Optical Line Emission from z$\sim$6.8 Sources with Deep Constraints on Ly$\alpha$ Visibility

We analyze a sample of $z$-dropout galaxies in the CANDELS GOODS South and UDS fields that have been targeted by a dedicated spectroscopic campaign aimed at detecting their Ly$\alpha$ line. Deep IRAC observations at 3.6 and 4.5 $\mu$m are used to determine the strength of optical emission lines affecting these bands at z$\sim$6.5-6.9 in order to i) investigate possible physical differences between Ly$\alpha$ emitting and non-emitting sources; ii) constrain the escape fraction of ionizing photons; iii) provide an estimate of the specific star-formation rate at high redshifts. We find evidence of strong [OIII]+H$\beta$ emission in the average (stacked) SEDs of galaxies both with and without Ly$\alpha$ emission. The blue IRAC [3.6]-[4.5] color of the stack with detected Ly$\alpha$ line can be converted into a rest-frame equivalent width EW([OIII]+H$\beta$)=1500$^{+530}_{-440}\AA$ assuming a flat intrinsic stellar continuum. This strong optical line emission enables a first estimate of f$_{esc}\lesssim$20% on the escape fraction of ionizing photons from Ly$\alpha$ detected objects. The objects with no Ly$\alpha$ line show less extreme EW([OIII]+H$\beta$)=520$^{+170}_{-150}\AA$ suggesting different physical conditions of the HII regions with respect to Ly$\alpha$-emitting ones, or a larger f$_{esc}$. The latter case is consistent with a combined evolution of f$_{esc}$ and the neutral hydrogen fraction as an explanation of the lack of bright Ly$\alpha$ emission at z$>$6. A lower limit on the specific star formation rate, SSFR$>$9.1$Gyr^{-1}$ for $M_{star}=2 \times 10^9 M_{\odot}$ galaxies at these redshifts can be derived from the spectroscopically confirmed sample.