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at a distance of about 2  mpc @xcite , the irregular galaxy ngc  1569 is one of the nearest starbursts @xcite .
it is rich in ionized and neutral gas , and recently underwent a global starburst that lasted at least 100  myr and ended 510  myr ago @xcite .
the starburst produced numerous hii regions and young star clusters , and still drives an x - ray superwind @xcite .
one of the most notable features of the starburst is the super star clusters ( sscs ) near the center of the galaxy @xcite .
they are some of the nearest and earliest - known examples of young , massive , compact star clusters .
these sscs , which may evolve into clusters resembling present - day globulars @xcite , have been found in all types of starburst environments , from dwarf irregulars to galaxy mergers .
we obtained spectra and images of the sscs in ngc  1569 on january 17 , 2000 ut using the near - infrared spectrometer nirspec on the keck ii telescope at the w. m. keck observatory .
the night was photometric , with seeing of about @xmath4 .
the _ k_-band image ( taken with the n7 filter by nirspec s slit - viewing camera ) in fig .
[ kimage ] shows the brightest central sscs of which we obtained _
k_-band spectra ( 2.032.47  @xmath5 m ) , along with many other clusters and stellar sources . for the brightest clusters ,
sscs a and b , we also obtained _ h_-band spectra ( 1.491.78  @xmath5 m ) .     seeing .
clusters for which spectra were obtained are labeled ]    date were reduced in the usual fashion , and the optimally extracted _
k_-band spectra are shown in fig .
[ spectra]a .
the strongest features in _
k _ band are the co first overtone bands longward of 2.295  @xmath5 m .
these saturated bands are found in the cool atmospheres of supergiants and giants .
their presence implies that the clusters contain stars that are at least 6 or 7  myr old , since that much time is required before the most massive stars evolve off of the main sequence .
stellar evolution models for a simple stellar population predict that the hot blue stars capable of driving nebular emission will have completely evolved off of the main sequence by the time red supergiants appear . thus the conjunction of strong co bands together with weak br@xmath6 and he emission in the spectra of clusters a and c1 suggests that they are not instantaneous bursts . in the case of cluster c1
we believe that the weak emission lines are explained by contamination from a nearby hii region @xcite .
the weak nebular emission from ssc a ( a double cluster @xcite ) is likely due to the wolf - rayet stars known to be present there @xcite .
thus the spectrum of ssc a can not be explained with a single simple stellar population according to current population synthesis models .
cluster c2 , on the other hand , shows both br@xmath6 and hei in absorption , which may be due to a much older population dominated by a stars and red giants .     and
he emission , while c2 shows both of these in absorption .
( * b * ) _ h_-band spectra of sscs a and b with slopes removed , compared with the spectrum of a k1.5 ib supergiant @xcite . note the correspondence of features between star and cluster spectra , and the richness of _ h _ band ]    optimally extracted _
h_-band spectra of sscs a and b are shown in fig .
[ spectra]b , together with the spectrum of a k1.5 ib supergiant from the kpno stellar atlases @xcite .
a comparison of the star and cluster spectra reveals that most of the features in the cluster spectra are real , not noise , and that _
photospheric spectra are remarkably rich in strong metallic and molecular features .
only the co bands stand out in the _ k_-band spectra , while many metal features in _ h _ band are as strong as the second overtone co bands .
most of the features in _
band are blends of lines from co , oh , and metals such as fe , si , al , and mg .
the most massive , evolved members of a single - aged stellar population tend to dominate its integrated light .
thus the simplest approach to interpreting the integrated light may be to ask , what is the dominant spectral type of the cluster ?
we attempt to characterize a cluster by an effective spectral type by fitting its _ h_- and _ k_-band spectra to a grid of nextgen model atmospheres @xcite , in order to determine an effective temperature , surface gravity , and metallicity for each object .
the nextgen atmospheres were available for spherically symmetric giant stars with a range in t@xmath2 of 3000  k to 6800  k , a range in @xmath7 of 0.0 to 3.5 , and metallicities of [ fe / h ] @xmath8 0.0 ( solar ) , @xmath90.3 , @xmath90.5 , and @xmath90.7 .
we first test the utility of this procedure by fitting the model atmospheres to an empirical spectrum of a star of known spectral type to evaluate the precision and accuracy with which it selects the atmospheric parameters .
[ chi2]a shows the resulting @xmath10 contours for a fit to a solar - metallicity k1.5  ib spectrum .
the resulting parameters , t@xmath11  k and @xmath12 , are a good match to those of the star . both _ h_- and _ k_-band spectra were required in order to remove degeneracies in the fits .
contours for fit of nextgen models for : ( * a * ) spectrum of a k1.5 ib star ; ( * b * ) ssc  b ; ( * c * ) ssc  a. white filled contour indicates 1  sigma confidence level , and line contours represent 90 , 95 , and 99% confidence limits .
best - fit parameters for ssc b imply an effective spectral type for the cluster light of k0 supergiant .
best - fit parameters for ssc a imply an effective spectral type for the cluster light of g5 supergiant with @xmath13 .
the temperature and range of @xmath7 are consistent with a mixed population of stars , either two short bursts or an extended epoch of star formation ]    next we fit the nextgen atmospheres at metallicity [ fe / h ] @xmath14 ( which is closest to that of ngc  1569 , [ fe / h ] @xmath15 to @xmath16 @xcite ) to the _ h _ + _ k _ spectra of the brightest _
k_-band cluster , ssc b. the resulting @xmath10 contours in fig .
[ chi2]b have the same shape as those found for the star in fig .
[ chi2]a , indicating that the light of cluster b is heavily dominated by stars with a very narrow range in spectral type .
the effective spectral type for ssc b is that of a k0 supergiant , with t@xmath11  k and @xmath17 .    for the double cluster , ssc a , the @xmath10 contours are less tightly constrained in the fit parameters than for ssc b. fig .
[ chi2]c shows them to be centered at a hotter t@xmath18  k and larger range of @xmath19 , typical for stars of types g5 i and g5 iii .
it is unlikely , however , that such stars dominate the cluster s emission , since optical / uv evidence indicates that hot blue wolf - rayet stars are present together with the red evolved stars creating the strong infrared co bands .
thus the inferred effective spectral type determined from the stellar atmospheres may simply result from the superposition of the two distinct populations .
since a cluster consists of stars with a range of stellar masses , luminosities , and temperatures , it is more informative to model the integrated population directly than to focus on its effective spectral type .
thus we employ the technique of population synthesis to calculate the distribution of stars in the h - r diagram of a cluster as a function of time .
we then calculate the integrated spectrum of the cluster by adding the appropriate numbers of stellar spectra  either empirical spectra or model atmospheres .      all models in this paper
were constructed using the updated evolutionary synthesis code starburst99 @xcite .
the code incorporates the most recent stellar evolutionary tracks from the geneva group at metallicities ranging from very metal - poor , to twice solar metallicity @xcite , and it has been updated to allow the use of isochrone synthesis .
starburst99 is a particular set of synthesis models which are optimized to reproduce properties of galaxies with active star formation , so it puts most of the emphasis on early evolutionary phases .
later phases , like agb stars or white dwarfs , are covered only crudely or not at all .
origlia et al .
@xcite show that low - metallicity tracks do not reproduce the co 1.62  @xmath5 m and co 2.29  @xmath5 m indices of young lmc clusters
. however , if the fraction of time spent as a rsg during the core - helium phase is forced to at least 50% , and if the rsg temperature is maintained to less than 4000  k , the models agree well with the observations .
our modeling technique was modified according to this prescription ( leitherer , private communication , 2000 ) .    in order to generate model cluster spectra
, we combine the starburst99 models with the empirical libraries of stellar spectra obtained at kitt peak by wallace & hinkle @xcite and meyer et  al .
for a given cluster population , we add up the spectra of component stars , and include nebular continuum emission ( but not the recombination lines ) based on the number of ionizing photons predicted for the cluster . thus we generate a time series of model cluster spectra such as that shown in fig .
[ mod]a for a 10@xmath20  m@xmath21 cluster with salpeter imf ranging from 0.1 to 100  m@xmath21 . for the first few myr ,
nebular emission powered by the hottest stars dilutes the photospheric emission from the cluster , but by an age of 67  myr , the most massive stars have evolved off of the main sequence to become red supergiants , whose spectra are marked by deep co bands .    finally , we can place observed cluster spectra in an evolutionary sequence by fitting them to the model sequences .
figure  [ mod]b displays the _ h_-band spectra of sscs a and b together with the three model cluster spectra ( 15 , 18 , and 21 myr ) which most closely resemble the observations . note the correspondence between features and the decrease in their strength with time . since the models are for solar metallicity clusters , they presumably have stronger metal features at a given age than expected for a lower - metallicity cluster .
thus the age estimates we derive from these models will be too large during this epoch of the cluster s evolution .
we have presented new high - quality near - infrared spectra of several of the sscs in the nearby irregular starburst , ngc  1569 , and demonstrated the utility of the rich _ h_-band spectral region for modeling stellar populations . we found that combining _ h_- and _ k_-band spectra removed some of the degeneracy in fitting just one band to model spectra .
we used population synthesis models together with model stellar atmospheres and empirical stellar spectra to fit for the effective spectral type of a cluster , and to generate sequences of synthetic cluster spectra to help determine the ages of observed clusters .
since the empirical libraries are only complete for solar metallicity , we are constructing models that use model atmospheres at lower metallicities that are more appropriate for systems like ngc  1569 .
we present _ h_- and _ k_-band nirspec spectroscopy of super star clusters ( sscs ) in the irregular starburst galaxy ngc  1569 , obtained at the keck observatory . 
 we fit these photospheric spectra to nextgen model atmospheres to obtain effective spectral types of clusters , and find that the information in both _ h- and k_-band spectra is necessary to remove degeneracy in the fits . 
 the light of ssc b is unambiguously dominated by k0 supergiants ( t@xmath0  k , @xmath1 ) . 
 the double cluster ssc  a has higher t@xmath2 ( g5 ) and less tightly constrained surface gravity ( @xmath3 ) , consistent with a mixed stellar population dominated by blue wolf - rayet stars and red supergiants . 
 we predict the time evolution of infrared spectra of sscs using starburst99 population synthesis models coupled with empirical stellar spectral libraries ( at solar metallicity ) . 
 the resulting model sequence allows us to assign ages of 1518  myr for ssc  b and 1821  myr for ssc  a.