CONSTRAINING JET PRODUCTION SCENARIOS BY STUDIES OF NARROW-LINE RADIO GALAXIES

Marek Sikora; Grażyna Stasińska; Dorota Kozieł-Wierzbowska; Greg M. Madejski; Natalia V. Asari

doi:10.1088/0004-637X/765/1/62

1. INTRODUCTION

It became clear already shortly after the discovery of the first radio galaxies (RGs) that their strong radio emission is associated with a presence of luminous optical emission lines (Baade & Minkowski 1954; Osterbrock 1977; Grandi & Osterbrock 1978). Such an association was later confirmed by finding a correlation of radio luminosities with narrow-line luminosities in Fanaroff–Riley type II (FRII; Fanaroff & Riley 1974) radio sources (Baum & Heckman 1989; Saunders et al. 1989; Rawlings et al. 1989; Rawlings & Saunders 1991; Zirbel & Baum 1995; Willott et al. 1999; Buttiglione et al. 2010; Kozieł-Wierzbowska & Stasińska 2011, hereafter KS11). Using the narrow-line luminosity as a proxy for the cold accretion disk luminosity and the radio luminosity as a proxy of the jet power, Rawlings & Saunders (1991) found an approximate proportionality between these two quantities, with jet powers approaching and in some cases, even exceeding the bolometric luminosities of the accretion disks.

Studies of the correlation of the jet powers with properties of central engines using radio and optical luminosities became more thorough and robust once methods of the black hole (BH) mass estimations have been developed (see, e.g., Woo & Urry 2002 and references therein). This allowed a determination of the properties of radio-loud active galactic nuclei (AGNs) as a function of their Eddington ratio, λ, defined as the ratio of the accretion bolometric luminosity to the Eddington luminosity. In particular, KS11 using the BH mass estimates from the stellar velocity dispersion (σ_*)–BH mass (M_BH) relation (Tremaine et al. 2002) found that FRII RGs span about four decades of the Eddington ratio and that, when scaled by their BH masses, their radio luminosities correlate with the Eddington ratio, similar to the correlation of absolute radio luminosities versus absolute narrow emission line luminosities. One might consider this similarity as resulting from the fact that distribution of the BH masses of FRII sources is rather narrow, with majority of them within the range of 10⁸–10⁹ M_☉. However, since the physics of the jet production is linked to the Eddington-scaled accretion rate rather than to its absolute value and powers of jets produced with the same efficiency scale with the BH mass, the "primary correlation" to be considered should be the one between the Eddington-scaled luminosities.

Such a correlation, however, contradicts the predictions of jet models which relate the strength of the central poloidal magnetic fields (those threading the innermost portions of the accretion disk and the BH) with maximal pressure in the disk. According to the standard accretion disk theory, innermost portions of disks accreting at a rate corresponding to the Eddington ratio in the range of 10⁻⁴–1 are dominated by radiation pressure. Since this pressure does not depend on the accretion rate, the powers of jets—believed to be initially dominated by Poynting flux—are not expected to depend on the accretion rate either. In consequence, such models predict maximal jet powers ∼100 times smaller than those observed in radio-loud quasars (RLQs) with extended radio structures (see, e.g., Ghosh & Abramowicz 1997).

The model which can account for the energetics of the most powerful jets and explain the observed radio–optical correlation is the one based on the so-called magnetically arrested/choked accretion flows (Narayan et al. 2003; Igumenshchev 2008; McKinney et al. 2012). In such a model, the amount of the net magnetic flux amassed in the central region is so large that innermost portions of accretion disks are dynamically affected by central magnetic fields. In this regime, the accretion onto a BH proceeds via interchange instabilities (≡ magnetic Rayleigh–Taylor instability; Stone & Gardiner 2007 and references therein) and magnetic flux threading the BH is supported by the ram pressure of the accreting plasma.

In order to directly confront this model with observations, we expand the sample of RGs studied by KS11 by including other types of radio morphologies, investigate the correlation of radio loudness ${\cal R}$ (radio-to-optical luminosity ratio) versus λ, and investigate the dependence of source sizes on the Eddington ratio. This paper is organized as follows. In Section 2 we describe our sample selection and data reduction and analysis. In Section 3 we present results of our analysis of optical and radio based correlations. In Section 4 we investigate a consistency of these results with the jet production model which involves the "magnetically choked" accretion scenario. Our main conclusions are listed in Section 5.

Throughout the paper we assume a Λ cold dark matter cosmology with H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_m = 0.27, and Ω_Λ = 0.73.

2. THE DATA

2.1. The Sample

To select our sample, we proceeded in a manner analogous to that described in KS11. Since we are primarily interested in RGs with elongated structures, we started with the Cambridge radio catalogs accessible via Vizier where such objects are well defined: 3C (Edge et al. 1959; Bennett 1962), 4C (Pilkington & Scott 1965; Gower et al. 1967), 5C (Pearson 1975; Pearson & Kus 1978; Benn et al. 1982; Benn & Kenderdine 1991; Benn 1995), 6C (Baldwin et al. 1985; Hales et al. 1988, 1990, 1991, 1993a, 1993b), 7C (Hales et al. 2007), 8C (Rees 1990; Hales et al. 1995), and 9C (Waldram et al. 2003). We considered all the radio sources from these catalogs and cross-identified them in an automatic fashion with the sample of 926,246 galaxies with optical spectra from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) main galaxy sample (Abazajian et al. 2009). Taking into account the sometimes large positional uncertainties in the Cambridge radio catalogs, we adopted a maximum distance between the position given for the radio source and that given for the optical galaxy varying from 0.2 arcmin to 1 arcmin, depending on the catalog. We thus obtained a list of 2633 RGs with available SDSS spectra. The final identification was done using the NRAO VLA Sky Survey (NVSS; Condon et al. 1998) and the Faint Images of the Radio Sky at Twenty centimeters (FIRST; Becker et al. 1995) radio maps, which have much better spatial resolution than the Cambridge catalogs, and have been obtained at the same frequency of 1.4 GHz. For all the pre-selected objects we constructed jpg images superimposing NVSS or FIRST contours on SDSS images in the r band. The images are centered on the galaxy which is supposed to correspond to the radio source. By visual inspection of all these images, we found that 307 cases were actually misidentifications (among which many of them corresponding indeed to a galaxy but for which the SDSS spectrum was that of another, nearby galaxy), and 14 corresponded to spiral galaxies whose radio emission is produced over the entire disk, most likely by star formation. For the remaining 2042 radio sources we carried out a morphological classification by eye resulting in the following subclasses:

1.
FRI type radio sources, considered as those where the maximum brightness of the lobes is closer to the center than to the extremity;
2.
FRII type, where the maximum brightness of the lobes is closer to the extremity;
3.
FRI/II type, where one lobe is of FRI type and the other of FRII type;
4.
double–double radio sources where two pairs of coaxial lobes are detected;
5.
X-shape radio sources with two pairs of lobes forming an X-shape structure;
6.
one-sided radio sources showing only one lobe;
7.
"elongated," i.e., radio sources that do not appear point-like, but whose angular size does not allow us to classify them more accurately;
8.
radio sources, for which no morphological class could be assigned because of an atypical, irregular shape;
9.
compact, unresolved radio sources.

This morphological classification, which is purely subjective, was carried out independently by two of the coauthors, D.K.-W. and G.S. For about 15% of the objects we considered, our initial classifications diverged, although we agreed on our final classification. For further considerations in this paper, we restricted our sample to objects that clearly show the presence of radio structures associated with radio lobes and/or jets, i.e., FRII, FRI, FRII/FRI, double–double, X-shape, and one-sided.

We excluded the radio sources whose parent galaxies have a redshift larger than 0.4, in order to insure that the Hα emission line—which is crucial for our study—falls within the SDSS spectral range. We also excluded those radio sources where a broad component was clearly seen in the hydrogen emission lines. This allows us to make more accurate computations of narrow-line luminosities as it avoids issues related to the decomposition of the narrow and the broad components. In addition, this limits our sample to objects which according to the Unified Scheme are observed at large inclination angles and by this step, we minimize viewing angle biases in our sample, in particular regarding source sizes. Finally, objects corresponding to galaxies where no emission lines were detected (after processing with the STARLIGHT code; Cid Fernandes et al. 2009, see below) were obviously removed from the sample, since all the considerations in this paper make use of emission line fluxes. After all these cuts, the entire sample on which this paper is based consists of 404 objects. They are listed in Table 1, together with the properties that will be used.

Table 1. Radio and Optical Properties of the Sample of Radio Galaxies

SDSS ID	Cambridge Cat. ID	Redshift	Radio Type	log L_1.4	log L_Hα	log L_[Oiii]	$\log _{M_{{\rm BH}}}$	Ang. Size	Lobe Size
SDSS ID	Cambridge Cat. ID	Redshift	Radio Type	(W Hz⁻¹)	(L_☉)	(L_☉)	(M_☉)	(arcsec)	(kpc)
0273.51957.633	4C+00.37	0.0968	FRI	25.65	6.839	6.644	8.87	170.64	151.02
0312.51689.471	4C+00.56	0.0524	FRII	25.34	7.605	7.572	8.74	255.62	128.83
0349.51699.169	6C B165818.4+630042	0.1063	FRII	25.45	6.417	6.579	7.83	139.2	135.45
0366.52017.349	6C B171944.8+591634	0.2212	FRII	25.59	7.486	6.889	8.29	52	92.72
0367.51997.294	4C+54.36	0.1852	X-shaped	26.00	7.195	6.740	8.16	78	121.12
0385.51877.485	4C−00.83	0.1848	FRI/II	26.28	6.482	0.000	9.01	67.2	104.18
0400.51820.424	4C+00.05	0.0793	FRI/II	25.37	6.127	0.000	8.55	45	33.71
0432.51884.345	7C B073404.1+402639	0.3905	FRII	25.59	0.000	6.806	8.66	32	84.73
0436.51883.010	6C B075738.1+435851	0.2554	FRII	25.66	6.899	6.740	8.42	26	51.63
0439.51877.044	6C B080758.9+434635	0.1432	X-shaped	25.55	6.886	0.000	8.26	28	35.21
0439.51877.436	7C B080310.1+452158	0.2439	FRI	25.06	0.000	7.105	8.17	30.46	57.97
0439.51877.637	7C B081405.1+450809	0.1422	FRII	25.43	5.690	6.322	8.17	35	43.76
0442.51882.241	6C B081421.2+500530	0.2804	FRI/II	25.93	7.272	0.000	8.67	33	70.12
0442.51882.258	6C B081520.7+495611	0.0952	One-sided	24.87	6.227	6.426	8.20	45.03	78.53
0448.51900.335	6C B084421.9+571115	0.1937	FRII	26.08	7.515	7.887	7.98	144	231.62
0449.51900.323	7C B084921.8+544832	0.1133	FRI	25.57	6.519	0.000	8.38	9.78	9.95
0450.51908.330	4C+56.17	0.1409	FRII	26.05	7.107	6.912	8.04	170	208.59
0451.51908.541	7C B091959.0+571901	0.2846	FRI	25.24	6.973	6.500	8.72	51.55	109.78
0484.51907.497	6C B090602.0+585910	0.2698	X-shaped	26.25	7.894	7.367	8.45	32.90	67.43
0486.51910.456	7C B093527.5+622203	0.2298	FRII	25.41	0.000	6.277	8.65	58	105.59
0487.51943.188	6C B095114.5+625546	0.2286	FRI	25.62	6.871	0.000	8.92	31.17	56.48
0488.51914.191	6C B101400.2+634442	0.1839	X-shaped	25.72	7.021	7.431	8.43	42	64.85
0490.51929.096	7C B105806.3+654923	0.1926	FRII	25.15	6.928	6.992	8.24	76.2	122.08

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as: Data Typeset image

There are some differences between our starting sample and the catalog of elongated radio sources published by Lin et al. (2010). The latter was assembled via cross-correlation of the SDSS DR6 with NVSS and FIRST. Those radio surveys have the advantage of being more homogeneous and deeper than the Cambridge catalogs. Indeed, the limiting radio flux density at 1.4 GHz in the Lin et al. sample is 3 mJy while that of the 3C catalog (when rescaled to 1.4 GHz) is 2 Jy, and those of the 4C–9C catalogs range between 400 mJy and 20 mJy (except for the 5C catalog which reaches 1.5 mJy but in very limited zones of the sky). One may wonder how many objects we are missing by using the Cambridge catalogs as a starting point rather than the NVSS one. It turns out that the number should not be very large, since our sample is limited to a redshift of 0.4, contains only objects with FRI, FRII, and related morphologies which are the most luminous radio sources, and, in addition, includes only objects with emission lines. All our objects have 1.4 GHz luminosities larger than 10²⁴ W Hz⁻¹. In Lin et al.'s catalog, there are only 120 objects with radio luminosities smaller than that out of a total of 1040 objects. This implies that, in our sample, we miss at the very most 12% of objects on the low-luminosity side. On the other hand, for some reason, our starting sample contains 112 objects that fulfill all the selection criteria of Lin et al. but do not appear in their catalog (such as, e.g., the well-known objects 3C198, 4C+00.56 which are bright in radio and have large angular sizes). Another difference between our approach and that of Lin et al. is that, while they attempted to define an objective way to trace the galaxy population smoothly from FRI sources to FRII (as opposed to a sharp and perhaps arbitrary distinction between type I versus type II), we adhered to more a classical morphological classification paying attention to other types than just FRI and FRII.

2.2. Data Processing

The 1.4 GHz radio luminosities, L_1.4, were obtained for each source from the sum of 1.4 GHz fluxes of each of its components listed in the NVSS catalog, including the central, compact point source. The NVSS catalog was used here in order to avoid a flux loss from the extended and faint components missed in the FIRST catalog.

The determination of the angular sizes of the radio sources depended on the morphologies. For FRII radio sources, the angular sizes were defined as the distances between the hot spots or the most distant bright structures in opposite lobes. They were estimated from the FIRST maps, if available, or from the NVSS maps otherwise. The determination of the sizes of FRI radio sources is less straightforward, since lobes and plumes of the FRI RGs fade away with the distance from the radio core. For each FRI source in our sample, we obtained the three rms contour using the FIRST map and we took for the source size the largest extent of this contour, measured along a straight line crossing the radio core (if present). This procedure works well with straight sources. In the case of bent sources, the size determined in that manner is an underestimate. For one-sided sources, we adopted a procedure similar to the one for FRI sources to determine the angular size of the only lobe. The linear (projected) sizes were then determined from the observed angular sizes using the redshift of the corresponding galaxy as obtained from the SDSS. To meaningfully compare the sizes of all the sources, we divided by two the sizes of all the two-sided radio sources: the result is called the characteristic lobe size in the remaining of this work.

The line luminosities of the galaxies associated with the radio sources are fundamental for our work. It is therefore important to determine them in the best possible way. For a removal of the stellar features from the observed optical spectrum, the best approach is to fit the observed continuum—excluding the spectral zones where emission lines are expected—with a composite stellar population obtained by spectral synthesis and subtract it from the entire observed spectrum. What remains is the pure emission line spectrum, whose intensities can then be measured. As in KS11, we have taken the [O iii] 5007, Hα, and Hβ line fluxes from the STARLIGHT database,⁷ where they have been obtained precisely in this manner.

As argued in KS11, we consider L_Hα to be a much better measure of the bolometric luminosity of the AGN than the commonly used L_[Oiii], because it does not depend on the ionization state. This has also been shown by Netzer (2009). The plots presented below are, however, presented in pairs, with one plot using L_Hα and the other using L_[Oiii], for easy comparison with works by other authors.

In only about 20% of objects in our sample are both the Hα and Hβ line fluxes measured with sufficient accuracy to allow a meaningful estimation of the extinction from their ratios. In the majority of those cases, the extinction A_V is smaller than 1 although in a couple of cases it reaches values of up to 4. Note that we find no correlation between A_V and the radio luminosity and the luminosity in the lines. There is then no other way than to ignore extinction in our work, if we want to work with a sample with significant size. Ignoring extinction will then simply add some dispersion to the properties derived from the comparison of optical and radio data, which is not really an issue in our work.

The BH masses of the galaxies were estimated from the observed stellar velocity dispersion given by the SDSS, σ_*, using the relation by Tremaine et al. (2002):

$\begin{equation} {\rm log} M_{\rm BH} = 8.13 + 4.02\, {\rm log} (\sigma _{*} / 200\,{\rm km\,s^{-1}}). \end{equation} \tag{ 1 }$

In considerations involving BH masses we disregard cases with σ_* < 60 km s⁻¹ as well as cases where the signal-to-noise ratio of the SDSS spectrum at 4000 Å is smaller than 10, to ensure that the estimate of M_BH is not significantly affected by observational errors.

3. RESULTS

3.1. Radio versus Optical Luminosities

To compare radio and optical luminosities, we consider three narrow redshift bins, 0.05 < z < 0.1, 0.1 < z < 0.2, and 0.2 < z < 0.4, to reduce the effect of the common parameter—distance—between these two quantities. Figures 1–3 present the three subsamples in the L_1.4–L_Hα and L_1.4–L_[Oiii] planes. RGs of FRI type are represented by filled red (gray in the printed edition) circles, FRII types by filled black circles, and the remaining types, i.e., FRI/II, double–double, X-shape, and one-sided, in open blue (gray in the printed edition) circles. As it is apparent from these figures, the radio luminosities clearly correlate with the narrow-line luminosities. The Spearman rank correlation coefficients are r_S = 0.62 for Hα lines and r_S = 0.58 for [O iii] lines in Figure 1, r_S = 0.57 and r_S = 0.55 in Figure 2, and r_S = 0.50 and r_S = 0.46 in Figure 3.⁸ In the left panels of Figures 1–3, we also labeled the axes in units of P_j and L_bol, where P_j is the jet power and L_bol is the AGN bolometric luminosity. They are obtained by using the following conversion formulae:

$\begin{equation} L_{{\rm bol}} = 2.0 \times 10^3 L_{{\rm H\alpha }} = 7.8 \times 10^{36} L_{{\rm H\alpha }}(L_{\odot }) \ {\rm erg\ s^{-1}} \, \end{equation} \tag{ 2 }$

(Netzer 2009), and

$\begin{equation} P_j = 1.6 \times 10^{18} (f/3)^{3/2} L_{1.4}[{\rm W\ Hz^{-1}}]\ {\rm erg\ s^{-1}} \,, \end{equation} \tag{ 3 }$

the latter being taken from Willott et al. (1999) with the following modifications: (1) conversion from 151 MHz to 1.4 GHz assuming the spectral index α = 0.8 (L_ν∝ν^−α); (2) replacement of P_j∝L^6/7_ν by P_j∝L_ν, the latter taken with a normalization factor giving equality of both at L_1.4 = 10²⁶ W Hz⁻¹. With this normalization the modified formula leads to overestimation of a jet power by a factor of 1.4 for L_1.4 = 10²⁷ W Hz⁻¹ and underestimation by a similar factor for L_1.4 = 10²⁵ W Hz⁻¹. These differences are not substantial when compared with uncertainties of an original formula expressed via the parameter f, with its 1–20 range. The figure was made, adopting f = 3. One can see that even for low values of f the jet powers of many objects exceed their bolometric luminosities.

**Figure 1.** Radio luminosities L_1.4 as a function of the optical line luminosities L_Hα (left panel) and L_[Oiii] (right panel) for the subsample within the redshift range 0.05 < z < 0.1. FRI types are represented by filled red circles (gray in the printed edition), FRII types by filled black circles, and the remaining types, i.e., FRI/II, double–double, X-shape, and one-sided, by open blue circles (gray in the printed edition). In the left panel, the values of the bolometric luminosity and of the radio luminosity *P_j* in ergs s⁻¹ calculated for f = 3 are also indicated.
Download figure:
Standard image High-resolution image

**Figure 2.** Same as Figure 1 for the redshift range 0.1 < z < 0.2.
Download figure:
Standard image High-resolution image

**Figure 3.** Same as Figure 1 for the redshift range 0.2 < z < 0.4.
Download figure:
Standard image High-resolution image

3.2. Radio Luminosities versus Eddington Ratio

In Figure 4, we plot the radio versus emission line luminosities normalized by the BH mass. The correlation is strong, with a Spearman rank correlation coefficient r_S = 0.77 and r_S = 0.71 for Hα and [O iii] lines, respectively. Noting that L_line/M_BH provides the proxy for the Eddington ratio defined to be λ ≡ L_bol/L_Edd and using the conversion formulae (2) and (3), one can see in the left panel of Figure 4 that narrow-line radio galaxies (NLRGs) cover about four decades of λ, from λ ∼ 10⁻⁴ up to λ = 1. The figure shows that our sample is dominated by objects with λ spanning the range of 10⁻⁴–10⁻². These AGNs are optically too weak to be considered as hidden quasars, but nonetheless, being emitters of strong and high excitation lines are expected to be powered like quasars by cold accretion disks and, if not obscured by torus, would appear to us as broad-line radio galaxies (BLRGs; Barthel 1989; Urry & Padovani 1995). However, one should note that the division of AGNs into RLQs and BLRGs does not have any physical grounds; they form a continuous "Eddington ratio sequence" with no signs of an accretion mode change (Sikora et al. 2007).⁹

The deficiency of AGNs with λ > 0.01 in our sample confirms the earlier indications of rarity of very high accretion rate sources at low redshifts located in massive galaxies (see, e.g., Kauffmann et al. 2008), while the presence of several FRI RGs at λ > 0.01 is consistent with a direct finding by Heywood et al. (2007) that radio morphologies of type FRI—which are usually associated with low-luminosity RGs—do happen in quasars as well.

3.3. Radio Loudness versus Eddington Ratio

In Figure 5, we plot the dependence of L_1.4/L_line on L_line/M_BH, where L_1.4/L_line can be considered to be the proxy of the radio loudness defined as the radio-to-optical flux ratio. Our results show a significant negative correlation of radio loudness with the Eddington ratio, with a Spearman rank correlation coefficient r_S = −0.54 and r_S = −0.63 when using the Hα and [O iii] lines, respectively. Such an anti-correlation was discovered previously by Ho (2002) for radio-quiet AGNs and by Sikora et al. (2007) for radio-loud AGNs; however, the statistics of their studies was too poor to claim its presence in the sample when limited only to strong-emission-line objects.

In the left panel of Figure 5 we have also indicated the values of P_j/L_bol and λ on the axes. We can see that most objects with λ < 0.01 have jet powers exceeding the bolometric luminosity of their AGNs, those with lowest λ even by a factor larger than 10 (f/3)^3/2 (see Equation (3)).

3.4. Sizes

Figure 6 shows the sizes of the radio lobes as a function of the Eddington ratio obtained using Hα (left panel) and [O iii] (right panel). To our knowledge, this is the first time that such a diagram is shown. There is only a weak correlation, with a Spearman rank correlation coefficient r_S = 0.34 and r_S = 0.27 when using the Hα and [O iii] lines, respectively. This suggests that the expansion of radio sources is not accompanied by monotonic, long-term changes of the accretion rate, and that the product of the expansion velocity multiplied by the source lifetime does not depend on the Eddington ratio. Furthermore, the fact that the source sizes show no dependence on morphological type suggests that radio morphologies do not form any evolutionary sequence. However, one cannot exclude "switches" between different morphologies caused by modulations of the jet power and the jet direction.

4. DISCUSSION

Amongst all AGNs, the most spectacular from the observational standpoint—yet most challenging theoretically—are probably those associated with extended, luminous radio structures. They appear to us as BLRGs and RLQs if oriented with respect to our line of sight such that their nuclei are not obscured by dusty tori, and as NLRGs otherwise. Their radio and optical luminosities imply an efficient energy transport from nuclei to radio lobes via narrow relativistic jets at a rate very often exceeding the bolometric luminosities of their host nuclei (Rawlings & Saunders 1991; Ghisellini et al. 2010; Fernandes et al. 2011; Punsly 2011; Section 3 in this paper).

As demonstrated by Tchekhovskoy et al. (2011) and McKinney et al. (2012), such powerful jets can be produced in the scenario which involves magnetically arrested/choked accretion flows. Such an accretion mode can well take place in the innermost portions of a disk, when the amount of the net magnetic flux, Φ, amassed in the central region is larger than the maximal flux which can be imparted on that region around the BH by the ram pressure of accreting plasma,

$\begin{equation} \Phi _{{\rm BH}} = \phi _{{\rm BH}} R_g (c \dot{M})^{1/2} \,, \end{equation} \tag{ 4 }$

where $\dot{M}$ is the accretion rate, R_g = GM_BH/c², and ϕ_BH is the dimensionless factor called by Tchekhovskoy et al. (2011) the "dimensionless magnetic flux." The value of ϕ_BH depends on the details of the model and according to the numerical simulations by McKinney et al. (2012) is typically on the order of 50.¹⁰ Jets powered by rotating BHs threaded by such magnetic flux appear to gain powers (Blandford & Znajek 1977; Tchekhovskoy et al. 2010)

$\begin{eqnarray} P_{j} & \simeq & 4.0 \times 10^{-3} \, {1 \over c} \, \Phi _{{\rm BH}}^2 \Omega _{{\rm BH}}^2 f(\Omega _{{\rm BH}}) \nonumber\\ & \sim & 10 \, (\phi _{{\rm BH}}/50)^2 \, x_a^2 f(x_a) \dot{M} c^2, \end{eqnarray} \tag{ 5 }$

where

$\begin{equation} x_a \equiv R_g \Omega _{{\rm BH}}/c = [2(1+\sqrt{1-a^2})]^{-1} \, a, \end{equation} \tag{ 6 }$

$\begin{equation} f(x_a) \simeq 1+ 1.4 x_a^2 - 9.2 x_a^4 \end{equation} \tag{ 7 }$

and a ≡ J_BH/J_{BH, max} = cJ_BH/GM²_BH is the dimensionless angular momentum of a BH, commonly named "spin." For maximal BH spins, a ∼ 1 (→ x_a ∼ 1/2),

$\begin{eqnarray} &&P_{j,{\rm max}} \simeq 1.9 (\phi _{{\rm BH}}/50)^2 \dot{M} c^2 = 19 (\phi _{{\rm BH}}/50)^2 L_{{\rm bol}} / (\epsilon /0.1), \nonumber\\ \end{eqnarray} \tag{ 8 }$

where $\epsilon =L_{{\rm bol}}/(\dot{M} c^2)$ is the radiation efficiency of an accretion disk. The jet power may also contain a contribution from the accretion flow. However, as it was shown by McKinney et al. (2012), this contribution is never dominant and therefore will be ignored in our further discussion. As it can be verified using Equations (5) and (8) and Figures 1–4, the model predicts domination of jet powers over AGN bolometric luminosities even for moderate spins.

As the next step, we will investigate whether—and how—such a model can explain the anti-correlation of radio loudness with Eddington ratio shown in Figure 5. We have

$\begin{equation} {\cal R} = L_{1.4}/L_{{\rm line}} \propto P_j/L_{{\rm bol}} = P_j/(\epsilon \dot{M} c^2) = \eta _j/\epsilon, \, \end{equation} \tag{ 9 }$

where $\eta _j \equiv P_j/\dot{M} c^2$ is often referred to as the jet production efficiency. Hence the negative correlation of ${\cal R}$ with λ may potentially arise from the respective dependencies of η_j and/or epsilon on λ. According to Equation (5), the dependence of η_j on λ can eventually result from the dependence of the spin on λ. However, that would require a negative correlation of spins with λ, which is the opposite of what one might expect by noting that the BHs are spun up more efficiently for larger rather than smaller accretion rates. Hence we are left with the option that the disk accretion efficiency decreases with the decrease of the Eddington ratio, i.e., that epsilon correlates with λ.

The correlation can be explained if we assume that all cold accretion episodes start with a similar total net magnetic flux Φ, which is sufficiently large to exceed Φ_BH for any accretion rate (see Equation (4)). In such a case, the dynamical dominance of magnetic field over the accreting plasma extends up to R_m ≫ R_in, where R_in is the inner edge of a standard accretion disk not affected by magnetic fields, and R_m, sometimes referred to as the magnetospheric radius, is the size of the region within which the magnetic flux Φ is enclosed. Since below that radius the accretion proceeds via interchange instabilities, no significant optical–UV radiation is expected to be produced within this region. Hence, being "truncated" at R_m, the accretion disk is expected to have radiation efficiency epsilon ∼ R_g/R_m. Noting that for a given BH mass $R_m/R_g \propto (\Phi)^{4/3} {\dot{m}}^{-2/3}$ (Narayan et al. 2003), where $\dot{m} \equiv \dot{M} c^2/L_{{\rm EDD}} = \lambda /\epsilon$ , one can find that epsilon ∝λ^2/5 and therefore that

$\begin{equation} {\cal R} \propto \eta _j/\epsilon \propto \lambda ^{-2/5} \,. \end{equation} \tag{ 10 }$

Some dispersion is expected to be imposed on this relation by distributions of BH masses and magnetic fluxes (unless Φ∝M^3/2_BH).

The large R_m/R_g ratios for AGNs with low values of λ are consistent with detailed observations of some individual BLRGs which strongly suggest existence of the truncation radius in their accretion disks (Eracleous et al. 2000; Grandi & Palumbo 2007; Sambruna et al. 2009; Tazaki et al. 2010; Cowperthwaite & Reynolds 2012). In those papers, the disk truncation radii inferred from observations were interpreted as an effect of obscuration of the central region by Thomson thick corona, or as a transition to the advection-dominated accretion flows. Since it predicts large truncation radii as determined by R_m, the model can explain the cases of objects with P_j/L_bol > 10 (see Punsly 2011 and references therein) without the necessity of postulating the jet production efficiency significantly greater than unity.¹¹

The scenario presented above needs to be verified by demonstrating how such a large net magnetic flux can be assembled in the central regions of AGN. This problem was raised by Lubow et al. (1994), who showed that it is possible only if the magnetic Prandtl number is ⩽H/R, where H is the height of the disk at a distance R from the BH center. Since the Prandtl number predicted in fluids with isotropic turbulence is expected to be on the order of unity (Parker 1979), the above condition is rather difficult to satisfy in cold, geometrically thin disks (Livio et al. 1999; Cao 2011). This problem can be alleviated if one considers a possibility of an accumulation of a large magnetic flux in the central regions of AGN at the onset, or even prior to the period of the cold accretion phase. Such an accumulation could occur by dragging magnetic fields by geometrically thick, advection-dominated accretion flows, such as those predicted for super-Eddington accretion rates (Jaroszynski et al. 1980; Beloborodov 1998; Abramowicz 2005) and also for very sub-Eddington accretion rates (Ichimaru 1977; Rees et al. 1982; Narayan & Yi 1994; Abramowicz et al. 1995). Since our studies of source sizes do not indicate any evolutionary trends of expansion of sources with decreasing Eddington ratio (Figure 6), the second option seems to be favored. This is also supported by probabilistic arguments. For a given frequency of the cold accretion events, which in turn are very likely to be triggered by mergers of giant ellipticals with less massive, cold gas-rich galaxies (see Ramos Almeida et al. 2012 and references therein), the fraction of those events accompanied by production of powerful jets is predicted to correspond to a reasonably significant fraction (∼3%–10%) of giant ellipticals to be in radio-active states (Sadler et al. 1989; Donoso et al. 2009; van Velzen et al. 2012). These ellipticals are most likely powered by the Bondi accretion of hot interstellar gas (Burns 1990; Hardcastle et al. 2007; Tasse et al. 2008; Dunn et al. 2010; Werner et al. 2012). For typical intensities of interstellar magnetic fields in such galaxies, ∼10 μG, and their coherence scales, ∼100 pc (Moss & Shukurov 1996; Mathews & Brighenti 2003 and references therein), the accumulation magnetic fluxes in the central regions of such objects needed to exceed Φ_BH for any accretion rate can occur within a small fraction of the Hubble time.

Obviously objects with luminous extended radio sources such as investigated by us NLRGs are exceptional and are only a minority among the radio-loud AGN (see, e.g., de Vries et al. 2006). Most of radio-loud AGN are compact or posses weak, diffuse, oval, or more complex extended radio structures. They usually have P_j ≪ L_bol and therefore do not require accumulation of very large magnetic fluxes and invoking the magnetically choked accretion flows. Production of jets in such objects may proceed via a variety of scenarios, including those where jets are directly launched by accretion disks (see, e.g., Blandford & Payne 1982).

5. CONCLUSIONS

Main results of our studies of radio and spectroscopic optical properties of NLRGs at z < 0.4 can be summarized as follows.

1.
Radio luminosities are found to correlate strongly with narrow-line luminosities. When converted to the jet powers and AGN bolometric luminosities, they indicate that the jet kinetic energy often exceeds the radiative output of accretion flows.
2.
NLRGs cover about four decades of the Eddington ratio, λ, with most of them having λ < 0.01. This indicates that their parent population is dominated by BLRGs. Together with RLQs, they form a continuous Eddington ratio sequence.
3.
The "radio loudness," ${\cal R} = L_{1.4}/L_{{\rm line}}$ , shows a strong negative correlation with λ. This would imply that the jet production efficiency is the largest at the lowest values of λ, provided that disk radiation efficiency is independent of λ.
4.
The lack of any signatures of correlation or anti-correlation of radio source sizes with Eddington ratio indicates the lack of any significant monotonic migration of objects (to lower or larger Eddington ratios).
5.
A promising scenario which can explain energetics of jets in powerful radio sources and observed radio versus optical luminosity correlations is the one involving the magnetically arrested/choked accretion flows. Such flows may support sufficiently large magnetic fluxes to power jets with P_j ≳ L_bol, while a truncation of accretion disks by a "poloidal magnetosphere" can relax requirements of having η_j ≳ 1.
6.
Our results suggest a connection of the cold accretion phase following a lower accretion rate, hot accretion phase taking place in extragalactic radio sources. Such a two-phase scenario can overcome the difficulty of accumulating large magnetic fluxes by geometrically thin accretion disks. Without such a pre-phase, the cold accretion events would not be accompanied by production of powerful jets.

M.S. and G.M. are grateful to R. Blandford and J. McKinney for many stimulating discussions regarding magnetically choked accretion scenarios. We acknowledge financial support by the Polish NCN grant DEC-2011/01/B/ST9/04845, by NASA Fermi grant No. NNX11AO39G, and by a Herschel Research Support Agreement (grant administered by NASA JPL) No. RSA 1433865. G.S. and D.K.-W. acknowledge financial support from the European Associated Laboratory "Astrophysics Poland-France." N.V.A. has been supported by CAPES (proc. No. 6382-10-0).

CONSTRAINING JET PRODUCTION SCENARIOS BY STUDIES OF NARROW-LINE RADIO GALAXIES

Article metrics

Permissions

Author e-mails

Author affiliations

Dates

ABSTRACT

1. INTRODUCTION