Mapping low-frequency carbon radio recombination lines towards Cassiopeia A at 340, 148, 54, and 43 MHz

Quantitative understanding of the interstellar medium requires knowledge of its physical conditions. Low-frequency carbon radio recombination lines (CRRLs) trace cold interstellar gas and can be used to determine its physical conditions (e.g. electron temperature and density). In this work, we present spatially resolved observations of the low-frequency (<= 390 MHz) CRRLs centred around C268 alpha, C357 alpha, C494 alpha, and C539 alpha towards Cassiopeia A on scales of <= 1.2 pc. We compare the spatial distribution of CRRLs with other interstellar medium tracers. This comparison reveals a spatial offset between the peak of the CRRLs and other tracers, which is very characteristic for photodissociation regions and that we take as evidence for CRRLs being preferentially detected from the surfaces of molecular clouds. Using the CRRLs, we constrain the gas electron temperature and density. These constraints on the gas conditions suggest variations of less than a factor of 2 in pressure over similar to 1 pc scales, and an average hydrogen density of 200-470 cm(-3). From the electron temperature and density maps, we also constrain the ionized carbon emission measure, column density, and path length. Based on these, the hydrogen column density is larger than 10(22) cm(-2), with a peak of similar to 4 x 10(22) cm(-2) towards the south of Cassiopeia A. Towards the southern peak, the line-of-sight length is similar to 40 pc over a similar to 2pc wide structure, which implies that the gas is a thin surface layer on a large (molecular) cloud that is only partially intersected by Cassiopeia A. These observations highlight the utility of CRRLs as tracers of low-density extended HI and CO-dark gas halo's around molecular clouds.