IMPLICATIONS OF INFALLING Fe ii-EMITTING CLOUDS IN ACTIVE GALACTIC NUCLEI: ANISOTROPIC PROPERTIES

Principal component analysis (PCA) of the emission-line spectra of quasars isolates several linearly independent components (Boroson & Green 1992). These are ascribed to distinct physical processes within these objects. Eigenvector 1, which is responsible for the largest part of the variability within the samples, anti-correlates with L/L_Edd, the ratio of the luminosity to the Eddington limit, while Eigenvector 2 represents the accretion rate (Boroson 2002). It has been proposed that Eigenvector 1 represents the effects of radiation pressure controlling the column densities of the surviving line-emitting clouds (Marconi et al. 2008; Netzer 2009; Dong et al. 2009). This paper is a specific, quantitative exploration of that idea.

Fe ii emission is one of the main spectroscopic signatures of Eigenvector 1. The physics of Fe ii emission is complex with many levels contributing to the spectrum, which occurs in a blended complex of muddled features (Wills et al. 1985; Verner et al. 1999; Baldwin et al. 2004). There has been only partial success in reproducing the observed Fe ii emission in a realistic model of AGN emission-line regions (Baldwin et al. 2004).

Gaskell (2009) recently discussed the considerable range of existing observational evidence indicating that QSO emission-line regions include infalling gas. Hu et al. (2008a) and Hu et al. (2008b) recently found that Fe ii emission is systematically redshifted relative to the QSO systemic velocities, and presented the reasons suggesting that this is because the Fe ii emission comes from infalling clouds. In a forthcoming paper (C. Hu et al. 2009, in preparation), we will further develop a model outlined by Hu et al. (2008b) in which the Fe ii emission comes from infalling clouds systematically viewed from their shielded faces. Such clouds must have a large enough column density to fall toward the black hole, despite L/L_Edd ∼ 10⁻¹ − 1. Here, we describe a preliminary exploration of the basic spectroscopic properties of clouds viewed from their non-illuminated sides, which is an important question in its own right independent of the exact dynamical model. If indeed the Fe ii emission does come from infalling clouds, our results have major consequences for the predicted emission-line spectrum and reveal one of the underlying drivers for Eigenvector 1.

Hu et al. (2008a, 2008b) find that much of the optical Fe ii emission comes from a redshifted intermediate-line region. The redshift of the Fe ii-emitting region inversely correlates with the L/L_Edd ratio as indicated by Eigenvector 1. The correlations are that, as the L/L_Edd ratio increases, Fe ii/Hβ increases (Boroson 2002; Boroson & Green 1992) and the Fe ii redshift relative to the systemic rest frame decreases (Hu et al. 2008b). These relations are the subject of this Letter.

For simplicity, we consider two Fe ii emission bands. The optical Fe ii λ4558 band is the integrated Fe ii emission between λ4434 and λ4684 as defined by Francis et al. (1992). UV Fe ii emission forms a blended pseudocontinuum with very few isolated Fe ii lines. We follow the Baldwin et al. (2004) definition of UV Fe ii λ2445 as the integrated Fe ii flux over the wavelength range λλ2240–2650.

We consider the properties of a typical Fe ii-emitting cloud. The observed spectrum is actually produced by a mix of clouds with a broad range of densities and distances from the central object (Baldwin et al. 1995). However, in this preliminary investigation, we consider only a single cloud.

We use a combination of line-continuum reverberation studies and theoretical predictions to determine the parameters of this typical cloud. Maoz et al. (1993) found that the UV Fe ii lines in NGC 5548 respond to the driving continuum on a timescale similar to that of C iv λ1549 and somewhat shorter than that of Hβ, but the optical Fe ii lines in this object are too weak for useful reverberation measurements (Vestergaard & Peterson 2005). Kuehn et al. (2008) studied the reverberation behavior of the optical Fe ii lines in Akn 120, for which there are no UV reverberation measurements but which has strong optical Fe ii lines. They found that in Akn 120 the optical Fe ii emission clearly does not originate in the same region as Hβ, and that there was some evidence of a reverberation response time of 300 days which implies an origin in a region several times further away from the central object than Hβ. A 300 day light-travel time corresponds to a source-cloud separation of ∼8 × 10¹⁷ cm. For a general AGN spectral energy distribution (SED), the quoted luminosity of Akn 120 (10⁴⁵ erg s⁻¹), and this separation, the flux of hydrogen-ionizing photons, Φ(H), at the derived position of the Fe ii emission is in the neighborhood of Φ(H) ≈ 10¹⁹ cm⁻² s⁻¹. From the results shown in Figure 7 of Baldwin et al. (2004), we estimate the gas density to be n(H) ∼ 10¹⁰ cm^-3 and the turbulence to be u_turb ∼ 10² km s⁻¹. The "standard cloud" considered in the remainder of this Letter has these quantities and solar abundances.

All calculations were done with version C10 of the spectral simulation code Cloudy, last described by Ferland et al. (1998). We concentrate on the emission from the shielded face of the cloud. Cloudy has long predicted the fraction of the emission that is beamed toward the central object (Ferland et al. 1992), but the outward emission, which is often quite faint for the large column densities we consider below, has not been an emphasis. The inward versus outward Fe ii emission, although calculated, was not reported. We have improved the adaptive logic used to define the spatial grid to better resolve the emission from the shielded face and added several output options to report these predictions. We now explicitly predict the inward, outward, and total Fe ii emission in the form presented by Baldwin et al. (2004).

We consider the ionizing flux versus gas density plane presented by Baldwin et al. (2004). For an isotropic radiation field, the ionizing flux Φ(H) ∝ r⁻² so this variable can be thought of as a proxy for the continuum source-cloud separation. All possible AGN clouds lie somewhere on this plane. Regions with the same ionization parameter form parallel lines with a slope of unity. Little observable emission comes from the large flux, small density quadrant which corresponds to highly ionized gas with temperatures near the Compton limit (Korista et al. 1997). Clouds in the small flux, large density quadrant have very low ionization, tend to be cool, and produce strong Fe ii emission.

3.1. The Force Multiplier

The fact that the Fe ii-emitting clouds, with L/L_Edd ∼ 10⁻¹, are falling into the center has major consequences for the cloud column density. The Eddington limit is the luminosity at which the force due to electron scattering balances the gravitational acceleration for optically thin gas,

$$\begin{equation} L_{\rm Edd} = \frac{4\pi {\it GM}m_p c}{\sigma _T }. \end{equation} \tag{ 1 }$$

Here, σ_T is the Thomson cross section. The ratio L/L_Edd is a dimensionless measurement of the specific luminosity of the AGN.

This acceleration limit is appropriate for very highly ionized gas. For gas with a higher total cross section σ, the outward force is greater by a force multiplier σ/σ_T. In general, σ ≫ σ_T for low-ionization gas due to the added opacity caused by line and photoelectric absorption (Castor 1974; Kippenhahn et al. 1974; Castor et al. 1975). The force multiplier over the range of densities and ionizing fluxes is shown in Figure 1, which also shows, as a shaded ellipse, the region that Baldwin et al. (2004) found could produce acceptable Fe ii emission.

Zoom In Zoom Out Reset image size

Figure 1 shows that typical Fe ii-emitting clouds should be strongly accelerated away from the central object unless the Eddington ratio is below L/L_Edd ∼ 10⁻³–10⁻⁴. The objects in the Hu et al. (2008b) sample have L/L_Edd ∼ 10⁻¹ so the gas would be expected to be accelerated outward. How can it be in a state of infall?

3.2. The Need for Large Column Densities

The outward radiation pressure corresponding to the force multiplier shown in Figure 1 will act only on the illuminated face of a large column density cloud. This is because the peak of the SED emitted by the AGN occurs at ionizing energies. The photons most capable of pushing the gas away ionize the gas and are absorbed.

An H⁺–H⁰ ionization front occurs when most ionizing photons have been absorbed. Most of the outward momentum acts on the H⁺ layer. Relatively little energy is in high-energy photons which penetrate into neutral regions. The result is that most of the radiative acceleration occurs in the H⁺ layer which then pushes on deeper neutral and molecular regions. The presence of shielded regions allows inflow to occur even at super-Eddington luminosities, as has been discussed previously (e.g., Shaviv 1998). Marconi et al. (2008) and Netzer (2009) have previously discussed radiation pressure from ionizing photons acting on large column-density AGN clouds, in terms of the effect on the deduced black hole masses and the L/L_Edd versus M_BH relation.

We quantify this with a calculation shown in Figure 2, using the standard conditions described in Section 2. The gas kinetic temperature is shown as a function of column density from the illuminated face of the cloud. A sharp drop in temperature occurs at the H⁺–H⁰ ionization front and an H⁺ layer with a column density of N(H) ≈ 5 × 10²¹ cm⁻² exists on the face of the cloud. The vast majority of the cloud consists of warm atomic gas where the Fe ii lines form.

Zoom In Zoom Out Reset image size

The dashed line shows the computed radiative acceleration. Within the H⁺ layer the force increases nearly linearly with increasing column density as more of the incident radiation field is absorbed. The force has nearly reached its asymptotic value when the H⁺–H⁰ ionization front is reached. This ionized layer then pushes against the much larger column density of cooler atomic gas. The atomic layer adds mass to the cloud without contributing to its outward acceleration.

In practice, the clouds may be subject to Rayleigh–Taylor instability (Mathews 1982, 1986). While the radiation force will suppress instability at the front surface of the cloud, it will enhance the instability at the ionization front. Within the ionized region, the structure may be subject to additional radiation-driven instabilities (Mestel et al. 1976; Williams 2000), as well as significant structural perturbations due to the varying continuum. These and other sources may support a level of turbulence similar to that which we model. We will not address the stability of the clouds we model further. The model does require that the cloud integrity must be maintained by other means, possibly magnetic, or, more likely, that the cloud is an evolving dynamic entity that survives long enough to be accelerated by the gravitational forces in the region.

Figure 2 establishes the minimum column density where infall is possible. The most useful way to consider the results in Figure 2 is by reference to the acceleration that would occur for pure electron scattering opacity in fully ionized gas since that is the opacity used in the definition of the Eddington limit. The dash-dotted line shows the equivalent radiative driving for the case where only electron scattering opacity acting on the incident radiation field is considered. The actual acceleration, the dashed line, is considerably larger than the electron scattering acceleration across the H⁺ region, as expected from Figure 1. The acceleration increases very slowly after the H⁺–H⁰ ionization front, while, with our definitions, the reference electron scattering acceleration increases linearly with column density N(H). The two lines cross at a column density of N(H) ≈ 1.2 × 10²⁴cm⁻², the point where the cloud would be neutrally buoyant for L/L_Edd = 1.

The minimum column density for which the inward gravitational force is stronger than the total outward radiation pressure on a cloud, N(H)_infall, may be estimated as

$$\begin{equation} N\left({\rm {H}} \right)_{\rm infall} \ge {f_{\rm thick}\over \sigma _T } \frac{L}{L_{\rm Edd}} \simeq 1.5 \times 10^{24}f_{\rm thick}\frac{L}{L_{\rm Edd}}{\rm \;cm^{-2}}, \end{equation} \tag{ 2 }$$

where f_thick ∼ 1 is the fraction of the incident radiation to which the cloud is optically thick. This establishes a relation between specific luminosity and the minimal column density of infalling clouds. In objects of higher specific luminosity, which tend to have stronger Fe ii emission, only high column density clouds will be able to fall inward.

Figure 3 shows how the total and, separately, the outward emission varies as the cloud column density is increased. The Fe ii lines begin to form when clouds have column densities N(H)>10^21.7 cm⁻², the point where the H⁺–H⁰ ionization front occurs. This is also the column density where Hβ becomes inwardly beamed. Lα is nearly fully emitted in the inward direction (Ferland & Netzer 1979).

Zoom In Zoom Out Reset image size

3.3. Isotropy of Optical Fe ii Emission

The upper panel of Figure 4 shows the total and outward Fe ii emission for our standard cloud. The spectrum is complex and it is hard to distinguish between the total and outward components in certain parts. The lower panel shows the ratio of the outward to the total emission. This shows the general trend for the inward fraction to increase with decreasing wavelength, mainly due to the larger optical depths of UV Fe ii transitions.

Zoom In Zoom Out Reset image size

Figure 5 compares the outward emission from our standard model with the Fe ii template presented by Vestergaard & Wilkes (2001) and Boroson & Green (1992). The agreement is good. We notice in particular that the predicted optical/UV ratio, which in the simulations by Baldwin et al. (2004) is always too small when both inward and outward Fe ii emission is considered, is actually larger than observed (i.e., the UV Fe ii strength is underpredicted). This allows for a component of UV Fe ii emission to form in the broad-line region (BLR), as suggested by reverberation results of NGC 5548 (Maoz et al. 1993).

Zoom In Zoom Out Reset image size

This is a major advance in the comparison between theory and observations for the Fe ii emission. It is important to keep in mind the fact that the deduced properties of emission-line clouds have, until now, come from comparing the total emission, not the outward emission, with observations. Future papers will further investigate the implications of asymmetric anisotropic emission.

Equation (2) suggests a linear relationship between the Eddington ratio and the column density of infalling clouds. Figure 3 shows that the Fe ii/Hβ ratio increases with increasing column density for N(H) ∼ 10²²–10²³ cm⁻². This implies that there will be a relation between L/L_Edd and Fe ii/Hβ. This explains one of the strongest systematic correlations captured by Eigenvector 1. As was recently suggested by Dong et al. (2009), the cloud column density is the physical variant which drives the spectroscopic variations.

The predicted Fe ii/Hβ reaches an asymptotic value of about 3 for large N(H) or L/L_Edd. This is close to the observed value for luminous quasars (Francis et al. 1991). Models which considered the full emission from the cloud do not reproduce this ratio (Baldwin et al. 2004).

Lα is strongly inwardly beamed, while C iv is nearly isotropic, as shown by Ferland & Netzer (1979) and Ferland et al. (1992). Hu et al. (2008b) found that all of the emission in the optical Fe ii band originates in the infalling clouds. Other lines are likely to form in both these and other regions, including the accretion disk, virialized broad-lined clouds and outflowing winds. High-resolution UV spectra of objects in which the infalling clouds have the largest velocity shift are needed to test this.

The infalling clouds must have a substantial covering factor. The observed Hβ equivalent widths of the broad and infalling components are similar (Hu et al. 2008a). The infalling clouds direct much of their Hβ emission away from the observer. They must have a covering factor approaching Ω/4π ∼ 0.5, consistent with an origin in the molecular torus (Hu et al. 2008b).

The net accretion rate due to these infalling clouds must be

$$\begin{eqnarray} &&\dot{M}_{\rm Fe\, \mathsc {ii}} > {\Omega \over 4\pi } 4\pi r^2 m_p (N_{\rm H}/r) v_{\rm infall}\nonumber \\ &&\simeq 17 \,{\Omega \over 2\pi } r_{18} N_{\rm H,24} v_8\; {M_\odot \rm \; yr^{-1}}, \end{eqnarray} \tag{ 3 }$$

where r = 10¹⁸r₁₈ cm, N_H = 10²⁴N_H,24 cm^-2, and v = 1000v₈ km s^-1. In this expression, the factor N_H/r is the mean density of the Fe ii-emitting material multiplied by the minimal line-of-sight filling factor if the clouds are evenly distributed. This may be compared to the accretion rate of 1.8L₄₅(η/0.01)⁻¹ M_☉ yr⁻¹ required to power an AGN of luminosity L = 10⁴⁵L₄₅ erg s^-1 with an accretion efficiency of η, where the scaling parameters are all ≃1 for Akn 120. The mass infall rate above that required by accretion is likely to be balanced by other outflows. Nevertheless, this suggests that the infalling Fe ii-emitting material constitutes a major element in the mass budget of high Eddington-ratio active nuclei.

We have investigated the effects of systematically viewing a low-ionization cloud from its shielded face. We focus on Fe ii and Hβ because of their importance in PCA analysis. Meaningful predictions about the full spectrum will require a much broader exploration of, and probably a weighted integration over, the ionizing flux versus gas density plane. A future paper will carry out that broader exploration and address predicted strengths and profiles of such lines, and also the open question of whether this infalling component should be seen in absorption particularly at UV or X-ray wavelengths.

• 1.  
  Low-ionization Fe ii-emitting clouds have force multipliers (the ratio of total to electron scattering opacities) that are large if the clouds are optically thin. Such clouds will be accelerated away from the central black hole if it has an Eddington ratio as large as those found in quasars, L/L_Edd ∼ 0.1.
• 2.  
  If the Fe ii-emitting clouds are infalling, as is suggested by their systemically positive velocity offsets (Hu et al. 2008b), they must have column densities significantly larger than previously thought if the inward pull of gravity is to offset the outward force of radiation pressure.
• 3.  
  There is a simple relationship between L/L_Edd and the minimum cloud column density required for infall. Fe ii/Hβ also depends on cloud column density. Cloud column density is the underlying driver that couples Eigenvector 1, L/L_Edd, and spectroscopic variations, as was previously proposed by Dong et al. (2009).
• 4.  
  Previous simulations of the emitting gas have assumed a symmetric distribution of clouds so that, on average, we see the same number of clouds from their illuminated as from their shielded faces. We have investigated here the result of seeing an asymmetric distribution of emitters, so that we mainly observe Fe ii emission from the shielded face of near-side infalling clouds, as is suggested by observations (Hu et al. 2008b; Gaskell 2009).
• 5.  
  Fe ii UV emission is emitted less isotropically than optical Fe ii lines. Previous work, which assumed a symmetric distribution of emitters, could not explain the larger-than-predicted ratio of optical to UV Fe ii emission or the Fe ii/Hβ ratio. The predicted emission ratios from the shielded face are in good agreement with observations. This is a major advance in understanding the nature of Fe ii emission in AGN.
• 6.  
  It is likely that there is a distribution of cloud column densities. If so, clouds with column densities smaller than that given in Equation (2) will be radiatively accelerated outward while those with larger column densities will fall in, with a column density cutoff depending on the AGN's luminosity. This would be the mechanism that accounts for the observed (Boroson 2002; Dong et al. 2009) coupling between L/L_Edd and the column density and Fe ii/Hβ ratio. Both outflow and infall are observed in AGN. Could this also be a natural consequence of a range of N(H) in the surviving clouds?

We thank the referee for very helpful comments. G.J.F. thanks NSF and NASA for support (AST0607028, AST0908877, and ATFP07-0124), J.A.B. acknowledges NASA HST grant AR-10932, and C.H. and J.M.W. acknowledge support from NSFC-10733010 and 10821061, CAS-KJCX2-YW-T03, and 973 project (2009CB824800).