Inclination

As mentioned earlier, photon packets are collected into inclination bins (parameterised with respect to the z-axis), which are then processed into energy bins forming spectra. The output spectra are then normalised to the input spectra. This leaves the deviations from the

input spectra to be fitted via the use of a multiplicative model, which modifies a continuum spectrum as f it_continuum × (output_spectrum/input_spectrum). It is important to note (as discussed later) that the input spectrum has an effect on the ionisation state of the wind which is not removed by this treatment; if possible the photon index should vary with that of the fit continuum. Failing that, the photon index of the fit continuum should be fixed or limited to be close to the photon index of the simulations.

The Monte Carlo method used to produce the output spectra causes high frequency noise, which can be seen in the thickness of the Compton hump around 30 keV in the (green) reflection spectrum in panels (b) to (d) of Fig. 3.8. This means that normalising the output to input spectrum can also sometimes be misleading as signal to noise (S/N) will fall off towards higher energies. Therefore, a Savitzky-Golay filter is used for plotting; this is a method for reducing the high frequency noise by fitting a low order polynomial to a moving window of points. However, this causes some highly blended features to appear as a single feature, but this is purely for plotting purposes as the data quality of X-ray spectra does not require smoothing of the output spectra.

Inclination is measured as the angle with respect to the polar (z) axis. The different sight lines from each inclination bin intercept increasing column densities with increasing polar angle. Fig. 3.7 shows that the column quickly increases into the optically thick regime. The d parameter controls the degree of collimation — this sets the lowest inclination at which the wind will intercept the line of sight (LOS), which is ∼ 45◦ for the standard geometric values in table 3.1. These inclinations can be split into three categories: low inclinations (polar), intermediate (along the wind) and high (edge on). The “typical” spectra for these categories are shown in Fig. 3.8 in the top-right-hand plot. A zoom-in on the Fe K region is shown in Fig. 3.9.

At close to polar inclinations the LOS does not intercept the wind, meaning that there is no modification to the directly observed spectrum. This can be seen in plot (b) in Fig. 3.8, which in this case is at an inclination of 32◦ (blue solid line). The deviations observed from the input spectra come from the reflection spectrum of the wind (green line of plot b) that

3.2 Input parameters 59

Figure 3.7: Angular dependence of the column density. Along a line of sight below 40◦ the wind does not intercept the line of sight to the X-ray source so the column density is 0, although the observed spectrum is modified by photons scattered into the line of sight. The column density increases from 44–90◦ as the line of sight becomes more edge on. The dashed red line represents one Compton depth where N_H= 1/σT = 1.5×1024cm−2

where the flux is suppressed to 38% of the unattenuated flux.

encompasses the Fe Kα emission seen at 6.4 keV which is blurred due to the Doppler shifts within the flow and a weak Compton hump (as described in section 1.3.2) produced in the scattered spectrum above 10 keV. The resultant spectrum (black line) is the superposition of the direct and scattered components.

In principle the broad Fe Kα emission lines seen in many type 1 Seyfert galaxies could be fitted with the Fe K emission line of the disk wind model such as the ones seen in panel (b) of Fig. 3.8 and panel (a) of Fig. 3.9. Indeed, Tatum et al. (2012) found acceptable fits for several bare Seyferts with relatively face-on inclinations. These objects are normally fit with the reflection spectrum blurred by transverse Doppler and gravitational redshift (as discussed in the previous chapter), and could in principle be fit with the reflection spectrum of a wind which is located out of the direct LOS of the observer (i.e. an angle_{. 40}◦) such

as the blue line in panel (a) of Fig. 3.8.

Figure 3.8: The effects on the observed spectra when intercepting the wind at different inclinations. The plot on the left is a colour map of the average charge of iron within each cell. Three lines corresponding to different lines of sight through the wind are overlaid. From top to bottom the inclinations (measured with respect to the z-axis) are 32◦ (blue solid line and panel b), 51◦ (red dashed line and panel c) and 73◦ (green dash-dot line and panel d). These sight lines intercept different column densities. The spectra in the right-hand panels show the deviations from the input continuum for each of the aforementioned inclinations. Along with the total spectrum (black). The direct (red) and scattered (green) spectra are also shown for each of the aforementioned inclinations. The direct spectrum shows the absorption due to the wind in the line of sight whereas the scattered spectrum primarily shows the emission/reflection from the wind.

3.2 Input parameters 61

Figure 3.9: Plot of the Fe Kα region of the output spectra. As in Fig. 3.8 the spectra show the deviations from the input. Along with the total spectrum (black) I also show the direct (red) and scattered (green) spectra for each aforementioned inclinations. The direct spectrum shows the absorption due to the wind in the line of sight whereas the scattered spectrum primarily shows the emission/reflection from the wind. The line of sight (an inclination of 32◦) for panel does (a)not intercept the wind so is dominated by the photons scattered off the inner edge of the wind and thus demonstrates the broad Fe Kα emission feature. Panel (b) shows the 51◦ inclination angle which shows modification from both emission and absorption with deep absorption troughs due to He-like and H-like iron. Finally, panel (c) shows the heavily absorbed equatorial inclination of 73◦, where the direct continuum is heavily suppressed by the large column and so is dominated by the scattered spectrum, showing a broad shallow absorption feature.

At intermediate inclinations (such as 51◦, red dashed line in Fig. 3.8 panel a) seen in panel (c) of Fig. 3.8 intercepting a column density of 2 × 1024_cm−2_{, the observed spectra}

will have emission and scattering into the LOS as before. However, now that the wind is intercepting the LOS to the X-ray source, it modifies the direct continuum (red line) by suppressing it. This can be seen in the reduced magnitude of the direct continuum (20% of the unattenuated direct component), and by imprinting absorption features at this ionisation where the 2–10 keV luminosity has been set to 0.8% of the Eddington luminosity (see Sec. 3.2.6).The strongest features are from He-like and H-like Fe, as illustrated in panel (b) of Fig. 3.9, where strong absorption lines from Fe XXV/XXVI are seen imprinted on

both the transmitted (direct) and reflected spectra. The lines are blueshifted with respect to the laboratory frame energies (6.7/6.97 keV). Higher-order (1s–3p) absorption features (Fe xxv Heβ and Fe xxvi Lyβ) are also seen at energies ∼ 10 keV in Fig. 3.9.

At an inclination of 73◦ (the green dash-dot line in panel (a) in Fig. 3.8), the scattered emission dominates over the direct continuum. This can be seen in panel (d) in Fig. 3.8. The column intercepting the LOS is ∼ 5 × 1024_cm−2_{, corresponding to an optical depth}

(τ ) of 3.3, meaning the direct continuum (in red) should be suppressed to ∼ 3% of the unattenuated flux in panel (d) of Fig. 3.8.

It can also be seen that the Compton hump is much weaker at 53◦ and 73◦ despite the reflection component being stronger compared to the direct continuum, due to the angular dependence of Compton scattering. It is also important to note that the observed velocity shift is dependent on the inclination. This can be seen when comparing direct spectra of the panels (b)–(d) in Fig. 3.8. In panel (b) in Fig. 3.9, the absorption line observed in the direct (red) spectrum is at 8.2 keV which corresponds to an outflow velocity (vout) of −0.16 c,

associated with Fe XXVI (H-like) Lyα. At the higher inclination in panel (c) the absorption line is seen at the lower energy of 7.2 keV, thus the resultant vout is −0.03 c. Thus along the

direct line of sight through the wind the observed velocity shift will be higher than for high inclination, due to shifting to slower streamlines. Along with this the observed width of the line will be larger at high inclinations when compared to lower inclinations due to the divergence of velocity streamlines.