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Detecting First Star Lyman-$α$ Spheres through Gravitational Telescopes

Lyman-$α$ spheres, i.e. regions around the first stars which are illuminated by Lyman-$α$ photons and show 21cm absorption feature against the CMB, are smoking guns at the dawn of the reionization epoch. Though overwhelming radio foreground makes their detections extremely difficult, we pointed out that, strong gravitational lensing can significantly improve their observational feasibility. Since Lyman-$α$ spheres have ~10" sizes, comparable to the caustic size of galaxy clusters, individual images of each strongly lensed Lyman-$α$ sphere often merge together and form single structures in the 21cm sky with irregular shapes. Using high-resolution N-body LCDM simulations, we found that the lensing probability to have magnification bigger than 10 is ~10^{-5}. This results in $\ga 10^6$ strongly lensed Lyman-$α$ spheres across the sky, which should be the primary targets for first detections of Lyman-$α$ spheres. Although the required total radio array collecting area for their detection is large (~100 km^2), the design of long fixed cylindrical reflectors can significantly reduce the total cost of such array to the level of the square kilometer array (SKA) and makes the detection of these very first objects feasible.