Modelling the Narrow Wind

The prescription of the wind kinematics is as provided in §3.2. Additionally, we also investigate the effects of optical depth and time delay of the emission lines. We choose to examine two optical depth cases, one where ξ is 1 s−1 _{and another where ξ is 10}10_s−1_. These values were chosen so that the optical depth of all the points in the wind are optically thin, τ < 1, in the first case, and optically thick for the other.

The time lag of each particle due to the light travel time is determined from the centre of the ionising source. During the line profile creation, the line profile is separated into the blue and red sides from the median velocity, and the mean time delays, hτi, are calculated for both sides. The difference in mean time delay between the blue and the red side, hτ

4.2. MODELLING THE NARROW WIND

4.2.1 Parameter Choice

The geometry of the narrow wind is similar to the models proposed byMurray et al.

(1995) and Elvis (2000, 2004) to describe the phenomenology of BELs and BALs in quasars. In our model, the vertical component of the wind proposed in Elvis (2000,

2004), where the wind is lifted vertically off the disk before being accelerated outwards, is not incorporated.

The list of parameters in the model is shown in Table 4.1. Two of the main parameter values, specifically the black hole mass and wind radius, are selected according to the funnel disk-wind model proposed by Elvis (2000, 2004). This is based on one of the most extensive RM AGN, Seyfert 1 NGC 5548, which is estimated to have MBH ∼ 7 × 107M with lower and upper limit wind radii of ∼ 10 light-days (2.59×1016_{cm or 175 r}

g, where rg = GMBH/c2 is the gravitational radius) and ∼ 30 light- days (7.77 × 1016_{cm or 526 r}

g) from the emitting region size of HIL C iv and LIL Mg ii respectively (Clavel et al. 1991;Peterson & Wandel 1999).

The size of the BLR wind region is bounded within rBLR = 2× 1017cm, in both radius and height. The value is chosen such that the effects of the poloidal velocity can be seen. This fiducial radius generally agrees with results from RM and microlensing. For a quasar with black hole mass of MBH∼ 108M, RM studies found that the size of the BLR using Balmer lines is about 1×1017_–5×1017_{cm (Wandel et al. 1999;Kaspi et al.}

2000). Microlensing measurements of the quasar QSO 2237+0305 estimates the BLR radius for HIL C iv to be ∼ 2 × 1017_{cm with M}

BH∼ 108.3M (Sluse et al. 2011). For

M_{BH∼ 4 × 10}8M BAL quasar H1413+117, the BLR size is & 2.9 × 1016cm (O’Dowd

et al. 2015).

Based on the evidence that the fraction of BAL quasars is around 20% of the overall quasar population (Weymann et al. 1991; Hewett & Foltz 2003;Knigge et al.

2008;Allen et al. 2011), we set the wind to have a narrow opening angle of 10°. This

is obtained assuming that the fraction is associated to sin θ = 20/100, which yields θ . 11.5°. However, due to the anisotropic continuum radiation from the accretion disk, the fraction of BALs in optical flux-limited samples might be larger when the outflowing wind opening angle is close to equatorial (Krolik & Voit 1998). Scattering attenuation of the continuum may also induce substantial bias on the true BAL covering fraction (Goodrich 1997). These factors are ignored for simplicity. We test ranges of minimum and maximum narrow wind opening angles from polar (θmin= 5°; θmax= 15°), intermediate (e.g., θmin= 40°; θmax= 50°), to equatorial (θmin = 75°; θmax= 85°). The intersections of the wind zone with inclination angle will be presented in §4.2.2.

The acceleration scale height, Rv, is set to 25 × 1016cm. The power law index that adjusts the acceleration of the wind, α, is taken to be 1, such that the acceleration increases slowly with increasing poloidal distance. Assuming an accretion efficiency of η = 0.1, the total mass accretion rate for a source with high luminosity of L ≈ 1046erg s−1

CHAPTER 4. NARROW DISK-WIND MODEL

and black hole mass of 108_M

 is ˙Macc≈ 2 Myr−1 (Peterson 1997). The total mass- loss rate of the wind, ˙M_wind, is fixed to be equal to the total mass accretion rate,

˙

M_acc= 2 My−1. The kinematics of the outflow for the fiducial BLR disk-wind model will be elaborated in § 4.2.3. Quantitative effects due to different choices of some parameter values will be explored in §4.4.6.

Table 4.1: Adopted parameter values in the fiducial narrow wind model.

Parameter Notation Value

Black hole mass M_BH (108_M

) 1.0

BLR size r_BLR (1016_{cm) 20.0}

r_BLR (light-days) 77.2

r_BLR (r_g) 1354.1

Wind radius r_min; r_max (1016_{cm) 1.0; 2.0}

r_min; r_max (light-days) 3.9; 7.7 r_min; r_max (r_g) 67.7; 135.4

Wind opening angle θ_min; θ_max Within 10°

Scale height Rv (1016cm) 25.0

Rv (light-days) 96.5

Rv (rg) 1692.6

Acceleration power law index α 1.0

Total mass-loss rate _M˙_{wind (Myr}−1_{) 2.0}

4.2.2 Wind Zone

As aforementioned, the rationale of partitioning the wind into ‘wind zones’ is to resemble the stratification of the different ionisation lines in the BLR geometry, which is consistent with the evidence of different time lags measured for LILs and HILs in RM studies. Essentially, this approach provides a way to examine the emission line properties in distinct emitting zone. To get an insight on which wind zones intersect with the sight lines, illustrations of the narrow winds viewed at various inclination angles are depicted in Fig.4.1.

In all cases, a close to pole-on viewing angle of i = 5° intercepts none of the wind zones, even for the polar wind since the initial baseline radius does not start at the centre of the rotation axis. A viewing angle near edge-on of i = 85° will certainly intersect zones [0, b] for all narrow wind models, and additionally zones [a, 3] for equatorial wind. Meanwhile, a viewing angle at i = 45° crosses zones [0, b] in polar wind model, mostly zones [a, 0] in intermediate wind model, but none in the equatorial wind model.

These are particularly useful in identifying the trends in the line width and blueshift of the line profiles, as will be shown later in the findings. In brief, when the line-of-sight and the outflowing wind are close to or intersect one another, the line profile will be

4.2. MODELLING THE NARROW WIND

broader and more blueshifted1_{. Though, it is also subjected to other factors including}

the wind zone position and the angle of outflow.

0 5 10 15 20 Radius, r [1016cm] 0 5 10 15 20 He ig ht , z [ 10 16cm ] i=5° i=45° i=85°

(a) Polar wind 5°–15°

0 5 10 15 20 Radius, r [1016cm] 0 5 10 15 20 He ig ht , z [ 10 16cm ] i=5° i=45° i=85° (b) Intermediate wind 40°–50° 0 5 10 15 20 Radius, r [1016cm] 0 5 10 15 20 He ig ht , z [ 10 16cm ] i=5° i=45° i=85° (c) Equatorial wind 75°–85°

Figure 4.1: Plot of intersections between wind zones and inclination angle. The discrete colours merely to distinguish the generated random points in each zone.

4.2.3 Wind Velocity and Density

Before delving into the characteristics of the line profile, first lets examine the kinematics of the narrow disk-wind model with the specified fiducial parameter values given in Table4.1. The physical properties of the outflow, which include the velocity components, total velocity, velocity gradient, and density, for three wind opening angles are shown in the contour plots in Figs.4.2 to4.4.

Initially, the wind is driven off the base of the accretion disk. For regions close to the streamline of the wind, the wind velocity is governed by the rotational component, vφ, and can be as large as ∼ 12 000 km s−1. This is due to the fact that matter is accreted into the disk and subsequently contributes to the Keplerian motion. As the wind spirals upward in a helical movement, the wind gradually gains an increase in the poloidal velocity while the rotational velocity continues to decrease. At some point, the poloidal part of the wind will dominate and be larger than the rotational part. This transition occurs at different positions depending on the angle of the wind, which can be seen in the total velocity plot. The total velocity is a combination of these two velocity components and represents the unprojected total velocity, i.e., without accounting for the projection onto the line-of-sight. Radially further from this location, a significant portion of the wind velocity comes from the poloidal term. It can achieve ∼ 8000 km s−1 at maximum height or a radius of 2 × 1017_cm.

One of the primary factors that determines whether a line profile will be single-peak is through the velocity gradient, defined by the poloidal over rotational velocity shear |(dvl/ dr)/(dvφ/ dr)| (Chiang & Murray 1996;Murray & Chiang 1997). If the poloidal

1_{Negative velocity indicates blueshift and positive velocity indicates redshift (see Fig.2.3).}

CHAPTER 4. NARROW DISK-WIND MODEL

shear is greater than the rotational shear |(dvl/ dr)/(dvφ/ dr)| & 1, then there is a higher likelihood of photons to travel radially, which will lead to the formation of single-peaked emission lines. As shown in Fig.4.2d, it is challenging for the polar wind model to attain single-peaked lines since the ratio is never more than 1 regardless of the wind zones. In contrast, the intermediate Fig. 4.3d and equatorial narrow wind Fig.4.4d are able to satisfy this limit for all wind zones except those that are near the wind base. Due to the higher rotational shear in those regions, the line profiles are expected to remain double-peaked. The radial shear increases as the wind travels further away; therefore, the increased ratio.

Considering the case for a uniform mass-loss rate of λ = 0, the densities for the intermediate and equatorial wind models have roughly the same range of values within ∼ 10−18_–10−12_{g cm}−3_{, whereas the range is slightly smaller within ∼ 10}−17_–10−13_{g cm}−3 for polar wind model. However, the variation in the densities are different in each model. The density gradient in polar wind model seems to be flatter compared to that of intermediate and equatorial wind. The inverse relationship between the density and poloidal velocity implies that the regions near the base of the outflow will be denser and becoming less dense with increasing poloidal distance, which complies with the continuity and mass conservations.

While the results presented here are for specific models, they serve as a vital insight on the motion of the particles in the BLR wind. Accordingly, this will enable us to infer whether a region in the wind is dominated by rotational or poloidal velocity component, and hence predicts the shape of the line profile. §4.4.6 will be dedicated to explore the sensitivity to the parameters.