  We propose a new scenario for supermassive star (SMS;>10^5Msun) formation in
shocked regions of colliding cold accretion flows near the centers of first
galaxies. Recent numerical simulations indicate that assembly of a typical
first galaxy with virial temperature (~10^4K) proceeds via cold and dense flows
penetrating deep to the center, where the supersonic streams collide each other
to develop a hot and dense (~10^4K, ~10^3/cc) shocked gas. The post-shock layer
first cools by efficient Ly alpha emission and contracts isobarically until
8000K. Whether the layer continues the isobaric contraction depends on the
density at this moment: if the density is high enough for collisionally
exciting H2 rovibrational levels (>10^4/cc), enhanced H2 collisional
dissociation suppresses the gas to cool further. In this case, the layer
fragments into massive (>10^5Msun) clouds, which collapse isothermally (~8000K)
by the Ly alpha cooling without subsequent fragmentation. As an outcome, SMSs
are expected to form and evolve eventually to seeds of supermassive black holes
(SMBH). By calculating thermal evolution of the post-shock gas, we delimit the
range of post-shock conditions for the SMS formation, which can be expressed
as: T>6000K/(n/10^4/cc) for n<10^4/cc and T>5000-6000K for n>10^4/cc, depending
somewhat on initial ionization degree. We found that metal enrichment does not
affect the above condition for metallicity below 10^-3Zsun if metals are in the
gas phase, while condensation of several percent of metals into dust decreases
this critical value of metallicity by an order of magnitude. Unlike the
previously proposed scenario for SMS formation, which postulates extremely
strong ultraviolet radiation to quench H2 cooling, our scenario naturally
explains the SMBH seed formation in the assembly process of the first galaxies,
even without such a strong radiation.
