A 10 deg$^2$ Lyman-$\alpha$ survey at z=8.8 with spectroscopic
  follow-up: strong constraints on the LF and implications for other surveys
  Candidate galaxies at redshifts of $z \sim 10$ are now being found in
extremely deep surveys, probing very small areas. As a consequence, candidates
are very faint, making spectroscopic confirmation practically impossible. In
order to overcome such limitations, we have undertaken the CF-HiZELS survey,
which is a large area, medium depth near infrared narrow-band survey targeted
at $z=8.8$ Lyman-$\alpha$ (Ly$\alpha$) emitters (LAEs) and covering 10 deg$^2$
in part of the SSA22 field with the Canada-France-Hawaii Telescope. We surveyed
a comoving volume of $4.7\times 10^6$ Mpc$^3$ to a Ly$\alpha$ luminosity limit
of $6.3\times10^{43}$ erg s$^{-1}$. We look for Ly$\alpha$ candidates by
applying the following criteria: i) clear emission line source, ii) no optical
detections ($ugriz$ from CFHTLS), iii) no visible detection in the optical
stack ($ugriz > 27$), iv) visually checked reliable NB$_J$ and $J$ detections
and v) $J-K \leq 0$. We compute photometric redshifts and remove a significant
amount of dusty lower redshift line-emitters at $z \sim 1.4 $ or $2.2$. A total
of 13 Ly$\alpha$ candidates were found, of which two are marked as strong
candidates, but the majority have very weak constraints on their SEDs. Using
follow-up observations with SINFONI/VLT we are able to exclude the most robust
candidates as Ly$\alpha$ emitters. We put a strong constraint on the Ly$\alpha$
luminosity function at $z \sim 9$ and make realistic predictions for ongoing
and future surveys. Our results show that surveys for the highest redshift LAEs
are susceptible of multiple contaminations and that spectroscopic follow-up is
absolutely necessary.
