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Edited by: Paola Marziani, Osservatorio Astronomico di Padova (INAF), Italy

Reviewed by: Alenka Negrete, Universidad Nacional Autónoma de México, Mexico; Milan S. Dimitrijevic, Astronomical Observatory, Serbia; Tomaz Zwitter, University of Ljubljana, Slovenia

*Correspondence: Swayamtrupta Panda

This article was submitted to Milky Way and Galaxies, a section of the journal Frontiers in Astronomy and Space Sciences

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Quasars are complex sources, characterized by broad band spectra from radio through optical to X-ray band, with numerous emission and absorption features. This complexity leads to rich diagnostics. However, Boroson and Green (

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,

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. (_{FeII} increases. According to Figure 1 from Shen and Ho (_{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.,

Most of the quasar radiation comes from the accretion disk and forms the Big Blue Bump (BBB) in the optical-UV (Czerny and Elvis, _{BBB}, maximum temperature corresponding to the Big Blue Bump; G, gravitational constant; M, black hole mass; _{in}, radius corresponding to the innermost stable circular orbit. M and _{Schw}) but at 4.08_{Schw}. The spectral energy distribution (SED) component peaks at the frequency
_{max}, frequency corresponding to T_{BBB}; L, accretion luminosity _{Edd}, Eddington limit _{max}/kT_{BBB} = 2.092. We expect that the thin-disk formalism applies to all the Type 1 AGN radiating above 0.01_{Edd} and below 0.3_{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. (

The values for the constants considered in Equation 3 are taken from the Clean Hβ R_{BLR}−L model from Bentz et al. (

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} = 10^{45} 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 × 10^{4}K and 1.53 × 10^{5}K. The corresponding range of the black hole mass range obtained from Equation (1) is [_{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., _{ox} = −1.6, we specify the optical-UV and X-ray luminosities. An example of SED is shown in upper panel of Figure

_{ox} = −1.6, α_{uv} = −0.36, α_{x} = −0.9, _{BLR}) = 17.208. The two-component power law serves as the incident radiation. _{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: _{H} = 10^{11} cm^{−3} and N_{H} = 10^{24} 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 (_{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., _{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 (

The results are shown in lower panel of Figure _{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,

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 _{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 (

Comparison between R_{FeII}–T_{BBB} for two different constant-density single cloud models. Observational data RE J1034+396 (Czerny et al.,

To understand the nature of this trend in our CLOUDY computations we plot Hβ and FeII emissivity profiles (Figures _{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 _{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

Emissivity profiles of Hβ and FeII for different local densities and column densities: T_{BBB} = 5.9 × 10^{4} K. X-axis label, geometrical depth (in cm); Y-axis label, geometrical depth (z) × emissivity (e).

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

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., _{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 (_{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.

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., _{FeII} dependence on other parameters (see Sulentic et al., _{bol}, α_{uv}, α_{ox}, n_{H}, N_{H}, cos(

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.

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.

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.