  Constraining the temperature and density structure of dense molecular cloud
cores is fundamental for understanding the initial conditions of star
formation. We use Herschel observations of the thermal FIR dust emission from
nearby isolated molecular cloud cores and combine them with ground-based
submillimeter continuum data to derive observational constraints on their
temperature and density structure. The aim of this study is to verify the
validity of a ray-tracing inversion technique developed to derive the dust
temperature and density structure of isolated starless cores directly from the
dust emission maps and to test if the resulting temperature and density
profiles are consistent with physical models. Using this ray-tracing inversion
technique, we derive the dust temperature and density structure of six isolated
starless cloud cores. We employ self-consistent radiative transfer modeling to
the derived density profiles, treating the ISRF as the only heating source. The
best-fit values of local strength of the ISRF and the extinction by the outer
envelope are derived by comparing the self-consistently calculated temperature
profiles with those derived by the ray-tracing method. We find that all
starless cores are significantly colder inside than outside, with the core
temperatures showing a strong negative correlation with peak column density.
This suggests that their thermal structure is dominated by external heating
from the ISRF and shielding by dusty envelopes. The temperature profiles
derived with the ray-tracing inversion method can be well-reproduced with
self-consistent radiative transfer models.
