The Physical Driver of the Optical Eigenvector 1 in Quasar Main Sequence

1. Introduction

Quasars are rapidly accreting supermassive black holes at the centers of massive galaxies. In type 1 AGN, we see the nucleus directly, the continuum emission dominating the energy output in the optical/UV band comes from an accretion disk surrounding a supermassive black hole (e.g., Czerny and Elvis, 1987; Capellupo et al., 2015), and the optical/UV emission broad emission lines, FeII pseudo-continuum and Balmer Component are usually considered to be coming from the Broad Line Region (BLR) clouds. Broad band spectral properties and line emissivity are highly correlated (Boroson and Green, 1992; Sulentic et al., 2000, 2002, 2007b; Yip et al., 2004; Shen and Ho, 2014; Sun and Shen, 2015), and the Principal Component Analysis (PCA) analysis is a powerful tool herein. As suggested by Sulentic et al. (2001), those correlations allow the identification of the quasar main sequence, analogous to the stellar main sequence on the HR diagram where the classification was also based purely on spectral properties of the stellar atmospheres. The stellar main sequence found the dependence of the spectra on the effective temperature of stars. Quasar main sequence was suggested to be driven mostly by the Eddington ratio (Boroson and Green, 1992; Sulentic et al., 2000; Shen and Ho, 2014) but also on the additional effect of the black hole mass, viewing angle and the intrinsic absorption (Sulentic et al., 2000; Kuraszkiewicz et al., 2009; Shen and Ho, 2014).

We postulate that the true driver behind the R_FeII is the maximum of the temperature in a multicolor accretion disk which is also the basic parameter determining the broad band shape of the quasar continuum emission. The hypothesis seems natural because the spectral shape determines both broad band spectral indices as well as emission line ratios, and has already been suggested by Bonning et al. (2007). We expect an increase in the maximum of the disk temperature as the R_FeII increases. According to Figure 1 from Shen and Ho (2014), increase in R_FeII implies increase in the Eddington ratio or decrease in the mass of the black hole. We expect that this maximum temperature depends not only on the Eddington ratio (Collin et al., 2006) but on the ratio of the Eddington ratio to the black hole mass (or, equivalently, on the ratio of the accretion rate to square of the black hole mass).

2. Theory

Most of the quasar radiation comes from the accretion disk and forms the Big Blue Bump (BBB) in the optical-UV (Czerny and Elvis, 1987; Richards et al., 2006), and this thermal emission is accompanied by an X-ray emission coming from a hot optically thin mostly compact plasma, frequently refered to as a corona (Czerny and Elvis, 1987; Haardt and Maraschi, 1991; Fabian et al., 2015). The ionizing continuum emission thus consists of two physically different spectral components. We parameterize this emission in the following way. For convenience, the BBB component is parameterized by the maximum temperature of an accretion disk. In the standard accretion disk model this temperature is related to the black hole mass and accretion rate

$\begin{array}{ll}{\mathrm{\text{T}}}_{\mathrm{\text{BBB}}}={\left[\frac{3\mathrm{\text{GM}}\dot{\mathrm{\text{M}}}}{8\pi \sigma {\mathrm{\text{r}}}^3}\left(1-\sqrt{\frac{{\mathrm{\text{R}}}_{\mathrm{\text{in}}}}{\mathrm{\text{r}}}}\right)\right]}^{0.25}=1.732\times 10^{19}{\left(\frac{\dot{\mathrm{\text{M}}}}{{\mathrm{\text{M}}}^2}\right)}^{0.25}& (1)\end{array}$

where T_BBB, maximum temperature corresponding to the Big Blue Bump; G, gravitational constant; M, black hole mass; $\dot{\mathrm{\text{M}}}$, black hole accretion rate; r, radial distance from the center; R_in, radius corresponding to the innermost stable circular orbit. M and $\dot{\mathrm{\text{M}}}$ are in cgs units. Similar formalism has been used by Bonning et al. (2007) although the coefficient differs by a factor of 2.6 from Equation 1. This maximum is achieved not at the innermost stable orbit around a non-rotating black hole (3R_Schw) but at 4.08$\bar{3}$ R_Schw. The spectral energy distribution (SED) component peaks at the frequency

$\begin{array}{ll}{\nu }_{\mathrm{\text{max}}}~{\left[\frac{\frac{\mathrm{\text{L}}}{{\mathrm{\text{L}}}_{\mathrm{\text{Edd}}}}}{\mathrm{\text{M}}}\right]}^{\mathrm{\text{0.25}}}.& (2)\end{array}$

where ν_max, frequency corresponding to T_BBB; L, accretion luminosity $(=\eta \dot{\mathrm{\text{M}}}{\mathrm{\text{c}}}^2)$; L_Edd, Eddington limit $(=\frac{4\pi {\text{GMm}}_{\text{p}}\text{c}}{{\sigma }_{\text{T}}},{\text{where m}}_{\text{p}},\text{mass of a proton},{\sigma }_{\text{T}},\text{Thompson cross section})$. The exact value of the proportionality coefficient has to be calculated numerically, and for a standard Shakura-Sunyaev disk hν_max/kT_BBB = 2.092. We expect that the thin-disk formalism applies to all the Type 1 AGN radiating above 0.01L_Edd and below 0.3L_Edd. Instead of a full numerical model of an accretion disk spectrum, we simply use a power law with the fixed slope, α_uv, and the value of T_BBB to determine an exponential cut-off. The X-ray coronal component shape is defined by the slope (α_x) and has an X-ray cut-off. The relative contribution is determined by fixing the broad band spectral index α_ox, and finally the absolute normalization of the incident spectrum is set assuming the source bolometric luminosity. We fix most of the parameters, and T_BBB is the the basic parameter of our model.

Some of this radiation is reprocessed in the BLR which produces the emission lines. In order to calculate the emissivity, we need to assume the mean hydrogen density (n_H) of the cloud, and a limiting column density (N_H) to define the outer edge of the cloud. Ionization state of the clouds depends also on the distance of the BLR from the nucleus. We fix it using the observational relation by Bentz et al. (2013)

$\begin{array}{ll}\left(\frac{{\mathrm{\text{R}}}_{\mathrm{\text{BLR}}}}{1\mathrm{\text{ lt-day}}}\right)=10^{\left[1.555+0.542\mathrm{\text{ log}}\left(\frac{\lambda {\mathrm{\text{L}}}_{\lambda }}{10^{44}{\mathrm{\text{erg s}}}^{-1}}\right)\right]}& (3)\end{array}$

The values for the constants considered in Equation 3 are taken from the Clean Hβ R_BLR−L model from Bentz et al. (2013) where λ = 5100 Å.

3. Results and Discussions

As a first test we check the dependence of the change in the R_FeII as a function of the accretion disk maximum temperature, T_BBB at constant values of L_bol, α_uv, α_ox, n_H, and N_H. We fix the bolometric luminosity at the AGN, L_bol = 10⁴⁵ erg s⁻¹ with accretion efficiency ϵ = 1/12, since we consider a non-rotating black hole in Newtonian approximation (see Equation 1). This determines the accretion rate, Ṁ. The BBB's exponential cutoff value is determined by the maximum temperature of the disk. Our branch of solutions covers the disk temperature range between 1.06 × 10⁴K and 1.53 × 10⁵K. The corresponding range of the black hole mass range obtained from Equation (1) is [$2.35\times 10^7{\text{M}}_{\odot }$, $4.90\times 10^9{\text{M}}_{\odot }$], and it implies the range of Eddington ratio (L/L_Edd) [0.002, 0.33] calculated from the mentioned range of maximum disk temperatures. Large disk temperature corresponds to low black hole mass, since we fix the bolometric luminosity. Finally, we use a two-power law SED with optical-UV slope, α_uv = −0.36, and X-ray slope, α_x = −0.91 (Różańska et al., 2014). The exponential cutoff for the X-ray component is fixed at 100 keV (Frank et al., 2002 and references therein). By setting a value for the spectral index, α_ox = −1.6, we specify the optical-UV and X-ray luminosities. An example of SED is shown in upper panel of Figure 1.

FIGURE 1

Figure 1. (A) An example of the spectral energy distribution of the AGN transmitted continuum and line emission produced by CLOUDY: ${\text{T}}_{\text{BBB}}=3.45\times 10^4\text{ K}$, α_ox = −1.6, α_uv = −0.36, α_x = −0.9, ${\text{n}}_{\text{H}}=10^{11}\text{ c}{\text{m}}^{-3}$, ${\text{N}}_{\text{H}}=10^{24}\text{ c}{\text{m}}^{-2}$ and log(R_BLR) = 17.208. The two-component power law serves as the incident radiation. (B) The family of solutions is parameterized by maximum accretion disk temperature: (i) composite Fe_II line luminosity [erg s⁻¹] − Hβ line luminosity [erg s⁻¹]; (ii) T_BBB − R_FeII; (iii) log R_BLR − R_FeII; (iv) T_BBB − log R_BLR. Trends plotted for the following values of the parameters: ${\text{L}}_{\text{bol}}=10^{45}\text{erg }{\text{s}}^{-1}$, n_H = 10¹¹ cm⁻³ and N_H = 10²⁴ cm⁻².

We now use this one-dimensional family of SED to calculate the line emission. We have dropped the X-ray power-law component in the subsequent analyses which we plan to re-introduce once we start to see the expected trend in the R_FeII − T_BBB. As a start, we use the values of parameters from Bruhweiler and Verner (2008) i.e., $\text{log}\left[{\text{n}}_{\text{H}}/(\text{c}{\text{m}}^{-3})\right]=11$, $\text{log}\left[{\text{N}}_{\text{H}}/(\text{c}{\text{m}}^{-2})\right]=24$, without including microturbulence (the motion that occurs within a cloud's line-forming region to whose variation the line formation and the emission spectrum is sensitive). The distance of the cloud from the source depends on adopted disk temperature. From the incident continuum, we estimate the L_5,100 that in turn is used to calculate the inner radius of the BLR cloud using Equation (3).

Knowing the irradiation, we produce the intensities of the broad FeII emission lines from the corresponding levels of transitions present in CLOUDY 13.04 (Ferland et al., 2013). We calculate the FeII strength (R_FeII = EW_FeII / EW_Hβ), which is the ratio of FeII EW within 4,434–4,684 Å to broad Hβ EW. This prescription is taken from Shen and Ho (2014).

The results are shown in lower panel of Figure 1. The rise of the disk temperature initially leads to weak change of the cloud distance from the source, since the SED maximum is close to 5,100 Å for such massive black holes, and later with increasing distance from the source it decreases. The FeII intensity changes monotonically with T_BBB but it is a decreasing, not an increasing trend. This is not what we have expected—high temperatures should correspond to low mass high accretion rate sources (Shakura and Sunyaev, 1973), Narrow Line Seyfert 1 galaxies, which show strong FeII component. This monotonic trend appears despite non-monotonic change with the disk temperature both in Hβ and FeII itself.

We thus extend our study for a broader parameter range, allowing for log(n_H) in the range 10–12, and log(N_H) from the range 22.0–24.0. The range of values obtained for R_FeII went up from [0.005, 0.4] to [0.4, 1.95] with increasing N_H. The change in the local density is also important. For a constant log(N_H) = 24, changing log(n_H) = 10–12 shifts the maximum of R_FeII from 1.93 [for log(n_H) = 10] down to 0.095 [for log(n_H) = 12], thus, there is a declining trend in the maximum of R_FeII with an increase in n_H at constant N_H. We see a definite change in the trend going from lower mean density to higher in the character of T_BBB − R_FeII dependence. In the case of the lower n_H case, we see the turnover peak close to log[T_BBB(K)] = 4.2 which couldn't be reproduced by the models generated using higher values of n_H and N_H owing to non-convergence of the CLOUDY code at lower values of T_BBB. But on the higher end of T_BBB we still get the same declining behavior of R_FeII. The two extreme cases of changing both parameters are in Figure 2. We thus find that the obtained values of R_FeII are heavily affected by the change in the maximum temperature of the BBB-component. The range of the R_FeII is well covered, in comparison with the plots of Shen and Ho (2014): higher density solutions reproduce large values and lower values are obtained by lowering the local density and column density. But, in general, there is a decay in the FeII strength with the rise of the disk temperature while it was expected to follow a rising curve.

FIGURE 2

Figure 2. Comparison between R_FeII–T_BBB for two different constant-density single cloud models. Observational data RE J1034+396 (Czerny et al., 2016) and Selsing quasar composite (Selsing et al., 2016) plotted on the simulated trends.

To understand the nature of this trend in our CLOUDY computations we plot Hβ and FeII emissivity profiles (Figures 3, 4) where we consider only the first five FeII transitions in the 4,434–4,684 Å range. We compute these profiles by varying n_H [log(n_H) = (10, 12)], N_H [log(N_H) = (22, 24)] and testing the dependence of T_BBB for three different temperature cases. The Hβ nearly always dominates over the selected FeII emissions. But close to the outer surface of the cloud i.e., as log(N_H) → 24, the Hβ emission starts to drop while the FeII increases with increasing N_H, and there is some overlap region (see Figure 3, 4). In Figure 3, we find that with increasing n_H, the peak of the Hβ formation shifts closer to the inner surface of the cloud, so the relative contribution of FeII rises. However, with increasing T_BBB the emissivity zones move deeper, and the relative role of Hβ (see the extreme right panel of Figure 4) goes down.

FIGURE 3

Figure 3. Emissivity profiles of Hβ and FeII for different local densities and column densities: T_BBB = 5.9 × 10⁴ K. X-axis label, geometrical depth (in cm); Y-axis label, geometrical depth (z) × emissivity (e).

FIGURE 4

Figure 4. Emissivity profiles of Hβ and FeII: comparison at three different T_BBB values and column densities. X-axis label, geometrical depth (in cm); Y-axis label, geometrical depth (z) × emissivity (e).

In general, the emissivity profile is much more shallow for Hβ while FeII emission is more concentrated toward the back of the cloud. Thus, an increase in N_H brings the R_FeII ratio up, but increasing irradiation pushes the Hβ and FeII emitting regions deeper into the cloud and R_FeII drops (see Figures 3, 4). Our sequence of solutions for fixed bolometric luminosity and rising accretion disk temperature creates an increasing irradiation, and apparently the change of the SED shape cannot reverse the trend.

Therefore, the question is whether our hypothesis of the dominant role is incorrect or the set of computations is not satisfactory. To answer it we used two objects with well measured SED as well as R_FeII: RE J1034+396 (Czerny et al., 2016) and an X-Shooter quasar composite from Selsing et al. (2016). In order to determine the parameter T_BBB for those sources we created a set of full-GR disk models following the Novikov-Thorne prescription, we simulate an array of SED curves with L_Edd parametrization where we consider simultaneous dependence on spin (0 ≤ a ≤ 0.998) and accretion rate ($0.01\le \dot{\text{m}}\le 10$; where $\dot{\text{m}}=\dot{\text{M}}/{\dot{\text{M}}}_{\text{Edd}}$, $\dot{\text{M}}=1.678\times 10^{18}\frac{\text{M}}{{\text{M}}_{\odot }}$). The value of the black hole mass has been taken from Capellupo et al. (2016). The two values represent the extreme tails of the possible trend, with X-Shooter composite having the SED peak in UV and RE J1034+396 peaikng in soft X-rays. The corresponding points are shown in Figure 2. Observations show a rise in the value of R_FeII with increase in T_BBB which the simulations have been unable to reproduce so far. However, the rise in R_FeII is not very large, from 0.3 to 0.5, despite huge change in the disk temperature difference implied by the observed SED in the two objects.

4. Future

The reason for starting the project from purely theoretical modeling of the line ratios is the fact that determinations of the black hole mass, accretion rate and the observational parameter R_FeII available in the literature are not accurate enough to be used to test our hypothesis about the nature of the EVI (Sniegowska et al., 2017). The subsquent tasks will be to check the R_FeII dependence on other parameters (see Sulentic et al., 2000; Mao et al., 2009; Marziani et al., 2015) which are used (L_bol, α_uv, α_ox, n_H, N_H, cos(i), a and others). We intend to incorporate the microturbulence as suggested in Bruhweiler and Verner (2008). Better, more physical description of the SED may be needed, i.e model of a disk + corona with full GR and more complex geometry of the BLR using Czerny et al. (2011), Czerny and Hryniewicz (2011), and Czerny et al. (2015). We intend to implement the constant density LOC (Locally Optimized Cloud) model and subsequently the constant pressure model to repeat the tests and check for discrepancies with respect to the current model. Next stage to consider is the possibility of shielding of some BLR regions by the puffed inner disk (e.g., Wang et al., 2014), or to consider independent production regions of Hβ and FeII. Different studies have proposed that FeII is mainly produced in BLR (Bruhweiler and Verner, 2008; Shields et al., 2010) while many others have suggested that these emissions are mostly produced in the accretion disk (Martínez-Aldama et al., 2015 and references therein). Finally, we have to test our theory observationally for more sources with known SED peak position. To have an overview of the EV1, it is necessary to study it in other ranges of frequencies, including X-ray, radio, UV, and IR spectral ranges. Considerable progress along these line have been made by Sulentic et al. (2007a) and Sulentic et al. (2017) (UV range), Dultzin-Hacyan et al. (1999) (Figure 4), and Martínez-Aldama et al. (2015) (IR range).

Author Contributions

SP has tested the basic model and carried out the photoionisation simulations based on the idea and formalism proposed by BC. CW has provided computational assistance and helped solve the T_BBB issue.

Funding

Part of this work was supported by Polish grant No. 2015/17/B/ST9/03436/.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The authors would like to acknoweledge the referees for their comments and suggestions to bring the paper to its current state. SP would like to acknowledge the organizing committee and the participants of the Quasars at all Cosmic Epochs conference held during 2nd Apr–7th Apr 2017 in Padova, Italy and, subsequently for providing the opportunity to present a talk on his research after being adjudged with the Best Poster award. SP would also like to extend his gratitude to the Center for Theoretical Physics and Nicolaus Copernicus Astronomical Center, Warsaw, the National Science Center (NSC) OPUS 9 grant for financing the project and Dr. Gary Ferland and Co. for the photoionisation code CLOUDY. SP would like to acknowledge the unending academic and personal support from Mr. Tek Prasad Adhikari. SP is also obliged to the Strong Gravity group at CAMK, Warsaw for engaging discussions resulting in this work.

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