Several lens models have been proposed for MG 2016+112 (Narasimha et al. 1984, 1987, 1989; Langston et al. 1991; Nair & Garrett 1997; Benítez et al. 1999). These models are constructed to match the optical and/or radio data such as image positions and flux ratios of the various components. The results of our spectroscopic observations can be used to put further constraints on the lens model.

As discussed in Sect. 3, the difference of CIII], CIV, and HeII line ratios in image B and C can be interpreted as a difference in ionization degree. Photoionization model predict smaller ionization parameter for C, which is a natural consequence if the component C is dominated by the light of a region at $\sim$ 1.5-2 times larger radius from the nucleus than the source region of the component B (assuming similar density).

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{yamada_9132_fig4.ps}\end{figure}$

Figure 4: Flux ratios of the emission lines seen in the spectrum of image B and C. Squares show those using only the narrow component of the C III] line and circles those using the C III] flux obtained with single-component fitting. The grids show the line flux ratio predicted by photo-ionization models calculated using CLOUDY90 (Ferland et al. 1988). The cases of hydrogen density of 100 cm^-3 and 1000 cm^-3 and input power-law spectra with energy index -1.0 and -1.4 are plotted for ranges of ionization parameter log $\Gamma$ = -1.0 to -2.5 (solid lines). The arrow shows the effect of the reddening calculated with the Calzetti's relation for starburst galaxies. 4 and E(B-V)=1

It is unlikely that the differences in line ratios of B and C is due to the contamination by a possible radio galaxy at the similar redshift assumed as the counterpart of the bright flat-spectrum radio component C₁. If the high CIII]/CIV ratio observed in the spectrum of image C is due to such a contamination, for example, the assumed radio galaxy should have CIII]/CIV ratio larger than $\sim$ 1. Radio galaxies rarely show such high CIII]/CIV ratio.

Our spectroscopic results thus support lens models like the ones proposed by Langston et al. (1991) and Benítez et al. (1999). In these models, the AGN and the narrow-emission-line region is located somewhat outside the fold caustic in the source plane, which results in forming the images A and B. The outer regions of the source extends over the caustic and the region which is very close to the caustic is largely amplified and form an arc-like lensed images at the position of component C. Radio sources at position C are interpreted as a lensed image of a "jet" which extends inside the caustic. The counter images of the component C will exist at position A and B but is mostly swamped by the AGN light due to a smaller amplification factor (compared to position C).

4.2 MG 2016+112: An obscured luminous radio-quiet quasar?

4.2.1 Intrinsic power of MG 2016+112

The observed radio flux density of image B at 1.47 GHz is 61.7 mJy (Lawrence et al. 1984), which corresponds to a luminosity density $L_{\rm 2.7~GHz} = 2.3~10^{34}$ ergs^-1 Hz^-1 $A_{\rm GL}^{-1}$ and $L_{\rm 8.4~GHz} = 9.1~10^{33}$ ergs^-1 Hz^-1 $A_{\rm GL}^{-1}$ at 2.7 and 8.4 GHz, respectively, with a luminosity distance of 26.5 Gpc and a spectral index $\alpha=-0.81$ (Lawrence et al. 1984). $A_{\rm GL}$ is a gravitational lensing amplification factor. According to the recent lens model by Benítez et al. (1999), the amplification factor of image B is estimated to be $\sim$ 6.

The radio power of MG 2016+112 is fairly large even corrected from the lensing amplification (e.g., Lawrence et al. 1984). Danese et al. (1987) obtained radio luminosity functions of at 2.4 GHz for various type of objects at $z\sim 0$ . Even the most luminous local objects have radio power $\sim$ 10³² ergs^-1 Hz^-1, which is more than a order of magnitude fainter than MG 2016+112. Dunlop & Peacock (1990) evaluated radio luminosity function of the radio-selected quasars and radio galaxies. Image B has radio power as large as those of very luminous radio sources at $z\sim 0.5$ which are definitely categorized as "quasars" or "powerful radio galaxies" ( 10³³-10³⁴ erg s^-1 Hz^-1 at 2.7 GHz). Thus it is very certain that the object harbors AGN as powerful as luminous as quasars.

Bischef & Becker (1998) investigated radio emissions for a sample of 4079 known quasars based on the NVSS radio catalog. These quasars are selected from the Verón-Cetty & Verón (VCV) catalog and constitute the largest compilation so far to study the radio properties of radio- and optically-selected quasars based on homogeneous radio observations in one frequency. In their Fig. 4, they presented a distribution of radio power at 8.4 GHz with redshift. The bimodal distribution of the radio power is evident at least to $z\sim 2.5$ . At higher redshift, the number of known radio-luminous quasars is too small to draw firm conclusion, but the tendency seems to hold. The radio power of MG 2016+112 at 8.4 GHz is likely to lie on the extension of the lower sequence, if we adopt an amplification factor of $\sim$ 10. In Fig 7 we plot the observed and amplification-corrected radio power of MG 2016+112 B superposed on the figure of Bischef & Becker's (their Fig. 4).

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{yamada_9132_fig6.ps}\end{figure}$

Figure 6: Line ratios for various kinds of high-redshift AGN. The solid squares are the average line ratios given in McCarthy (1993) and the open squares are those of USS HzPRGs in Röttgering et al. (1997). Triangles are the infrared-selected type-2 AGN, 10214, using the narrow-component (filled) and total (open) C III] flux. The ratios of broad lines quasar quoted from Baldwin (1979) are shown as crosses

4.2.2 Radio loudness

Radio loudness of AGN is conventionally defined by the radio to optical (or ultra violet) flux ratio. Bischef & Becker (1998) also obtained the distribution of the radio loudness for VCV quasars. According to their definition, radio-loud quasars have log $(L_{\rm 8.4~GHz}/L_{B})$ larger than 1. The upper sequence in Fig. 4 of Bischef & Becker (1998) corresponds to radio-loud quasars and the lower to radio-quiet quasars. It is difficult, however, to evaluate the radio loudness of MG 2016+112 by using the radio to optical flux ratio since it is an obscured narrow-line object. We may see only a scattered light of the nucleus in the optical wavelength and the contamination by light from the host galaxy must be relatively large. The nominal value, log $L_{\rm 8.4~GHz}$ / L_B = 3.4, thus does not mean that this object is a radio-loud AGN. Indeed, as mentioned in the previous subsection, the observed radio power of MG 2016+112 after lensing amplification correction seems too faint to be classified as radio-loud, which suggests that this object is a radio-quiet AGN. It is not surprising that the scattered component is more than hundred times smaller than the intrinsic luminosity and the intrinsic log $L_{\rm 8.4~GHz}$ /L_B value of the object can be $$\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displaystyle ...$ 1.

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{yamada_9132_fig7.eps}\end{figure}$

Figure 7: The observed (thick open circle) and the lensing amplification corrected (filled circle) radio luminosities of MG 2016+112 superposed in Fig. 4 of Bischof & Becker (1990) (scanned by us) which shows the distribution of radio luminosity at 8.4 GHz vs redshift for VCV quasars. Crosses are values for the broad lines of type-1 quasars

How typical the radio power is if MG 2016+112 is a radio-quiet AGN? Figure 7 suggests that it may be one of the most radio active object among the radio-quiet quasars at this redshift. Kukula et al. (1998) recently investigated the correlation between radio and optical luminosity of a sample of nearby radio-quiet quasars and Seyfert galaxies (z < 0.2). The most luminous nearby quasars with $M_{V} \sim -26$ have log $L_{\rm 8.4~GHz}$ $\sim 10^{31}$ ergs^-1 Hz^-1. If the correlation holds for high-redshift quasars which are typically 50-100 times more luminous than nearby AGNs, MG 2016+112 ( $L_{\rm 8.4~GHz}$ $\sim 10^{33}$ erg s^-1 Hz^-1) may be one of the most luminous quasars in optical wavelength, too, even if there is some radio excess.

4.2.3 Morphologies

HST NICMOS observations (Falco et al.) revealed that the rest-frame optical light of MG 2016+112 A and B is dominated by the point sources. The resolution limit of NICMOS is $\sim$ 0.15 arcsec. If we adopt the lens model of Benítez et al. (1999), the size of the unresolved lensed object must be smaller than 0.03 arcsec, which corresponds to $\sim$ 200 pc at z=3.27. It may not be surprising that A and B are not resolved if we observe only the obscured nucleus or its scattered light which may come from inside the narrow-line region.

Many of HzPRGs show resolved faint extension in NIR images which may be star lights of their host galaxies. On the other hand, the known type-2 AGN or obscured quasars at $z\sim$ 1-2.5 are not resolved or only marginally resolved (Ohta et al. 1995; Almani et al. 1995; Ivison et al. 1998). There could be some difference between observable properties of host galaxies of HzPRGs and radio-quiet type-2 AGN or obscured quasars. The radio images of A and B are also point-like with $\sim$ 15 mas resolution (Garrett et al. 1996). 15 mas corresponds to about 40 pc in the physical scale at z=3.27. Kukula et al. (1998) presented the 1.4 GHz maps of the nearby radio-quiet quasars with $\sim$ 0.5 arcsec resolution. They found a significant fraction of the radio emission in radio-quiet quasars originates in a compact nuclear source directly associated with the quasar. Therefore the point-like morphology of the radio emission of MG 2016+112 is not surprising if it is a radio-quiet quasar. At the same time, some outer structures are also seen in the radio maps of the nearby radio-quiet quasars. The maximum extent of the radio emission of resolved sources is typically a few kpc. It is possible that such a structure associated with the lensed object extends over the diamond caustic of the source plane to form the strongly amplified radio image at the position of component C.

4.2.4 Summary of the possible type-2 quasar nature of MG 2016+112

Since only the narrow emission lines are observed in UV wavelength, MG 2016+112 is very likely to be an obscured luminous AGN. Although it is need to see the properties of lines in the rest-frame optical wavelength redshifted to near infrared before concluding whether it is really a luminous analogue of the Seyfert 2 galaxies (namely, type-2 quasars) or just a partially-obscured normal quasars, it is interesting to summarize the possible type-2 quasar nature of MG 2016+112 since the number of known radio-quiet luminous type-2 quasars and candidates are still very limited. Only several examples of type-2 AGN or candidates at high redshift which are serendipitously discovered in far-infrared, sub-mm, and X-ray source surveys. If MG 2016+112 at z=3.27 is really a type-2 quasar, it is the highest-redshift one identified so far and thus provides a unique and important example for further studies of type-2 quasars. The properties of MG 20116+112 are summarized as follows.

(1) The central engine of MG 2016+112 must be obscured since only the narrow emission lines are observed. (2) The radio and optical morphologies are both compact, which is not compatible with typical properties of HzPRGs but common for radio-quiet AGNs. (3) The radio power is much smaller than typical radio-loud quasars at $z\sim 3$ but consistent with luminous radio-quiet quasar. (4) Finally, the emission line flux ratios of image B are not compatible with typical HzPRGs.

We thus consider that MG 2016+112 is not a typical powerful radio galaxies but may be naturally classified as a rare example of a high-redshift radio-quiet type-2 quasar.

Since 10214 and SMM 02399-0136 are detected in CO in sub-millimeter (Rowan-Robinson et al. 1993; Ivison et al. 1998; Frayer et al. 1998), it will be interesting to investigate the cold gas and dust properties of MG 2016+112. As expected from the obscuration of the nucleus, large dust content may be a general property of type-2 quasars.

4 Discussion

4.1 Lens models

4.2 MG 2016+112: An obscured luminous radio-quiet quasar?

4.2.1 Intrinsic power of MG 2016+112

4.2.2 Radio loudness

4.2.3 Morphologies

4.2.4 Summary of the possible type-2 quasar nature of MG 2016+112