  Aims Determining the intensity of lines and continuum airglow emission in the
H-band is important for the design of faint-object infrared spectrographs.
Existing spectra at low/medium resolution cannot disentangle the true
sky-continuum from instrumental effects (e.g. diffuse light in the wings of
strong lines). We aim to obtain, for the first time, a high resolution infrared
spectrum deep enough to set significant constraints on the continuum emission
between the lines in the H-band. Methods During the second commissioning run of
the GIANO high-resolution infrared spectrograph at La Palma Observatory, we
pointed the instrument directly to the sky and obtained a deep spectrum that
extends from 0.97 to 2.4 micron. Results The spectrum shows about 1500 emission
lines, a factor of two more than in previous works. Of these, 80% are
identified as OH transitions; half of these are from highly excited molecules
(hot-OH component) that are not included in the OH airglow emission models
normally used for astronomical applications. The other lines are attributable
to O2 or unidentified. Several of the faint lines are in spectral regions that
were previously believed to be free of line emission. The continuum in the
H-band is marginally detected at a level of about 300
photons/m^2/s/arcsec^2/micron, equivalent to 20.1 AB-mag/arcsec^2. The observed
spectrum and the list of observed sky-lines are published in electronic format.
Conclusions Our measurements indicate that the sky continuum in the H-band
could be even darker than previously believed. However, the myriad of airglow
emission lines severely limits the spectral ranges where very low background
can be effectively achieved with low/medium resolution spectrographs. We
identify a few spectral bands that could still remain quite dark at the
resolving power foreseen for VLT-MOONS (R ~6,600).
