\documentstyle{preprint}

\def\gta{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}}
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\def\lta{\mathrel{\spose{\lower 3pt\hbox{$\mathchar"218$}}
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\def\HI{\hbox{H~$\scriptstyle\rm I\ $}}

\begin{document}

\title{HIGH REDSHIFT GALAXIES IN THE HUBBLE DEEP FIELD.\\
~\\
COLOR SELECTION AND STAR FORMATION HISTORY TO ${\bf z\sim 4}$~\thanks{Based on observations with the
NASA/ESA {\it Hubble Space Telescope} obtained at the Space Telescope Science Institute which is operated by AURA
under NASA contract NAS5-26555.}}

\author{Piero Madau, Henry C.~Ferguson, Mark E.~Dickinson\thanks{Space Telescope Science Institute,
3700 San Martin Drive, Baltimore MD 21218}\\
~\\
{e-mail: madau@stsci.edu, ferguson@stsci.edu, med@stsci.edu}\\
~\\
~\\
{\it Mauro Giavalisco}\thanks{Hubble Fellow}$^,$\thanks{Carnegie Observatories,
813 Santa Barbara Street, Pasadena, CA 91101-1292}\\
~\\
{e-mail: mauro@ociw.edu}\\
~\\
~\\
{\it Charles C. Steidel}~\thanks{Alfred P.~Sloan Foundation Fellow}$^,$\thanks{NSF Young
Investigator}$^,$\thanks{Palomar Observatory, California Institute of Technology, Mail
Stop 105-24, Pasadena, CA 91125}\\
~\\
{e-mail: ccs@astro.caltech.edu}\\
~\\
~\\
{\it Andrew Fruchter}~\samethanks{2}\\
~\\
{e-mail: fruchter@stsci.edu}\\
~\\}

\pub{MNRAS}

\recacc{10 July 1996}{8 August 1996}

\maketitle

\setcounter{footnote}{0}

\begin{abstract}
The Lyman decrement associated with the cumulative effect of \HI in QSO
absorption systems along the line of sight provides a distinctive feature
for identifying galaxies at $z\gta2.5$. Color criteria, which are sensitive to
the presence of a Lyman-continuum break superposed on an otherwise flat UV
spectrum, have been shown, through Keck spectroscopy, to successfully identify 
a substantial population of star-forming galaxies at $3\lta z\lta 3.5$
(Steidel \etal 1996a). Such
objects have proven surprisingly elusive in field-galaxy redshift surveys;
quantifying their surface density and morphology is crucial for determining how
and when galaxies formed. The {\it Hubble Deep Field} (HDF) observations offer
the opportunity to exploit the ubiquitous effect of intergalactic absorption
and obtain useful statistical constraints on the redshift distribution of
galaxies considerably fainter than current spectroscopic limits. We model the
\HI cosmic opacity as a function of redshift, including scattering in 
resonant lines of the Lyman series and Lyman-continuum absorption, and use
stellar population synthesis models with a wide variety of ages, metallicities,
dust contents, and redshifts, to derive color selection criteria that provide a
robust separation between high redshift and low redshift galaxies. From the HDF
images we construct a sample of star-forming galaxies at $2\lta z\lta 4.5$.
While none of the $\sim 60$ objects in the HDF having known Keck/LRIS 
spectroscopic redshifts in the range $0\lta z\lta 1.4$ is found to contaminate
our high-redshift sample, our color criteria are able to efficiently select the
$2.6\lta z\lta 3.2$ galaxies identified by Steidel \etal (1996b). 

The ultraviolet (and blue) dropout technique opens up the possibility of
investigating cosmic star and element formation in the early universe. We set a
lower-limit to the ejection rate of heavy elements per unit comoving volume
from Type II supernovae at $\langle z\rangle=2.75$ of $\approx 3.6\times
10^{-4}\msunits$ (for $q_0=0.5$ and $H_0=50\kmsmpc$), which is 3 times
higher than the local value, but still 4 times lower than the rate observed at
$z\approx 1$. At $\langle z\rangle=4$, our lower limit to the cosmic metal
ejection rate is $\approx 3$ times lower than the $\langle z\rangle=2.75$
value. We discuss the implications of these results on models of galaxy
formation, and on the chemical enrichment and ionization history of the
intergalactic medium. 
\end{abstract}