Diffuse radio sky models using large-scale shapelets

Aims . Sky models used in radio interferometric data-processing primarily consist of compact and discrete radio sources. When there is a need to model large-scale diffuse structure such as the Galaxy, specialized source models are sought after for the sake of simplicity and computational efficiency. We propose the use of shapelet basis functions for modeling the large-scale diffuse structure in various radio interferometric data-processing pipelines. Methods . The conventional source model construction using shapelet basis functions is restricted to using images of smaller size due to limitations in computational resources such as memory. We propose a novel shapelet decomposition method to lift this restriction, enabling the use of images of millions of pixels (as well as a wide spectral bandwidth) for building models of large-scale diffuse structure. Furthermore, the application of direction-dependent errors onto diffuse sky models is an expensive operation that is often performed as a convolution. We propose using some specific properties of shapelet basis functions to apply these direction-dependent errors as a product of the model coefficients, which avoids the need for convolution. Results . We provide results based on simulations and real observations. In order to measure the efficacy of our proposed method in modeling large-scale diffuse structure, we considered the direction-dependent calibration of simulated as well as real LOFAR observations that have a significant number of diffuse large-scale structure. The results show that by including large-scale shapelet models of the diffuse sky, we are able to overcome a major problem of existing calibration techniques, which do not model this large-scale diffuse structure, that is, the suppression of this large-scale diffuse structure because the model is incomplete.