  By combining high resolution, radiative transfer cosmological simulations of
z~6 galaxies with a sub-grid multi-phase model of their interstellar medium we
derive the expected intensity of several far infrared (FIR) emission lines ([C
II] 158 micron, [O I] 63 micron, and [N II] 122 micron) for different values of
the gas metallicity, Z. For Z = Z_sun the [C II] spectrum is very complex due
to the presence of several emitting clumps of individual size < 3 kpc; the peak
is displaced from the galaxy center by ~100 km/s. While the [O I] spectrum is
also similarly displaced, the [N II] line comes predominantly from the central
ionized regions of the galaxy. When integrated over ~500 km/s, the [C II] line
flux is 185 mJy km/s; 95% of such flux originates from the cold (T~250 K) H I
phase, and only 5% from the warm (T~5000 K) neutral medium. The [O I] and [N
II] fluxes are ~6 and ~90 times lower than the [C II] one, respectively. By
comparing our results with observations of Himiko, the most extended and
luminous Lyman Alpha Emitter (LAE) at z = 6.6, we find that the gas metallicity
in this source must be sub-solar. We conclude that the [C II] line from z~6
galaxies is detectable by the ALMA full array in 1.9 < t_ON < 7.7 hr observing
time, depending on Z.
