Illustration of the scaling method with the ratio of two different blackbody curves and that many pairs of T_ref,1 and T_ref,2 can produce the same blackbody ratio curve. In the top panel, the RGS1 spectrum of RS Oph from 2021d55.6 (black) is multiplied with the ratio of two blackbody models corresponding to T_ref,1 = 5 × 10⁵ K (=500 kK) and T_ref,2 = 4 × 10⁵ K (=400 kK), respectively and normalised (see legend). The resulting spectrum (orange) is a factor 20 brighter but is also harder. The bottom panel shows the results of fitting only T_ref,2 with (black) and without (orange) additional normalisation while T_ref,1 is fixed at given grid values (x-axis) to reproduce the 500 kK/400 kK ratio curve. The bottom right legend provides empirical analytic relationships between fixed grid value and T_2,best values reproducing the same ratio curve. The same relationships are found for any other pairs of reference temperatures T_ref,1 and T_ref,2; see Sect. 3.2.2 for details.