SILVERRUSH XI: Constraints on the Ly$\alpha$ luminosity function and cosmic reionization at $z=7.3$ with Subaru/Hyper Suprime-Cam

The Ly$\alpha$ luminosity function (LF) of Ly$\alpha$ emitters (LAEs) has been used to constrain the neutral hydrogen fraction in the intergalactic medium (IGM) and thus the timeline of cosmic reionization. Here we present the results of a new narrow-band imaging survey for $z=7.3$ LAEs in a large area of $\sim 3\ \mathrm{deg}^2$ with Subaru/Hyper Suprime-Cam. No LAEs are detected down to $L_{\mathrm{Ly}\alpha}\simeq 10^{43.2}\ \mathrm{erg\ s^{-1}}$ in an effective cosmic volume of $\sim 2\times 10^6$ Mpc$^3$, placing an upper limit to the bright part of the $z=7.3$ Ly$\alpha$ LF for the first time and confirming a decrease in bright LAEs from $z=7.0$. By comparing this upper limit with the Ly$\alpha$ LF in the case of the fully ionized IGM, which is predicted using an observed $z=5.7$ Ly$\alpha$ LF on the assumption that the intrinsic Ly$\alpha$ LF evolves in the same way as the UV LF, we obtain the relative IGM transmission $T^\mathrm{IGM}_{\mathrm{Ly}\alpha}(7.3)/T^\mathrm{IGM}_{\mathrm{Ly}\alpha}(5.7)<0.77$, and then the volume-averaged neutral fraction $x_\mathrm{HI}(7.3)>0.28$. Cosmic reionization is thus still ongoing at $z=7.3$, being consistent with results from other $x_\mathrm{HI}$ estimation methods. A similar analysis using literature Ly$\alpha$ LFs finds that at $z=6.6$ and 7.0 the observed Ly$\alpha$ LF agrees with the predicted one, consistent with full ionization.