4.5 Microstructures in Arcs and Minilensing by Small Dark Halos

Perturbations of caustics by intervening masses can locally change the length and shape of arcs or locally increase the intensity of unresolved arc substructures. Dramatic perturbations could even be responsible for the complete vanishing of an arc segment (Hammer 1987). The perturbation of caustics by a smaller interloping lens can be understood by considering that the magnification matrix degenerates to a single eigenvector tangent to the critical curve. Indeed the distortion of the images of objects close to the critical line corresponds mainly to a stretching along the direction of merging. Therefore, the angular coordinates of the source can be developed in polynomial form along the direction of merging (Kassiola, Kovner & Fort 1992). Fig. 19 gives a short description of the effect of perturbations on two merging images of an extended object near a fold. In this case the functional form of the unperturbed fold is approximated by a second-degree polynomial. If a large perturbation from a nearby galaxy is added, the image can be split into many components (Fig. 19).

Figure 19. Gravitational distortion induced by a perturbation close to a giant fold arc. The top left panel shows the formation of two elongated images by a fold catastrophe. The vertical segment (A,B) is the length of the source in the source plane. The images are given by the antecedent of the parabola (fold caustic) and therefore two images are formed. In the next panel we introduce a perturbation represented as the dashed line which co-adds to the parabola. This perturbation roughly represents the deviation angle expected from an isothermal sphere with soft core, assuming its influence is zero beyond a given radius. The difference between the three configurations is the intensity of the perturbation. When the intensity is large enough (top right panel) it can break the nearest image and form multiple small images. When the intensity decreases (bottom left) the perturbation can break the images but can also form sub-ellipses of merging sub-images. For the case of very small perturbation (bottom right), sub-images can be formed, but if the spatial resolution is low, one cannot distinguish multiple images and we observe a locally (de)amplified region (a bright or dark spot) which looks like the spot observed in Cl2244-02. If the local amplification applies to a bright substructure of the source itself (HII regions for instance), the spot can be bright and clearly visible on the arc. Minilensing can be strong on the critical line. Note that such a bright spot only appears on one of the two segments of the fold arc.

When the amplitude of the perturbation decreases, the multiple components come closer and closer until they merge into one single image. If a perturbation of a caustic is small but falls right on a substructure of the source having the same angular size it may appear as a bright spot within the arc. Remember that for multiply-imaged systems the same structural details must be present in all images taking into account the parity changes of the images. Each image is a linear mapping of the others. However, additional bright granules have been noticed on some arcs that most likely arise via minilensing from superposed dark interlopers (Fig. 13). This granularity is an exciting observational development and one hopes for exploitation with the refurbished HST. One goal will be to determine the spectra of small mass substructures in rich clusters or along the line of sight. Large perturbations of caustics were already used by Hammer (1987) and Hammer & Rigaut (1989) to give upper mass limits for galaxies located on arcs in A370 and Cl2244. A similar study of the cusp arc in Cl0024+1654 by Kassiola, Kovner & Fort (1992) explained why the length of the central segment of the triple arc is so small. It does not satisfy the length theorem: the length of the middle image equals the sum of the other two for a cusp configuration! In summary, the investigation of caustic perturbations could be useful to probe galaxy masses as well as dark halos along the line of sight toward large arcs, and give interesting constraints on the clumpiness of dark matter on small scales. It is important to mention here another class of bright spots. They can also be produced on extremities of arcs close to critical lines when a bright giant star, or a globular cluster is just crossing the caustic. Kovner & Paczynski (1988), and Miralda-Escudé (1991c) discussed the variability of such events which would appear as single spots due to the time delay effect. However, contrary to local perturbations, these intrinsic events should change locally the color of the arc and therefore we should be able to separate the two kinds of effects.