The density and temperature structures of dense cores in the L1495 cloud of the Taurus star-forming region are investigated using Herschel SPIRE and PACS images in the 70 $mu$m, 160 $mu$m, 250 $mu$m, 350 $mu$m and 500 $mu$m continuum bands. A sample
consisting of 20 cores, selected using spectral and spatial criteria, is analysed using a new maximum likelihood technique, COREFIT, which takes full account of the instrumental point spread functions. We obtain central dust temperatures, $T_0$, in the range 6-12 K and find that, in the majority of cases, the radial density falloff at large radial distances is consistent with the $r^{-2}$ variation expected for Bonnor-Ebert spheres. Two of our cores exhibit a significantly steeper falloff, however, and since both appear to be gravitationally unstable, such behaviour may have implications for collapse models. We find a strong negative correlation between $T_0$ and peak column density, as expected if the dust is heated predominantly by the interstellar radiation field. At the temperatures we estimate for the core centres, carbon-bearing molecules freeze out as ice mantles on dust grains, and this behaviour is supported here by the lack of correspondence between our estimated core locations and the previously-published positions of H$^{13}$CO$^+$ peaks. On this basis, our observations suggest a sublimation-zone radius typically $sim 10^4$ AU. Comparison with previously-published N$_2$H$^+$ data at 8400 AU resolution, however, shows no evidence for N$_2$H$^+$ depletion at that resolution.
Utilizing multi-wavelength dust emission maps acquired with $Herschel$, we reconstruct local volume density and dust temperature profiles for the prestellar cores B68 and L1689B using inverse-Abel transform based technique. We present intrinsic radia
l dust temperature profiles of starless cores directly from dust continuum emission maps disentangling the effect of temperature variations along the line of sight which was previously limited to the radiative transfer calculations. The reconstructed dust temperature profiles show a significant drop in core center, a flat inner part, and a rising outward trend until the background cloud temperature is reached. The central beam-averaged dust temperatures obtained for B68 and L1689B are 9.3 $pm$ 0.5 K and 9.8 $pm$0.5 K, respectively, which are lower than the temperatures of 11.3 K and 11.6 K obtained from direct SED fitting. The best mass estimates derived by integrating the volume density profiles of B68 and L1689B are 1.6 M_sol and 11 M_sol, respectively. Comparing our results for B68 with the near-infrared extinction studies, we find that the dust opacity law adopted by the HGBS project, $kappa_{lambda} =0.1(lambda/300 mu m)^{-2}$, agrees to within 50% with the dust extinction constraints
