the relation between polytropic index and concentration, as well as a self-consistent scheme to derive the non-linear scaling relations expected for any cosmology and the best-fitting normalizations of the M – T , L – T and F – T relations appropriate for a Λ cold dark matter universe. The predicted scaling relations reproduce observational data reasonably well for massive clusters, where the effects of cooling and star formation are expected to play a minor role.     

Galaxy activity in merging binary galaxy clusters

We present the results of a study of galaxy activity in two merging binary clusters (A168 and A1750) using the Sloan Digital Sky Survey (SDSS) data supplemented with the data in the literature. We have investigated the merger histories of A168 and A1750 by combining the results from a two-body dynamical model and X-ray data. In A168, two subclusters appear to have passed each other and to be coming together from the recent maximum separation. In A1750, two major subclusters appear to have started interaction and to be coming together for the first time. We find an enhanced concentration of the galaxies showing star formation (SF) or active galactic nuclei (AGN) activity in the region between two subclusters in A168, which were possibly triggered by the cluster merger. In A1750, we do not find any galaxies with SF/AGN activity in the region between two subclusters, indicating that two major subclusters are in the early stage of merging.     

The optical/X-ray connection: intra-cluster medium iron content and galaxy optical luminosity in 20 galaxy clusters

X-ray observations of galaxy clusters have shown that the intra-cluster gas has iron abundances of about one-third of the solar value. These observations also show that part (if not all) of the intra-cluster gas metals was produced within the member galaxies. We present a systematic analysis of 20 galaxy clusters to explore the connection between the iron mass and the total luminosity of early- and late-type galaxies, and of the brightest cluster galaxies (BCGs). From our results, the intra-cluster medium (ICM) iron mass seems to correlate better with the luminosity of the BCGs than with that of the red and blue galaxy populations. As the BCGs cannot produce alone the observed amount of iron, we suggest that ram-pressure plus tidal stripping acts together to enhance, at the same time, the BCG luminosities and the iron mass in the ICM. Through the analysis of the iron yield, we have also estimated that SN Ia are responsible for more than 50 per cent of the total iron in the ICM. This result corroborates the fact that ram-pressure contributes to the gas removal from galaxies to the ICM, being very efficient for clusters in the temperature range  2 < kT (keV) < 10  .     

Projection effects in X-ray cores of cooling flow galaxy clusters

Recent analyses of Newton-XMM and Chandra data of the cores of X-ray bright clusters of galaxies show that modelling with a multi-phase gas in which several temperatures and densities are in equilibrium might not be appropriate. Instead, a single-phase model seems able to reproduce properly the spectra collected in annuli from the central region. The measured single-phase temperature profiles indicate a steep positive gradient in the central  100–200 kpc  and the gas density shows a flat profile in the central few 10s of kpc. Given this observational evidence, we estimate the contribution to the projected-on-the-sky rings from the cluster emissivity as function of the shell volume fraction sampled. We show that the observed projected X-ray emission mimics the multi-phase status of the plasma even though the input distribution is single-phase. This geometrical projection affects (i) analyses of data where insufficient spatial resolution is accessible, (ii) the central bin when its dimension is comparable to the extension of any flatness in the central gas density profile.     

Undistorted lensed images in galaxy clusters

To date, the study of high-magnification gravitational lensing effects of galaxy clusters has focused upon the grossly distorted, luminous arc-like features formed in massive, centrally condensed clusters. We investigate the formation of a different type of image, highly magnified yet undistorted, in two widely employed cluster mass density profiles, namely an isothermal sphere with a core, and a universal dark matter halo profile derived from the numerical simulations of Navarro et al. We examine the properties of images of extended sources produced by these two cluster profiles, paying particular attention to the undistorted images. Using simple assumptions about the source and lens population, we estimate the relative frequency of the occurrence of highly magnified, undistorted images and the more commonly known giant arcs.     

Dynamic evolution of nearby galaxy clusters

A study of the evolution of 377 rich ACO clusters with redshift z < 0.2 is presented. The data concerning galaxies in the investigated clusters were obtained using FOCAS packages applied to Digital Sky Survey I. The 377 galaxy clusters constitute a statistically uniform sample to which visual galaxy/star reclassifications were applied. Cluster shape within 2.0 h^–1 Mpc from the adopted cluster centre (the mean and the median of all galaxy coordinates, the position of the brightest and of the third brightest galaxy in the cluster) was determined through its ellipticity calculated using two methods: the covariance ellipse method (hereafter CEM) and the method based on Minkowski functionals (hereafter MFM). We investigated ellipticity dependence on the radius of circular annuli, in which ellipticity was calculated. This was realized by varying the radius from 0.5 to 2 Mpc in steps of 0.25 Mpc. By performing Monte Carlo simulations, we generated clusters to which the two ellipticity methods were applied. We found that the covariance ellipse method works better than the method based on Minkowski functionals. We also found that ellipticity distributions are different for different methods used. Using the ellipticity‐redshift relation, we investigated the possibility of cluster evolution in the low‐redshift Universe. The correlation of cluster ellipticities with redshifts is undoubtly an indicator of structural evolution. Using the t‐Student statistics, we found a statistically significant correlation between ellipticity and redshift at the significance level of α = 0.95. In one of the two shape determination methods we found that ellipticity grew with redshift, while the other method gave opposite results. Monte Carlo simulations showed that only ellipticities calculated at the distance of 1.5 Mpc from cluster centre in the Minkowski functional method are robust enough to be taken into account, but for that radius we did not find any relation between e and z. Since CEM pointed towards the existence of the e (z) relation, we conclude that such an effect is real though rather weak. A detailed study of the e (z) relation showed that the observed relation is nonlinear, and the number of elongated structures grows rapidly for z > 0.14 (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heating rate profiles in galaxy clusters

In recent years, evidence has accumulated suggesting that the gas in galaxy clusters is heated by non-gravitational processes. Here, we calculate the heating rates required to maintain a physically motivated mass flow rate, in a sample of seven galaxy clusters. We employ the spectroscopic mass deposition rates as an observational input along with temperature and density data for each cluster. On energetic grounds, we find that thermal conduction could provide the necessary heating for A2199, Perseus, A1795 and A478. However, the suppression factor of the classical Spitzer value is a different function of radius for each cluster. Based on the observations of plasma bubbles, we also calculate the duty cycles for each active galactic nucleus (AGN), in the absence of thermal conduction, which can provide the required energy input. With the exception of Hydra-A, it appears that each of the other AGNs in our sample requires duty cycles of roughly 10⁶–10⁷ yr to provide their steady-state heating requirements. If these duty cycles are unrealistic, this may imply that many galaxy clusters must be heated by very powerful Hydra-A type events interspersed between more frequent smaller scale outbursts. The suppression factors for the thermal conductivity required for combined heating by AGN and thermal conduction are generally acceptable. However, these suppression factors still require 'fine-tuning' of the thermal conductivity as a function of radius. As a consequence of this work, we present the AGN duty cycle as a cooling flow diagnostic.