Astron. Astrophys. 329, 809-820 (1998)

4. Nature of the Faraday screen

The identity of the principal Faraday screen(s) responsible for the RM is discussed in this section.

4.1. Faraday screens non-local to the radio source

4.1.1. Galactic ISM

All the sources in the MRC/1 Jy sample, from which the HRRGs are drawn, were selected to lie at Galactic latitudes 20 where the RM of the Galactic ISM is minimal. Further, the RM gradients in the ISM are known to be 10 rad m^-2 over 1' arc (Simonetti & Cordes, 1986; Leahy 1987). The much larger gradients observed in the HRRGs (implied by the difference in the RMs of the two lobes which have a typical separation of 10 arc) indicates that the origin of the RM is extragalactic.

The RM contributed by the Galactic ISM was estimated by averaging the RMs of all known radio sources within a cone of 15^o radius centred on the HRRG. The RM data and the method used are described in Simard-Normandin et al (1981) and Simard-Normandin & Kronberg (1980). The extreme RM values ( from the mean) were discarded and the mean recalculated to obtain the values listed in Table 3. It was also confirmed that this mean value from the subsample was consistent with the median for the whole sample. However, when the RM values of the different sources within the cone were widely discrepant, the values listed in Table 3 are the mean values for the sources nearest to the HRRG; the 3 nearest sources (all with similar RMs) were considered for 1138-262 and the 4 nearest sources for 2025-218.

Table 3. Intrinsic rotation measures in the lobes of MRC/1Jy galaxies at z 2. The columns are redshift (z), remarks (R), observed RM (RM_obs), Galactic RM towards the source (GRM), intrinsic RM not corrected for Galactic RM (RM_int = RM_obs (1+z)²) and intrinsic RM corrected for GRM (RM = (RM_obs - GRM) (1+z)²). The remarks are as described in Table 2.

4.1.2. Intervening galaxies and clusters

Disk galaxies and the centres of rich clusters at low redshifts can introduce Faraday rotation in background radio sources. The probability of intersecting an object at redshift z along a line of sight is given by

where R_c is the radius of cross-section and N_o (z) is the comoving number density. ²

Intervening clusters Kim et al. (1991) reported excess RMs in radio sources located behind the centres (inner 500 kpc) of Abell clusters which indicated that cluster cores introduce Faraday rotation in the background sources. From the observed density of 8.8.10^-7 Mpc^-3 of Abell clusters richer than Class 1 (Efstathiou et al. 1992) and assuming a constant co-moving space density between z = 0 and 1, the probability of intercepting the inner 500h^-1 of a cluster along a line of sight is only 0.5%. This value is a robust upper limit since rather liberal values have been used for all the parameters. The small probability, coupled with the fact that not all clusters introduce large RMs makes it very unlikely that foreground clusters are the Faraday screens of the HRRGs.

Absorption-line Systems The abundance of disk galaxies and their presumed progenitors at high redshifts, the damped Ly absorbers, can be estimated from their presence in the optical spectra of distant quasars. Their estimated line-of-sight number density, (Rao et al. 1995), gives a probability of 16% for intersecting one along a line of sight between z = 0 and 2.

It was believed that the presence of damped Ly systems (as against other absorption systems) in the optical spectra of quasars greatly increased the probability of detection of RM of extragalactic origin (ie. an RM larger than 3 times the error after subtracting the galactic contribution) at radio wavelengths (Wolfe et al. 1992). However, the result was based on a heterogeneous sample of 5 quasars with damped Ly absorbers. A more recent study of 11 radio quasars with damped Ly absorbers (from a complete sample of 60 quasars) detected extragalactic RMs in only 2 sources (Oren & Wolfe, 1995). Eight of the 11 quasars had RMs less than 40 rad m^-2, all of which were smaller than the quoted errors.

Estimating the RM contribution of intervening objects in the spectra of compact quasars is very unsatisfactory because RMs can be estimated along only one line of sight per object. The single value makes it very difficult to separate the contributions from the Galactic ISM, intervening galaxies/clusters and regions local to the quasars (both nuclear and in the extended environment). On the other hand the RMs of extended radio sources provide diagnostics like the gradient in the values which have been used in this work to rule out the Galactic ISM.

An estimate of the RM contribution from the intervening systems may be obtained from RMs of 14 extended radio lobes in 7 galaxies at z 0.6-1.2 () (Pedelty et al., 1989). Seven of the 14 RM_obs values are 10 rad m^-2 and only 3 are greater than 40 rad m^-2 (highest 60 rad m^-2). The variation of RMs across the lobes indicates that much of the RM is local to the radio galaxies.

The small probability of intersecting disk galaxies and Ly absorbers along the line of sight and the small RMs observed in many of them makes it very unlikely that they are responsible for the large RMs observed in HRRGs.

4.1.3. Gravitational lenses

It has also been suggested that many of the HRRGs may be lensed by intervening galaxies (Hammer & Le Fevre 1990). Lensed background radio sources may be preferentially selected in flux limited samples due to magnification of the intrinsic flux. If the lenses (at much lower redshifts) were the Faraday screens, the intrinsic RMs would be much smaller than estimated here and would also account for the large differences in the RMs of the two lobes. However, we find no preference for the brighter lobe to have a larger RM as would be expected in this model. Further the deep optical/IR images of these HRRGs show no other galaxies in the close vicinity except in the case of 0406-244 (see McCarthy et al. 1991a; Rush et al. 1996).

4.2. Faraday screens local to the radio source

Having argued that intervening systems are unlikely to be the Faraday screens of HRRGs in most cases, we shall ascribe all the RM to screens in the vicinity of the HRRGs themselves. The intrinsic RMs, corrected for cosmological redshifts, are listed in Table 3. In addition, the intrinsic RMs have also been calculated by subtracting the Galactic RM (GRM) from the observed RM before correcting for the redshift. We have listed the intrinsic RM values obtained by both subtracting and not subtracting the GRM because the uncertainties in many GRM values are an appreciable fraction of the values themselves.

It must be noted that significant RM contributions from damped Ly systems at z 2 would change the identity of the Faraday screen (from local to the radio source to intervening galaxies) but would not alter the conclusion regarding RMs and magnetic fields at high redshift.

An examination of the highest RM measured in a source shows that four of the 13 sources have values in excess of 1000 rad m^-2 with the highest value of 5911 rad m^-2 in 1138-262 (z = 2.17). In fact, over half the sources have values of well over 500 rad m^-2 (i.e. RM 500 + 3 error) while only 3 sources are consistent with values 100 rad m^-2 (RM - 3 100). This is in sharp contrast to the much smaller fraction of high RM sources at z 0.5 (Taylor et al. 1992). It must be noted that higher resolution observations have always resulted in the detection of higher RM values in other radio galaxies; the RM values obtained from our low resolution observations may in fact be underestimating the highest RM in the HRRGs (see 0156-252 in this sample). These numbers are somewhat modified when the GRM corrected values of the intrinsic RM are used; however, the large RM sources, particularly those with values in excess of 1000 rad m^-2, are hardly affected by the GRM. The two other HRRGs with known RMs, 4C 41.17 at z = 3.8 and 0902+343 at z = 3.4, have intrinsic RMs of 6250 and 1100 rad m^-2, respectively (Carilli et al. 1994a; Carilli 1995). The RMs of the two radio lobes in each source show differences of several thousand rad m^-2.

Several sources in our sample show a rotation of more than 90 (Fig. 2); an internal screen, i.e. thermal plasma mixed with the synchrotron plasma, can be ruled out in such cases (Laing 1984). Going by the prevalence of external rotation in FR II radio sources, it is assumed here that the rotation occurs outside the emitting region in all the HRRGs of this sample; the rotation in the PPA of 90 seen in many of them is likely to be due to the small range in rest frame at which they have been observed. One of the radio lobes in 0943-242 shows a higher fractional polarisation at a lower frequency, which may be due to an internal screen. However, higher resolution observations are required to confirm this as low resolution observations have the same effect as an internal Faraday screen in case of unresolved magnetic field structure.

All the high RM radio galaxies at low redshifts are known to be associated with dense environments; the radio sources are either compact (sub-galactic in size) or associated with cooling-flow clusters (Taylor et al. 1992, 1994). That the HRRGs, which are also presumed to be in dense environments, show large RMs is, perhaps, an indication that dense ambient gas plays a key role in forming a deep Faraday screen. Before going into the problem of Faraday screens at high redshift, we shall first outline briefly the situation in low redshift objects with high RMs.

Several workers have dealt with the problem of generating the large RMs seen in low redshift clusters. Using a typical intracluster medium (ICM) electron density of 0.01 cm^-3, the observed RMs of thousands of rad m^-2 require magnetic fields of a few to tens of G correlated over tens to hundreds of kpc (Perley & Taylor 1991; Taylor & Perley 1993; Taylor et al. 1994; Feretti et al. 1995). However, there is very little direct observational evidence of such strong magnetic fields on such a large scale. It is generally assumed that the fields are organised on the cluster core scales (100-200 kpc) and the magnetic fields are calculated by using these values of L in Eqn. 2. It has been suggested that the turbulence due to galaxies moving through the ICM generates the large scale magnetic fields (Jaffe 1980; Ruzmaikin et al. 1989). However, most non-linear calculations indicate that the magnetic fields generated cascade quickly to much smaller length scales and maintaining G fields correlated over a kpc is a tough proposition; most models produce tenths of G correlated over a few kpc at best (de Young 1992; Goldman & Rephaeli 1991). Indeed, there is observational evidence from the correlation analyses of RM variations in the transverse direction that the magnetic fields are tangled on scales of 1-5 kpc (Feretti et al. 1995; Perley et al. 1984; Ge & Owen 1993, Taylor & Perley 1993). The Laing-Garrington effect, wherein the radio lobe on the counter-jet side (presumably the farther lobe in the relativistic beaming models) is more depolarised, also indicates considerable tangling up of the fields in the ambient medium on scales much smaller than the radio lobes. It is difficult to envisage magnetic fields correlated over tens or hundreds of kpc along one direction while the correlation is only a few kpc in the perpendicular direction. However, it has been suggested that cluster cooling flows may result in such an anisotropy, though not to such a large degree (Soker & Sarazin 1990). Cooling material flowing into the deep potential well of clusters may result in the stretching (and alignment) of the frozen-in magnetic field in the radial direction. This may also result in a moderate amplification of the radial component. However, since the stretching of the field lines is due to differential infall as a function of radius, the radial alignment and amplification would be appreciable only in the case of cooling flows extending from several hundreds of kpc to an inner radius of 10-20 kpc.

Even if the field is stretched radially by a cooling flow, it must be noted that field reversals could occur on scales similar (apart from the stretching by a factor of few) to that seen in the transverse direction. This random walk situation should result in an RM distribution with zero mean and an rms given by RM_c, where N is the number of individual cells along the line of sight and RM_c is the typical RM of an individual cell. So the distribution of RMs of a large number of independent pixels within a radio lobe obtained from sufficiently high resolution observations, should be a gaussian with a zero mean. However, high resolution observations of several sources have shown a gaussian RM distribution but with a non-zero mean of up to thousands of rad m^-2 (for e.g. Taylor & Perley 1993), indicating that, the cooling-flow scenario, while likely, is not the whole answer. The non-zero mean RM may be a result of a Faraday screen in the immediate vicinity of the individual radio lobes.

As the previous discussion shows, it is not clear if the mechanisms proposed to generate and align large magnetic fields in low redshift galaxies are actually appropriate. Explaining the large RMs at high redshift is even more problematic due to the added constraint of insufficient time. The Universe was just a sixth of its present age at z = 2.5; it is not clear if the time available at those redshifts is sufficient for the mechanisms to generate and align strong magnetic fields on a large scale. We have investigated below several mechanisms to see if they are plausible at high redshifts.

4.2.1. High redshift cooling-flows

In the cooling-flow scenario, a mass M_t (total mass baryonic (M_b) + dark matter (M_d); 10% in baryons) turns around from the Hubble flow at a redshift z_m and collapses by a redshift z into an isothermal sphere with a temperature T_vir (due to virialisation). It is essential that the collapse occurs on a timescale () smaller than the cooling time-scale () so that much of the material is still outside the core. Further, the cooling timescale should be substantially smaller than the Hubble time () at the redshift at which the galaxies are being observed. Subsequent cooling and the resulting slow and ordered infall of the material into the potential well is called a cooling flow. Cooling, being a function of density and hence radius, will lead to a radial gradient in the infall velocity. The timescale constraints define the inner and outer radii within which plasma cools and flows in. The differential infall within the cooling shell results in a radial stretching of the frozen-in magnetic field leading to correlated magnetic fields in that direction.

We consider below a simple model for the formation of a high redshift cluster with a cooling flow. The relationships governing the formation of a cluster, derived from rather general considerations of gravitational collapse, are given in Padmanabhan & Subramanian (1992) and have been reproduced below. The formation of a cooling flow is constrained by the requirements that (i) it is formed by z 2.5 (ii) as required by an ordered inflow and (iii) the central density of the cluster is not higher than what is observed in clusters/galaxies today, i.e. M 2. in baryons within 10 kpc radius. The last constraint is not central to the cooling flow model but it ensures that the high redshift cluster in our model is consistent with the clusters seen at low redshifts.

where, h is the Hubble's constant in units of 100 km s^-1 Mpc^-1, V is the total velocity dispersion in the cluster in km s^-1, T is the temperature, is the total density (dark + baryon) in gm cm^-3, N_b is the electron density in cm^-3, R is the radial co-ordinate of the isothermal sphere formed during the collapse and R_c its core radius. f_m takes metal enrichment into account for the cooling rate (f_m is 0.03 for primordial abundance and 1 for Solar abundance; See Peacock & Heavens 1990). The other symbols are as already described in the previous two paragraphs. All masses are in , timescales in Gigayear, lengths in kpc and temperatures in 10⁶ K.

We have used R_c = 10 kpc, f_m = 0.03 and h = 0.5 in the calculations which follow. We assume that 10% of the total matter is in baryons, the rest being dark matter. The dark matter component is not expected to deviate from its initial isothermal density profile even over 10 Gyr while the peripheral baryonic matter cools and accumulates at the centre of the cluster potential resulting in similar amount of dark and baryonic mass (2. each within 10 kpc) seen in galaxies at the centres of present day clusters. The constraint on the central density requires [M_t (1+z 68.5. For z 5, which is essential for forming cooling flows by z = 2.5, we get M 4. . The virialised temperature would be 10⁷ K. The cooling timescale depends on the baryon density and so will be a function of radius within this isothermal sphere. The upper and lower constraints on the cooling time (described previously) define the shell within the collapsed sphere where a cooling flow can operate. The numbers and the constraints used above limit the cooling-flow to between 20 and 35 kpc. The picture that emerges here for a cluster at z 2.5 is that of about 20 galaxies with a galactic scale cooling-flow.

The cooling-flows in low redshift clusters operate between 15 and 100-200 kpc. It is this ratio of 10 which is responsible for the alignment of the field. One can hardly expect any alignment of the magnetic field with the mini cooling-flows possible in HRRGs where the ratio is less than 2. Further, the 25 kpc size of the radio lobes hardly makes for any path length through a Faraday screen formed by such a cooling flow. Pushing the parameters to their limits would only change the cooling shell to between 30 and 45 kpc. The problem is even more severe to get cooling flows to form Faraday screens by z = 3.8! It seems unlikely that cooling flows play a significant role in generating Faraday screens at z 2.

4.2.2. Large magnetised plasma clouds in the vicinity of the radio lobes

The large integrated RMs for the individual lobes and the differences between the two lobes suggests approximate sizes for the Faraday screens of a few kpc to 25 kpc (the lower limit from the presence of net RM and the upper limit from the difference). If the initial gravitational collapse is rapid and fragmentary (such a model is less constrained in parameter space and perhaps more likely than the cooling flow model), it would result in the formation of many clouds in the range of 10⁸ - with little constraint on the total mass. These clouds could be responsible for the RMs seen in HRRGs. The optical continuum and line images of high redshift galaxies (see McCarthy 1993 and references therein) and the large differences in the properties of the two lobes of their radio sources (Pedelty et al. 1989; Athreya 1996) are indicative of the dense and clumpy environments at those redshifts required by this model.

A further refinement of this model is a collapsed object with correlated G field in the path of the radio jet. A cloud of thermal plasma in the path of the jet would be stretched along the bow-shock. The resulting shear would stretch and align the magnetic field along a sheath around the radio hotspot. The passage of the shock would also increase the plasma density by a factor of 4 and may even amplify the magnetic field. A cloud with a baryonic density of just 1 particle cm^-3 and 5 kpc diameter (baryonic mass of only 2. ) and a magnetic field of 1 G (all numbers refer to the unshocked cloud) can lead to an RM of several thousands of rad m^-2 for a wide range of angles between the observer and the orientation of the bow-shock. An added appeal of this model is that the large differences in the RM values of the two lobes are naturally explained by Faraday screens local to each lobe rather than by a global screen. Structures in RM maps similar to what may be expected from a sheath around the bow shock have been seen in, for e.g., Cygnus A (Carilli et al. 1988), 3C 194 (Taylor et al. 1992a) and 0902+343 at z = 3.4 (Carilli 1995). Similarly, the RM structure seen in the high resolution images of 0156-252 in Fig. 3 is consistent with the above model; the highest RM values are in an arc in front of the hotspot and at a knot in the jet where it has bent considerably, presumably due to a collision with a clump of matter in the ambient medium.

© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997
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