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).
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.