We have obtained images of the Trapezium Cluster ( 140 \arcsec \times 140 \arcsec ; 0.3 pc \times 0.3 pc ) with the Hubble Space Telescope Near-Infrared Camera and Multi-Object Spectrometer ( NICMOS ) .
Combining these data with new ground-based K -band spectra ( R = 800 ) and existing spectral types and photometry , we have constructed an H-R diagram and used it and other arguments to infer masses and ages .
To allow comparison with the results of our previous studies of IC 348 and \rho Oph , we first use the models of D ’ Antona & Mazzitelli .
With these models , the distributions of ages of comparable samples of stars in the Trapezium , \rho Oph , and IC 348 indicate median ages of \sim 0.4 Myr for the first two regions and \sim 1 -2 Myr for the latter .
The low-mass IMFs in these sites of clustered star formation are similar over a wide range of stellar densities ( \rho Oph , n = 0.2 - 1 \times 10 ^ { 3 } pc ^ { -3 } ; IC 348 , n = 1 \times 10 ^ { 3 } pc ^ { -3 } ; Trapezium , n = 1 - 5 \times 10 ^ { 4 } pc ^ { -3 } ) and other environmental conditions ( e.g. , presence or absence of OB stars ) .
With current data , we can not rule out modest variations in the substellar mass functions among these clusters .
We then make the best estimate of the true form of the IMF in the Trapezium by using the evolutionary models of Baraffe et al .
and an empirically adjusted temperature scale and compare this mass function to recent results for the Pleiades and the field .
All of these data are consistent with an IMF that is flat or rises slowly from the substellar regime to about 0.6 M _ { \odot } , and then rolls over into a power law that continues from about 1 M _ { \odot } to higher masses with a slope similar to or somewhat larger than the Salpeter value of 1.35 .
For the Trapezium , this behavior holds from our completeness limit of \sim 0.02 M _ { \odot } and probably , after a modest completeness correction , even from 0.01-0.02 M _ { \odot } .
These data include \sim 50 likely brown dwarfs .
We test the predictions of theories of the IMF against 1 ) the shape of the IMF , which is not log-normal , in clusters and the field , 2 ) the similarity of the IMFs among young clusters , 3 ) the lowest mass observed for brown dwarfs , and 4 ) the suggested connection between the stellar IMF and the mass function of pre-stellar clumps .
In particular , most models do not predict the formation of the moderately large numbers of isolated objects down to 0.01 M _ { \odot } that we find in the Trapezium .