We present a study of molecular-hydrogen absorption lines in the continuum
spectra of three early-type stars in the Carina Nebula, HD 93129a, HD 93250
, and HD 303308, made with the Berkeley Extreme and Far-Ultraviolet Spectro
meter (BEFS) on the ORFEUS telescope in 1993 September. The instrument poss
esses an intermediate spectral resolving power (lambda/Delta lambda = 3000)
over the wavelength range lambda lambda 390-1170. We derive column densiti
es for the H-2 rotational levels up to J" = 6 and estimate the kinetic temp
erature and the UV radiation fields at the surface of the clouds in the neb
ula. All three stars show strong H-2 absorption features, indicating that t
he Carina Nebula contains abundant molecular hydrogen. The UV radiation fie
ld strength seems to be correlated with the angular distance of the target
star from eta Car, implying that the clouds might be located close to eta C
ar. We derive the absolute distances between the clouds and eta Car, which
are in good agreement with the angular positions of these stars. We also ex
amine the morphology of the Carina Nebula based on the present result, as w
ell as previous CO observations, and derive the conversion factor N(H-2)/W(
(CO)-C-12) in this region.