Free-bound emission from cosmological hydrogen recombination

In this letter we compute the emission coming from the direct recombination of free electrons to a given shell (n = 2) during the epoch of cosmological hydrogen recombination. This contribution leads to a total of one photon per recombined hydrogen atom and therefore a similar to 30-88% increase in the recombination spectrum within the frequency range 1 GHz <= v <= 100 GHz. In particular, the Balmer-continuum emission increases the distortion at v similar to 690 GHz by roughly 92%. With our 100 shell calculations for the hydrogen atom, we find that a total of similar to 5 photons per hydrogen atom are emitted when including all the bound-bound transitions, the 2s two-photon decay channel, and the optically thin free-bound transitions. Since the direct recombination continuum at high n is very broad, only a few n-series continuua are distinguishable and most of this additional emission below v less than or similar to 30 GHz is completely featureless.