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tokens: spectroscopy leads to more detailed models being needed to fully describe the data. Our knowledge of many aspects of these models is not yet complete (for example the possible presence of additional astrophysical components in the line of sight towards the source and imperfect atomic data) and we also have to deal with imperfect instrumental calibration, systematic effects and statistical fluctuations, so there will necessarily be differences between the data and the best physical model that can be found. As discussed in Blustin et al. (2002) , the use of goodness-of-fit statistics when modelling RGS data must be coupled with careful consideration of the physical meaning of the models, as physical self-consistency is more important than reaching a nominally “acceptable” goodness-of-fit value. 3.1. Testing the 2012–13 stacked spectrum with continuum model and Gaussian lines As Braito et al. (2014) have previously analysed the Jan. 2013 observation (Obs. 3, the least absorbed of the four 2012–13 observations), we began our analysis using their continuum and absorption model. Their use of EPIC data allows much better contraints of the continuum than is possible using just the RGS data. As observation 3 has lower absorption than the other 2012–13 observations, it reveals ionised absorber phases not previously seen. For this we used a power law model, absorbed by three ionised absorbers ( of 3.77, 2.15 and 0.17, as in their Table 4). We allowed our power law normalisation to vary, and fixed to a value of 2.1 to match their EPIC fits. At this stage we have not fitted any of the emission lines, so have an unacceptable -statistic value of 7000. Table 2 Narrow emission line best fit intensities from the 2012–2013 stacked spectrum and 2004–2007 stacked spectrum. Notes. A star marks uncertainty in the assigned transition. Overall -statistic 1445 (2012–13) and 1548 (2004–07). (a) r, i and f represent the resonance, intercombination and forbidden lines of an He-like triplet, respectively. Fig. 1 2012–13 RGS spectrum and line labels for detected emission lines. r, i and f represent the resonance, intercombination and forbidden lines of a He-like triplet, respectively. A * indicates uncertainty in the line identification. The data are binned by two for display purposes. The data are shown in black, and the model in red. For details of the model shown here, see Sect. 3.5 . We then fitted Gaussian lines to the data, adding a Gaussian if the best fit -statistic improves by , corresponding to a 90% confidence level for three extra free parameters (normalisation, width and central wavelength of each Gaussian model). These Gaussian models are only absorbed by our Galactic , and none of the absorption intrinsic to NGC 1365. For the He-like triplets in this wavelength range we included three components (resonance, intercombination and forbidden) if at least one was detected at the 90% level. These “triplets” really include four components, but at RGS resolution