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Appendix A: Ionic columndensity measurements
The columndensity associated with a given ion as a function of the radial velocity v is defined as: (A.1)where f_{j}, λ_{j} and ⟨ τ_{j}(v) ⟩ are respectively the oscillator strength, the rest wavelength and the average optical depth across the emission source of the line j for which the optical depth solution is derived (see Edmonds et al. 2011). The optical depth solution across a trough is found for a given ion by assuming an absorber model. As shown in Edmonds et al. (2011), the major uncertainty on the derived columndensities comes from the choice of absorption model. In this study we investigate the outflow properties using columndensities derived from three common absorber models.
Assuming a single, homogeneous emission source of intensity F_{0}, the simplest absorber model is the one where a homogeneous absorber parameterized by a single optical depth fully covers the photon source. In that case, known as the apparent optical depth scenario (AOD), the optical depth of a line j as a function of the radial velocity v in the trough is simply derived by the inversion of the BeerLambert law: τ_{j}(v) = −ln(F_{j}(v) /F_{0}(v)), where F_{j}(v) is the observed intensity of the line.
Early studies of AGN outflows pointed out the inadequacy of such an absorber model, specifically its inability to account for the observed departure of measured optical depth ratio between the components of typical doublet lines from the expected laboratory line strength ratio R = λ_{i}f_{i}/λ_{j}f_{j}. Two parameter absorber models have been developed to explain such discrepancies.
Observations and flux values for all epochs.
The partial covering model (e.g. Hamann et al. 1997; Arav et al. 1999, 2002, 2005) assumes that only a fraction C of the emission source is covered by absorbing material with constant optical depth τ. In that case, the intensity observed for a line j of a chosen ion can be expressed as (A.2)Our third choice are inhomogeneous absorber models. In that scenario, the emission source is totally covered by a smooth distribution of absorbing material across its spatial dimension x. Assuming the typical power law distribution of the optical depth τ(x) = τ_{max}x^{a} (de Kool et al. 2002; Arav et al. 2005, 2008), the observed intensity observed for a line j of a chosen ion is given by (A.3)Once the line profiles have been binned on a common velocity scale (we choose a resolution dv = 20 km s^{1}, slightly lower than the resolution of COS), a velocity dependent solution can be obtained for the couple of parameters (C,τ_{j}) or (a,τ_{max}) of both absorber models as long as one observes at least two lines from a given ion, sharing the same lower energy level. Once the velocity dependent solution is computed, the corresponding column density is derived using Eq. (A.1) where ⟨ τ_{j}(v) ⟩ = C_{ion}(v)τ_{j}(v) for the partial covering model and ⟨ τ_{j}(v) ⟩ = τ_{max,j}(v) / (a_{ion}(v) + 1) for the power law distribution. Note that the AOD solution can be computed for any line (singlet or multiplet), without further assumption on the model, but will essentially give a lower limit on the columndensity when the expected line strength ratio observed is different from the laboratory value.
UV columndensities for the outflow components in NGC 5548.
Fig. A.1
2013 spectrum of NGC 5548. The vertical axis is the flux in units of 10^{14} erg s^{1} cm^{2} Å^{1}, and the quasarrestframe and observerframe wavelengths are given in Angstroms on the top and bottom of each subplot, respectively. Each of the six kinematic components of the outflow shows absorption troughs from several ions. We place a vertical mark at the expected center of each absorption trough (following the velocity template of Si iv and N v) and state the ion, restwavelength and component number (C_{1}–C_{6}). We also assign a color to each component number that ranges from blue (C_{1}) to red (C_{6}). Absorption lines from the ISM are likewise marked in black with dashed lines. 

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Fig. A.2
Spectrum of NGC 5548 during the five epochs of observation. The 2013 spectrum is obtained by coadding visits 1 through 5. Spectral regions where absorption troughs from five ions are shown in subplots a) through e) and the six kinematic components associated with such absorption are labelled C_{1} through C_{6}. 

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Fig. A.3
Normalized spectrum of NGC 5548 during the five epochs of observation, plotted in the velocity restframe of the quasar (same annotation as Fig. A.2). 

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© ESO, 2015