J. Astrophys. Astr. (1993) 14, 121–129

Straight Arc in Abell 2390

D. Narasimha & S. M. Chitre Theoretical Astrophysics Group, Tata Institute of Fundamental 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 -cluster Abell 2390 is investigated in the framework of a gravitational lens model that invokes a single background source galaxy. An extended source galaxy at a of 0·913 is being marginally lensed by the foreground X-ray cluster of at a redshift of 0·231. It is demonstrated that a single lensed galaxy lying on or very near to the lip caustic of the cluster lens is capable of reproducing the linear morphology with the observed breaks.

Key words: Gravitational lensing—straight arc—lip caustic—galaxy clusters

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 opened up a whole new area to study features associated with high redshift objects. A sufficient amount of evidence has been accumulated to demonstrate that the luminous arcs observed in the cores of rich clusters are manifestations of background galaxies being distorted and magnified by the gravitational lensing action of the intervening clusters. Besides, Fort et al. (1988) have reported detection of several small elongated structures in the cluster Abell 370, which finds a straightforward interpretation in terms of distorted singly-lensed images of distant galaxies by a foreground cluster. About a dozen galaxy clusters have revealed the presence of giant arcs or arclets since 1986 (refer Fort 1991). Amongst these, in at least four cases the features lying close to the centre of the cluster are observed to have a linear morphology. Even though the presence of tangentially amplified curved arcs extending over several arc seconds has been revealed in the cores of rich clusters, this, of course does not mean that there are no linear features present in these clusters; it merely shows that the linear features may not have been revealed in the magnitude-limited searches. In fact, it is expected that there should be a range of , with values smaller than those associated with the giant arcs, at which a number of background galaxies may be located that could be imaged into linear structures. Such source-galaxies may be intrinsically faint to have manifested in the present searches. The first such unusual configuration with a nearly linear morphology was reported by Pello et al. (1991) in the rich cluster of galaxies, Abell 2390 (z = 0·23). This extended straight feature is made up of segments which are tangentially amplified; a high resolution imaging of the 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 a bimodal potential for the lens with the source located at the saddle point between the two deflecting objects, which was, however, not supported by observations (Soucail et al. 1987). Another possibility was discussed by Kassiola, Kovner & Blandford (1992), who proposed a model to explain the observed features including the breaks in the straight arc-like image of Abell 2390 by invoking two source galaxies at a redshift z = 0·913 that are lensed by a cluster aided by a visible and a . In the present work we outline a theoretical lens model to account for the observed morphology of Abell 2390 that employs only a single background source galaxy. We present 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 and just above the critical value for multiple imaging and that straight arcs should be largely oriented along the minor axis of the lensing cluster. We suggest that in a flux-limited sample of rich galaxy-clusters, a good many should exhibit the presence of highly magnified background galaxies, some of which are likely to display the long linear structures extending over 10 arcsec. Our main motivation is to get an idea of the 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, as seen in Abell 370, can be simulated with the background source galaxy lying on a fold 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 observed morphology of the straight arc in Abell 2390, Kassiola et al. (1992) invoke two background galaxies for the source that is situated very close to a beak-to-beak calamity formed by the potentials of the foreground cluster aided by a visible galaxy on 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 2390 which is a long linear structure of over 15 arcsec extent and an approximate width of 1·3 arcsec. It has two breaks which separate the arc in three segments of comparable optical brightness. We adopt a scenario wherein there is only a single extended source galaxy at a redshift z = 0·913 that is being marginally lensed by the foreground at a redshift z = 0·231 (refer Kovner (1987) for a detailed discussion of the phenomenon of marginal lensing; also Narasimha (1993)). For this purpose the gravitational lens parameters are so chosen as to be close to the critical values, i.e., the surface mass density, 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 specified by eccentricity e and a mass density distribution which is taken to be the truncated King-type:

where rc is the core-radius and n is the cut-off radius in units of rc. With this smooth distribution 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 a family of parameters, rc ,σv ,e , . . ., which should be carefully chosen to lie in a physically and 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 the straight arc Abell 2390. The solid curve indicates the line-like morphology of the lip caustic in the source plane, while the corresponding critical curve in the image plane is shown by the large dotted ellipse. The cluster-centre is marked by a cross and one of the elliptical contours of the background source galaxy is seen intersecting the lip caustic with its major axis almost orthogonal to the caustic. With such a configuration, a large part of the background galaxy is singly imaged and only a part is mapped into a three-image region. We can clearly see from the model contour plot of the straight arc in Abell 2390 the presence of prominent breaks in the form of two necks in its morphology. The constricted feature in the extended segment of the map is the result of the merging of images; the exact nature of the merging region would naturally depend on the surface brightness of the source in the region of the lip caustic. We have obtained the 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 with the help of a reasonable set of parameters for the lensing cluster (Table 1), assuming a King-type density distribution. This yields a transversely amplified linear structure of over 20 arcsec extent, with a width of nearly 1·3 arcsec. We find that the most natural model to account for the straight arc observed in the rich cluster Abell 2390 should involve the lensing of a single high redshift galaxy by a foreground cluster just at the critical surface mass density. The linear structure is evidently an outcome of a marginally lensed galaxy with the formation of a line-like cusp caustic intersecting the 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 the lip caustic in the source plane, while the corresponding critical curve in the image plane is indicated by the larger dotted ellipse. The cross represents the centre of the cluster lens and one of the contours of the background source is shown by the small broken ellipse lying practically inside the lip caustic. The contour map (thin broken lines) is produced by convolving the image with a beam-size of (0".45, 0"45). who invoke two background source galaxies in order to simulate the straight arc in Abell 2390. We are not too certain about the bright feature extending from the larger segment 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 theoretical model. The linear features supply us with a very valuable handle to probe the structure of 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 provides us with an important observational diagnostic for studying the cluster properties; thus, straight arcs reveal the orientation of the minor axis of the cluster. There will always exist a range of redshifts at which a source galaxy may be located behind the lensing cluster. The linear arc-like morphology would, however, result only from marginally lensed galaxies that are situated behind the cluster in a narrow range of redshifts corresponding to the critical surface mass density. These should manifest as tangentially amplified straight features of ≳ ten arcsec extent and oriented approximately 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; this has 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 centre located behind the deflecting cluster at redshifts in the vicinity of the one that is responsible for producing the straight arc. These should be distorted in shape as arclets which will manifest as features largely aligned with the straight arc, being elongated orthogonal to the major axis of the cluster. But such arclets will be placed progressively at larger radial distances from the centre within a core-radius, although fainter by some 4–5 magnitudes in relation to the dominantly luminous straight arcs. With the favourable placement of the background source galaxies producing such arclets, one might even be able to locate the position of the cluster-centre from the observed curvature of these small arcs. We have shown in Fig. 2(a), typical linear features 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 redshift z = 0.231 by its lensing action on two background galaxies shown by broken ellipses, located at redshifts (a) zs = 0·86 and zs= 1.2, with the eccentricity ε = 0.85 for the cluster, (b) zs = 1.4 and zs = 1.65 with its eccentricity ε = 0.7 for the cluster. The solid curves show the lip caustic for zs = 1.2 and line-like caustic for zs = 0.86 in the source plane. The solid ellipse-like curve represents the critical curve corresponding to the smaller redshift and the broken ellipse-like curve represents the critical curve corresponding to the higher redshift. The contour map is generated 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 redshift zs = 0.86 and the other at zs = 1.2, lying on the lip caustic. Notice the feature associated with the image of the source galaxy at z = 1.2, which appears as a detached segment of the main linear arc. Likewise, Fig. 2(b) displays the image configuration with two nearly parallel linear features that result from the lens action of a rich cluster at a redshift z = 0·231 and eccentricity ε = 0·7, with the background source-galaxies located at zs=1.4 and zs = 1.65. We imagine such image morphologies to be reasonably common, if our model for generating linear features is tenable. It is remarkable that linear features in this model can arise from background source-galaxies, having redshifts in the range ∆z ≃ 0·4. We should also like to point out that for extended arc-like morphologies, a very powerful diagnostic probe could become available by observing the spatial velocity profile. Thus, the spectroscopic analysis in the emission line of the linear arc Abell 2390 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 , then by invoking the Tully-Fisher relation, one might hope to deduce the absolute magnitude of the source and infer the intrinsic source luminosity to within an accuracy of half a magnitude. But one should be aware of some of the limitations of this method. In the first place, we do not have a priori information of the inclination of the source spiral galaxies with respect to the line of sight. But, to some extent, this is a problem for the validity and application 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 one might be able to estimate the inclination of the background galaxy with the line of sight. On the other hand, a reliable knowledge of the accurate velocity-gradient along 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 velocity in the two or three segments could provide a few extra constraints on the rotational velocity than what might be expected for an unlensed spiral in, say, Coma cluster, despite other limitations. A comparison with the observed magnitude would then supply us with the information about the magnification due to the lensing action of the cluster. One can also surmise the linear magnification from the shape and size of the observed images. Alternatively, the number count of galaxies in the X-ray map of the cluster Abell 2390 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 the observed image configuration, for comparison with the values derived using the Tully-Fisher relation or the linear size estimates. It is hoped that since extended arcs in rich clusters are likely to be background galaxies that are magnified typically by an order of magnitude, these features could provide valuable information regarding the luminosity-function of galaxies at large redshifts. By undertaking an imaging of the field of the lensing cluster upto faint limits and carrying out a spectroscopic analysis of the arcs, it might be possible to study 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 was substantially different in the past, like the faint blue galaxies detected by Guhathakurta et al. (1990). This, of course, would require an accurate knowledge of the magnification of the arcs. A more definitive result could become available on the mass function of rich clusters of galaxies. This would result from imaging of all the clusters having a range of redshifts in a given region and measuring the minimum redshift associated with the linear 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 available with the cluster redshifts varying in the range ~ 0.2–0.56. Consequently, the exercise of making any rough statistical estimate of probabilities would become unreliable.

In the theoretical models simulating linear features, one must examine the possible

role of a cD galaxy located in the⋝ central region of the lensing cluster. In general, if 12 the mass of the cD galaxy is 10 Μ☼ 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 we adopt a departure of not more than ~ 1/2 arc sec from the collinearity of individual image segments (i.e. typical angular scale of the source flux profile) and the ratio of major to minor axes of the image morphology to exceed typically a value of 5, in order to designate a generally acceptable definition of a straight arc. Clearly, the eccentricity of the lensing cluster also has a significant influence on the morphology of the image system. Thus, for obtaining a largely linear structure we require a modest to 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 of 0.83–1.25, while for ε = 0.7 the corresponding redshift range for providing a linear morphology is 1.4–1.65, with the foreground cluster located of z = 0.231 and having a core radius ~ 160 kpc and velocity dispersion ~ 1000 km/sec. It is clear from the foregoing discussion that in lensing scenarios involving straight arcs, 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-light ratio, or even estimate the masses of individual galaxy-members in the cluster, and convert any of the above three possibilities into a surface mass density for the deflecting cluster. In short, we should make every effort to gain some decent observational handle on the surface luminosity, redshift, mass density of the rich clusters which exhibit straight arcs, if we wish to use the properties of these features for deriving cosmological parameters. It is tempting to use the straight arc morphologies in rich clusters as distance indicators, 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 lensing cluster will give a reasonably reliable estimate, to within 20%, of Σ, the surface mass density of the cluster. Since the appearance of a linear feature necessarily involves

2 c marginal lensing with Σ close to, but just above ∑ c = , we can reasonably 4πGDeff adopt the equation Σ = Σc to solve for Deff. With the knowledge of the lens and source redshifts and possibly reliable estimate of Σ from a variety of considerations, we should in principle be able to 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 indication of 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 Fort for making available some of the unpublished maps of A2390.

References

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