Caught in Swallowtails: Discovery of Two Swallowtail Image Formations in MS 0451.6-0305

We report the discovery of two swallowtail image formations at $z=2.91$ and $z=6.70$ behind the galaxy cluster MS 0451.6-0305 in JWST-NIRCam imaging. We find that in both of the above lensed systems, the complex image morphology cannot be reproduced by simple fold/cusp caustics, and detailed lens modeling reveals higher-order swallowtail caustic configurations. In the $z=2.91$ lens system, a small part of the source galaxy (which itself is part of a galaxy group) containing atleast two compact knots sits inside the swallowtail caustic, producing a quadruply imaged arc. At two of the image positions of these knots, we infer point source magnifications of $\gtrsim 300$, implying lensing-corrected effective radii of $\lesssim 0.8-1.5$ pc. The $z=6.70$ system exhibits even more complex image formation. We therefore only use the most confidently identified counter-images of knots in this system as constraints in our lens modeling. The resulting model predicts magnifications $\sim20-200$ and lensing-corrected effective radii of $\lesssim 0.8-18.5$ pc for various knots. Together, these two systems represent the first example of observations of multiple swallowtail image formations in a single galaxy cluster and demonstrate the ability of swallowtail caustics to magnify individual substructures at sub-parsec scales, from intermediate redshifts to the first billion years of the Universe.