  We study the H2 cooling emission of forming galaxies, and discuss their
observability using the future infrared facility SAFIR. Forming galaxies with
mass >10^11 Msun emit most of their gravitational energy liberated by
contraction in molecular hydrogen line radiation, although a large part of
thermal energy at virialization is radiated away by the H Ly alpha emission.
For more massive objects, the degree of heating due to dissipation of kinetic
energy is so great that the temperature does not drop below 10^4 K and the
gravitational energy is emitted mainly by the Ly alpha emission. Therefore, the
total H2 luminosity attains the peak value of about 10^42 ergs/s for forming
galaxies whose total mass 10^11 Msun. If these sources are situated at redshift
z=8, they can be detected by rotational lines of 0-0S(3) at 9.7 micron and
0-0S(1) at 17 micron by SAFIR. An efficient way to find such H2 emitters is to
look at the Ly alpha emitters, since the brightest H2 emitters are also
luminous in the Ly alpha emission.
