Strong dependence of the physical properties of cores on spatial resolution in observations and simulations

The angular resolution of a telescope is the primary observational parameter, along with the detector sensitivity in defining the quality of the observed images and of the subsequent scientific exploitation of the data. During the last decade in star formation research, many studies have targeted low- and high-mass star formation regions located at different distances, with different telescopes having specific angular resolution capabilities. However, no dedicated studies of the spatial resolution effects on the derived sizes and masses of the sources extracted from the observed images have been published. We present a systematic investigation of the angular resolution effects, with special attention being paid to the derived masses of sources as well as the shape of the resulting source mass functions (SMFs) and to their comparison with the initial stellar mass function. For our study, we chose two star-forming regions observed with Herschel, NGC 6334 and Aquila distant of 1750 and 460 pc respectively, and three (magneto)-hydrodynamical simulations, virtually positioned at the same distances as the observed regions. We built surface density maps with different angular resolutions by convolving the surface density images of the five regions to a set of four resolutions differing by a factor of two (9, 18, 36, and 72′′), which allowed us to cover spatial resolutions from 0.6 down to 0.02 pc. Then we detected and measured sources in each of the images at each resolution using getsf and we analysed the derived masses and sizes of the extracted sources. We find that the number of sources does not converge from 0.6 to ≳0.05 pc. It increases by about two when the angular resolution increases with a similar factor, which confirms that these large sources are cluster-forming clumps. Below 0.05 pc, the number of source still increases by about 1.3 when the angular resolution increases by two, suggesting that we are close to, but not yet at, convergence. In this regime of physical scales, we find that the measured sizes and masses of sources linearly depend on the angular resolution with no sign of convergence to a resolution-independent value, implying that these sources cannot be assimilated to isolated prestellar cores. The corresponding SMF peak also shifts with angular resolution, while the slope of the high-mass tail of the SMFs remains almost invariant. We propose that these angular resolution effects could be caused by the underestimated background of the unresolved sources observed against the sloping, hill-like backgrounds of the molecular clouds. If prestellar cores physically distinct from their background exist in cluster-forming molecular clouds, we conclude that their mass must be lower than reported so far in the literature. We discuss various implications for the studies of star formation: the problem of determining the mass reservoirs involved in the star-formation process; the inapplicability of the Gaussian beam deconvolution to infer source sizes; and the impossibility to determine the efficiency of the mass conversion from the cores to the stars. Our approach constitutes a simple convergence test to determine whether an observation is affected by angular resolution.