Free-bound emission from cosmological hydrogen recombination

In this paper 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 ~30-88% increase of the recombination spectrum within the frequency range 1 GHz<=nu<=100 GHz. In particular the Balmer-continuum emission increases the distortion at nu~ 690 GHz by ~92%. With our 100 shell calculations for the hydrogen atom we find that a total of ~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 nu<~30 GHz is completely featureless