Abstract
Abstract. The presence of obscuring material (or a dusty 'torus') in active galactic nuclei (AGN) is central to the unification model for AGN. Two models, the multi-population model for radio sources and the receding torus model, are capable of describing observational properties of powerful radio galaxies and radio quasars. Here, I study the changes of the opening angle of the obscuring torus with radio luminosity at 151 MHz, [O III] emission-line luminosity and cosmic epoch aiming to discriminate between two working models. An analytical expression relating the half opening angle of the torus to the mean projected linear sizes of double radio galaxies and quasars is derived. The sizes of powerful double radio sources taken from the combined sample of 3CRR, 6CE and 7CR complete samples are used to estimate the torus opening angle. I found a statistically significant correlation between the half opening angle of the torus and [O III] emission-line luminosity. The opening angle increases from 20
Abstract
• to 60
Abstract
• with increasing [O III] emission-line luminosity. This correlation is interpreted as direct evidence of the receding torus around central engines of powerful double radio sources.
Introduction
Spectropolarimetric observations of Seyfert 2 galaxies (Antonucci & Miller 1985; Miller & Goodrich 1990) suggested an orientation-based unification scheme for active galactic nuclei (AGN). An optically thick molecular torus obscuring the AGN permits a unification of Seyfert 1 and Seyfert 2 galaxies by proposing that they are intrinsically the same objects viewed at different angles to the axis of the torus. This model was invoked by Scheuer (1987) and Barthel (1989) to account for the orientation-dependent appearance of powerful radio sources, which can appear as radio galaxies or quasars. According to the standard picture, the torus hides the AGN and broad-line region of a radio galaxy, whereas for quasars these are viewed directly for a quasar down the ionization cone. The opening angle of the torus defines the cone angle and the half opening angle is the critical angle (θ c ∼ 45
Introduction
• ; Barthel 1989) at which the transition between radio galaxies and quasars occurs. The narrow-line regions have extended kpc-scale structure and therefore are visible for any orientation of the torus. There is considerable multi-band observational evidence supporting the unification scheme for radio galaxies and quasars. This comes from the X-ray detection of inverse Compton scattered photons (Brunetti et al. 1997 ) and polarized (scattered) emission lines from hidden quasars in some radio galaxies (Antonucci & Miller 1985) , from the direct detection of unabsorbed soft and hard X-ray emissions from quasars (e.g. 3C 109, Allen and Fabian 1992; Cyg A, Ueno et al. 1994; 3C 295, Brunetti et al. 2001; 3C 265, Bondi et al. 2004) , from the detection of comparable far-infrared emission from the high-redshift (z > 0.8) radio galaxies and quasars (e.g. Meisenheimer et al. 2001; Haas et al. 2004) , from the difference of the mid-infrared spectral energy distribution in the broad-line and narrow-line AGN (Siebenmorgen et al. 2004) , from the detection of superluminal radio knots on parsec-scales (Vermuelen & Cohen 1994) , and from the presence of supermassive black holes and relativistic jets in both radio galaxies and quasars (McLure & Dunlop 2002; Laing 1988; Garrington et al. 1988) .
Introduction
A single opening angle can not account for two pieces of observational evidence: (i) at a given radio power the [O III] lines are weaker in radio galaxies than in quasars (Lawrence 1991; Simpson 2003) , and (ii) the increase of the quasar fraction with increasing radio luminosity (Hill et al. 1996; Willott et al. 2000; Grimes et al. 2004 ). Lawrence (1991) suggested the receding torus model in which the dust evaporation radius of the torus depends on the luminosity of the photoionizing radiation of the AGN, which is assumed to be independent of the height of the torus. In this scenario the opening angle of the torus increases with increasing luminosity of the ionizing radiation, L phot , from the AGN. This model accounts for the fact that quasars are brighter in L phot than radio galaxies (Lawrence 1991; Simpson 2003) in samples selected at low radio frequencies, and that the fraction of quasars increases with radio luminosity. Gopal-Krishna et al. (1996) showed that a wider opening angle with increasing radio luminosity could explain the problem of unification posed by the difference between the radio luminosity-size correlations for radio galaxies and quasars. In addition, Willott et al. (2000) found that the fraction of quasars decreases at low luminosities. They argued that this can be explained either by the receding torus model (decrease of θ c with decreasing radio luminosity), or by the existence of a second population of low-luminosity radio galaxies. Grimes et al. (2004) used a combined complete sample at 151 MHz to show that, in the luminosity-dependent unified scheme, a twopopulation model may explain the increase of the quasar fraction with L phot as well as the emission-line differences between radio galaxies and quasars. They conclude that the effect of the receding torus may be important but it is not clear yet whether the receding torus is present in both populations.
Introduction
The opening angle of the torus, θ c , defines the geometry of the torus (the inner radius and height) and appears to be an important parameter for understanding the evolutionary behaviour of the obscuring material and testing the torus model. In the Appendix, I derive an equation that allows the mean half opening angle of the torus θ c to be estimated by means of the projected linear sizes of radio galaxies and quasars. In section 2 the equations for estimating θ c are presented. The combined complete sample of radio sources is described in section 3. In section 4, the relations between the critical angle with the 151 MHz radio luminosity L 151 , [O III] 5007-Å emission-line luminosity L [O III] and cosmic epoch are investigated. In section 5, the receding torus model is discussed.
Introduction
Throughout the paper a flat cosmology (Ω m + Ω Λ = 1) with non-zero lambda, Ω m = 0.3 and H 0 = 70 km s −1 Mpc −1 is used.
Equations for the opening angle of the torus
Powerful FRII (Fanaroff & Riley 1974 ) radio galaxies and quasars are associated with bipolar relativistic radio jets emerging from the AGN which form extended radio lobes on both sides of the AGN. The radio jets are almost aligned with the axes of the tori in FRII (Cyg A; Canalizo et al. 2004 ) and FRI radio sources (3C270, Jaffe et al. 1993; Verdoes Kleijn et al. 2001) . The half opening angle of the torus is defined by the angle between the radio axis and the direction at which the division between radio galaxies and quasars occurs. Then the half opening angle of the torus can be estimated by means of the projected linear sizes of FRII radio galaxies and quasars; linear sizes of quasars appear to be systematically smaller than the linear sizes of radio galaxies (Barthel 1989 ) as a result of projection effects. In the Appendix, I derive an equation (7) for estimating the mean critical angle θ cs from the ratio of the mean projected linear sizes of quasars l Q and the whole sample l. The problem is solved for the sample of FRII radio sources having an isotropic distribution of radio axes over the sky. Lowfrequency radio samples of radio sources are thought to be free from orientation biases and can be used in this analysis. Another independent way to estimate the half opening angle is to consider the number of quasars N Q and the number of radio galaxies and quasars N G+Q in the low-frequency radio samples,
Equations for the opening angle of the torus
If the unified schemes for FRII radio galaxies and quasars is valid then one should expect a correlation between θ cf and θ cs , which are independent estimates.
The sample and selection criteria
I use a combined sample of three complete low-frequency samples (Grimes et al. 2004) 1 , made up of the 3CRR, 6CE and 7CRS samples (Laing, Riley & Longair 1983; Rawlings, Eales & Lacy 2001; Willott et al. 2002) . This contains 302 radio sources all having extended radio structure on kiloparsecscales. I then excluded 3C48, 3C287 and 3C343 because they are complex with no clear double lobe structure (Laing et al. 1983) . Three other sources were excluded: 3C231 because its radio emission is due to a starburst, 3C345 and 3C454.3 because their inclusion in the 3CRR sample is a result of Doppler boosting of the jet. I adopted the classification of radio sources used by Grimes et al. (2004) : high-and low-excitation narrow-line radio galaxies (HEGs and LEGs), weak quasars (WQs) and broad-line radio quasars. The category of weak quasars includes HEGs which are objects with weakly or heavily obscured broad-line nuclei seen indirectly (e.g., in broad wings of Hα and Paschen lines, in optically-polarized light) and unobscured objects with weak broad-line optical nuclei.
The sample and selection criteria
There are 39 low-excitation radio galaxies in the sample which are believed to be a separate population independent from the high-excitation radio galaxies and radio quasars (Laing et al. 1994) . Exclusion of these sources and FRI radio sources leaves a sample consisting of 237 FRII radio sources. The projected linear sizes (the apparent distance between radio lobes) of 3CRR sources are adopted from the 3CRR database 2 , and the sizes of 6CE and 7CRS sources are taken from the electronic version of the combined database 1 . The projected linear sizes vary over (1 to 2000) kpc over the range (1.6 × 10 24 to 4.6 × 10 28 ) W Hz −1 sr −1 of the 151 MHz radio luminosity. The structure of FRII radio sources is influenced by environmental asymmetry, which becomes more important on small scales (Arshakian & Longair 2000) . I excluded the compact steep-spectrum radio sources with typical sizes < 20 kpc to avoid contamination of projection effects by interaction effects between a radio jet and interstellar medium (Barthel 1989) . Their inclusion or exclusion does not introduce perceptable change in the results described below. The final sample consists of 206 FRII radio sources: 134 HEGs, 20 weak quasars and 52 quasars. (Fig. 3) . The values of mean linear sizes of weak quasars are larger than those of quasars in three equal subsamples divided by [O III] emission-line luminosity. The same result is obtained when the sample is binned by 151 MHz radio luminosity. This supports the idea that HEGs and weak quasars are the same objects, where the later ones appear to have broad emission lines as a result of scattered light from the nucleus. Therefore in this analysis, the weak quasars are grouped with the HEGs rather than quasars. On the other hand, some of the WQs appear to be transitional objects (between quasars and HEGs) which are oriented near to the critical angle where the broad-line region is reddened but not totally obscured (Laing et al. 1994; Simpson et al. 1999 ) and hence they can be grouped with quasars. Therefore it is important to see how an exclusion of 20 WQs influences the final results and this will be discussed later in this section.
Relations for the torus opening angle
For the whole sample, I calculate the number of all radio sources N G+Q = 206 and quasars N Q = 52, and their mean linear sizes l = (279 ± 21) kpc and l Q = (162 ± 19) kpc respectively. Then the critical viewing angles, θ cs = 42
Relations for the torus opening angle
• ± 7
Relations for the torus opening angle
• and θ cf = 42
Relations for the torus opening angle
• ± 12 • , are estimated using equations (7) and (1). Two independent equations give similar results with the error being 4 T. G. Arshakian: Direct evidence of the receding 'torus' in powerful radio sources Table 2 . Estimates of critical angles, θ cs and θ cf and their errors in equal subsamples binned by L [OIII] . The first line of the table refers to the two sets of binned data, and the second line shows results of three sets of binned data.
Relations for the torus opening angle
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) [OIII] in the bin; (4,5) -Number of radio galaxies and quasars in the log L [OIII] bin; (6) -The half opening angle of the torus estimated by fraction of quasars (eq. 1), and its standard error σ θ cf is calculated assuming that σ N G+Q = N G+Q and σ N Q = N Q ; (7) -The confidence level of rejecting the null hypothesis that half opening angles θ cf of the torus estimated in different L [O III] bins are equal. The variance analysis (the Fisher test) is used with two degrees of freedom, N bin − 1 and N bin (N G+Q − 1); (8,9) -The mean linear sizes of all sources (radio galaxies and quasars) and quasars, and their standard errors; (10) -The half opening angle of the torus and its standard error from eqs, (7) and (8); (11) Table 2 ). Critical angles θ cs estimated by the mean linear sizes of radio galaxies and quasars (eq. (Table 2) . Both, θ cs and θ cf , increase by a factor of two Fig. 4 ). The mean half opening angle increases from ∼ 20
Relations for the torus opening angle
• to ∼ 40 • and to ∼ 60 • in three subsamples binned by [O III] emission-line luminosity, and the difference between the angles is still very significant (97 %). The difference becomes less significant (< 85 %) when the sample is divided on four or more subsamples. The division into subsamples smaller than ∼ 50 objects does not allow a statistically significant correlation between θ c and L [O III] to be investigated. Also, the small samples may introduce fluctuations of θ c due to statistical fluctuations in the orientation of radio sources (Saikia & Kulkarni 1994) .
Relations for the torus opening angle
I repeated the analysis for the θ c − L 151 and θ c − z relations. Both θ cs and θ cf estimated for two equal subsamples binned by 151 holds for the combined 3CRR, 6CE and 7CRS samples (Grimes et al. 2004 ). A Fisher test shows that the increase of θ cs with L 151 is not statistically significant (Table 3 ; Fig. 5 ). No significant evolution of θ cs or θ cf is found with cosmic epoch z.
Relations for the torus opening angle
The results of this section stand even after excluding the WQs from the sample (Table 3 ). This indicates that the positive correlation in the θ cs − L [O III] plane is mainly due to HEGs and quasars. The significance of the correlation is still high after exclusion of transitional sources from the sample of 206 radio sources.
Relations for the torus opening angle
Let us consider the selection effects which might cause the positive correlation θ c − L [O III] seen in Fig. 4 . Although there are problems with identifying the broad-line radio galaxies as low-luminosity quasars, Hardcastle et al. (1998) suggest that some of the low-luminosity broad-line radio galaxies are true quasars which are not sufficiently bright to be classified as such in the optical. If so, then reassigning them to the HEGs rather than to the quasars will decrease the fraction of quasars, resulting in small opening angles and the consequence of this is that θ cf = 24
Relations for the torus opening angle
• is underestimated in the L [O III] low-luminosity bin (Table 2 ). In a L [O III] high-luminosity bin the fraction of quasars may increase if the [O III] emitting region is partially obscured in radio galaxies causing a factor of 5 to 10 depression of the [O III] emission (Hes et al. 1996) which may result in the overestimation of θ cf . The selection effects at low-and highluminosities may reproduce a positive correlation between θ cf and L [OIII] . To understand the bias introduced in the fraction of quasars one may consider the independent measurements of the opening angle θ cs ( Table 2 ). The fact that θ cs is independent of the fraction of quasars (eq. 7), θ cs positively correlates with L [O III] (Fig. 4) and θ cs ≈ θ cf across L [O III] range indicates that the θ cf − L [O III] correlation is real and if there is a bias in the fraction of quasars it is not significant. The χ 2 test is used to estimate the significance of the null hypothesis that two independent measurements of θ cs and θ cf are equal across the L [O III] and L 151 ranges. For two and three sets of binned data the values of θ cs and θ cf are not significantly different (P < 80 %).
Relations for the torus opening angle
Figs. 4 and 5 show that θ cs ≃ θ cf in different bins of L [O III] and L 151 . The equality of two independent estimates confirms the validity of the orientation-based unification scheme for radio galaxies and quasars and it indicates that the relative mean size of quasars (l Q /l) and the relative number of quasars (N Q /N G+Q ) are indeed good measures of the critical viewing angle in the low-frequency radio samples.
Relations for the torus opening angle
Another possible selection effect is related to the measured projected sizes of FRII sources which may be overestimated as a result of projection of the volume of radio lobes. It is clear that independent of the plausible geometry of radio lobes the projection effects may be important for sources having small inclinations of radio axes to the line of sight. The fact that the exclusion of small sizes (< 20 kpc, see section 3) does not change the final results indicates that the projection effect is not likely to influence strongly the estimates of θ cs .
Relations for the torus opening angle
The assumption that the axis of a dusty torus is aligned with the radio axis of FRII sources can be partially relaxed (e.g., Capetti & Celotti 1999) in real life allowing some distribution of angles between the axes of the torus and the jet. In this scenario there should be a difference between the true critical angle (θ ct ) defined by the geometry of the torus and the critical angle θ cs (eq. 7) estimated by means of projected sizes of FRII sources. It is important to understand how this difference varies depending on the value of true critical angle and whether it can lead to a positive correlation found between θ cs and L [O III] . To test this, I model random angles between the axes of the torus and the jet by generating a pair of 5000 random directions: for every random axis of the torus the random jet direction is generated within the specified cone angle 2δ max . For simplicity, a single linear size (300 kpc) for radio galaxies and quasars is adopted. Then, given the true critical angle (θ ct ), I generate the projected linear sizes for both quasars and all sources using the inclination angles of the jet. The mean sizes of quasars and the whole sources are used to estimate the critical angle θ cs (eq. 7). The deviation of estimated critical angle θ cs from the true θ ct one is presented in Table 4 for different δ max . δ max = 0 corresponds to the case where the axes are aligned and here there is an excellent agreement between θ ct and θ cs , which provides a good test of the formalism involved in equation (7). For larger values of δ max the estimated critical angle appears to be larger than the true critical angle (θ cs > θ ct ) (Table 4) . One may conclude that the effect of misalignment of axes of the torus and the jet leads to the overestimation of critical angles θ cs , which is higher for small θ ct . If there is a significant misalignment of axes then the critical angles in the θ cs − L [O III] relation plane are overestimated with the effect of making flatter the slope of the real θ ct − L [O III] relation. This demonstrates that the misalignment effect makes the real correlation weaker and thus can not produce the positive correlation found between θ cs and L [O III] .
Discussion and conclusions
The key result of the previous section is that the opening angle of the ionizing cone of the torus becomes larger at high [O III] emission-line luminosities. The half opening angle tan θ c = Table 4 . The values of true critical angles θ ct and their deviations (θ cs ) simulated for different half cone angles δ max within which the angles between the axes of the torus and the jet are distributed. (ii) decrease of the height with L [OIII] . The first relation naturally follows from the receding torus model (Lawrence 1991; Hill et al. 1996 ). In this model (i) the ionizing radiation from the AGN evaporates the circumnuclear dust forming the inner wall of the torus at a distance r which increases as r ∼ L
Discussion and conclusions
(where L [O III] is assumed to be a measure of the ionizing luminosity), and (ii) the height of the torus h is independent of L [O III] . There is observational evidence in favour of an r−L [O III] relation. Minezaki et. al. (2004) used multi-epoch observations of the Seyfert 1 galaxy NGC 4151 to show that the time lag between the optical and near-infrared light curves grows with optical luminosity as log △t ∝ L 0.5 . They interpreted this as thermal dust reverberation in an AGN to relate a △t to the inner radius of the dusty torus (△t ∝ r). Willott et al. (2002) found that 3C/6C quasars have higher submillimetre luminosities by a factor > 2 than radio galaxies. They argued that this is in quantitative agreement with the receding torus model if there is a positive correlation between optical and far-infrared luminosities. Another piece of evidence comes from the studies of the mid-infrared spectra of 3C radio sources (Freudling et al. 2003) . They showed that the bands of polycyclic aromatic hydrocarbons (PAHs) are weak in broad-line radio galaxies and they are much stronger in narrow-line radio galaxies of similar luminosities. They interpreted this difference as a result of the heating radiation from the central nucleus: the hard radiation destroys PAHs in the broad-line regions and heats larger dust grains at intermediate distances. The spectra of broad-line galaxies and quasars originate in the broad-line region where only few PAHs survive. In the narrow-line radio galaxies this region is obscured and the spectra are dominated by cooler dust at larger distances where more PAHs can survive. Simpson & Rawlings (2000) showed that the near-infrared spectral slopes of 3CR quasars are steeper for less luminous objects and that the fraction of moderately obscured, red quasars decreases with increasing radio luminosity. Both relations are in agreement with the receding torus model.
Discussion and conclusions
As indicated by Simpson (2003) there are several lines of evidence indicating that the height of the torus is not a strong function of luminosity. If so, the half opening angle of the torus tan θ c = 2r/h ∝ L , which is somewhat stronger than is expected from my results. A larger sample of radio sources is needed to confirm the increase of the torus thickness with photoionizing radiation of the AGN.
Discussion and conclusions
The second relation, i.e. the negative correlation between h and L [O III] which may be a cause for an increase of θ c with L [O III] , seems to be unrealistic since it requires the inner radius of the torus to be independent of L [O III] . One may conclude that the growth of the opening angle of the torus with increasing L [O III] is a direct evidence of the receding-torus-like structures around central nuclei of FRII radio sources. This result apparently breaks the degeneracy (multi-population or receding torus) in the interpretation of data in favor of the receding torus model.
Discussion and conclusions
The main conclusions of this analysis are as follows:
Discussion and conclusions
1. On the basis of an inverse problem approach, an equation for estimating the opening angle of the torus by means of the mean projected linear sizes of FRII radio galaxies and quasars has been derived. The small errors involved in estimation of the opening angle makes the linear size statistics a powerful tool for investigating the orientation-dependent structures in AGN.
Discussion and conclusions
T. G. Arshakian: Direct evidence of the receding 'torus' in powerful radio sources 7
Discussion and conclusions
2. An application of this equation to the combined complete sample of FRII radio sources revealed the following: -The mean half opening angle of the torus is 42 • ± 7
Discussion and conclusions
• for the whole sample. 

{'paper_id': '12466629', 'title': 'Direct evidence of the receding “torus” around central nuclei of powerful radio sources', 's2_url': 'https://api.semanticscholar.org/CorpusID:12466629', 'source': 'S2ORC'}