A possible formation mechanism of hydrogen molecules on a galactic scale is
examined. We are interested especially in the role of hydrogen molecules f
or the formation and evolution of primordial galaxies. Thus, the formation
process of hydrogen molecules in a very low-metallicity galaxy (I Zw 18; th
e most typical metal-deficient galaxy) is studied. Adopting a recent observ
ational result of the absorption lines of hydrogen molecules in I Zw 18, we
obtain the upper limit for the ionization degree in the case where hydroge
n molecules can form via the H--process, although they are generally believ
ed to form on the surface of dust grains. Furthermore, we present a critica
l ionization degree, above which the H--process can be dominant over the fo
rmation process on the surface of grains. Interestingly, this critical ioni
zation degree is comparable to the upper limit of the ionization degree for
I Zw 18. For determining the formation process of hydrogen molecules, futu
re observational facilities can be useful. Thus, we examine the detectabili
ty in some wavelengths for metal-deficient galaxies. According to our estim
ate, the near-infrared line emission of hydrogen molecules is observable at
the level of 10 mu Jy, the free-free radio emission is at the level of mJy
, and the far-infrared emission from the dust on which hydrogen molecules f
orm can also be detected at the 10-mJy level with its temperature of 16 K.
The near-infrared line and the far-infrared continuum are feasible for ASTR
O-F observations.