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.
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