The majority of quasars detected at high redshifts ( ) strongly emit ultraviolet radiation with absolute magnitudes at rest-frame . Some of them have high luminosities in [CII] line and in far-infrared (FIR) continuum, which leads to the expectation of a large amount of much cold dusty gas in these quasars. We have studied the relation between luminosities in the [CII] and the FIR continuum for a slightly absorbed supermassive black hole (SMBH) obscured by an ensemble of dense clouds with a low covering factor. We have found that dense clouds with a low covering factor can give sufficient luminosities in [CII] line and the underlying FIR continuum to reproduce the [CII]-FIR ratio observed in high-redshift quasars for a reasonable SMBH mass of . We note that many distant mildly/heavily obscured active galactic nuclei are to avoid detection in near-infrared (IR) wavelengths; if this is the case, blind IR/FIR surveys are needed.
In recent years, many supermassive black holes (SMBHs) have been discovered at redshifts (e.g. Bañados et al. 2018, Wu et al. 2015, Yang et al. 2020). They appear to be quite massive, their masses lay around or exceed , and bright in the rest-frame ultraviolet (UV) range; their absolute magnitude values at rest-frame are high as (see, e.g. Bañados et al. 2018, Wu et al. 2015, Yang et al. 2020). The existence of such SMBHs testifies to the rapid growth of black holes in the early Universe (Latif et al. 2018, Pacucci et al. 2017, Volonteri and Rees 2005) and raises the question of the accompanying star formation rate (Habouzit et al. 2021).
Extremely high UV luminosity may be explained by the fact that the observed emission is from either an almost naked active galactic nucleus (AGN), i.e. the emission inherent to an accreting SMBH, or a very massive stellar population, or both of them. Usually, the masses of SMBH and stellar population follow each other (Heckman and Best 2014). The high mass of stars corresponded to such high-redshift SMBH is believed to be associated with an enormous quantity of dust produced during stellar evolution and cold gas (Kennicutt and Evans 2012). Then, the SMBH radiation is supposed to be attenuated significantly by a massive cold dusty torus, especially, its UV part (e.g. Hickox and Alexander 2018). In light of this it is interesting to search high-redshift galaxies with SMBH in the far-infrared (FIR) range.
Using the Atacama Large Millimeter Array, Decarli et al. (2018) have studied UV bright quasars at in the [CII] line emission and the underlying FIR dust continuum. These quasars have been selected by requiring that they are more luminous at rest-frame UV than . They appeared to be bright in both the FIR continuum and CII line. The FIR luminosities are similar to the values for ultra-luminous infrared galaxies (ULIRGs) in local universe (see their Figure 8 in Decarli et al. 2018). The most remarkable result is that such galaxies demonstrate a higher (about an order of magnitude higher, Decarli et al. 2018) ratio between black hole (BH) and dynamical masses than that in the local universe (Heckman and Best 2014). That may reflect more rapid BH growth during the dark ages epoch (Latif et al. 2018, Pacucci et al. 2017, Volonteri and Rees 2005).
Further insight into the relationship between stellar population and SMBH in these galaxies has been made by Venemans et al. (2020). This set of quasars has been observed in the FIR with higher spatial (about 1 kpc) resolution. They have found that the [CII] emission in the quasar hosts is located within the central region of several (1–4.8) kpc, so that high infrared (IR) emission could be associated with star-forming bursts. This may also argue in favour of the similarity to local ULIRGs. However, local ULIRGs are significantly dust-obscured systems, and their UV luminosities are quite low (Goldader et al. 2002) in comparison with the values of the quasars studied by Decarli et al. (2018).
Motivated by these results, we are interested in whether the [CII]-FIR ratio could be explained by the SMBH emission being slightly absorbed by a lot of small dense clouds located in the ionization cone.
According to the unified model for AGNs (Antonucci 1993, Hickox and Alexander 2018), we assume that the quasars selected by Decarli et al. (2018) are so bright in UV because almost naked nucleus is observed in these cases. Note that a significant part of local AGNs (Ricci et al. 2015) have low obscuration (Ramos Almeida and Ricci 2017) with a small covering factor of clouds. In the ionization cone, there are many clumps; they may be a result of jet-wind interaction and further cloud entrainment process (e.g. Murthy et al. 2022). We expect that the emission of these cloudlets exposed to a naked AGN will become a small supplement to that inherent to AGN emission except for the FIR range, where the cold/warm gas of clouds emits efficiently in both the FIR continuum and [CII] line.
Following Kubota and Done (2018), the SMBH radiation is supposed to be generated by a slim disc (Abramowicz et al. 1988) with the Novikov–Thorne spectrum (Novikov and Thorne 1973) modified by a comptonised extension up to the energy keV (see details in Kubota and Done 2018). Figure 1 presents an example of such a spectrum depicted by the red line. Note that the SMBH spectrum looks like thermal radiation, with an effective temperature depending on the SMBH mass (Kubota and Done 2018). An inherent feature of the SMBH spectrum is a powerful high-energy part with , and such a spectrum is believed to be consistent with a composite spectral energy distribution (SED) for radio-quiet AGNs (see, e.g. Ho 2008).
We assume that a part of the SMBH radiation is absorbed in the inner region of the dusty torus, i.e. in gaseous layers located on the border between the ionization cone and the torus, and that it is added to the radiation from the naked accreting SMBH. This relatively rarefied gas produces a low absorption of the UV photons emitted by SMBH and re-radiates them in the IR range to form the common dusty IR bump in the spectrum. Such gas is heated efficiently, and it cannot give any meaningful CII emissions. An example of the spectrum for such a slightly attenuated SMBH is depicted by green line in Figure 1. Then, we add the contribution to SED from many small dense clouds. They are dense enough to re-radiate SMBH emission in the CII line; moreover, they can be located at different distances from the central SMBH, so those placed closely may be ionized higher, whereas those located further are left cold and slightly ionized.
We use the CLOUDY code (Ferland et al. 2017) to calculate a library for SEDs of both AGN slightly obscured by a gaseous layer and clouds immersed in the ionization cone of an AGN. To model the SEDs for slightly obscured AGNs, we assume the gas layer thickness 10–100 pc with a relatively low density of 10–30 . After we add to this spectrum, the emission from clouds exposed to the unabsorbed radiation from the BH. Because of the low surface/volume covering factor of clouds, we can do this independently for different realizations of the following parameters: gas density, metallicity, size of each cloud, and distance of a cloud from the AGN. The number density of clouds varied in the range of , and the metallicity is assumed to be equal to the solar value, which is based on the reasonable estimates of the dust mass in the host galaxies (Decarli et al. 2018) and close to the values detected in the gaseous component of similar high-redshift AGNs (Venemans et al. 2020). Their sizes ranged from 1 to 30 pc. An ensemble of such clouds is distributed within from AGN. At small distances, the radiation of a naked AGN remains high enough to completely ionize the CII ion. We assume an open geometry and a total solid angle equal to 1/16, which is expected from the observations (e.g. Zakamska et al. 2006, Fischer et al. 2013), however, this value is quite poorly constrained (e.g. Ramos Almeida et al. 2014).
Figure 2 presents several spectra for the models of SMBH with absorption by small clouds. The unabsorbed spectrum of SMBH is presented in Figure 1 by red line. The SMBH mass is set to for all models. One can see that these spectra show sufficiently high UV luminosities: the values of absolute magnitude are about . A small attenuation in X-ray/UV bands produces significant IR dust and CII line emission. So these SEDs demonstrate high luminosity in both the UV background and the FIR continuum and CII line as well.
Using our statistical model, we calculate a set of different realizations, with a surface covering factor lower than 0.1, and then pick up those with the [CII]–FIR ratio close to the observed set (Decarli et al. 2018). Figure 3 presents the luminosity ratio of the [CII] line to the FIR continuum versus the FIR continuum for our models shown by filled grey circles and for the quasars observed by (Decarli et al. 2018, the data are taken from their Table 5) depicted by open red circles. The SMBH mass is set to in these models. One can see that the loci of points obtained in our statistical models and observed by Decarli et al. (2018) are close to each other. The values of absolute magnitude ranged in . As a result, the [CII]-FIR ratios observed in high-redshift AGNs are similar to the ratios for slightly obscured SMBH with small covering factor by cold dense clouds. Certainly, the locus of the ratio values depends on many parameters, i.e. SMBH mass, covering factor of clouds, and distances of clouds from SMBH, as well as cloud features like their density, metallicity, size, and so on. A detailed analysis of its influence on the [CII]-FIR ratio will be given elsewhere.
Here, we would like to pay attention to two issues. First, it seems that there is lower limit of SMBH mass at which absolute magnitude at rest-frame remains higher for a given threshold. For the selection criterion adopted by Decarli et al. (2018), the SMBH mass cannot be lower than . Second, higher absorption corresponds to the population of mildly/highly obscured AGNs, which have been observed in significant quantity in the local universe (e.g. Ricci et al. 2015) and are expected to be at high redshifts. Recently, a heavily obscured AGN candidate has been discovered at (Vito et al. 2019). It is expected that there are numerous similar objects at high redshifts. In general, such objects should be low-luminous or even unseen in the near-IR band, where rest-frame UV emission is shifted for high-redshift objects. In the former, these objects look similar to red dwarfs and the detection of Lyman-break or high FIR luminosity leads to the confirmation as AGN. In the latter case, blind IR/FIR surveys are needed, and possible X-ray detections are useful as well.
We have studied the relation between luminosities in the [CII] and the FIR continuum for SMBH slightly obscured by an ensemble of dense clouds with a low covering factor. The low obscuration of SMBH results in extremely high UV luminosity, which is detected from known high-redshift quasars (see, e.g. Bañados et al. 2018, Yang et al. 2020, Wu et al. 2015, and so on). Decarli et al. (2018) have selected a set of AGNs, which are UV bright, and investigated their FIR radiation. We have found that dense clouds with a low covering factor (to remain the majority of UV emission from unobscured AGNs) can give sufficient luminosities in [CII] line and underlying FIR continuum to reproduce the [CII]-FIR ratio observed from the set of high-redshift AGNs for reasonable SMBH mass of . One can think that many distant, mildly/heavily obscured AGNs are to avoid detection in near-IR wavelengths (i.e. UV range at rest-frame), if so blind IR/FIR surveys as well as possible X-ray detections are needed to confirm this conclusion.
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Conflict of interest: The authors state that there is no conflict of interest.
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