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We present a new method to quantify the value of the escape fraction ofionizing photons, and the existence of ultra-faint galaxies clustered aroundbrighter objects during the epoch of cosmic reionization, using the diffuseLy$\alpha$, continuum and H$\alpha$ emission observed around galaxies at$z\sim6$. We model the surface brightness profiles of the diffuse halosconsidering the fluorescent emission powered by ionizing photons escaping fromthe central galaxies, and the nebular emission from satellite star-formingsources, by extending the formalisms developed in Mas-Ribas & Dijkstra (2016)and Mas-Ribas et al. (2017). The comparison between our predicted profiles andLy$\alpha$ observations at $z=5.7$ and $z=6.6$ favors a low ionizing escapefraction, $f_{\rm esc}^{\rm ion}\sim5\%$, for galaxies in the range $-19\gtrsimM_{\rm UV} \gtrsim -21.5$. However, uncertainties and possible systematics inthe observations do not allow for firm conclusions. We predict H$\alpha$ andrest-frame visible continuum observations with JWST, and show that JWST will beable to detect extended (a few tens of kpc) fluorescent H$\alpha$ emissionpowered by ionizing photons escaping from a bright, $L\gtrsim 5L^*$, galaxy.Such observations can differentiate fluorescent emission from nebular emissionby satellite sources. We discuss how observations and stacking of severalobjects may provide unique constraints on the escape fraction for faintgalaxies and/or the abundance of ultra-faint radiation sources.

Small-scale Intensity Mapping: Extended Halos as a Probe of the Ionizing Escape Fraction and Faint Galaxy Populations during Reionization