L/M-ratios (left-hand figure) and the effective dust temperatures (right-hand figure) for embedded passively heated cores. The values obtained using ray-tracing (symbols) are compared with the approximate solutions for cores in spheres (solid curves) and cylinders (dashed curves). The different symbols refer to the external pressures (shown as vertical grey lines) assumed in the calculations: diamonds 2  ×  10⁴   K/cm³, triangles 10⁵   K/cm³, and squares 10⁶   K/cm³. They are labelled according to the extinction A_V through the filament center. The dotted line in the left-hand figure shows the asymptote Eq. (17) for non-embedded cores (A_V = 0   mag), where the external radiation heating the core is completely absorbed.