Inaccuracies and biases of the Gaussian size deconvolution for extracted sources and filaments

A simple Gaussian size deconvolution method is routinely used to remove the blur of observed images caused by insufficient angular resolutions of existing telescopes, thereby to estimate the physical sizes of extracted sources and filaments. The size deconvolution method is expected to work when the structures, as well as the telescope beams, have Gaussian shapes. This study employs model images of the spherical and cylindrical objects with Gaussian and power-law shapes, representing the dense cores and filaments. The images are convolved to a wide range of angular resolutions to probe various degrees of resolvedness of the models. Simplified flat, convex, and concave backgrounds are added to the images, then planar backgrounds across the footprints of the structures are subtracted and sizes are measured and deconvolved. When background subtraction is inaccurate, the structures acquire profoundly non-Gaussian profiles. The deconvolved half maximum sizes can be strongly under- or overestimated, by factors of up to ~20 when the structures are unresolved or partially resolved. For resolved structures, the errors are within a factor of ~2, although for some power-law models show the factors of up to ~6. The size deconvolution method cannot be applied to unresolved structures, it can be used only for the Gaussian-like structures, including the critical Bonnor-Ebert spheres, when they are at least partially resolved. The method must be considered inapplicable for the power-law structures with shallow profiles. This work also reveals subtle properties of convolution for different geometries. When convolved with different kernels, spherical objects and cylindrical filaments with identical profiles obtain different widths and shapes. A filament, imaged by the telescope with a non-Gaussian PSF, could appear substantially shallower than the structure is in reality, even when it is resolved.