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

Abstract

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. To ensure that the physical conclusions derived from observations are correct, it is necessary to know the inaccuracies and biases of the size deconvolution method, which is expected to work when the structures, as well as the telescope beams, have Gaussian shapes. This study employed model images of the spherical and cylindrical objects with Gaussian and power-law shapes, representing the dense cores and filaments observed in star-forming regions. The images were convolved to a wide range of angular resolutions to probe various degrees of resolvedness of the model objects. Simplified shapes of the flat, convex, and concave backgrounds were added to the model images, then planar backgrounds across the footprints of the structures are subtracted and sizes of the sources and filaments were measured and deconvolved. When background subtraction happens to be inaccurate, the observed 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 generally within a factor of ~2; although, the deconvolved sizes can be overestimated by factors of up to ~6 for some power-law models. The results show that Gaussian size deconvolution cannot be applied to unresolved structures, whereas it can only be applied to the Gaussian-like structures, including the critical Bonnor-Ebert spheres, when they are at least partially resolved. The deconvolution method must be considered inapplicable for the power-law sources and filaments with shallow profiles. This work also reveals subtle properties of convolution for structures of different geometry. When convolved with different kernels, spherical objects and cylindrical filaments with identical profiles obtain different widths and shapes. In principle, a physical filament, imaged by the telescope with a non-Gaussian point-spread function, could appear substantially shallower than the structure is in reality, even when it is resolved.