Observations of submillimeter lines of CO, HCO+, HCN and their isotopes fro
m circumstellar disks around low mass pre-main sequence stars are presented
. CO lines up to J = 6 -->5, and HCO+ and HCN lines up to J = 4 -->3, are d
etected from the disks around LkCa 15 and TW Hya. These lines originate fro
m levels with higher excitation temperatures and critical densities than st
udied before. Combined with interferometer data on lower excitation lines,
the line ratios can be used to constrain the physical structure of the disk
. The different line ratios and optical depths indicate that most of the ob
served line emission arises from an intermediate disk layer with high densi
ties of 10(6) -10(8) cm(-3) and moderately warm temperatures in the outer r
egions. The data are compared with three different disk models from the lit
erature using a full 2D Monte Carlo radiative transfer code. The abundances
of the molecules are constrained from the more optically thin C-13 species
and indicate depletions of approximate to 1-30 for LkCa 15 and very high d
epletions of >100 for TW Hya with respect to dark cloud abundances. Evidenc
e for significant freeze-out (factors of 10 or larger) of CO and HCO+ onto
grain surfaces at temperatures below 22 K is found, but the abundances of t
hese molecules must also be low in the warmer upper layer, most likely as a
result of photodissociation. A warm upper layer near the surface of a flar
ing disk heated by stellar and interstellar radiation is an appropriate des
cription of the observations of TW Hya. LkCa 15 seems to be cooler at the s
urface, perhaps due to dust settling. The density constraints are also well
fitted by the flared disk models.