Finding bright $z \geq 6.6$ Lyman-$\alpha$ emitters with lensing: prospects for Euclid

We model the $z \geq 6.6$ Ly$\alpha$ luminosity function to estimate the number of lensed high$-z$ Ly$\alpha$ emitters that may be detected by the Euclid Deep Survey. To span the whole range of possible predictions we exploit two Ly$\alpha$ luminosity function models and two strong gravitational lensing models from the literature. We show that the planned Euclid Deep Survey observing 40 deg$^2$ over the 920-1850 nm wavelength range down to a flux limit of $F_{lim}=5\times10^{-17}\,$erg s$^{-1}\,$cm$^{-2}$ will enable us to find between $\sim 0.85$ and $\sim 1.82$ deg$^{-2}$ lensed Ly$\alpha$ emitters at $z \geq 6.6$ depending on the adopted Ly$\alpha$ luminosity function and strong gravitational lensing model. The obvious [OII], [OIII] and H$\beta$ contaminants of the Ly$\alpha$ lensed population will be identified with the help of Euclid's spectral resolving power, while the SKA will enable the identification of the interloper population of H$\alpha$ emitters. By combining Euclid and the SKA, we will thus be able to identify, for the first time, a sample of $\sim 34$ to $\sim 73$ lensed Ly$\alpha$ emitters at $z \geq 6.6$.