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With the Hubble Frontier Fields program, gravitational lensing has provided apowerful way to extend the study of the ultraviolet luminosity function (LF) ofgalaxies at $z \sim 6$ down to unprecedented magnitude limits. At the sametime, significant discrepancies between different studies were found at thevery faint end of the LF. In an attempt to understand such disagreements, wepresent a comprehensive assessment of the uncertainties associated with thelensing models and the size distribution of galaxies. We use end-to-endsimulations from the source plane to the final LF that account for all lensingeffects and systematic uncertainties by comparing several mass models. Inaddition to the size distribution, the choice of lens model leads to largedifferences at magnitudes fainter than $M_{UV} = -15~$ AB mag, where themagnification factor becomes highly uncertain. We perform MCMC simulations thatinclude all these uncertainties at the individual galaxy level to compute thefinal LF, allowing, in particular, a crossover between magnitude bins. The bestLF fit, using a modified Schechter function that allows for a turnover at faintmagnitudes, gives a faint-end slope of $\alpha = -2.01_{-0.14}^{+0.12}$, acurvature parameter of $\beta = 0.48_{-0.25}^{+0.49}$, and a turnover magnitudeof $M_{T} = -14.93_{-0.52}^{+0.61}$. Most importantly our procedure shows thatrobust constraints on the LF at magnitudes fainter than $M_{UV} = -15~$ ABremain unrealistic. More accurate lens modeling and future observations oflensing clusters with the James Webb Space Telescope can reliably extend the UVLF to fainter magnitudes.

monthly notices of the royal astronomical society

The Extreme Faint End of the UV Luminosity Function at $z\sim6$ Through  Gravitational Telescopes: a comprehensive assessment of strong lensing  uncertainties