  We study the physical properties of 216 z ~ 2.1 LAEs discovered in an
ultra-deep narrow-band MUSYC image of the ECDF-S. We fit their stacked Spectral
Energy Distribution (SED) using Charlot & Bruzual templates. We consider star
formation histories parametrized by the e-folding time parameter tau, allowing
for exponentially decreasing (tau>0), exponentially increasing (tau<0), and
constant star formation rates. These LAEs are characterized by best fit
parameters and 68% confidence intervals of log(M_*/M_sun)=8.6[8.4-9.1],
E(B-V)=0.22[0.00-0.31], tau=-0.02[(-4)-18] Gyr, and age_ SF=0.018[0.009-3] Gyr.
Thus, we obtain robust measurements of low stellar mass and dust content, but
we cannot place meaningful constraints on the age or star formation history of
the LAEs. We also calculate the instantaneous SFR to be 35[0.003-170] M_sun/yr,
with its average over the last 100 Myr before observation giving
<SFR>_100=4[2-30] M_sun/yr. When we compare the results for the same star
formation history, LAEs at z~2.1 are dustier and show higher instantaneous SFRs
than z~3.1 LAEs, while the observed stellar masses of the two samples seem
consistent. LAEs appear to occupy the low-mass end of the distribution of star
forming galaxies at z~2. We perform SED fitting on several sub-samples selected
based on photometric properties and find that LAE sub-samples at z~2.1 exhibit
heterogeneous properties. The IRAC-bright, UV-bright and red LAEs have the
largest stellar mass and dust reddening. The UV-faint, IRAC-faint, and high
equivalent width LAE sub-samples appear less massive (<10^9 M_sun) and less
dusty, with E(B-V) consistent with zero.
