J. Astrophys. Astr. (1993) 14, 121–129 Straight Arc in Abell 2390 D. Narasimha & S. M. Chitre Theoretical Astrophysics Group, Tata Institute ofFundamental Research, Homi Bhabha Road, Bombay 400 005 and School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London Received 1993 May 18; accepted 1993 October 29

Abstract. The straight arc in the galaxy-cluster Abell 2390 is investigatedin the framework of a gravitational lens model that invokes a singlebackground source galaxy. An extended source galaxy at a redshift of0·913 is being marginally lensed by the foreground X-ray cluster of galaxies at a redshift of 0·231. It is demonstrated that a single lensed galaxy lyingon or very near to the lip caustic of the cluster lens is capable of reproducingthe linear morphology with the observed breaks. Key words: Gravitational lensing—straight arc—lip caustic—galaxyclusters

1. Introduction

The detection of the first giant luminous arc in the Central region of the rich galaxy-cluster Abell 370 by Lynds & Petrosian (1986) and Soucail et al. (1987) has openedup a whole new area to study features associated with high redshift objects. A sufficientamount of evidence has been accumulated to demonstrate that the luminous arcsobserved in the cores of rich clusters are manifestations of background galaxies beingdistorted and magnified by the gravitational lensing action of the intervening clusters.Besides, Fort et al. (1988) have reported detection of several small elongated structuresin the cluster Abell 370, which finds a straightforward interpretation in terms ofdistorted singly-lensed images of distant galaxies by a foreground cluster.

About a dozen galaxy clusters have revealed the presence of giant arcs or arcletssince 1986 (refer Fort 1991). Amongst these, in at least four cases the features lyingclose to the centre of the cluster are observed to have a linear morphology. Eventhough the presence of tangentially amplified curved arcs extending over several arcseconds has been revealed in the cores of rich clusters, this, of course does not meanthat there are no linear features present in these clusters; it merely shows that thelinear features may not have been revealed in the magnitude-limited searches. In fact,it is expected that there should be a range of redshifts, with values smaller than thoseassociated with the giant arcs, at which a number of background galaxies may belocated that could be imaged into linear structures. Such source-galaxies may beintrinsically faint to have manifested in the present searches. The first such unusualconfiguration with a nearly linear morphology was reported by Pello et al. (1991) inthe rich cluster of galaxies, Abell 2390 (z = 0·23). This extended straight feature ismade up of segments which are tangentially amplified; a high resolution imaging ofthe centre of Abell 2390 with an I-band filter clearly shows two breaks in the linear 121

122 D. Narasimha & S. M. Chitre morphology (Fort 1992). The infrared observations by Ellis in the K-band, however,shows a substantially bright feature extending from the longer segment of the arc.

One of the first suggestions for the linear shape of the arc was the existence of abimodal potential for the lens with the source located at the saddle point betweenthe two deflecting objects, which was, however, not supported by observations (Soucailet al. 1987). Another possibility was discussed by Kassiola, Kovner & Blandford(1992), who proposed a model to explain the observed features including the breaksin the straight arc-like image of Abell 2390 by invoking two source galaxies at aredshift z = 0·913 that are lensed by a cluster aided by a visible and a dark galaxy.

In the present work we outline a theoretical lens model to account for the observedmorphology of Abell 2390 that employs only a single background source galaxy. Wepresent arguments that it is possible to simulate the linear morphology of the arc,provided the projected surface mass density of the deflecting cluster is close to andjust above the critical value for multiple imaging and that straight arcs should belargely oriented along the minor axis of the lensing cluster. We suggest that in aflux-limited sample of rich galaxy-clusters, a good many should exhibit the presenceof highly magnified background galaxies, some of which are likely to display the longlinear structures extending over 10 arcsec. Our main motivation is to get an idea ofthe range of redshifts at which the lensed structures could exhibit linear morphology.

2. Lens model for Abell 2390

It has been demonstrated by Grossman & Narayan (1988) and Narasimha & Chitre(1988) that a single giant, tangentially amplified, luminous arc-like morphology, asseen in Abell 370, can be simulated with the background source galaxy lying on afold caustic. But, while large curved arc-like images result from a general fold caustic,one requires the presence of lip catastrophes for producing straight arcs (refer Kassiola,Kovner & Blandford (1992) for a very elegant and illuminating analysis of the ‘lip’and ‘beak-to-beak’ configurations). However, in order to generate the observedmorphology of the straight arc in Abell 2390, Kassiola et al. (1992) invoke twobackground galaxies for the source that is situated very close to a beak-to-beakcalamity formed by the potentials of the foreground cluster aided by a visible galaxyon one side of the arc and a comparable dark galaxy on the other.

We propose to outline a theoretical lens model for the straight arc in Abell 2390which is a long linear structure of over 15 arcsec extent and an approximate widthof 1·3 arcsec. It has two breaks which separate the arc in three segments of comparableoptical brightness.

We adopt a scenario wherein there is only a single extended source galaxy at aredshift z = 0·913 that is being marginally lensed by the foreground galaxy cluster ata redshift z = 0·231 (refer Kovner (1987) for a detailed discussion of the phenomenonof marginal lensing; also Narasimha (1993)). For this purpose the gravitational lensparameters are so chosen as to be close to the critical values, i.e., the surface massdensity, Σ, of the lensing cluster must be just above the critical surface density,

Straight Arc in Abell 2390 123

We consider an oblate spheriodal lens cluster given by

For the purpose of computation we adopt a model for the lensing cluster specifiedby eccentricity e and a mass density distribution which is taken to be the truncatedKing-type:

where rc is the core-radius and n is the cut-off radius in units of rc. With this smoothdistribution the total mass of the cluster is given by

The line-of-sight velocity dispersion, σν is given by

Clearly, the resulting lens model will be, by no means unique, as it depends on afamily of parameters, rc ,σv ,e , . . ., which should be carefully chosen to lie in a physicallyand observationally admissible region of the parameter space (refer Narasimha,Subramanian & Chitre (1982) for an outline of the mathematical formalism).

3. Discussion and conclusions We have illustrated in Fig. 1 the source and image planes corresponding to thestraight arc Abell 2390. The solid curve indicates the line-like morphology of the lipcaustic in the source plane, while the corresponding critical curve in the image planeis shown by the large dotted ellipse. The cluster-centre is marked by a cross and oneof the elliptical contours of the background source galaxy is seen intersecting thelip caustic with its major axis almost orthogonal to the caustic. With such aconfiguration, a large part of the background galaxy is singly imaged and only a partis mapped into a three-image region.

We can clearly see from the model contour plot of the straight arc in Abell 2390the presence of prominent breaks in the form of two necks in its morphology. Theconstricted feature in the extended segment of the map is the result of the mergingof images; the exact nature of the merging region would naturally depend on thesurface brightness of the source in the region of the lip caustic. We have obtainedthe image-map by convolving the image with a beam-size of 0·45 arcsec FWHM.

It is thus possible to reproduce the observed linear morphology of Abell 2390 withthe help of a reasonable set of parameters for the lensing cluster (Table 1), assuminga King-type density distribution. This yields a transversely amplified linear structureof over 20 arcsec extent, with a width of nearly 1·3 arcsec. We find that the mostnatural model to account for the straight arc observed in the rich cluster Abell 2390should involve the lensing of a single high redshift galaxy by a foreground clusterjust at the critical surface mass density. The linear structure is evidently an outcomeof a marginally lensed galaxy with the formation of a line-like cusp caustic intersectingthe source galaxy. Note that our model differs from that of Kassiola et al. (1992)

124 D. Narasimha & S. M. Chitre

Figure 1. The morphology of the straight arc Abell 2390, where the solid curve shows thelip caustic in the source plane, while the corresponding critical curve in the image plane isindicated by the larger dotted ellipse. The cross represents the centre of the cluster lens andone of the contours of the background source is shown by the small broken ellipse lyingpractically inside the lip caustic. The contour map (thin broken lines) is produced by convolvingthe image with a beam-size of (0".45, 0"45). who invoke two background source galaxies in order to simulate the straight arc inAbell 2390. We are not too certain about the bright feature extending from the largersegment of the arc which Ellis has reported as being manifest in the K-band. However,there is no obvious evidence for such a feature in the I-band observations of Fort(1992). We have, therefore, opted not to incorporate this feature in our theoreticalmodel.

The linear features supply us with a very valuable handle to probe the structureof the deflector and the source. We can see from Fig. 1 that the major axes of the

Table 1. Lens model.

Straight Arc in Abell 2390 125

lensing cluster and the critical curve are pretty much aligned. Such a feature providesus with an important observational diagnostic for studying the cluster properties;thus, straight arcs reveal the orientation of the minor axis of the cluster. There willalways exist a range of redshifts at which a source galaxy may be located behind thelensing cluster. The linear arc-like morphology would, however, result only frommarginally lensed galaxies that are situated behind the cluster in a narrow range ofredshifts corresponding to the critical surface mass density. These should manifestas tangentially amplified straight features of ten arcsec extent and orientedapproximately perpendicular to the major axis of the cluster. We would thus expect,in any flux-limited sample, to detect the nearly straight arc-like morphologies; thishas been borne out by the discovery of some 4 straight arcs in the last few years(refer Fort 1990; Mathez et al. 1992).

There will naturally be other galaxies within a core-radius from the cluster centrelocated behind the deflecting cluster at redshifts in the vicinity of the one that isresponsible for producing the straight arc. These should be distorted in shape asarclets which will manifest as features largely aligned with the straight arc, beingelongated orthogonal to the major axis of the cluster. But such arclets will be placedprogressively at larger radial distances from the centre within a core-radius, althoughfainter by some 4–5 magnitudes in relation to the dominantly luminous straight arcs.With the favourable placement of the background source galaxies producing sucharclets, one might even be able to locate the position of the cluster-centre from theobserved curvature of these small arcs. We have shown in Fig. 2(a), typical linearfeatures that might result from the lensing action of a foreground cluster at redshift

Figure 2(a)

≳

126 D. Narasimha & S. M. Chitre

Figure 2(b) Figure 2(b) Two parallel linear features produced in the core-region of a cluster at a redshiftz = 0.231 by its lensing action on two background galaxies shown by broken ellipses, locatedat redshifts (a) zs = 0·86 and zs= 1.2, with the eccentricity ε = 0.85 for the cluster, (b) zs = 1.4and zs = 1.65 with its eccentricity ε = 0.7 for the cluster. The solid curves show the lip causticfor zs = 1.2 and line-like caustic for zs = 0.86 in the source plane. The solid ellipse-like curverepresents the critical curve corresponding to the smaller redshift and the broken ellipse-likecurve represents the critical curve corresponding to the higher redshift. The contour map isgenerated by convolving the images with a beam-size of (0".45, 0".45).

z = 0.231 and eccentricity ε = 0·85, on two background galaxies, one at redshiftzs = 0.86 and the other at zs = 1.2, lying on the lip caustic. Notice the feature associatedwith the image of the source galaxy at z = 1.2, which appears as a detached segmentof the main linear arc. Likewise, Fig. 2(b) displays the image configuration with twonearly parallel linear features that result from the lens action of a rich cluster at aredshift z = 0·231 and eccentricity ε = 0·7, with the background source-galaxies locatedat zs=1.4 and zs = 1.65. We imagine such image morphologies to be reasonablycommon, if our model for generating linear features is tenable. It is remarkable thatlinear features in this model can arise from background source-galaxies, havingredshifts in the range ∆z 0·4.

We should also like to point out that for extended arc-like morphologies, a verypowerful diagnostic probe could become available by observing the spatial velocityprofile. Thus, the spectroscopic analysis in the emission line of the linear arc Abell2390 by Pello et al. (1991) and later detailed investigation by Soucail & Fort (1991)indicate a velocity gradient along the arc. If this were interpreted as reflecting an

≃

Straight Arc in Abell 2390 127

intrinsic rotation in the background spiral galaxy, then by invoking the Tully-Fisherrelation, one might hope to deduce the absolute magnitude of the source and inferthe intrinsic source luminosity to within an accuracy of half a magnitude. But oneshould be aware of some of the limitations of this method. In the first place, we donot have a priori information of the inclination of the source spiral galaxies withrespect to the line of sight. But, to some extent, this is a problem for the validity andapplication of the Tully-Fisher relation even for the local spirals. However, if a two-dimensional velocity profile in the extended linear structure were available, then onemight be able to estimate the inclination of the background galaxy with the line ofsight. On the other hand, a reliable knowledge of the accurate velocity-gradientalong the linear feature might prove sufficient, provided, of course, the intensity-weightage was properly incorporated in the model computation of the rotation-profile(refer Narasimha & Chitre 1993). The positions of breaks and comparison of velocityin the two or three segments could provide a few extra constraints on the rotationalvelocity than what might be expected for an unlensed spiral in, say, Coma cluster,despite other limitations. A comparison with the observed magnitude would thensupply us with the information about the magnification due to the lensing action ofthe cluster. One can also surmise the linear magnification from the shape and sizeof the observed images.

Alternatively, the number count of galaxies in the X-ray map of the cluster Abell2390 would give us a reasonable measure of the core-radius of the cluster. In addition,if we are able to determine independently the velocity dispersion of the galaxy-cluster,then the theoretical models are expected to give the magnification required for theobserved image configuration, for comparison with the values derived using theTully-Fisher relation or the linear size estimates.

It is hoped that since extended arcs in rich clusters are likely to be backgroundgalaxies that are magnified typically by an order of magnitude, these features couldprovide valuable information regarding the luminosity-function of galaxies at largeredshifts. By undertaking an imaging of the field of the lensing cluster upto faintlimits and carrying out a spectroscopic analysis of the arcs, it might be possible tostudy the luminosity function of galaxies. We can examine the question, for example,if there were phases in the galactic evolution in which the luminosity-function wassubstantially different in the past, like the faint blue galaxies detected by Guhathakurtaet al. (1990). This, of course, would require an accurate knowledge of the magnificationof the arcs.

A more definitive result could become available on the mass function of rich clustersof galaxies. This would result from imaging of all the clusters having a range ofredshifts in a given region and measuring the minimum redshift associated with thelinear feature or substantially magnified one in the cases of those clusters manifesting the lensed features. The statistics would then tell us the value of the surface mass density.Σ Σc' for those clusters which reveal the existence of these features; for other cases,the statistics will furnish bounds on the surface mass density. At present, however,only for about half of the twelve galaxy-clusters, the redshift information is availablewith the cluster redshifts varying in the range ~ 0.2–0.56. Consequently, the exerciseof making any rough statistical estimate of probabilities would become unreliable.

In the theoretical models simulating linear features, one must examine the possiblerole of a cD galaxy located in the central region of the lensing cluster. In general, ifthe mass of the cD galaxy is 1012Μ☼ and its linear size is around 100 Kpc, the

≃

⋝

128 D. Narasimha & S. M. Chitre extended image structure will then be expected to show a more pronounced curvature.This curvature would essentially reflect the clumpiness in the cluster mass-distribution(refer Narasimha 1993).

For our purpose, for distinguishing between linear features and curved arcs weadopt a departure of not more than ~ 1/2 arc sec from the collinearity of individualimage segments (i.e. typical angular scale of the source flux profile) and the ratio ofmajor to minor axes of the image morphology to exceed typically a value of 5, inorder to designate a generally acceptable definition of a straight arc. Clearly, theeccentricity of the lensing cluster also has a significant influence on the morphologyof the image system. Thus, for obtaining a largely linear structure we require a modestto large eccentricity for the lens cluster. It turns out that for an eccentricity ε = 0.85,we get such features with background source galaxies lying in the redshift range of0.83–1.25, while for ε = 0.7 the corresponding redshift range for providing a linearmorphology is 1.4–1.65, with the foreground cluster located of z = 0.231 and havinga core radius ~ 160 kpc and velocity dispersion ~ 1000 km/sec.

It is clear from the foregoing discussion that in lensing scenarios involving straightarcs, what we can determine from observations is the cosmology-dependent quantity

. This should enable us to deduce the value of Σc, according to our

prescription of marginal lensing for producing the morphology of straight arcs. At this stage we can use the observational information in one or more of the

following manners: 1. We can count the number of galaxies per unit angular area, in the rich clusters

exhibiting straight arcs. 2. We can measure the optical flux per unit angular area, from the rich clusters. 3. We can similarly measure the flux-density of the rich cluster in any other waveband,

such as its X-ray emission.

It should then be possible to make a plausible assumption about the mass-to-lightratio, or even estimate the masses of individual galaxy-members in the cluster, andconvert any of the above three possibilities into a surface mass density for thedeflecting cluster. In short, we should make every effort to gain some decentobservational handle on the surface luminosity, redshift, mass density of the richclusters which exhibit straight arcs, if we wish to use the properties of these featuresfor deriving cosmological parameters.

It is tempting to use the straight arc morphologies in rich clusters as distanceindicators, provided, of course, we have a measurement of the velocity dispersion (or,the mass) and the core-radius to better than 10%. Such an information on the lensingcluster will give a reasonably reliable estimate, to within 20%, of Σ, the surface massdensity of the cluster. Since the appearance of a linear feature necessarily involves

marginal lensing with Σ close to, but just aboveeffGD

cc

π4

2=∑ , we can reasonably

adopt the equation Σ = Σc

to solve for Deff. With the knowledge of the lens and source redshifts and possiblyreliable estimate of Σ from a variety of considerations, we should in principle be ableto determine the Hubble constant, H0, for an assumed value of q0. We suggest that

Straight Arc in Abell 2390 129

properties of linear features in cores of rich clusters might very well provide indicationof the value of the Hubble constant, and hopefully, also the deceleration parameter.

Acknowledgements

We are grateful to Rajaram Nityananda for helpful comments and to Bernard Fortfor making available some of the unpublished maps of A2390.

References

Fort, B. 1990, in Toulouse Workshop on Gravitational Lensing Eds. Y. Mellier, B. Fort &G. Soucail (SpringerVerlag), p. 221.

Fort, B. 1991, in “Gravitational Lenses”, Proceedings, Hamburg Eds. R. Kaysar, T. Schramm &L. Nieser (Springer-Verlag), p 267.

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