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4.1. Faraday rotation and x-ray probes of galaxy cluster magnetic fields

Intergalactic gas in galaxy clusters has a typical electron density of 10-4 -10-2 cm-3, temperature in the range 107 -108 K, and an extent of ~ 1 Mpc. At this temperature range, which makes clusters significant x-ray sources (Lx approx 1043 -1045 erg s-1), the ion sound speed is comparable to the galaxies' velocity dispersion in the cluster, which is ~ 400 - 1200 km s-1. A minority of clusters contain cosmic ray electrons which, over dimensions comparable to that of the hot gas, emit a diffuse `halo' of synchrotron radiation, thus revealing an intracluster magnetic field. Our discussion here focuses specifically on cluster magnetic fields and their measurement: the extensive subject of intergalactic gas has been covered in a recent review in this journal by Fabian and Barcons (1991).

4.1.1. Radio and x-ray methods for probing cluster magnetic fields.     Intracluster magnetic fields can be most easily detected via synchrotron radiation (equation (1.1)) from co-extensive cosmic rays (cf also section 4.3 below). Thus, the first evidence for magnetic fields came via detection of a synchrotron halo: in the Coma cluster of galaxies (Wilson 1970, Jaffe et al 1976, Hanisch et al 1979, Kim et al 1990), in Abell 754 (Waldthausen 1980), Abell 2256 Bridle et a1 1979, Kim 1993), Abell 2319 (Harris and Miley 1978), and subsequently several others - see Hanisch (1987) for a more extensive bibliography.

Unfortunately the synchrotron emissivity does not give the field strength (equation (1.1)) unless we have independent knowledge of the true number density of relativistic electrons. Apart from detecting the synchrotron-emitting halo, ICM magnetic fields can be probed in three further ways: (i) multi-frequency polarization mapping of the synchrotron halo emission which, due to the co-extensive thermal gas, will undergo differential Faraday rotation and depolarization as a function of radio wavelength. Because the Faraday rotation law (equation (1.3)) also contains the (non-relativistic) electron density and an unknown number of field reversals, independent estimates of these latter two quantities lead to an estimate of |B|. (ii) Comparing the Faraday rotation of background radio sources shining through the cluster (cf Lawler and Dennison 1982, Kim et a1 1990) with comparable sources whose ray path to us avoids the cluster, to test for excess Faraday rotation due to the cluster's ICM. (iii) Using Faraday rotation mapping of extended radio sources embedded within the cluster as a polarized `surface', against which foreground intra-cluster variations of Delta chi = 8.1 × 105 lambda2 integ ne B|| dl can be measured. This assumes that the Faraday rotation internal to the radio lobes of cluster sources is smaller than that being probed in the ICM. Each of these methods requires, ideally, a companion x-ray image, with x-ray spectral information so that estimates of both Te, and ne, within the cluster can be made. Then a weighted <|B|> can be estimated. In the following we review recent attempts to make cluster magnetic field estimates using the above three types of observations.

4.1.2. Recent magnetic field measurements in the ICM of `normal ' galaxy clusters and groups.     Method (i) is difficult, because of the extreme faintness of the steep-spectrum halo emission at a useful resolution at lambda < 10 cm. Although the synchrotron emissivity becomes rapidly stronger at longer lambdas, only few radio telescopes have the required (< 1') angular resolution. Furthermore, the `Faraday depth' (cf Burn 1966, Tribble 1991) at lambda > 20 cm is so high that the linear polarization can become completely self-depolarized by its own differential Faraday rotation. One of the few such observations attempted, by Kim et al (1990) for the Coma cluster, indeed found the Coma cluster's halo to be largely depolarized at 21 cm, and loo weak at shorter radio lambdas. Method (ii) is promising for nearby clusters, and was successfully used by Kim et al (1990) to make the first, relatively firm estimate of magnetic field strength in the intracluster medium. Their result, for the Coma cluster core region, is 1.7 ± 0.9µG, and was obtained using 18 background source RMs near in position to the Coma cluster (see figure 12). This field strength estimate used x-ray data from Abramopoulos and Ku (1983) to estimate ne (cf equation (l.3)), and an estimate-of the field reversal scale was obtained from the RM variation scale in an extended head-tail galaxy within the cluster. By interstellar medium standards, the field is surprisingly strong. being comparable with the disk interstellar field in our galaxy (~ 3 - 4 µG). It is likely that the field strength near the Coma cluster core (not well sampled with the RM data in figure 12) is even higher. A field strength estimate for another relatively nearby cluster, Abell 2319, was made by Vallée et al (1986). The density of suitable background RM probes on the sky is insufficient to apply this method to most other clusters, so attempts have been made to compare RMs for large numbers of background sources at differing impact parameter distances for a sample of many clusters. Using this technique, Lawler and Dennison (1982) obtained the first tentative positive statistical signal of cluster ICM rotation measures.

Figure 12

Figure 12. RM distribution of 18 background radio sources relative to the x-ray boundary of the Coma cluster of galaxies, which shows a clear excess RMs added by the intracluster medium (source Kim et a1 1990). Filled and open circles show positive. and negative RM's respectively. The dashed line shows the ROSAT x-ray boundary at approx. 0.12 counts/ 400 arcsec2 for the ROSAT PSPC detector, in the range 0.5-2.4 keV (from Brie1 et al 1992).

More recently, Kim et a1 (1991) used a sample of 53 Abell galaxy clusters, 19 of which had x-ray core size measurements, and obtained the surprising and interesting result that magnetic field strengths near ~ 1 µG extend typically to ~ 0.5 Mpc from the cluster centers. Since clusters with strong radio halos are rare, their result further suggests that µG-level fields are widespread in the ICM whether or not a cluster has a strong radio halo. The fact that magnetic fields near µG level are widespread in galaxy clusters is, independently, consistent with a lower limit of 0.3 - 0.5 µ G which is implied by the observed general absence of inverse-Compton-generated x-rays in clusters (cf Gursky and Schwartz 1977, Harris and Grindlay 1979, Henriksen and Mushotzky 1986, Rephaeli and Gruber 1988).

Evidence of a different kind, and a version of method (iii) above, has been produced by Garrington et a1 (1988), and Garrington and Conway (1991), who discovered a systematic side-to-side asymmetry of the depolarization ratio between two frequencies in a large sample of FR II radio sources covering a substantial redshift range. They interpret this near (jet) side/far side difference relative to the radio galaxy nucleus to be due to a 30 - 100 kpc radius ionized gas halo having a magnetic field strength of at least 1 µG in the low redshift sources, and tangled on a scale of < 5 kpc. They ascribe this environment to that which is typical around cD galaxies in galaxy groups or poor clusters of galaxies. Although these more 'typical' radio sources are not usually in rich clusters, the result is important, in that it supports the findings described above, by suggesting that µG level magnetic fields are widespread, at least wherever there is significant hot gas in galaxy systems. Although the energy density in 1-2 µG fields is usually much less than that in the hot gas, their influence on conductivity is sufficient to indirectly influence the dynamics of the ICM, and the long term evolutionary scenario of galaxies in clusters. What remains to be understood is how, and when, these fields were generated and amplified to these levels.

4.1.3. Detection of strong magnetic-fields in cooling flow clusters     High resolution, multi-frequency VLA radio images of extended radio galaxies associated with cD galaxies in the centers of dense, 'cooling flow' clusters have, using method (iii), revealed extremely large Faraday rotations from kpc-scale, ordered magnetic fields: Examples are Cygnus A (Dreher et al 1987), M87 (Owen et a1 1990), Hydra A (Taylor et al 1990, Taylor and Perley 1993), 3C295 (Perley and Taylor 1991) and Abell 1795 (Ge and Owen 1993).

The Cygnus A radio source contains systematic RM gradients of 100 to 600 rad m-2 kpc-1, and regions of large scale magnetic field coherence. In other regions, RM jumps of up to 3000 rad m-2 occur over scales < 400 pc in the cluster (Perley 1990). Hydra A, also associated with a cD galaxy and x-ray emission (David et al 1990), has RM fluctuations of close to 12 000 rad m-2 with organized magnetic field changes on scales of up to 100 kpc (Taylor and Perley 1993). The large extent of the RM probe offered by Hydra A shows that magnetic field strengths of up to approx 30 µG exist in its host cluster. Furthermore, the magnetic pressure closer to the cluster core is roughly two orders of magnitude greater than the dynamic gas inflow pressure as inferred from the model of White and Sarazin (1987) - cf Taylor el al (1990). Cluster field values of ~ 30 µG, have also been found around the radio galaxy 3C295 at a redshift of 0.461 (Perley and Taylor 1991). As for Cygnus A and Hydra A, evidence for the lack of depolarization within the magnetized zones generating the high RM gradients favors their location outside, rather than within, the boundary of the radio lobes (Perley 1990).

These results suggest prima facie that, at least in cooling flow clusters, individual galaxies may form out of a strongly magnetized environment having prior magnetic field strengths at least as large as in the ISM of `evolved' galaxy disks.

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