Cumulative χ2 distributions when Td and βd are fixed in the filtering (solid red curve) or when they are left free (solid blue curve). Top panel: distribution for a dust-only filtering on a dust-only mock catalogue. Bottom panel: distribution for a dust + tSZ filtering on a dust + tSZ mock catalogue. In both cases (dust-only or dust + tSZ), fixing Td and βd leads to a χ2 distribution with seven degrees-of-freedom (corresponding to our seven maps), while leaving them free reduces the number of degrees-of-freedom to five.
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