\documentstyle[12pt,moriond,psfig]{article}
\newcommand{\siiv}{Si~IV $\lambda$1400}
\newcommand{\civ}{C~IV $\lambda$1550}
\newcommand{\Ha}{H$\alpha$}
\newcommand{\Myr}{M$_{\odot}$~yr$^{-1}$}
\newcommand{\Ms}{M$_{\odot}$}
\newcommand{\Ls}{L$_{\odot}$}
\newcommand{\kms}{km~s$^{-1}$}
\newcommand{\vinf}{v$_{\infty}$}
\newcommand{\Zs}{Z$_{\odot}$}
\newcommand{\Md}{$\dot{M}$}
\newcommand{\Mlow}{$M_{\rm{low}}$}
\newcommand{\Mup}{$M_{\rm{up}}$}
\newcommand{\erga}{erg~s$^{-1}$~cm$^{-2}$~\AA$^{-1}$}
\begin{document}
%
\heading{THE STELLAR INITIAL MASS FUNCTION IN LOCAL DWARF GALAXIES}

\author{Claus Leitherer } 
{Space Telescope Science Institute, Baltimore, Maryland}
 
\begin{moriondabstract}
The stellar initial mass function (IMF) for dwarf galaxies in the local 
universe is reviewed. These galaxies are at distances between 50~kpc (LMC)
and tens of Mpc. This distance range allows IMF determinations from star
counts in conjunction with photometry/spectroscopy, color-magnitude
diagrams, and integrated spectral energy distributions. There
is no observational evidence for a significant IMF variation among local
dwarf galaxies. Small variations, however, could be hidden by systematic and
experimental uncertainties. Environment and metallicity in particular have
little observable effect on the IMF. The high-mass end of the IMF above
$\sim$10~\Ms\ follows a power-law slope with a Salpeter exponent. At 
intermediate masses between 3 and 10~\Ms\ the slope is close to Salpeter, or
somewhat steeper (richer in less massive stars). This trend is reversed at
lower masses where a flattening of the IMF or even a truncation may occur,
somewhat similar to the solar neighborhood case. Extrapolating the Salpeter
slope to the hydrogen-burning limit of $\sim$0.1~\Ms\ would lead to an 
overestimate of the star-formation rate by a factor of several. 
A power-law fit with a Salpeter slope truncated at 1 and 100~\Ms\ is an
acceptable approximation for the IMF and gives reasonable star-formation rates.
  
\end{moriondabstract}

\section{Introduction}

The shape of the stellar initial mass function (IMF) and its theoretical 
interpretation are fundamental to our understanding of the star-formation
process. Yet, more than 40 years after the influential paper on the solar 
neighborhood IMF by \cite{sa55} we are still lacking a concise theory, and 
observational studies are subject to substantial uncertainties. Rather than
repeating the current state of the IMF in this review, I refer the reader
to the comprehensive articles written by \cite{ms79}, \cite{sc86}, \cite{sc98},
and \cite{el99}. The goals I have set for this paper are
(i) to highlight the challenges of deriving the IMF in local dwarf galaxies,
(ii) to present a consensus 
view of the IMF shape (if there exists one), and (iii)
to make a recommendation for the choice of the IMF in dwarf galaxies at
cosmological distances. 

\section{Relevant parameters}

Figure~\ref{Scalo} shows the ``classical'' solar neighborhood field star
IMF of \cite{sc86}. A few more recent IMF studies over the full mass 
range have become available since then. A complete literature 
survey is in \cite{sc98}. Since few of these investigations have revised 
the basic functional behavior of the IMF (at least not to a degree that would 
affect the interpretation of the IMF in dwarf galaxies), I will use 
Figure~\ref{Scalo} for a qualitative discussion of the main relevant issues.

The solar neighborhood IMF can be approximated by a power-law with an exponent
close to Salpeter's value of $\Gamma = -1.35$ for masses higher than 
$\sim$10~\Ms. The IMF becomes steeper towards lower masses but can still be
reasonably well approximated by a power-law exponent down to $\sim$2~\Ms. The
IMF is scale-free over 1 to 2 orders of magnitude in mass. Below about 2~\Ms,
the IMF flattens, or may even turn over --- although this is under debate
(see \cite{kr95}). 
Uncertainties become prohibitive at the lowest masses but it may well be 
(and is plausible) that the trend in Figure~\ref{Scalo} continues, and the
IMF over the full mass range is symmetric with respect to the maximum at 
$\sim$0.3~\Ms. This would suggest a preferred mass of $\sim$0.3~\Ms, and the
mass range accessible to observations would merely be the tip of the iceberg.

\begin{figure}
\psfig{figure=pp1254f1.ps,height=14cm,width=11cm}
\caption[fig]{\label{Scalo} Field star IMF in the solar neighborhood.
Plotted are star numbers per logarithmic mass interval.
Crosses: solar-neighborhood IMF of \cite{ms79}; points with error bars: 
revised field star IMF of \cite{sc86}. The
straight lines indicate slopes of --1.35 (Salpeter slope), and  --2.3 (power-law
approximation to the high-mass end of the Miller-Scalo IMF) at
arbitrary normalization.
The extrapolation of the Salpeter IMF to 0.1~\Ms\
highlights the difference between this IMF and a more realistic IMF with a
flattening at low masses.}
\end{figure}

It is worth recalling that even if the IMF is truncated close to 1~\Ms, most
of the mass of a stellar population is locked in low-mass stars. 
For a Salpeter IMF, stars with masses between 1 and 10~\Ms\
contribute six times more mass to the total mass than all stars above 40~\Ms.
Conversely, most of the stellar light is provided by the most massive stars
due to the steep stellar mass-luminosity relation.

Is the IMF of Figure~\ref{Scalo} universal? There are suggestions that
this is not the case. The slope of the IMF could vary with environment, with
a steeper IMF found in more metal-rich star-formation regions (e.g., 
\cite{me92}). There could also 
be a metallicity dependent upper mass limit \Mup\ to
the IMF, in particular in dust-enshrouded starbursts (e.g., \cite{lv96}). Or
low-mass stars could be deficient or completely absent. A mass cut-off around
\Mlow~$\approx$~5~\Ms\ was derived for M82 by \cite{ri80}. 
An IMF with a deficit of intermediate and low-mass stars was suggested by
\cite{lm96} to account for the large amount of oxygen observed in galaxy 
clusters.  

In order to illustrate the effect of even a moderate variation of the IMF, I
took the models of \cite{lh95} to make predictions for a few
key quantities related to dwarf galaxies. I assumed a ``standard'' IMF
($\Gamma = -1.35$ between 1 and 100~\Ms) for this exercise and considered three
variants whose normalization leaves the total star-formation rate unchanged:
\begin{itemize}
\item $\Gamma = -2.3$: The non-thermal luminosity of stellar winds and
supernovae at 10~Myr would be reduced by a factor of 10, thereby reducing
the energization of dwarf galaxy superbubbles and outflows (e.g., \cite{ma96}).
The output of
ionizing photons at 3~Myr would be down by a factor of 20, and so would be
the [O~II] line flux (e.g., \cite{gbh89}, \cite{ke92}).
\item \Mup~=~30~\Ms. If most Wolf-Rayet stars are the evolved descendants of
very massive stars, such an IMF would predict very few Wolf-Rayet galaxies
(cf. \cite{kj85}, \cite{co91}). Along the same
argument, the O3 star cluster in the center of R136 (\cite{mh98})
could not have formed in a galaxy with \Mup~=~30~\Ms.
\item \Mlow~=~5~\Ms. The mass converted into stars 
would be reduced by a factor of 3. Galaxies would consume only a small 
fraction of their gas supply over a Hubble time
at their currently observed star-formation
rates (\cite{sa86}). Starbursts with a truncated IMF would become invisible 
after about 100~Myr without ongoing star formation (cf. \cite{no91} and could
remain undetected in galaxy number counts.
\end{itemize}

These examples should be motivation enough to seriously investigate the evidence
for deviations from the solar neighborhood IMF in local dwarf galaxies.

\section{Results for the Large Magellanic Cloud}

The proximity of the Large Magellanic Cloud (LMC) allows IMF determinations
whose precision is often comparable to those obtained in the Galaxy. Therefore
I will review selected LMC results to have a baseline for comparison with
more distant dwarf galaxies. I will begin with a discussion of the 
field population at low and high masses and then move on to 
the IMF in clusters.  

The LMC populations were reviewed by \cite{ma92}. Ground-based work, as pushed
to the limits by \cite{vc96}, is restricted to main-sequence 
turn-off masses $>$1~\Ms. Recent deep WFPC2 imagery of an outer LMC field by
\cite{ho97} reaches $V \approx 28$, with a completeness
limit of $V = 26$. The corresponding main-sequence mass limit is 0.6~\Ms. The
luminosity function provides constraints on the star-formation history and the
IMF between 0.6 and 3~\Ms. The data favor an IMF with a Salpeter or somewhat
steeper slope. However, disentangling IMF and star-formation history is far
from trivial. The look-back times corresponding to the sampled masses are a
few Gyr, and significant variations in the star-formation history of the LMC
have occurred over that period (e.g., \cite{be92}). 
                                                                         
Most of the work on the high-mass end of the {\em field} IMF was done by 
P.~Massey and collaborators (e.g., \cite{ma95}). The IMF for masses above
$\sim$40~\Ms\ is clearly steeper than Salpeter, a trend found in the Milky
Way and the SMC as well. Most likely, this is the result of an increasing 
concentration of O stars  with earlier spectral type in clusters and 
associations (\cite{ga90}). The earliest types (which correspond to
 the most massive 
stars) are predominantly observed in clusters due to their short lifetimes, 
whereas older stars are commonly found in the field, presumably after becoming 
gravitationally unbound. Note that the earliest O stars do not contribute
significantly to the integrated light of a galaxy, even at 2200~\AA. Therefore
the fact that these stars are almost exclusively found in clusters is not
in conflict with the result of \cite{me95} that clusters do not account
for the bulk of the UV light in starburst galaxies.  

{\em Star clusters} form quasi-instantaneously in comparison with stellar 
evolutionary lifetimes. Therefore star-formation histories are generally
not an issue when converting luminosity functions (and, for the most
extreme masses, spectral types) into an IMF. An abundance of cluster work
is available in the literature (see \cite{sc98}). I will concentrate on 
R136, the central cluster of the 30 Doradus region (\cite{wa91}) because
(i) the cluster is massive enough ($\sim$10$^5$~\Ms) that the high-mass
end of the IMF is well populated and (ii) recent deep HST imagery sheds light
on the top-heavy IMF controversy in starburst galaxies.

\begin{figure}
\psfig{figure=pp1254f2.ps,height=11cm,width=15cm}
\caption[fig]{\label{R136} Low-mass end of the IMF in the central R136 
region derived from deep HST WFPC2 V and I imagery (\cite{si98}). 
The dashed lines are the results of \cite{hu95} and \cite{hu96}, based
on less deep photometry. The data point at $\log M = 0.2$ is the average over
the mass interval $0.1 < \log M < 0.3$. The completeness level for all mass
intervals is $>$50\%.}
\end{figure}

\cite{pg93} derived the IMF above $\sim$20~\Ms\ by matching 
spectral types to stellar evolutionary models. Indications for spatial
variations of the IMF slope were found, but uncertainties are large. The mean 
IMF slope is $\Gamma = -1.5 \pm 0.2$, similar to the Salpeter value.  
Deep HST imaging and crowded-field photometry are
complementary: the lack of spectroscopic information prevents
mass determinations of the most massive stars due to the color degeneracy
(\cite{ma95}) but photometric analysis of fainter, less massive stars becomes
possible. \cite{mh94}, using HST $UBV$ photometry, compared the 
properties of 30~Dor within and outside R136. They find a flatter IMF in the 
central region of R136. The positions of massive stars can either reflect the
initial condition at the cluster's birth or they can result from mass 
segregation due to dynamical evolution. It is not clear what applies to 
R136 but models for the Orion Trapezium cluster indicate that the
timescale for significant mass segregation due to dynamical evolution is longer
than the cluster age (\cite{bd98}). 
A near-infrared view of R136 was presented by \cite{br96} 
who used adaptive optics to
achieve diffraction limited H- and K-photometry. Their results
confirm an average IMF slope of --1.6 and a flatter IMF towards the
center of R136. 
The census of R136 at the high-mass end was recently
completed by \cite{mh98} who detected about 40 previously unknown O3
stars in the very center. Combining their detections with other existing 
spectroscopy indicates a power-law IMF with $\Gamma = -1.35$ between 100 and
10~\Ms. 

HST is needed for spatially resolved photometry of intermediate- and low-mass
stars. \cite{hu95} and \cite{hu96} detected stars down to $V \approx 25$
within the central pc of R136. Comparison with stellar evolution models leads
to an IMF slope consistent with results at higher masses: stars form with
a power-law IMF down to
the detection limit of $\sim$3~\Ms. This limit could  be pushed further down 
to about 1~\Ms\ by \cite{si98} (see Figure~\ref{R136}). R136 is clearly 
forming stars in this mass range but not at the rate observed at higher 
masses: the IMF is flattening around 2 to 3~\Ms. Extrapolation of a Salpeter
IMF down to and beyond this mass range would lead to a significant  
overestimate  of the
number of low-mass stars and the total cluster mass. In the future, deep
near-infrared imaging with HST's NICMOS camera allows a search for 
pre-main-sequence stars which are still embedded in dust and therefore not 
included in the optical census. Measuring individual
stellar velocities could independently verify the total cluster mass --- if
virial equilibrium applies. Such a program is underway (R.~Terlevich,
private communication). 

Similar (but less detailed) results are available for the intermediate- and
high-mass star content of other Local Group galaxies.
There are few observationally significant variations of the IMF, and
the average slope tends to cluster around the Salpeter value (see also 
Figure~5 of \cite{sc98}). The surveyed regions cover more than one order of
magnitude in metallicity.

\section{A biased sample of local dwarf galaxies}

Space limitations preclude a systematic review of the available literature. An
excellent overview can be found in the conference volume edited by \cite{gi98}.
I will instead present my own view of the most important issues
by choosing a ``biased'' sample of five local dwarf galaxies with relevant 
observational data. The galaxies are in Table~1. They are ordered in terms
of increasing distance from 2 to 50~Mpc and cover a broad range of luminosity
and metallicity. Each of the five galaxies is particularly suited to address
the issues quoted in column~5 of Table~1.

\begin{center}
{\bf Table 1.} Sample galaxies.
\end{center}
\begin{center}
\begin{tabular}{|c|c|c|c|l|}
\hline Galaxy & $d$ & $\log L_{\rm{IR}}$ & $Z$ & IMF Aspect \\ 
 &  (Mpc) & (\Ls) &  (\Zs) & \\ \hline
NGC 1569 & 2.2  & 9.2  & 1/4  &  clusters versus field stars \\
M 82     & 3.2  & 10.5 & 1/3  &  IMF in dusty, metal-rich environments\\
NGC 5253 & 4.1  & 8.9  & 1/6  &  low-mass stars and cluster evolution\\
I Zw 18  & 10   & 8.1  & 1/50 &  IMF at extremely low metallicity\\
NGC 1741 & 50   & 10.3 & 1/4  &  IMF from integrated light analysis\\ \hline
\end{tabular}
\end{center}
\medskip

\subsection{NGC 1569: clusters and field stars}

The dwarf irregular NGC~1569 is the closest example of a starburst galaxy.
Most of its field population of stars with masses higher than a few \Ms\
was formed during a global star-formation episode beginning more than
100~Myr ago, and ending as recently as $\sim$10~Myr ago (\cite{gr98}). The IMF
in this mass range is a power law somewhat steeper than Salpeter, and the
associated star-formation rate over the whole galaxy is about 1~\Myr\ if the
mass is distributed between 1 and 100~\Ms. While this value may not sound too
impressive (it is comparable to the total star-formation rate of the Milky
Way), the {\em normalized} star-formation rate per unit surface reveals  the
extraordinary nature of this object. NGC~1569 forms stars at a rate of a few
\Myr~kpc$^{-2}$, which is three orders of magnitude higher than
in our Galaxy and a factor of 100 above the highest rates 
measured in dwarf irregular
galaxies of the Local Group (\cite{mt95}, \cite{to96}, \cite{ga96}).

The low-mass end of the IMF in the NGC~1569 field
 is inaccessible to direct observations,
even with HST. An innovative study of the low-mass regime was done by 
\cite{hf96}. NGC~1569 hosts several ``super star clusters'' (\cite{oc94}),
highly concentrated (half-light radius of a few pc), gravitationally bound 
stellar clusters which rival entire dwarf galaxies in luminosity
($M_{\rm B} = -14$). Faint red supergiant features were detected and resolved
with Keck spectroscopy. The velocity dispersion of $\sigma = 15.7$~\kms\ 
suggests a mass of $3 \times 10^5$~\Ms\ for the super star cluster. This mass
and the mass-to-light ratio are consistent with a single stellar population
formed about 10~Myr ago if the IMF has a Salpeter slope with stars forming
down to 1~--~2~\Ms\ (cf. Figure~9 of \cite{lh95}). A similar result was found
for the super star cluster in NGC~1705. If the simple dynamical model is 
correct, the IMF extends down to 1~--~2~\Ms\ but there is no dynamical
evidence for less massive stars.

\subsection{M 82: a case for a top-heavy IMF}

M~82 is the prototype of a dusty starbursting dwarf galaxy. The terminology 
of a ``top-heavy IMF'' for this galaxy was coined in an influential paper by
\cite{ri80}. Top-heavy indicates a higher proportion of red supergiants over
giants and dwarfs than expected for a normal IMF. 
In terms of mass, a top-heavy IMF has an excess of
stars in the mass range 10~--~20~\Ms\ over stars of 5~\Ms\ and less. 
Observational evidence for a top-heavy IMF in M~82 comes from the relatively
high K-band luminosity of the nucleus, together with its relatively low
dynamical mass. This results in a low $M/L$ ratio which can only be understood
if red giants and dwarfs (which produce mass) are deficient with respect to
supergiants (which
produce near-IR light). Low-mass cut-offs around 3~--~5~\Ms\ are required. 
Additional support for a top-heavy IMF has been found in some other 
galaxies as well, although the case is far from settled (see \cite{sc90}).

Whether the M~82 IMF is indeed top-heavy is critically dependent on the
adopted dynamical mass, the extinction correction, and the star-formation
history. If the starburst is not condensed in a central cluster but
rather spread out over a few hundred pc as a result of sequential star
formation, all observational constraints can be satisfied with a standard
Salpeter IMF extending to 0.1~\Ms\ (\cite{sa97}). However, such 
a model would use up 30\% of the total dynamical mass. This is an uncomfortably
large percentage since it is
unlikely that the starburst accounts for most of even the stellar mass due
to the presence of an older pre-existing population. 

The obvious alternative
would be an IMF with a somewhat larger value of \Mlow, closer to the
original top-heavy IMF concept. Although quantitative modeling has yet to be
done, my feeling is that the low-mass IMF in R136 of \cite{si98} may be
consistent with all constraints in M~82 as well. If so, the starburst IMF is
indeed mildly top-heavy.

\subsection{NGC 5253: age gradients from clusters}

Star clusters may provide useful constraints on the low-mass IMF even if a
dynamical mass determination is not available. NGC~5253, a dwarf galaxy in the
Centaurus group serves as an example (\cite{ca97}). Star formation in this
galaxy is concentrated in numerous star clusters whose properties are very
similar to those in NGC~1569 or NGC~1705. \cite{ca97} studied the six brightest
clusters and found ages ranging between a few to 60~Myr. Older clusters may
exist but are beyond the detection limit. The properties of the {\em cluster 
population} can (at least in principle) give constraints in the IMF.

The maximum cluster age of 60~Myr corresponds to a main-sequence turn-off mass
of $\sim$7~\Ms. This immediately suggests that the IMF extends to at least
\Mlow~$\approx$~7~\Ms. If the IMF were truncated at this mass, the cluster
color should turn very red: when the turn-off mass reaches \Mlow, the cluster
becomes unusually red since
a ``naked'' red giant population is observed in the absence of a bluer
main-sequence population (\cite{ch93}). If clusters with ages of more than
a few hundred Myr are found, a stability argument can be made in favor of
a large cluster mass, or equivalently, for the presence of low-mass stars. 
Otherwise the  cluster evaporation timescales are shorter than the observed
ages (cf. \cite{te87}). The underlying assumption of all these arguments is
of course that the clusters themselves form nearly instantaneous, with little 
subsequent star formation. Observations of individual clusters in the Galaxy
and the Magellanic Clouds generally support this assumption (\cite{mdg95}).
   
\subsection{I Zw 18: formation of Wolf-Rayet stars}

I will now turn to the high-mass end of the IMF. Wolf-Rayet stars are
a particularly sensitive tracer since they are considered the evolved 
descendants of the most massive O stars (\cite{mc94}). Wolf-Rayet stars form
out of more massive progenitors by stellar mass loss via radiatively
driven winds. The mass-loss efficiency scales with the far-ultraviolet
radiation field so that the most luminous, and therefore the most massive
stars have the strongest winds and are the most important evolutionary channel
for Wolf-Rayet formation. Wolf-Rayet features
have been detected in some fraction of H~II galaxies. Their strength requires
a massive star population following a Salpeter (or even slightly flatter) IMF
(\cite{mc94}, \cite{my95}, \cite{sv98}).

I~Zw~18 is still the most metal-poor galaxy known (\cite{it98}). The recent
detection of Wolf-Rayet stars in I~Zw~18 (\cite{le97}, \cite{iz97},
\cite{du98}) imposes rather stringent limits on the upper end of the IMF.
Mass loss becomes less and less efficient at lower metallicity due to the
weakening of the driving spectral lines. Therefore only the most massive 
main-sequence stars evolve into Wolf-Rayet stars at low metallicity.
As a caveat, the assumption is made that Wolf-Rayet stars originate
predominantly from single stars. If binaries are important, this argument
would be weakened (\cite{vb97}).
Quantitative modeling by \cite{du98} suggests that the observed Wolf-Rayet
population in I~Zw~18 evolved from progenitor stars with masses of at least
100~\Ms. These masses are similar to those derived for individual hot stars
in the R136 cluster by \cite{ko97}, indicating a similar IMF at the high-mass 
end.

\subsection{NGC 1741: high-redshift analog (?)}

NGC~1741 is a luminous ($L \approx L^\star$) Magellanic-type irregular at
a distance of 50~Mpc. The spatial morphology is dominated by two main
starburst centers, each being about 100 times as luminous as 30~Doradus.
Both starburst centers are composed of several intense knots of recent star
formation. The starburst region NGC~1741B1  was observed in the ultraviolet
with HST's GHRS and analyzed by \cite{co96} and
\cite{jo98}. A section of the ultraviolet
spectrum is shown in Figure~\ref{profiles}.
The most prominent lines are \civ\ and \siiv. These lines
have broad absorptions and/or emissions due to their origin in stellar
winds from hot stars. They can be used to constrain the IMF of the underlying
stellar population (\cite{lrh95}, \cite{le96}): the profiles contain 
information on the wind momentum flux, and since radiation pressure is the 
driving force, on the stellar luminosity. 
Evolution models predict a stellar mass-luminosity relation so that
the line profiles are eventually tied to the stellar mass. 
Evolutionary synthesis modeling leads to a
prediction for the ultraviolet spectrum of a population of massive stars.

\begin{figure}
\psfig{figure=pp1254f3.ps,height=14cm,width=16cm}
\caption[fig]{\label{profiles} Comparison between the observed spectrum 
of NGC~1741B1 around
\siiv\ and \civ\ (full lines) and synthetic spectra for three IMF slopes
(dashed lines). Upper panel: $\Gamma = -0.5$; middle: $\Gamma = -1.35$
(Salpeter slope); lower: $\Gamma = -2.0$. Other parameters of the
synthetic spectra are: continuous star formation, $t = 5$~Myr, $Z$~=~\Zs,
\Mlow~=~1~\Ms, \Mup~=~100~\Ms\ (from \cite{jo98}).}
\end{figure}

The purpose of Figure~\ref{profiles} is to illustrate how an IMF can be derived
from the analysis of integrated light but also to raise the awareness for the
limits of this method. The general trend in the figure is easy to understand: 
the larger the fraction of early-O stars (responsible for the stellar-wind 
lines) relative to late-O/early-B  stars (responsible for the continuum), the 
more pronounced the observed P~Cygni profiles. A larger fraction of early-O 
stars translates into a flatter IMF.
The \civ\ and \siiv\ profiles indicate a standard IMF
with a Salpeter slope ($\Gamma = -1.35$) in the mass range between 15 and
100~\Ms. A much flatter IMF produces an excess of blueshifted wind absorption
whereas a much steeper IMF underpredicts the wind emission. Note that the
narrow absorptions at rest wavelength are interstellar and therefore not
included in the wind modeling. The conclusion from Figure~\ref{profiles} is
that it is difficult to constrain the IMF exponent to better than 
$\pm 0.5$.

NGC~1741 has become the favorite local analog of star-forming dwarf galaxies
at high redshift (e.g., \cite{lo97}) whose restframe ultraviolet spectra 
are quite similar to that of NGC~1741B1. The lensed star-forming galaxy
cB58 at a redshift of $z = 2.723$ has been discussed, e.g., by \cite{ye96}
and \cite{pe97}. A quantitative comparison with NGC~1741 should be taken cum
grano salis due to the metallicity difference but it is safe to conclude that
a young population with stellar masses above $\sim$30~\Ms\ and age of 10~Myr
or less is present. Otherwise the observed stellar lines could not be 
understood. Nothing is known about the low-mass star content but if local
starbursts are taken as analogs, there should be few recently formed stars
below $\sim$1~\Ms. Star-formation rates derived from an extrapolation of the IMF
below $\sim$1~\Ms\ would likely be an overestimate.
                                                        
\section{Conclusions and recommendations to ``IMF users''} 

The IMF in local dwarf galaxies has been derived using several independent
observational techniques. The accessible stellar masses are between 100~\Ms,
where stochastic effects due to small-number statistics set in, and 1~\Ms,
where the observational sensitivity limit is reached. Additional constraints
on the IMF can be obtained from the galactic chemical composition and its time 
evolution (e.g., \cite{ws93}, \cite{ca95}). This field is reviewed elsewhere
in this conference.

A major source of uncertainty is stellar evolutionary theory, which enters 
in essentially all
IMF determinations: at the high-mass end for O supergiants and Wolf-Rayet stars,
at intermediate masses for red supergiants and red giants, and at the lowest
masses for pre-main-sequence stars. Other areas of concern are stellar
atmospheres and cluster dynamics.

Most studies suggest a rather uniform IMF in dwarf galaxies. Considering the
very different observational techniques used and the prevailing theoretical
uncertainties, this result appears to have some significance. In general, the
IMF in dwarf galaxies is not too different from the IMF in the solar 
neighborhood, except perhaps for the lowest masses. In the absence of tighter
observational constraints, and since observers have a preference for power
laws, I will use a power-law approximation for the derived IMF. Note, however,
that this may detract from the actual astrophysical meaning of the initial
mass function. 
\begin{itemize}
\item At the high-mass end ($>10$~\Ms), the average IMF has a slope
of $\Gamma \approx -1.35 \pm 0.5$, where the range is due to the measurement
uncertainties. Correlations with environmental parameters have been searched
for, but none have been found.
\item There is a trend for a somewhat steeper IMF ($\Gamma \approx -1.6$)
at lower masses between
3 and 10~\Ms, although the effect is barely significant. This value is similar
to that of the solar neighborhood found by \cite{sc86}.
\item The low-mass end below 3~\Ms\ is most controversial. Observational 
methods are too crude and results too sparse to quote an average IMF. There
appears to be a deficit stars which could be due to a low-mass cut-off, or
more likely, a flattening of the IMF.
\end{itemize}

Although the IMF is the major link between the theory of the star-formation
process and galaxy evolution, it is often only needed by observers as a
parameter to model the energy output of a galaxy, such as the spectrum, the
metal production, or the supernova rate. A power-law approximation with a 
slope of $\Gamma = -1.35$ between 1 and 100~\Ms\ should be adequate for this 
purpose. This IMF reproduces the distribution of those stars which are
the most important contributors to the observed spectrum. It also
mimics the total mass and therefore the star-formation rate by neglecting
both the IMF steepening between 3 and 10~\Ms\ and the flattening or cut-off
at lower masses. For comparison, the commonly used extrapolation of a 
Salpeter IMF to 0.1~\Ms\ would overestimate the star-formation rate by a
factor of 2.5. 

\bigskip
\bigskip
\noindent {\bf Acknowledgements.} It is a pleasure to thank the organizers for 
setting up this conference in such a stimulating environment. Financial 
support from
the STScI DDRF and from the conference organizers is gratefully acknowledged.
Torsten B\"oker, Daniel Devost, Daniel Kunth, Denise Smith, and Monica Tosi 
 provided comments and suggestions which improved the
paper significantly. I am grateful to Ariane Lan\c{c}on for French language
assistance. 

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