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.
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