We present 2D Monte Carlo radiative transfer simulations of prestellar cores . We consider two types of asymmetry : disk-like asymmetry , in which the core is denser towards the equatorial plane than towards the poles ; and axial asymmetry , in which the core is denser towards the south pole than the north pole . In both cases the degree of asymmetry is characterized by the ratio e between the maximum optical depth from the centre of the core to its surface and the minimum optical depth from the centre of the core to its surface . We limit our treatment here to mild asymmetries with e = 1.5 and 2.5 . We consider both cores which are exposed directly to the interstellar radiation field and cores which are embedded inside molecular clouds . The SED of a core is essentially independent of the viewing angle , as long as the core is optically thin . However , the isophotal maps depend strongly on the viewing angle . Maps at wavelengths longer than the peak of the SED ( e.g . 850 \mu m ) essentially trace the column-density . This is because at long wavelengths the emissivity is only weakly dependent on temperature , and the range of temperature in a core is small ( typically T _ { max } / T _ { min } \la 2 ) . Thus , for instance , cores with disk-like asymmetry appear elongated when mapped at 850 \mu m from close to the equatorial plane . However , at wavelengths near the peak of the SED ( e.g . 200 \mu m ) , the emissivity is more strongly dependent on the temperature , and therefore , at particular viewing angles , there are characteristic features which reflect a more complicated convolution of the density and temperature fields within the core . These characteristic features are on scales 1 / 5 to 1 / 3 of the overall core size , and so high resolution observations are needed to observe them . They are also weaker if the core is embedded in a molecular cloud ( because the range of temperature within the core is then smaller ) , and so high sensitivity is needed to detect them . Herschel , to be launched in 2007 , will in principle provide the necessary resolution and sensitivity at 170 to 250 \mu m .