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We study the production rate of ionizing photons of a sample of 588 H$\alpha$emitters (HAEs) and 160 Lyman-$\alpha$ emitters (LAEs) at $z=2.2$ in the COSMOSfield in order to assess the implied emissivity from galaxies, based on theirUV luminosity. By exploring the rest-frame Lyman Continuum (LyC) withGALEX/$NUV$ data, we find f$_{\rm esc} < 2.8\, (6.4)$% through median (mean)stacking. By combining the H$\alpha$ luminosity density with IGM emissivitymeasurements from absorption studies, we find a globally averaged$\langle$f$_{\rm esc}\rangle$ of $5.9^{+14.5}_{-4.2}$ % at $z=2.2$ if we assumeHAEs are the only source of ionizing photons. We find similarly low values ofthe global $\langle$f$_{\rm esc}\rangle$ at $z\approx3-5$, also ruling out ahigh $\langle$f$_{\rm esc}\rangle$ at $z<5$. These low escape fractions allowus to measure $\xi_{ion}$, the number of produced ionizing photons per unit UVluminosity, and investigate how this depends on galaxy properties. We find atypical $\xi_{ion} \approx 10^{24.77\pm0.04}$ Hz erg$^{-1}$ for HAEs and$\xi_{ion} \approx 10^{25.14\pm0.09}$ Hz erg$^{-1}$ for LAEs. LAEs and low massHAEs at $z=2.2$ show similar values of $\xi_{ion}$ as typically assumed in thereionization era, while the typical HAE is three times less ionizing. Due to anincreasing $\xi_{ion}$ with increasing EW(H$\alpha$), $\xi_{ion}$ likelyincreases with redshift. This evolution alone is fully in line with theobserved evolution of $\xi_{ion}$ between $z\approx2-5$, indicating a typicalvalue of $\xi_{ion} \approx 10^{25.4}$ Hz erg$^{-1}$ in the reionization era.

The production and escape of Lyman-Continuum radiation from star-forming galaxies at z~2 and their redshift evolution