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In all cases involving short spacings, the relative weight of the single dish data to interferometer data is critical. Within the restrictions imposed by the noise level, this relative weight is a free parameter. It is all the more important that the Fourier transform of the uv plane density of weights is the dirty beam, a key parameter of the deconvolution. The general goal is to have a dirty beam as close as possible to a Gaussian. As the Fourier transform of a Gaussian is a Gaussian, we search for obtaining a uv plane density of weights as close as possible to a Gaussian. In general, the short spacing frequencies are small compared to the largest spatial frequency measured by an interferometer. This implies we can use the linear approximation of a Gaussian, i.e. a constant, in the range of frequencies used for the short spacing processing. We thus end up with the need to match (as far as possible) the Single-Dish and interferometric densities of weights in the uv plane. In practice, we compute the density of weights from the single-dish in a uv circle of radius 1.25 d and we match it to the averaged density of weights from the interferometer in a uv ring between 1.25 and 2.5 d. Experience shows that this gives the right order of magnitude for the relative weight and that a large range of relative weight around this value gives very similar final results.
When processing IRAM-30m data to combine to NOEMA data, this criterion implies a large down-weighting of the IRAM-30m data which may make think that too much observing time was used at the IRAM-30m data. However, just using the above criterion to determine the observing time needed at the IRAM-30m would in general lead to very low signal-to-noise ratio of the single-dish map. In such a case, it is very difficult to detect problems which would translate in strong artifacts in the IRAM-30m + NOEMA combination. We recommend to ask for enough IRAM-30m time to get a median signal-to-noise ratio of 5 on the single-dish map. This ratio should be achieved for all velocity channels of interest (which may include the line wings).