Gravitational Lens Systems to probe Extragalactic Magnetic Fields
aa r X i v : . [ a s t r o - ph ] F e b Gravitational Lens Systems to probe Extragalactic Magnetic Fields
D. Narasimha ∗ and S.M. Chitre † Tata Institute of Fundamental Research, Mumbai 400 005, India Department of Physics, University of Mumbai, Mumbai 400 098, IndiaAccepted .... Received ..... ; in original form ....
Abstract
The Faraday rotation measurements of multiply-imaged gravitational lens systems can be effectively used to probethe existence of large-scale ordered magnetic fields in lensing galaxies and galaxy clusters. The available sample of lenssystems appears to suggest the presence of a coherent large-scale magnetic field in giant elliptical galaxies somewhatsimilar to the spiral galaxies. keywords: gravitational lensing – galaxies: magnetic fields – polarization. ∗ E-mail: [email protected] (DN) † [email protected] (SMC) Introduction
The origin of extragalactic magnetic fields is one of themost challenging problems in astronomy. Clearly, the de-tection and measurement of large-scale magnetic fields incosmological objects would be important for our under-standing of their role in theories of galaxy formation andevolution. It is hoped that observations of extragalacticobjects and high redshift galaxies can, in principle, illumi-nate the basic issues relating to their origin and dynamicalamplification.Magnetic fields in external galaxies have been mea-sured using radio observations of their synchrotron emis-sion to have strengths of about microgauss and they havebeen detected to have a coherence over a scale of few kilo-parsecs. The large-scale ordered magnetic fields in sev-eral spiral galaxies were reported byBeck et al to haveaverage field strength ∼ µ G with a coherence scale ofseveral kpc. However, it is desirable to have completelyindependent tools to ascertain the global characteristics ofthe pervading magnetic fields in galaxies, both spiral andelliptical, at a much earlier epoch. Equally, estimation ofthe strength of galactic magnetic fields over a range ofredshifts will be highly valuable for understanding theirorigin and evolution with the age of the Universe.Cosmological magnetic fields could be generated inthe early universe by some mechanism such as the first-order phase transition Hogan , coupling of electromag-netic field with curvature Turner & Widrow or by athermal battery operating in expanding ionization/shockfronts impinging on density inhomogeneities in the inter-galactic medium Subramanian et al , Kulsrud et al . Butthese seed field values ( ≤ − G) need to be enhancedand maintained at the observed microgauss level by somekind of a dynamo process. We note parenthetically thatthe energy density of average galactic magnetic fields isof the same order as the energy density of cosmic raysof intergalactic thermal energy, and of cosmic microwavebackground radiation (of order 10 − erg/cm ).The radiation emitted by distant sources, during its pas-sage over cosmological distances, is likely to encountera variety of objects en route such as galaxies, galaxy–clusters, Ly α clouds, magnetic fields and metal line ab-sorbers. The imprints left by these intervenors in the formof spectral absorption features and Faraday rotation of thepolarized flux of the background source can, in principle, furnish valuable information about the chemical compo-sition or magnetic fields associated with the interveningobjects. The observed correlation of the Faraday rota-tion measure (RM) of high red-shift quasars with the op-tically detected absorption-line systems along the sight-lines prompted Kronberg and Perry (1982)Kronberg &Perry to estimate the magnetic field strength in high red-shift objects. For studying magnetic fields in high redshiftgalaxies and galaxy clusters we should first identify ex-tragalactic radio sources with polarized flux that are lo-cated within or behind these intervening deflectors andmeasure the Faraday rotation of radio waves coming fromthe background source. The Faraday rotation will natu-rally have contributions from (i) our Galaxy, (ii) interven-ing objects and absorption systems, and (iii) the source it-self. Clearly, for inferring the average strength of high redshift magnetic fields, it is essential to subtract out the con-tributions to the Faraday rotation occurring at the sourceand in our own Galaxy. We need, of course, to have areasonably independent estimate available of the electroncolumn density in the intervening objects. The connec-tion between damped Lyman systems and galaxies andestimation of the hydrogen column density from the opti-cal lines is extensively discussed in the literature (Blasi etal , Sargent et al ) As discussed by Blasi et al the elec-tron column density could be assumed to follow the cor-responding density of neutral hydrogen in the intervenorwhich can be estimated from absorption line strengths.All these requirements may be very conveniently ful-filled for the case of radio-selected gravitationally lensedsources. In gravitational lens systems we often encounterpolarized radio sources (e.g. quasars, radio galaxies) thatare being multiply imaged by an intervening ‘normal’galaxy or a galaxy cluster. In such lensed systems thedifference in the rotation measures between various im-ages is not expected to be severely affected by the back-ground source or by our Galaxy, except for possible con-tributions from absorption systems located en route andperhaps, contamination from small-scale inhomogeneitiesin our own Galaxy. In short, because there is more thanone sightline to the polarized radio source available for amultiply imaged system, it should be possible to filter outcontributions from the source and our Galaxy by takingdifferences between rotation measures of various images.We propose to apply this technique for deducing the esti-mates of magnetic fields in galaxy and cluster lenses and1articularly enquire about the nature and strength of mag-netic fields in elliptical galaxies. It will be valuable if wecan adopt this technique for inferring the large-scale mag-netic fields in the intergalactic medium and even more il-luminating if we can use the polarized Cosmic MicrowaveBackground as a source for probing the cosmic magneticfields. We can only hope this may conceivably becomefeasible with rapidly advancing technology. For the sake of illustration, we have sketched the phe-nomenon of gravitational lensing in Figure 1. A polar-ized source such as a quasar, S, is lensed by an intervein-ing galaxy L producing the multiple images I1 and I2.The phenomenon of gravitational lensing preserves sur-face brightness and also the polarization properties of theoriginal lensed source. The fractional polarization as wellas the direction of the electric field in the images shouldfollow the value in the source; we have, therefore, shownthe polarization vectors with same length and direction inthe source as well as in all the images. However, the pathof the light rays forming the two images sample differentregions of the lens galaxy (shown through C1 and C2 inthe figure) and hence will be affected differently by the in-terstellar medium of the lens. It was, therefore, recognisedafter the discovery of the first gravitational lens systemQ0957+561 Walsh et al that radio observations of suchlens systems could furnish valuable information about thephysical properties of the intervening lens and of absorp-tion system along the lines of sight.The magneto-ionic plasma in the intervening lenses isexpected to cause Faraday rotation of the radiation whichwill, of course, vary for each of the light paths from var-ious images. The angle of rotation of the plane of polar-ization is given by Ψ F = e πm e c Z B k ( l ) n e ( l ) λ dl, (1) where n e is the electron number density, λ is the wave-length of the radiation as seen by the absorber medium, B k is the line of sight component of the magnetic field Figure 1: Schematic diagram of the phenomenon of grav-itational lensing. Background source S is lensed by theintervening galaxy L and multiple images I1 and I2, hav-ing identical intrinsic properties are formed. The regionsof the lens sampled by the light rays forming images I1and I2, shown by C1 and C2, are separated by typically afew kiloparsecs.2nd the integral is over the path length through the inter-vening absorbers.The rotation measure, as measured by the observer atredshift of zero is given by RM = Ψ F λ obs = e πm e c Z B k ( l ) n e ( l ) (cid:20) λ ( l ) λ ( obs ) (cid:21) dl (2) For the Faraday Rotation produced by a deflector atredshift z , the rotation measure of the intervening galaxywith the average line of sight magnetic field component, < B k > = R n e ( z ) B k ( z ) dl ( z ) R n e ( z ) dl ( z ) (3) and the electron column density, N e = R n e ( z ) dl ( z ) maybe expressed as RM ≃ . × ( N e ) < B k > µG / (1 + z ) rad m − . (4) Here ( N e ) is expressed in units of 10 cm − and < B k > µG in units of microgauss. Even though the Fara-day Rotation may be caused by the source, the intervenorand the Milky Way, the difference in the rotation anglebetween the multiple images is practically due to the lenswhich is contained in Eq. (4). Consequently, the magni-tude of the difference in rotation measures (RM) betweenimages turns out to be a valuable probe for estimating theaverage line of sight component of magnetic field in thelenses.There have been a number of multi-frequency VLApolarization observations of gravitational lens systemsthrough the 1980s and 1990s. The Faraday rotation mea-sures and intrinsic polarization angles of the multiple im-ages of some selected lenses Patnaik et al , Subrah-manyan et al , Patnaik et al ; , King et al , Chen& Hewitt , Patnaik & Narasimha , Patnaik are sum-marised in column 3 of Table I, while column 4 is the bestfit estimation of the differential Faraday Rotation Measurebetween various images. The last column denotes the dif-ference between polarization angles at zero wavelengthwhich, in principle, would have the value 0, were there noFaraday rotation in the source. Most of the radio sources have substructures like core,knot and jet and generally the source polarization vec-tor among these components is not aligned. A good il-lustration of the change in polarization angle across thesubstructures can be found Biggs et al for the 8.4 GHzVLBA images of the lens system B0218+357 The relativeflux contribution between these components also happensto change gradually with frequency. There is an added un-certainty introduced in the estimation of Faraday rotationfrom the position angles of the polarization vector if themeasurements at various frequencies are not made simul-taneously.The change in polarization vector with time, for ex-ample as illustrated by Patnaik & Narasimha Patnaik &Narasimha can also be a factor. But, in principle, thisuncertainty can be eliminated by getting the maps at sim-ilar spatial resolution and at close epochs and correctingfor the time delay between the images. Here we argue that(a) if we ignore the effects of non–simultaneous measure-ments of the position angle, (b) further make the reason-able assumption that the Faraday rotation introduced byan intervening object does not vary considerably at mil-liarcsecond scale, and (c) the source variability and thetime–delay together do not seriously affect the differen-tial Faraday Rotation measurements, then we can estimatethe difference between the Rotation Measure between thelines of sight along the multiple images of a backgroundsource. The Milky Way is amenable to detailed analysis of itsmagnetic field structure due to pulsar and other observa-tions. There is evidence for the presence of magnetic fieldas well as its direction reversal from very small scale tothe global scale of kiloparsec. However, there is a con-troversy about the magnetic field reversal due to difficul-ties in the analysis of Faraday rotation measurements spe-cially when the line of sight passes through multiple spi-rals Rand & Kulkarni , Sofue et al . Nevertheless, itmight be fair to accept that the Milky Way has (a)an or-dered component of magnetic field of 2 to 10 µ G on thescale of spiral arms, with the field strength generally in-3able 1: Faraday Rotation in selected Lens systemsSystem Lens RM Diff. RM Excess χ ∗∗ no. of Time Referencesredshift (rad m − ) (rad m − ) P.A. degree delay(degree) of(literature) (best fit) ∗ ( λ =0) freedom (days)SpiralsB0218+357 0.684 A-8920 AB: 913 ±
31 -10 0.3 2 10.5 Patnaik et al B-7920PKS1830–211 0.89 A -157 AB: 1480 ±
83 24 7 2 26 Subrahmanyan et al B 456EllipticalsQ0957+561 0.36 A-61 ± ± ± B1422+231 0.31 A -4230 ±
60 AB: 125 ±
125 4.7 16.1 2 1.5 Patnaik et al ,B -3440 ±
88 AC: 20 ±
70 3.4 5 2 7.6 Patnaik et al C -3340 ±
90 BC: 105 ±
77 -1.3 6.1 2 8.21938+666 0.878 A 665 ±
14 AB: 960 ±
202 -26 27 1 King et al B 465 ±
14 BC1:85 ±
39 -10.5 19 1C1 441 ± ± ± ±
10 Chen & Hewitt R2 -72 ± ± ± ± ± ∗ In some cases, the differential RM listed in column 4 are at variance with the direct difference because of theambiguity modulo π . ∗∗ See the text for discussion on the χ .4reasing as we go inwards to the central regions of theGalaxy and (b) at scales of star forming regions or stel-lar environment ( ∼ cm), there is evidence for mil-ligauss magnetic field. Consequently, we could expectdifferential Rotation Measures of a few tens of rad m − if we pass through a star forming region. However, itcould also produce substantial depolarization on subarc-second scale and a change in the direction of polariza-tion. More importantly, in such a case we are unlikelyto observe the lensed images. On the other hand, nearthe galactic plane we might expect Faraday Rotation dueto the global magnetic field almost aligned along the spi-ral arms. But the differential Faraday rotation measurebetween the arcsecond scale images of gravitational lenssystems would be marginal at less than about 10 rad m − ,and could be safely ignored unless the image separation istens of arcseconds. Nevertheless, this becomes important,for instance, when we attempt to estimate magnetic fieldsof galaxy–clusters using differential Faraday rotation be-tween multiple images produced by the gravitational lens-ing action of the cluster. Consequently, it would be diffi-cult to separate effects due to our Galaxy and an inter-vening galaxy-cluster located almost along the Galacticplane, unless the cluster magnetic field is at least of theorder of 100 nG. Nair et al had, indeed, pointed out suitability of the po-larization vector as a cosmological probe. The thrust ofthe analysis was that modification of the position angledue to inhomogeneities such as individual stars or gasclouds in the lens would have no role to play providedthe scale over which the polarization direction changesis always larger than the scale over which the inhomo-geneities can affect the background source. The problemwill, of course, be serious if the scale length of the sourcepolarization vector and the lens inhomogeneity conspireto become comparable. It is evident from the discussionin the previous section that the depolarization and Fara-day rotation introduced in our own Galaxy will be similarbetween the multiple images with separation of the or- der of arcseconds. Thus, if the depolarization is substan-tial when an image is intercepted by a cloud having par-tially ionized matter, the extinction in optical wavelengthswould be noticeably high. The image B in PKS1830–211,for instance, could be one such case, and we should treatsuch rare configurations with proper care. The rotation measure and the excess position angle at zerowavelength are computed from the best fit straight linebetween the measured polarization position angle and thesquare of the observed wavelength. The absolute rotationmeasure will have the uncertainty in the position angle bya multiple of π . In the case of differential Faraday Rota-tion, this problem is, by and large, absent and hence weexpect that the differential rotation measure is possibly abetter indication of the magnetic field in the lens than theabsolute rotation measure. For typical Faraday rotation inthe case of nearby galaxies, the expected rotation of theposition angle can exceed π at frequencies lower than ∼ , and − , this factor has been incorporated and as suchthere is no ambiguity of π . The errors in the observed po-sition angles are available only for , and Pat-naik (private communications) gives a value of 2 ◦ for thesystem . For systems like , the errorsare given only for one frequency and no error informationis available for other systems. Consequently, the χ val-ues shown in Table 1, with an assumed error of 2 ◦ shouldbe taken with caution. However, the errors in the differen-tial Faraday Rotation Measure are not severely affected bythis lack of error information in the data. For instance, asKing et al have demonstrated for the absolute FaradayRotation for the system , the fit and the un-certainty in the rotation measure are fairly good if we ac-cept the data at all the frequencies with equal weight. Fordifferential Faraday rotation between the multiple imagesin gravitational lens systems, the excess position angle atzero wavelength should be ideally zero, which providesan independent check on the reliability of the fits given inTable 1.5 .3 Faraday Rotation due to Spiral Galax-ies In our sample we have two lens systems, B0218+357 andPKS1830–211, where the lens is confirmed to be a spiralgalaxy. There is a large rotation measure ∼ − that is common to both the images A, B in the lens sys-tem B0218+357. The large intrinsic RM could be fromabsorbing clouds en route. On the other hand, the rela-tive fluxes of the two VLBI components change with fre-quency. We cannot, therefore, rule out the possibility thatpart of the change in the Faraday Rotation as function offrequency may be caused by the presence of milliarcsec-ond substructures. This is amply borne out by the detailed8.4 GHz VLBA images of Biggs et al . The polarizationimages of the core of both images exhibit a difference ofthe order of 10 degrees in the polarization direction be-tween the hot spots separated by a milliarcsecond. Con-sequently, in the absence of detailed VLBA polarizationmaps, we may not be in a position to estimate the rota-tion measure at the source. However, the difference inRM between images B and A, which is found to be 980 ±
10 rad m − when the Faraday Rotation angle for fourfrequencies between 8.4 and 43 GHz in Patnaik et al isused. This could conceivably be the contribution of thelens galaxy. The result should be trustworthy consideringthe error estimate, since for an uncertainty in the Posi-tion Angle of polarization vector of ∼ ◦ , the χ is 0.65for 2 degrees of freedom. With the neutral hydrogen col-umn density of ∼ × cm − and using the electroncolumn density N e ∼ cm − , we get from eq. (3),the mean field magnetic component, along the sightline,in the lensing galaxy of order µG . The magnetic fieldcould be even higher, provided the relative RM is not sig-nificantly overestimated. Both the lens systems Q0957+561 and B1422+231 havea giant elliptical galaxy as the dominant lens. While theformer is part of a galaxy-cluster, the latter might be asso-ciated with a group of galaxies. An analysis of the Fara-day Rotation measurements in these and similar systemscould provide evidence for possible existence of coherentlarge–scale magnetic fields in elliptical galaxies. Two important problems need to be addressed:(a)effects of time delay between the multiple images,which could become important for large time delays and(b)the Faraday Rotation introduced at the source. Possi-bly the first lens system Q0957+561, with a time delay of ∼
420 days is a good example for examination of these is-sues. The earlier measurements by Greenfield et al forthe system Q0957+561 reported rotation measures of Aand B images to be respectively -61 ± − and -160 ± − . This gives difference in the RM between Aand B images of ∼
100 rad m − which is at variance withthe corresponding difference of ∼
30 rad m − measuredby Patnaik et al . Indeed, Nair et al had pointed out theimportance of polarization measurements for time–delayestimations. Following the work of Biggs et al , the wellestablished time variability of the polarization vector wasused by Patnaik and Narasimha Patnaik & Narasimha tonumerically derive the time delay between the images inthe system 0218+357, thereby demonstrating the possibleeffects of time–delay on the differential Faraday Rotation.The discrepancy between Greenfield et al and Patnaik etal might be indicative of time–variability of the polar-ization vector in the system Q0957+561 over a time-scaleof a decade. This is a major problem while comparing po-larization position angles at two or more different epochs.There is also a need to discuss contribution of the in-tervening medium to the Faraday Rotation. Greenfield etal attributed the difference between the rotation mea-sures along the sightlines to the two images, of ∼ − entirely to the lensing cD galaxy with intra-cluster medium making a negligible contribution. Thisseems to be a reasonable deduction as also implied by ourbest fit excess P.A. of 2 degrees. Perry et al argue thatbecause of the availability of separate rotation measuresalong two sightlines to images A, B, it should be possi-ble to identify the contribution from the absorption linesystems detected en route at redshifts z abs = 1 . and z abs = 1 . . They speculate that the RM of -63 rad m − that is common to both images A and B should be as-signed to the absorption system located at z abs = 1 . because of its large inferred electron column density. Thisimplies ( N e ) < B k > µG ≃ cm − µG . With thereported N e ≈ . × cm − , the mean line-of-sight magnetic field in the lensing galaxy is inferred tobe < B k ≈≥ µG . On the other hand, the commonRotation Measure might merely be an artifact of the sub-6tructure in the source. A systematic analysis of the Ro-tation Measure along the multiple images of an extendedfeature like a jet, similar to what Kronberg et al did fora single image, will help resolve this important issue.Possibly the source structure in the lens systemB1422+231 has similarities with B0218+357 at VLBscales, and, not surprisingly, straightforward estimationof the absolute Faraday Rotation along individual imagesresults in a large value of RM for both these systems. Thesource in B1422+231 has smaller fraction of polarizationand hence, the change of polarization direction within themilliarcsecond scale structures is expected to affect therotation measure estimates. Interestingly, the differen-tial RM is coincidentally similar to the value arrived atfor 0957+561, where the rotation is probably caused by asimilar giant elliptical galaxy at comparable redshift. Thedifferent ratio of flux between the images in radio and op-tical is possibly an indication of extinction.The nature of the lensing object in the systemsMG1131+0456 and 1938+666 has remained enigmaticfor a long time, although the redshifts have now be-come available Kochanek et al ,Tonry & Kochanek .The main lens in both the systems appears to be a pas-sively evolving giant elliptical, but probably there aretwo clusters or rich groups of galaxies in the field ofMG1131+0456. Still, we believe that Rotation Measureestimates for these systems are important due to the pres-ence of extended structures in the background source. Weexpect Einstein Rings and giant arcs to provide valuableprobes of the large–scale magnetic field in the interven-ing object because, in principle, we can trace the gradualvariation of the position angle of the field vector along thequasi–linear image structure. With better long term obser-vations of these systems, we should be able to determinethe length scale, signature and strength of magnetic fieldin the lenses.For the system MG1131+0456, the reported FaradayRotation measurements Chen & Hewitt are primarilyfor bright regions of the Einstein Ring. It is conceiv-able that these features are, perhaps not identifiable withimages of the same source-region and hence we cannotspeculate on intrinsic magnetic field of any absorbers nearthe source. However, based on their detailed analysis (cf.Fig.6 Chen & Hewitt ), we speculate that the differencein Rotation Measure between spots R1 and R4, of ∼ − , is an indication of the presence of a magnetic field in the lens galaxy. This value is practically simi-lar to what is estimated for B0218+357. As emphasisedearlier, Faraday Rotation measurements for the systemMG1131+0456 will be valuable even if the image iden-tification may not be very robust.For the 4-image system 1938+666, the images C1 andC2 are highly magnified and are at sub–arcsecond sepa-ration; so they are unlikely to be affected by many of theother systematics discussed earlier. They have a small dif-ferential rotation measure of 56 rad m − , for the two im-ages separated by approximately 5 kiloparsecs at the lensand the excess position angle extrapolated to zero wave-length is negligible. But they have a common RotationMeasure of almost 500 rad/m which is also seen in theother two images.Thus, based on the differential Faraday Rotation be-tween the multiple images in 0957+561, 1938+666,MG1131+0456 and B1422+231, there appears to be sug-gestive evidence that giant elliptical galaxies may alsohave ordered magnetic field with strength comparable tothat of spiral galaxies. The fit for differential FaradayRotation is overall reasonable, but with lower fraction ofpolarization, it is certainly not as good as in the case ofB0218+357. In spite of the range of Faraday Rotationmeasure common to the images, it is remarkable that forthe four systems having small image separation, the dif-ferential Faraday Rotation (introduced by the main lens-ing galaxy alone) is of order 1000 rad m − for systemswith vastly different properties. This possibly suggeststhat by the redshift of 1, most of the magnetic fields we seein galaxies (of the order of a few microgauss) which werepresumably generated in the pre-galactic epochs, mighthave become saturated. It is tempting to surmise that per-haps already by redshift ∼
1, magnetic fields of strengthof the order of µ G are generated over length scales of ∼
10 kpc in the Universe. However, we should emphasiseagain that we have put together data on polarized imagestaken by various groups for different purposes and hence,the result may not be as robust as we might hope. Kro-nberg Kronberg emphasised the need for co-ordinatedVLBA/VLBI observations of extended multiply–imagedsystems to overcome many of the defects we have men-tioned, and make an attempt to get a reliable magneticfield profile at least in a few lens systems.It should, of course, be conceded that the presentmethod based on differential Faraday Rotation measure7aps is not without its limitations. The primary reasonfor the inadequacy of the data is that observations werenot intended for the measurement of the lens magneticfields. However, considering the importance of prob-ing the large–scale cosmic magnetic fields at high red-shift, we have used the available data for deducing theexistence of ordered magnetic field in external galaxies.Clearly, a determination of the large–scale magnetic struc-tures in the Universe at all scales is a fundamental prob-lem in astronomy and to address this question it is im-perative to undertake coordinated multifrequency, multi–epoch VLBI/VLBA observations. A selection of non-varying sources (e.g. knots) will help alleviate some ofthe problems associated with time delays between the im-ages. The existence of µ G global fields on kpc scale, that arealmost aligned along the spiral structure has been obser-vationally well established Beck et al . It is evident fromthe foregoing discussions that probably the global mag-netic field we see in the nearby spirals is not very differentfrom that found in galaxies at redshift of 0.5 to 1. We haveattempted to demonstrate that there is evidence suggestingthe existence of magnetic fields of microgauss strength,coherent over tens of kiloparsec scale even in giant el-liptical galaxies. Naturally, as the next step it is worth-while searching for global scale cluster magnetic fields.Galaxy–clusters are the largest gravitationally bound sys-tems and probably, the rich galaxy–clusters virialise afterthe formation of spiral galaxies.Many independent observations over the past decadehave provided evidence for cluster magnetic field of theorder of µ G . The synchrotron emission from radiohalos associated with several galaxy clusters has now beendetected. In particular, the radio halos of the Coma andseveral other clusters have been extensively studied re-cently to find that the halos have typically sizes ∼ Mpcand are concentrated close to the centre of X-ray emis-sion Kemper & Sarazin . Indeed, observations of thediffuse radio source in Abell 85 showing enhanced X-rayemission was effectively used by Bagchi et al to de- duce a magnetic field of ∼ µ G. The estimates of mag-netic fields in cluster halos, based on minimum energyarguments Miley range from a fraction of a microgaussto one microgauss. Thus, from radio observations of theComa cluster Beck , a lower bound on the magnetic fieldof a tenth of a microgauss in the halo region has beenplaced Raphaeli et al . A similar bound has also beenobtained from the gamma-ray flux above 100 MeV ob-served by EGRET Sreekumar et al . Remarkably, themagnetic field strength derived by Kim et al using theminimal energy arguments also yields similar estimatesfor the field.It should be recognized that the results for intraclus-ter global fields within the galaxy–clusters are not so ro-bust, although there is reliable information on the mag-netic fields in member radio galaxies in the clusters Bran-denberg & Subramanian . An impressive study of a sam-ple of sixteen Abell clusters was undertaken by Clarkeet al to probe intracluster magnetic fields using radioand X-ray data. From a statistical analysis of clustersources situated in the hot cluster gas and of the controlledbackground sources located behind the cluster medium,they found evidence for intracluster magnetic fields in theAbell clusters of order ∼ µ G ( l B / kpc) − / , l B beingthe coherence scale-length of the magnetic field. This ledthem to conclude that the high Faraday Rotation in em-bedded radio sources in galaxy–clusters indeed originatesfrom the foreground ICM Carilli & Taylor , Clarke ,Kronberg . However, Rudnick & Blundell argue thecase in favour of source–local magnetic fields. Greenfield,Roberts & Burke(1985) had earlier pointed out the use ofa radio lobe associated with the lensed image 0957+561Ato rule out a significant contribution to the Rotation Mea-sure from the ICM of the lens cluster for this system.It is clear that Faraday Rotation studies of both radiogalaxies in clusters as well as background radio sourcesaligned with the cluster can provide valuable probes forcluster magnetic fields. Thus, in the core of the cool-ing flow cluster 3C295, a magnetic field of order 12 µ Ghas been estimated with a coherence scale-length of about5–10 kpc based on the patchiness of RM Allen et al somewhat similar to the value given for 3C129 Taylor etal . The multi–frequency observations of the radio galax-ies embedded in the X-ray cluster 3C129 reveal signifi-cant difference in the Faraday RMs towards radio galax-ies 3C129.1 located at the cluster centre and 3C129 at its8eriphery, implying cluster magnetic field strength of ∼ µ G out to a distance of ∼
450 kpc. There is observeda remarkable trend of the rotation measures in Hydra Awhich is positive to the north of the nucleus and negativeto the south indicating a field strength ∼ µ G with a co-herence scale of ∼
100 kpc Taylor & Perley . The Fara-day Rotation measurements of multiply–imaged extendedbackground sources will be valuable to probe this kind ofstructures. The differences in RMs between various im-ages should filter out contributions from the backgroundsource and from our Galaxy with the residual RM pro-viding a value of N e < B > for a suitably averagedline-of-sight magnetic field component. An independentestimate of the electron column density from the thermalX-ray emission or from the measurements of Sunyaev–Zel’dovich effect would provide an estimate of the mag-netic field strength in the cluster and the change in thefield strength along the images of an extended structurewill, further pinpoint the coherence length of this field En-sslin & Vogt .Ideally, we should attempt to search for radio arcs inwell-studied Abell Clusters and measure the Faraday ro-tation along the arcs in order to deduce intracluster mag-netic field strength and its coherence length. Assumingthere is no active radio source in the lensing cluster con-tributing to the RM, we should enquire if we can deducean intracluster magnetic field of strength ∼ µ G coher-ent over a scale-length exceeding 100 kpc. Such an ex-ploration will be facilitated if we should be able to locatemagnetized sources such as polarized radio jets, starburstgalaxies and the associated synchrotron jets and even su-pernovae in distant galaxies which are suitably aligned be-hind the foreground lensing clusters. A multiply imagedpolarized Gamma Ray Burst (GRB) source together withits afterglow in radio located behind a foreground clusterlens would also serve a useful purpose of indicating thestrength of the intervening cluster magnetic field.It will be valuable to have radio maps in polarizationat a few closely separated frequencies to estimate theRMs. A candidate lens system like B , whichis a six–image configuration of a high redshift source ( z source = 3 . having a flux of 66 mJy at 5 GHz fre-quency (with unknown lens redshift) could have the ad-vantage of tracing the large-scale magnetic field of the in-tervening lens. Due to the six image nature of the system,the problem associated with time delay between the im- ages might be alleviated. It will be useful to examine un-confirmed lens candidates, especially radio-weak systemswith substantial image separations. These could serve asideal clusters mass dark lenses for probing the intraclus-ter magnetic fields. Amongst the six dozen or so lensedquasars discovered to date most have few arcsecond im-age separations which can be produced by galaxy-masslenses. However, theoretical CDM models of structureformation predict large quasar image separations of sev-eral arcsec capable of being generated by dark matter ag-gregates. Indeed, Inada et al have recently reported thediscovery of a quadruply lensed quasar with a maximumimage separation of 14.62 arcsec, an evident case of grav-itational lensing by a dark matter dominated interveningobject. There should be several such large-separation im-age configurations with hitherto undetected dark clustermass objects acting as lenses.A favourable set of observations for Faraday Rotationof lensed background sources as well as embedded radiosources within the cluster, for a range of cluster redshifts,could provide valuable information on the possible originof magnetic fields in galaxy clusters:1. Seed magnetic field produced during the protoclus-ter formation Subramanian et al . This will be aglobal field spread over Mpc scale which is likelyto be rather weak, unless clusters grew by mergers.2. Field produced by embedded radio sources: The jetpropagating into the intracluster medium will intro-duce an oriented field, the strength of which will de-crease away from the radio source.3. Local fields due to anisotropic electron velocity dis-tribution Okabe & Hattori : Chandra observationsof rich galaxy clusters show evidence for sharp dis-continuity in the density of X-ray emitting regions aswell as temperature over length scales of a few hun-dred kpc in systems like Abell2142 where the elec-tron anisotropic velocity could drive a Biermann cur-rent.A systematic observational study of these three effectswill be valuable in understanding the substructures ingalaxy clusters.9 Conclusions
The multiply-imaged gravitational lens systems can be ef-fectively used to establish the presence of global orderedmagnetic fields in lensing galaxies and to estimate theiraverage field strength. It turns out that the difference inPosition Angles between various images is generally areliable indicator of the existence of magnetic fields inintervening lenses. An advantage of multiple path RMmeasurements is that they are potentially capable of sens-ing the direction as well as coherence length-scale of themagnetic field. We have further argued that the contribu-tions due to inhomogeneities in our Galaxy need not be amajor hurdle in estimating these ordered magnetic fields,unless the depolarization effects between images turns outto be substantial. The compact flat–spectrum sources willhave substructures in polarization which will naturally besubject to differential magnification across the image, ifthe source is in the vicinity of a caustic. Evidently, a non–varying polarized radio source would be ideal for diferen-tial Faraday Rotation measurements and equally to moni-tor the lensed images for polarization changes in order tocorrect for the time–delay. The main conclusions of ourstudy are the following:1. There appears to be suggestive evidence for the pres-ence of coherent, large scale magnetic field in thelens systems we have examined, in particular, in gi-ant elliptical lens galaxies.2. Substantial amount of Rotation Measure common toall the images is observed in almost all the cases,which probably originates in the medium in theneighbourhood of the source or may even be a resultof not resolving the source substructures.3. In spite of a range of absolute Rotation Measures forthe various systems and along different images, thedifferential Rotation Measure appears to be in therange of several hundred rad m − for the ellipticalgalaxy lenses and ∼ − for the spirals.4. The available sample of lens systems do not seem toindicate any obvious evolution with redshift of theobserved Rotation Measure. Acknowledgements
We are grateful to Professor P. Kronberg for his encour-agement and valuable comments which have led to a con-siderable improvement in the manuscript. We thank Pro-fessors J.P. Ostriker, A. Olinto, G. Memon and K. Subra-manian for several useful discussions. DN is grateful toJapan Society for the Promotion of Science for an Invita-tional Research Fellowship. SMC is grateful to the DAE–BRNS Senior Scientist scheme for a fellowship and to theInstitute of Astronomy, Cambridge for hospitality.
References [1] Beck, R., 2004, ApSpS, 289, 293[2] Hogan, C.H., 1983, Phys. Rev. Lett., 51, 1488[3] Turner, M.S. and Widrow, L.M., 1988, Phys. Rev.,D37, 2743[4] Subramanian, K., Narasimha, D. and Chitre, S.M.,1994, MNRAS, 271, P et al. , 1999, MNRAS, 307, 1 P [16] Patnaik, A.R., Menten, K.H., Porcas, R.W. andKemball, A.J., 2001, in Gravitational Lensing: Recentprogress and future goals. ASP, proceedings, eds. T.G.Brainerd, C.S. Kochaneck, P et al , 2003, MNRAS, , 599.[22] Rand, R.J., Kulkarni, S.R., 1989, ApJ, 343, 760[23] Sofue, Y., Fujimoto, M., Wielebinski, R., 1986,ARA & A, 24, 459[24] Nair, S., Narasimha, D., Rao, A.P., 1993, ApJ, 407,46.[25] Biggs, A.D. et alet al