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\title{MOLECULES AT HIGH REDSHIFT: THE EVOLUTION\\
~\\
OF THE COOL PHASE OF PROTOGALACTIC DISKS}

\author{Colin A.\ Norman\\
\\
Space Telescope Science Institute\\
\\
3700 San Martin Drive\\
\\
Baltimore, MD 21218\\
\\
and\\
\\
The Johns Hopkins University\\
\and
Marco Spaans\\
\\
Department of Physics and Astronomy\\
\\
The Johns Hopkins University\\
\\
3400 N.\ Charles Street\\
\\
Baltimore, MD 21218}

\tobe{1 May 1997}{ApJ}

\maketitle

\begin{abstract}
\medskip
 
We study the formation of molecular hydrogen, after the epoch of
re-ionization, in the context of canonical galaxy formation theory due
to hierarchical clustering. There is an initial epoch of $H_2$
production in the gas phase through the $H^-$ route which ends at a
redshift of order unity. We assume that the fundamental units in the
gas phase of protogalaxies during this epoch are similar to diffuse
clouds found in our own galaxy and we restrict our attention to
protogalactic disks although some of our analysis applies to
multi-phase halo gas. Giant molecular clouds are not formed until
lower redshifts. Star formation in the protogalactic disks can become
self-regulated. The process responsible for the feedback is heating of the gas 
by the internal stellar radiation field which can dominate the background
radiation field at various epochs. If the gas is heated to above
2000--3000~K the hydrogen molecules are collisionally dissociated
and we assume that in their absence the star formation process is
strongly suppressed due to insufficient cooling. As we demonstrate by
analysis of phase diagrams, the H$_2$-induced cool phase disappears. A~priori,
the cool phase with molecular hydrogen cooling can only achieve
temperatures $ \geq 300$~K. Consequently, it is possible to define a
maximum star formation rate during this epoch. Plausible estimates
give a rate of $ \lesssim 0.2-2 M_{\odot}~{\rm yr}^{-1}$ for condensations
corresponding to 1$\sigma$ and 2$\sigma$ initial density fluctuations. For more
massive structures, this limit is relaxed and in agreement with observations
of high redshift galaxies. Therefore, the
production of metals and dust proceeds slowly in this phase. This
moderate epoch is terminated by a phase transition to a cold dense and
warm neutral/ionized medium once the metals and dust have increased
to a level $Z\approx 0.03-0.1Z_{\odot}$. Then: (1)~atoms and molecules
such as C, O and
CO become abundant and cool the gas to below 300~K; (2)~the dust abundance
has become sufficiently high to allow shielding of the molecular gas and;
(3)~molecular hydrogen formation can occur rapidly on grain
surfaces. This phase transition occurs at a redshift of approximately 1.5,
with a fiducial range of $1.2\le z\le 2$, and
initiates the rapid formation of molecular species, giant molecular clouds and
stars. The delayed initiation of the cold phase in the interstellar
medium of protostellar disks at a metallicity of $Z \lesssim 0.1
Z_{\odot}$ is consequently a plausible physical reason that the
formation phase of the stellar disks of the bulk of the galaxies
only occurs at a redshift of order unity.
The combination of feedback and a phase transition provides a natural
resolution of the G-dwarf problem.

\end{abstract}