Active Galactic Nuclei with a Low-Metallicity Narrow-Line Region
Kota Kawasaki Tohru Nagao Yoshiki Toba Koki Terao Kenta Matsuoka
astro-ph.GA





kawasaki@cosmos.phys.sci.ehime-u.ac.jp
1
   Department of Physics, Graduate School of Science and Engineering, 
   Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan 
2
   Research Center for Space and Cosmic Evolution, 
   Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan 
3
   Academia Sinica Institute of Astronomy and Astrophysics,
   PO Box 23-141, Taipei 10617, Taiwan 
4
   Department of Astronomy, Kyoto University, Kitashirakawa-
   Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan  
 5
   Dipartimento di Fisica e Astronomia, Università di Firenze, Via G.
   Sansone 1, I-50019 Sesto Fiorentino, Italy         
 6
   INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5,
   I-50125 Firenze, Italy    

  

Low-metallicity active galactic nuclei (AGNs) are interesting to study 
the early phase of the AGN evolution. 
However most AGNs are chemically matured and accordingly 
low-metallicity AGNs are extremely rare. 
One approach to search for low-metallicity AGNs systematically is utilizing 
the so-called BPT diagram that consists of the [O iii]λ5007/Hβλ4861 and 
[N ii]λ6584/Hαλ6563 flux ratios. 
Specifically, photoionization models predict that low-metallicity
AGNs show a high [O iii]λ5007/Hβλ4861 ratio
and a relatively low [N ii]λ6584/Hαλ6563 ratio,
that corresponds to the location between the sequence of star-forming galaxies
and that of usual AGNs on the BPT diagram (hereafter “the BPT valley”). 
However, other populations of galaxies such as star-forming galaxies and AGNs with a high 
electron density or a high ionization parameter could be also located in the BPT
valley, not only low-metallicity AGNs.
In this paper, we examine whether most of emission-line galaxies at 
the BPT valley are low-metallicity AGNs or not. We select 70 BPT-valley objects 
from 212,866 emission line galaxies obtained by the Sloan Digital Sky Survey. 
Among the 70 BPT-valley objects, 43 objects show
firm evidence of the AGN activity; i.e., the He iiλ4686 emission 
and/or weak but significant broad Hα emission.
Our analysis shows that those 43 BPT-valley
AGNs are not characterized by a very high gas density nor ionization parameter, inferring that 
at least 43 among 70 BPT-valley objects (i.e., >60%) are low-metallicity AGNs. 
This suggests that the BPT diagram is an efficient tool to search for low-metallicity AGNs. 








§ INTRODUCTION


The active galactic nucleus (AGN) is one of the most luminous class of objects 
in the Universe, whose huge radiative energy is released through the mass 
accretion onto the supermassive black hole (SMBH). The mass of SMBHs 
(M_ BH) is tightly correlated with the mass or the stellar velocity 
dispersion of their host galaxies <cit.>, 
implying that SMBHs and 
galaxies have evolved with closely interacting in each other (the so-called 
co-evolution of SMBHs and galaxies). However, the physics behind the 
co-evolution is still unclear. To understand the total picture of the 
co-evolution, examining the scaling relations for AGNs in the early phase of the 
co-evolution is an interesting approach since different theoretical models predict 
different redshift dependences of scaling relations <cit.>. One simple strategy to explore 
the early phase of the co-evolution is measuring the scaling relations at high 
redshifts, where the typical age of AGNs is much younger than low-redshift 
AGNs. Many attempts have been made for measuring the scaling relations for 
high-redshift AGNs <cit.>, and a higher M_ BH with respect to the mass 
or velocity dispersion of host galaxies has been sometimes reported 
<cit.>. On the other hand, there are some reports 
claiming that such a possible evolution in the scaling relation is a result of 
observational bias through the sample selection <cit.>. Measuring the properties of AGN host galaxies at high 
redshift is generally very challenging, that prevents us from assessing the scaling
relations at high redshifts.

Another possible approach to study the early phase of the co-evolution is 
focusing on young AGNs at low redshifts, where detailed observations are much 
easier than high redshifts. In this context, low-metallicity (i.e., chemically young) 
AGNs in the low-redshift Universe are particularly interesting. However, the 
typical metallicity of AGNs inferred for broad-line regions (BLRs) and narrow-line
regions (NLRs) is high (Z ≳ 2 Z_⊙; e.g., 
) and low-metallicity AGNs
are very rare <cit.>. <cit.>
proposed a method to search for AGNs with a low-metallicity NLR, that utilizes 
an optical emission-line diagnostic diagram which consists of the flux ratios of
[N ii]λ6584/Hαλ6563 and
[O iii]λ5007/Hβλ4861. This diagnostic diagram
was originally investigated for classifying emission-line galaxies into star-forming
galaxies and Seyfert 2 galaxies (BPT diagram, ).
<cit.> established the “maximum” 
starburst line in the BPT diagram by combining stellar population synthesis 
models and photoionization models. On the other hand, <cit.> derived empirical classification criteria for star-forming 
galaxies while <cit.> derived empirical 
classification criteria for low-ionization nuclear emission-line regions (LINERs;
), using emission-line data taken from the database 
of Sloan Digital Sky Survey (SDSS; ).

<cit.> pointed out that AGNs with a low-metallicity 
NLRs (i.e., characterized by the solar or sub-solar metallicity) should have a flux ratio of 
[O iii]λ5007/Hβλ4861 as high as usual AGNs
(∼ 10^0.5-10^1) but have an intermediate flux ratio of
[N ii]λ6584/Hαλ6563 between usual AGNs and
low-mass (i.e., low-metallicity) star-forming galaxies (∼ 10^-1-10^-0.5). 
This is because the nitrogen relative abundance is in proportion to the metallicity 
due to its nature as a secondary element <cit.>. In 
the BPT diagram, there are only few objects located at the region characterized 
by a high flux ratio of [O iii]λ5007/Hβλ4861 and 
an intermediate flux ratio of [N ii]λ6584/Hαλ6563
(hereafter “BPT valley”; see Figure <ref>). 
<cit.> specifically focused on AGNs with a low-mass
host galaxy (i.e., M_ host < 10^10 M_⊙), and then they selected 
low-metallicity AGNs using another diagnostic
diagram that consists of [N ii]λ6584/[O ii]λ3727 and
[O iii]λ5007/[O ii]λ3727 flux ratios. However, it is not
clear whether low-metallicity AGNs should be always found in a sample of AGNs with a
low-mass host galaxy. Also, the method adopted by <cit.>
requires a wide wavelength coverage (λ_ rest∼ 3700-6600 Å), 
that is not convenient for future applications to expand the search of low-metallicity
AGNs toward the high-redshift Universe. 

Therefore, we focus on BPT-valley selection (requiring a moderately narrow 
wavelength coverage; λ_ rest∼ 4800-6600 Å) to select 
low-metallicity AGNs without any host-mass cut.
However, there is a potentially serious problem in the BPT-valley selection for 
identifying low-metallicity AGNs. 
That is, not only low-metallicity AGNs are located in the BPT valley. 
As <cit.> showed, star-forming galaxies with 
a very hard radiation field or high-density H ii regions are expected 
to be seen in the BPT valley (see also, e.g., ). 
Also, star-forming galaxies with a high ionization parameter 
<cit.>, a high nitrogen-to-oxygen 
abundance ratio (N/O; e.g., ), 
or shocks <cit.> are also expected to be seen in the BPT valley. 
Not only star-forming galaxies, AGNs with a high electron density or high ionization parameter 
(i.e., not characterized by a low metallicity) could be also seen in the BPT valley 
<cit.>. 
Therefore, it is not completely clear whether the BPT-valley objects are really low-metallicity AGNs 
and whether the BPT diagram is a useful tool to search for low-metallicity AGNs. 
This problem prevents us from selecting chemically-young AGNs observationally.

In this paper, we investigate the optical spectra of BPT-valley objects for 
examining whether most of emission-line galaxies at the BPT valley are really 
low-metallicity AGNs or not. Through this examination, it will be tested whether 
the optical BPT diagram is an efficient and appropriate method to search for 
low-metallicity AGNs. In Section 2, we present our selection procedure of the 
BPT-valley sample. In Section 3, we show how we identify BPT-valley AGNs to 
avoid contaminating star-forming galaxies at the BPT valley. In Section 4, we 
investigate gas properties of the selected BPT-valley AGNs such as electron 
density and ionization parameter, for examining whether the BPT-valley AGNs
are characterized by a low metallicity or not. 
In Section 5, we disccus physical properties of the BPT-valley AGNs.
Section 6 describes the summary of this work.




§ SAMPLE


In order to select the BPT-valley objects, we use Max-Planck-Institute for 
Astrophysics (MPA)-Johns Hopkins University (JHU) SDSS Data Release 7 
() galaxy catalog[http://www.mpa-garching.mpg.de/SDSS/]. 
The MPA-JHU DR7 catalog of spectral measurements contains various
spectral properties such as emission-line fluxes and their errors, based on
the analysis for 927,552 objects without showing dominant broad Balmer lines 
(i.e., star-forming galaxies, composite galaxies, LINERs, and type-2 Seyfert galaxies) 
in the SDSS DR7.  
Our sample selection is based on the following procedure (the flow chart of our 
sample selection process is shown in Figure <ref>).

First, we select the initial sample according to the following criteria. 
We require the reliable redshift measurement (i.e., z_ warning = 0) and also z> 0.02. 
This redshift limit is required to cover [O ii]λ3727.
This results in 906,761 galaxies.
Then we require a signal-to-noise ratio (S/N) > 3 for some key emission lines, i.e., 
Hβλ4861, [O iii]λ5007, 
[O i]λ6300, Hαλ6563, 
[N ii]λ6584 and [S ii]λλ6717, 31 (212,866 galaxies).

Next, we classify these 212,866 galaxies and extract the BPT-valley sample 
according to the following steps. 


  * Using the  empirical line,
   
    log(  [O  III]/ Hβ) 
       > 0.61/ log ([N  II]/Hα) -0.05+1.3,

   for removing usual star-forming galaxies (56,217 galaxies).

  * Using the  maximum starburst line,
   
    log(  [O  III]/ Hβ) > 
       0.61/ log ([N  II]/Hα) -0.47+1.19,

   for removing so-called composite galaxies (22,865 galaxies).

  * Using the  empirical criterion,
   
    log(  [O  III]/ Hβ) > 
       1.36log(  [O  I]/ Hα) + 1.4,

   for obtaining Seyfert sample by removing LINERs (14,253 galaxies).

  * Adopting the following criterion,
   
    log(  [N  II]/ Hα) < -0.5,

   for finally selecting the BPT-valley sample (71 galaxies).

Note that 1 object in the 71 BPT-valley objects was observed twice and 
duplicated in the final sample, i.e., the final BPT-valley sample consists of 70 objects. 
The BPT-valley criterion (Equation <ref>) is determined empirically, 
by taking account of the frequency distribution of the [N ii]λ6584/Hαλ6563 
flux ratio of Seyfert galaxies. 
Figure <ref> shows the [N ii]λ6584/Hαλ6563 frequency distribution of 
Seyfert galaxies, 
where the average and standard deviation of the logarithmic [N ii]λ6584/Hαλ6563 
flux ratio are -0.058 and 0.145, respectively.
Accordingly, the 3 σ bounding from the average value is -0.493, 
and therefore we adopt the threshold to categorize BPT-valley objects as described 
by Equation <ref>.
Figure <ref> shows the finally selected 70 BPT-valley objects 
in the BPT diagram that consists of
[N ii]λ6584/Hαλ6563 versus 
[O iii]λ5007/Hβλ4861.
Table 1 shows the basic properties of the selected BPT-valley objects.











ccrrrrrrrrc

The BPT-valley sample
0pt

ID     SDSS Name     Plate     MJD     Fiber    
z     Hβλ4861     [O iii]λ5007    
[O i]λ6300     Hαλ6563    
[N ii]λ6584

(1)     (2)     (3)     (4)     (5)     
(6)     (7)     (8)     (9)     (10)     
(11)

1..........     SDSS J102310.97-002810.8     0272     51941     0238     0.11274     253.97      2279.29     125.19     881.10       235.20  

2..........     SDSS J111006.26-010116.5     0278     51900     0096     0.10949     382.92      1837.07     129.44     1484.61      438.76  

3..........     SDSS J230321.73+011056.4     0380     51792     0565     0.18136     235.38      1692.71     12.29      816.35       247.33  

4..........     SDSS J024825.26-002541.4     0409     51871     0150     0.02467     10.35       41.33       4.71       47.65        14.92   

5..........     SDSS J073506.37+393300.8     0432     51884     0316     0.03479     29.46       163.57      8.55       109.51       21.85   

6..........     SDSS J023310.78-074813.4     0455     51909     0388     0.03097     97.71       707.20      12.83      433.29       104.88  

7..........     SDSS J092907.78+002637.3     0475     51965     0205     0.11732     259.86      2602.18     56.12      1173.36      274.70  

8..........     SDSS J090613.76+561015.1     0483     51902     0016     0.04668     188.36      1144.93     73.96      621.46       189.46  

9..........     SDSS J144328.78+044022.0     0587     52026     0374     0.11411     36.11       300.13      3.37       137.53       32.98   

10.........     SDSS J114825.71+643545.0     0598     52316     0189     0.04169     349.08      1347.75     60.17      1302.50      392.24  

11.........     SDSS J213439.57-071641.9     0641     52199     0487     0.06377     215.60      2079.35     78.83      800.93       182.94  

12.........     SDSS J001050.35-010257.4     0686     52519     0020     0.11299     223.89      1669.57     109.74     940.89       275.90  

13.........     SDSS J124738.52+621243.1     0781     52373     0076     0.12112     171.82      915.80      33.03      697.15       162.91  

14.........     SDSS J131659.37+035319.9     0851     52376     0219     0.04541     127.05      1399.96     80.91      698.40       136.73  

15.........     SDSS J115908.55+525823.1     0881     52368     0623     0.06644     392.77      2812.16     52.13      1218.45      379.53  

16.........     SDSS J104632.21+543559.7     0906     52368     0169     0.14475     83.71       938.64      19.52      375.92       101.46  

17.........     SDSS J104600.36+061632.0     1000     52643     0035     0.18447     146.67      637.74      31.28      586.86       177.72  

18.........     SDSS J101945.65+520608.6     1008     52707     0378     0.06492     29.60       115.17      6.75       92.29        28.00   

19.........     SDSS J205111.11+000913.2     1023     52818     0393     0.06644     7.37        44.11       4.92       37.11        9.68    

20.........     SDSS J214930.43+010509.4     1031     53172     0369     0.11399     28.14       210.35      3.43       109.29       31.13   

21.........     SDSS J081653.27+285423.1     1206     52670     0530     0.05740     246.45      1610.19     131.99     1145.34      203.60  

22.........     SDSS J095319.42+422912.2     1217     52672     0349     0.22343     207.67      1835.79     83.29      698.87       115.09  

23.........     SDSS J110504.94+101623.5     1221     52751     0359     0.02076     104.02      466.39      29.14      481.20       151.62  

24.........     SDSS J114440.53+102429.3     1226     52734     0435     0.12688     51.67       304.73      39.93      241.38       67.83   

25.........     SDSS J124110.10+104143.7     1233     52734     0611     0.15613     214.49      1004.84     29.37      703.65       188.71  

26.........     SDSS J092620.42+352250.3     1274     52995     0147     0.24729     118.98      868.18      81.24      513.89       75.74   

27.........     SDSS J131756.07+491531.3     1282     52759     0390     0.09231     215.30      2050.51     105.88     711.65       176.30  

28.........     SDSS J090107.41+085459.2     1300     52973     0335     0.08380     172.61      1116.69     153.30     822.23       210.37  

29.........     SDSS J120134.05+581421.1     1313     52790     0527     0.04636     28.83       136.20      5.78       87.43        20.49   

30.........     SDSS J152723.47+334919.1     1354     52814     0044     0.09116     44.63       173.46      24.18      254.04       79.05   

31.........     SDSS J112314.89+431208.7     1365     53062     0119     0.08005     56.52       226.87      33.20      183.08       52.19   

32.........     SDSS J152328.09+313655.6     1387     53118     0210     0.06850     382.47      1707.84     67.32      1300.98      322.89  

33.........     SDSS J120900.89+422830.9     1448     53120     0075     0.02364     100.07      614.24      24.50      320.70       61.56   

34.........     SDSS J121839.40+470627.6     1451     53117     0190     0.09389     478.35      5046.81     101.68     1861.68      380.45  

35.........     SDSS J005231.29-011525.2     1496     52883     0089     0.13485     251.99      2400.52     55.68      826.34       254.44  

36.........     SDSS J011341.11+010608.5     1499     53001     0522     0.28090     191.99      2118.06     38.27      779.72       162.79  

37.........     SDSS J001901.52+003931.8     1542     53734     0375     0.09669     58.06       296.69      15.99      242.69       58.75   

38.........     SDSS J034019.39+002530.6     1632     52996     0467     0.35296     40.58       375.40      10.78      167.65       46.21   

39.........     SDSS J032224.64+401119.8     1666     52991     0048     0.02608     121.08      1388.24     50.70      428.76       130.77  

40.........     SDSS J135855.82+493414.1     1670     53438     0061     0.11592     56.67       385.56      14.74      189.76       50.29   

41.........     SDSS J160452.78+344540.4     1682     53173     0201     0.05493     87.33       437.20      37.34      364.99       111.94  

42.........     SDSS J132011.71+125940.9     1698     53146     0327     0.11398     25.43       174.93      4.92       92.99        24.68   

43.........     SDSS J143523.42+100704.1     1711     53535     0306     0.03122     128.18      530.61      15.31      473.30       123.16  

44.........     SDSS J072637.94+394557.8     1733     53047     0326     0.11141     505.82      3357.26     23.23      1744.03      120.42  

45.........     SDSS J095914.76+125916.4     1744     53055     0385     0.03432     1298.59     8418.94     361.09     4396.86      1088.11 

46.........     SDSS J113714.22+145917.2     1755     53386     0463     0.03484     74.19       364.47      25.99      276.40       77.15   

47.........     SDSS J120847.79+135906.7     1764     53467     0013     0.29030     136.33      659.31      28.11      554.94       137.92  

48.........     SDSS J135429.05+132757.2     1777     53857     0076     0.06332     312.80      3422.56     111.50     1005.37      306.94  

49.........     SDSS J130431.99+061616.7     1794     54504     0046     0.06283     184.84      1202.46     41.38      702.29       217.24  

50.........     SDSS J134316.52+101440.1     1804     53886     0433     0.08132     186.67      960.51      170.90     635.68       198.21  

51.........     SDSS J160032.89+052608.8     1822     53172     0012     0.11653     281.02      1630.88     69.22      1204.67      280.09  

52.........     SDSS J081212.84+541539.8     1871     53384     0060     0.04417     93.10       809.73      34.28      326.93       94.82   

53.........     SDSS J084038.99+245101.6     1931     53358     0396     0.04334     137.37      770.11      39.75      579.80       151.50  

54.........     SDSS J122451.88+360535.4     2003     53442     0112     0.15094     25.95       148.22      11.11      126.62       35.77   

55.........     SDSS J134237.37+273251.3     2017     53474     0127     0.04947     12.67       97.69       10.27      60.02        17.32   

56.........     SDSS J140952.03+244334.6     2128     53800     0358     0.05215     45.42       220.76      12.29      198.30       41.19   

57.........     SDSS J142535.21+314027.1     2129     54252     0618     0.03324     91.61       362.11      42.31      323.51       95.49   

58.........     SDSS J145505.97+211121.1     2148     54526     0122     0.06751     82.30       441.80      12.31      437.94       126.61  

59.........     SDSS J083200.51+191205.8     2275     53709     0472     0.03753     549.64      6069.28     42.46      15422.57     419.58  

60.........     SDSS J103731.01+280626.9     2356     53786     0468     0.04263     54.57       447.10      24.55      216.95       65.48   

61.........     SDSS J104403.52+282628.3     2356     53786     0618     0.16286     225.46      1047.00     17.43      794.20       193.30  

62.........     SDSS J104724.40+204433.5     2478     54097     0541     0.26515     102.51      751.70      37.17      391.58       66.16   

63.........     SDSS J160635.22+142201.9     2524     54568     0498     0.03245     162.66      621.83      41.72      517.08       160.44  

64.........     SDSS J171901.28+643830.8     2561     54597     0345     0.08954     152.42      709.97      21.69      586.95       174.32  

65.........     SDSS J084658.44+111457.5     2574     54084     0382     0.06296     130.82      638.15      41.04      557.91       161.29  

66.........     SDSS J095745.49+152350.6     2584     54153     0442     0.05183     96.42       702.55      24.58      514.46       117.37  

67.........     SDSS J133014.91+242153.9     2665     54232     0388     0.07151     50.49       244.84      15.74      284.46       76.98   

68.........     SDSS J135007.07+164227.2     2742     54233     0551     0.13043     99.01       903.05      38.82      495.52       137.00  

69.........     SDSS J153941.67+171421.9     2795     54563     0509     0.04583     157.66      758.85      14.76      500.33       119.40  

70.........     SDSS J143730.46+620649.4     2947     54533     0227     0.21862     66.97      290.54      22.39      219.25       65.39   

Col. (1): Identification number assigned in this paper. 
Col. (2): Object name. 
Col. (3)–(5): Plate-MJD-Fiber ID in the SDSS observation for analyzed spectra. 
Col. (6): Redshift measured by the SDSS pipeline.
Col. (7)–(11): Emission-line fluxes in units of 10^-17 erg s^-1 cm^-2.







§ SELECTION OF SECURE-AGN SAMPLE


As described in Section 1, the BPT-valley sample potentially includes star-forming galaxies with 
special gas properties, not only AGNs. 
Thus we first select objects showing secure evidence of the AGN from the BPT-valley sample. 
Specifically, we regard objects showing at least one of the following two features 
in their SDSS spectra as secure AGNs; (1) a broad Hαλ6563 emission, 
and (2) a He iiλ 4686 emission line. 
Details of the selection procedure of secure AGNs are given below.




 §.§ Broad Hαλ6563 emission line


The velocity profile of recombination lines is a powerful tool to examine 
the presence of AGNs, since star-forming galaxies never show a velocity 
width wider than ∼1000 km s^-1 in full-width at half maximum (FWHM). 
Generally the optical spectra of type-1 AGNs show broad permitted lines whose 
velocity width is ≳ 2000 km s^-1 emitted from BLRs. 
The origin of recombination lines with FWHM ∼ 1000 - 2000 km s^-1 is 
not very clear, since such lines may arise at BLRs in so-called narrow-line 
Seyfert 1 galaxies (NLS1s; e.g., Osterbrock & Pogge 1985) or 
at NLRs in type-2 AGNs with a relatively large velocity width 
(such as NGC 1068 and NGC 1275; see, e.g., ). 
However, in either case, the detection of recombination lines with 
FWHM > 1000 km s^-1 strongly suggests the presence of AGNs. 
Therefore we search for the broad Hαλ6563 component 
in the optical spectrum of the BPT-valley objects. Here we do not search for 
the broad component of the Hβλ4861 emission, 
since it is intrinsically fainter than that of the Hαλ6563 emission 
and it is sometimes affected significantly by the Fe ii multiplet emission
<cit.>.

We use an IRAF routine specfit <cit.> to find the broad 
Hαλ6563 component.
Specifically, we fit the SDSS optical spectrum of the BPT-valley objects 
in the range of λ_ rest = 6200-6800 Å with and 
without the broad Hαλ6563 component, and examine 
whether the addition of the broad component improves the spectral fit significantly. 
The details of the fitting procedure are as follows. 
First, we fit the optical spectrum with a linear continuum component and 
single-Gaussian emission-line components for [O i]λ6300, 
[O i]λ6363, [N ii]λ6548, Hαλ6563, 
[N ii]λ6584, [S ii]λ6717, and [S ii]λ6731 
(hereafter “nobroad fitting”). 
Here we assume that the velocity width of all emission lines is the same, 
and the relative separation of the emission lines is fixed to be the same as 
that of their laboratory wavelengths. 
The flux ratios of [O i]λ6300 to [O i]λ6363 and 
[N ii]λ6584 to [N ii]λ6548 are fixed to be 3.00 and 2.96 
respectively <cit.>, and the flux ratios among the remaining 
emission lines are kept to be free. 
Then, we add a broad component for the Hαλ6563 emission to 
the nobroad fit, where the flux, wavelength center and width of this additional 
component are kept to be free (hereafter “broad fitting”). 
Here we recognize that the additional broad component significantly improves 
the fit by the following criterion:

    χ̃^2_ nobroad-χ̃^2_ broad/χ̃^2_ nobroad>0.4,

where χ̃^2_ nobroad and χ̃^2_ broad are the reduced 
chi-square of the nobroad fitting and broad fitting, respectively. 
Note that the threshold, 0.4, is determined empirically, so that the result 
becomes consistent with the visual inspection. 
As a result, 13 BPT-valley objects with a broad component are identified from the 70 BPT-valley objects.
Figures <ref> and <ref> show the SDSS spectrum with the best-fit result 
for the BPT-valley objects with a broad Hαλ6563 component. 
Figure <ref> shows an example of objects (ID = 48) whose fitting result does not satisfy the 
criterion defined by Equation <ref> (for this case, the improvement of the fit is slightly less than 
the threshold, 0.32).
Note that we regard object ID = 8 as an object with a broad Hα component, 
though the FWHM of the broad Hα component is less than 
1000  km s^-1 (Figure <ref>). 
This is because this object shows [Fe vii]λ6087 and [Fe x]λ6374 
lines, that are seen only when the AGN presents. Note that such high-ionization forbidden 
emission lines are preferentially seen in type-1 AGNs 
<cit.>. 
Note that the [Fe vii]λ6087 line is seen in 8 objects 
while [Fe x]λ6374 line is seen in 3 objects 
(including ID = 8, note that 2 objects in addition to ID = 8 show both [Fe vii]λ6087 
and [Fe x]λ6374). 
The spectral properties of the BPT-valley objects with a broad Hαλ6583 
component are summarized in Table 2.
Only 1 BPT-valley object (ID = 25) shows the broad Hβ component among  
the 13 BPT-valley objects showing a broad Hα component (see Figure <ref>).



 §.§ He iiλ4686 emission line

The presence of a He iiλ4686 emission line indicates the existence of 
the hard ionizing radiation since the ionization potential for 
He^+ is 54.4 eV. 
This hard radiation is naturally produced by AGNs. 
Therefore, the He iiλ4686 emission line is a good indicator of AGNs. 
We examine whether the SDSS optical spectrum of the BPT-valley objects show 
the He iiλ4686 line by the visual inspection, 
since the He iiλ4686 information is not given in the MPA-JHU database. 
As a result, 38 BPT-valley objects with the He ii emission line are identified from 
the 70 BPT-valley objects. 
Some of the SDSS spectra of BPT-valley objects with the He ii detection are shown 
in Figures <ref>, while those without the He ii detection are shown 
in Figure <ref>.














 §.§ Classification result of the BPT-valley sample


 The results of the classification of the BPT-valley objects are summarized in Table 3. 
 Among the 70 BPT-valley objects, 8 objects show both broad Hα component and 
 He ii emission line, that are now confirmed to be AGNs. 
 There are 5 objects showing the broad Hα component but without He ii emission line, 
 that are also regarded as AGNs. 
 The non-detection of the He ii line is likely due to insufficient signal-to-noise ratio, 
 since the He ii line is very weak. In addition, 30 objects show the He ii line 
 but without broad Hα component, that are thought to be typical type-2 AGNs. 
 Here we should mention that the stellar absorption lines (mainly Hα) are not 
 considered in our fitting procedure. 
 Though the stellar Hα absorption line could impact the narrow component of the Hα 
 emission, the absorption effect is negligible for examining the presence of the broad Hα 
 component. 
 This is because the equivalent width of the detected broad Hα component is higher than 
 20 Å (the median value of EW_rest(Hα)_b is 44.74 Å, Table 2) 
 while the typical equivalent width of the stellar Hα absorption is ∼ 2-3 Å 
 in nearby galaxies <cit.>.
 Note that the detected He ii line is not caused by Wolf-Rayet stars, 
 because the typical velocity width of the detected He ii line is not 
 broad (≲ 1000  km s^-1). 
 Therefore, at least 43 among the BPT-valley objects are regarded as AGNs. 
 There may be some additional AGNs in the remaining 27 objects, possibly 
 owing to insufficient S/N to detect any AGN indicators in their spectra. 
 Instead, some of those 27 objects could be non-AGNs, i.e., star-forming 
 galaxies with a relatively high N/O ratio or fast shocks. 
 We do not discuss further about those 27 objects since the main interests 
 of this work are on the BPT-valley AGN sample. 
 Accordingly, we conclude that at least 43 objects of the BPT-valley sample 
 (or ∼ 60%, but probably more) are confirmed to be AGNs.
  
 As described in Section 3.1, at least one of the [Fe vii]λ6087 and 
 [Fe x]λ6374 lines are seen in 9 BPT-valley objects. 
 Interestingly, a large fraction of objects showing both the broad Hα component and He ii 
 emission show such high-ionization iron lines (5 among 8 objects). 
 On the other hand, objects showing neither the broad Hα component nor He ii emission 
 never shows those high-ionization iron lines. 
 Then, a few objects in the remaining two classes show high-ionization iron lines (4 among 35 objects). 
 This may infer that our classification is well tracing the presence of the AGN, 
 but the absence of high-ionization iron lines could be simply due to a low S/N ratio of the spectra. 
 
 Figure <ref> shows how various populations of galaxies classified in this work 
 are populated in the BPT diagram. 
 There are no significant segregation except for two BPT-valley objects whose 
 [N ii]λ6584/Hαλ6563 flux ratio is very low, < 0.1. 
 Both of these two galaxies show no broad Hα component nor He ii line, 
 which is consistent with the idea that these two objects are not low-metallicity AGNs 
 but somewhat extreme low-metallicity galaxies, characterized probably by a very 
 high ionization parameter and/or very hard ionization radiation.




lrrrrr
0pt
6 
Broad-line AGNs in the BPT valley

ID     f( Hα)_n     f( Hα)_b     FWHM_Hα     FWHM_[S  II]     EW_ rest(Hα)_b

(1)     (2)     (3)     (4)     (5)     (6)

6cbroad Hα and He ii

3.........     991.96     1834.96     7162.24     245.05     88.10

8.........     414.20     309.70     875.811     247.31     27.02

12........     524.87     830.66     1682.70     324.79     57.25

13........     748.78     728.55     2033.36     223.68     72.83

25.........     607.56     930.70     1974.28     248.66     159.88

34........     2072.41     797.10     2083.37     377.39     33.06

65........     573.27     761.34     4830.02     263.52     44.61

66........     448.38     768.76     2430.79     221.86     47.03

6cbroad Hα and noHe ii

17........     719.07     392.29     3396.57      270.94     44.74

21........     1014.89     1145.11     2440.19     337.97     44.13

47........     515.66     726.01     3569.90     273.99     246.77

58........     390.35     801.51     4347.42     307.51     28.83

67........     276.51     335.10     2372.32     276.41     25.14    
1Classified as an object with a broad Hα component through the FWHM 
of the additional Hα component is less than 1000 km s^-1 (see the main text).

Col. (1): Identification number assigned in this paper. 
Col. (2): Flux of the nallow component of Hα in units of 10^-17 erg s^-1 cm^-2.
Col. (3): Flux of the broad component of Hα in units of 10^-17 erg s^-1 cm^-2.
Col. (4): FWHM of the broad component of Hα in units of km s^-1.
Col. (5): FWHM of the [S ii]λ6717 (i.e., narrow component) in units of km s^-1.
Col. (6): Rest-frame equivalent width of the broad component of Hα in units of Å.




lcc
3 

0pc
Classification result of the BPT-valley sample
 
     broad     nobroad 

He II      8     30 

    noHe II       5     27 





§ SELECTION OF LOW-METALLICITY AGNS


The 43 BPT-valley objects confirmed to be AGNs are not necessarily low-metallicity AGNs, 
because AGNs with a very high electron density or very high ionization parameter are 
also expected to be populated in the BPT valley as mentioned in Section 1. 
More specifically, the [N ii]λ6584 emission in AGNs with a density higher than 
the critical density of the [N ii]λ6584 transition (∼8.7 × 10^4 cm^-3) 
is significantly suppressed due to the collisional de-excitation effect. 
On the other hand, a very high ionization parameter results in a higher relative ionic abundance of 
N^2+ (i.e., a lower relative ionic abundance of N^+), that results in a weaker 
[N ii]λ6584 emission.
Therefore, in this section, we examine whether the 43 BPT-valley AGNs are characterized 
by a very high electron density or very high ionization parameter or not, and test whether 
the AGNs in the BPT-valley are characterized by low-metallicity gas or not.



 §.§ Electron density

The emission-line flux ratios of [S ii]λ6717/λ6731 and 
[O ii]λ3729/λ3726 are famous good indicators of the electron density 
<cit.>.
In this work, we use the [S ii]λ6717/λ6731 line ratio to estimate electron density, 
because the wavelength separation of the [O ii] doublet is too small to be well resolved with 
the SDSS spectral resolution.
We use an IRAF routine temden for deriving the electron density from the 
[S ii]λ6717/λ6731 ratio, by assuming the electron temperature of 10,000 K. 
Here we derive the electron density whose [S ii]λ6717/λ6731 ratio is 
within the range of 0.5–1.4. 
No BPT-valley objects show the [S ii]λ6717/λ6731 ratio lower than 0.5 
(i.e., the high-density limit) while 11 among the 70 BPT-valley objects show the flux ratio 
higher than 1.4 (i.e., the low-density limit). 
Among 14,252 Seyfert sample, only 12 objects show the [S ii]λ6716/λ6731 
ratio lower than 0.5 while 2,880 objects show the flux ratio higher than 1.4.

Figure <ref> shows the frequency distribution of the inferred gas density for objects whose 
[S ii]λ6717/λ6731 ratio is within the range of 0.5–1.4; i.e.,  41 BPT-valley AGNs 
(showing a broad Hα component and/or He ii emission), 59 BPT-valley objects 
(including objects without any AGN signatures), and 11,360 Seyfert galaxies. 
Here we show the histograms for both BPT-valley AGNs and BPT-valley objects, because some of 
BPT-valley objects without any AGN signatures could be also AGNs (see Section 3.3). 
The median density of the BPT-valley AGNs, BPT-valley objects, and Seyfert galaxies are 
210 cm^-3, 210 cm^-3, and 270 cm^-3, respectively. 
In order to investigate whether the frequency distribution of the gas density is statistically different 
among the samples, we apply the Kolmogorov-Smirnov (K-S) statistical test with a null hypothesis that 
the frequency distribution of the gas density of two classes of objects comes from 
the same underlying population. 
The derived K-S probability for the BPT-valley AGNs and Seyferts is 0.207, while that for 
the BPT-valley objects and Seyferts is 0.146. 
These results strongly suggest that the BPT-valley sample is not characterized by the higher gas density 
with respect to the Seyfert sample.





 §.§ Ionization parameter

The ionization palameter is the ratio of the number density of hydrogen-ionizing photons 
to that of Hydrogen atoms. 
In order to investigate the ionization parameter, the [O iii]λ5007/[O ii]λ3727 
flux ratio is a useful indicator because this ratio does not suffer significantly from chemical properties of 
the gas in both AGNs and star-forming galaxies 
<cit.>.
Note that this flux ratio is sensitive also to the gas density if the density is higher than 
the critical density of [O ii] (∼10^3.5 cm^-3), 
but the typical density of NLRs inferred from the [S ii] doublet ratio is much lower than 
that as described in Section 4.1.
Though the dust reddening is not corrected to study the BPT diagram due to the small wavelength 
separation of emission-line pairs used for the BPT diagram (Section 2), we should correct for the reddening 
effect to investigate the [O iii]λ5007/[O ii]λ3727 flux ratio. 
For this correction, we assume R_V = A_V/E(B-V) = 3.1 and the intrinsic flux ratio 
of Hαλ6584/Hβλ4861 = 3.1, and adopt the reddening curve 
of <cit.>.

Figure <ref> shows the histogram of the [O iii]λ5007/
[O ii]λ3727 line 
ratio of the BPT-valley AGNs, BPT-valley objects, and Seyferts, with S/N([O ii]λ3727) > 3.
Here it should be noted that the BPT-valley objects show 
log([O iii]λ5007/Hβλ4861) > 0.5 by definition, 
while the Seyfert galaxies could have much lower [O iii]λ5007/Hβλ4861 flux ratios 
down to ∼ -0.2. 
This may introduce a selection effect in the sense that strong [O iii] emitters could be selectively 
included in the BPT-valley sample. 
Therefore, for reducing this selection effect, only objects with 
log([O iii]λ5007/Hβλ4861) > 0.5 are examined for assessing 
the ionization parameter. 
After adopting this additional criterion, the numbers of the BPT-valley AGNs, BPT-valley objects, and 
Seyferts examined in Figure <ref> are 42, 69, and 8,500, respectively. 
This figure shows that the BPT-valley samples seem to show systematically higher 
[O iii]λ5007/[O ii]λ3727 flux ratios than the Seyfert sample. 
The median values of the logarithmic [O iii]λ5007/[O ii]λ3727 flux ratios of 
the BPT-valley AGNs, 
BPT-valley objects, and Seyferts are 0.67, 0.65, and 0.46, respectively. 
In order to investigate whether or not the distributions of the 
[O iii]λ5007/[O ii]λ3727 line ratio are 
statistically different between BPT-valley sample and Seyfert sample, we apply the K-S statistical test. 
The K-S probability that the underlying distribution of these two
distributions is the same is 3.925× 10^-6 for the BPT-valley AGNs and Seyferts, 
while 1.803 × 10^-5 for the BPT-valley objects and Seyferts. 
These results suggest that the BPT-valley samples have statistically higher 
[O iii]λ5007/[O ii]λ3727 flux ratios, i.e., the ionization parameter, 
than the Seyfert sample. 
Note that it is well known that low-metallicity galaxies are generally characterized by a relatively 
high ionization parameter, at least for star-forming galaxies <cit.>. 
It may be interesting that the BPT-valley objects show a clear edge at the lower side of the 
[O iii]λ5007/[O ii]λ3727 distribution in Figure <ref>.
However, probably this feature is not statistically significant, because the number of BPT-valley objects 
is not enough to discuss the tail of the frequency distribution of the 
[O iii]λ5007/[O ii]λ3727 flux ratio.

In the next subsection, we will examine whether or not this difference in the ionization parameter can be 
responsible for the lower [N ii]λ6584/Hαλ6563 ratio observed in the 
BPT-valley samples with respect to the Seyfert sample.






 §.§ Model calculations

As shown in Section 4.2, the ionization parameter of the BPT valley sample is higher than that of 
the Seyfert sample. 
Since it is interesting to examine either the BPT-valley AGNs are characterized by a low metallicity or 
a high ionization parameter, we perform photoionization model calculations.

We perform photoionization model calculations for simulating the NLR of AGNs, 
using the code CLOUDY version 13.03 <cit.>. 
Here the main parameters for CLOUDY calculations are as follows 
<cit.>:

 
  * The hydrogen density of the cloud (n_ H).
 
  * The ionization parameter (U).
 
  * The chemical composition of the gas.
 
  * The shape of the input SED.

We calculate photoionization models covering the following ranges of parameters:
10^1  cm^-3≤ n_ H≤ 10^6  cm^-3 and
10^-4≤ U ≤ 10^-1. 
We set the gas-phase elemental abundance ratios to be the solar ones. 
The adopted solar abundances relative to hydrogen are taken from <cit.> 
with extensions by <cit.>.
The adopted metallicity (i.e., the solar one) is not typical for usual Seyfert galaxies 
(whose NLR metallicity is generally higher than the solar metallicity), possibly nor BPT-valley AGNs 
(that could have sub-solar metallicity). 
However, as described below, it is useful to fix the metallicity to examine whether the ionization 
parameter alone can account for the difference in the emission-line flux ratios between 
BPT-valley objects and Seyferts. 
For the input SED, we adopt the following one:

    f_ν=ν^α_UVexp( -hν/kT_ BB) exp( -kT_ IR/hν) 
    + aν^α_  X

as a typical spectrum of AGNs (see ). 
kT_ IR is the infrared cutoff of the big-blue bump, and we adopt 
kT_ IR=0.01 ryd <cit.>. 
α_ UV is the slope of the low-energy side of the big-blue bump.
We adopt α_ UV = 0.5, which is typical for AGNs 
<cit.>. 
α_ ox is the UV–to–X-ray spectral slope, which determines the parameter a in equation (6).
We adopt α_ ox=-1.35, which is the average value of nearby Seyfert 1 galaxies
<cit.>.
α_ x is the X-ray slope, and we adopt α_ x=-0.85 (see ).
T_ BB is the characterizing the shape of the big-blue bump, and we adopt 490,000 K 
(see ).
The calculations end at the depth where the temperature falls to 3,000 K, 
below which gas does not contribute significantly to the flux of optical emission lines.

Figure <ref> shows the results of the photoionization model calculations, overlaid 
on the BPT diagram. 
Though the density effect is not significant in the range of 
10^1 cm^-3 < n_ H < 10^5 cm^-3, 
we can see the effect of the collisional de-excitation at n_ H > 10^4 cm^-3. 
However, this figure suggests that the difference in the [N ii]λ6584/Hαλ6583 
flux ratio is more easily explained by the difference in the ionization parameter rather than by the difference 
in the gas density. 
More specifically, a higher ionization parameter by 0.5–1 dex in the BPT-valley objects with respect to 
the Seyfert sample is required to explain the lower [N ii]λ6584/Hαλ6583 
flux ratio of the BPT-valley objects. 

For examining whether the BPT-valley objects have a higher ionization parameter than the Seyfert sample, 
we investigate another diagnostic diagram that consists of the emission-line flux ratios of 
[O iii]λ5007/[O ii]λ3727 and [O i]λ6300/[O iii]λ5007 
(Figure <ref>). 
This diagram is useful to examine the effect of ionization parameter without suffering from 
the metallicity effect, because only oxygen lines are used and thus less sensitive to the metallicity. 
Figure <ref> shows that the BPT-valley sample and Seyfert sample have a similar gas density, 
that is consistent with our analysis presented in Section 4.1. 
More interestingly, Figure <ref> shows that the BPT-valley sample shows a systematically 
higher ionization parameter than the Seyfert sample, but the inferred difference in the ionization 
parameters is only less than 0.5 dex. 
This strongly suggests that the lower [N ii]λ6584/Hαλ6563 flux ratio 
in the BPT-valley sample with respect to the Seyfert sample is not explained by the ionization parameter 
(nor the gas density, as described in Section 4.1). 
Therefore we conclude that the BPT-valley AGNs are characterized by a systematlcally lower metallicity 
than the Seyfert sample, as originally proposed by <cit.>.








§ DISCCUSIONS

As mentioned Section 1, low-metallicity AGNs are interesting to study the early phase of 
the AGN evolution.
However low-metallicity AGNs are very rare, so that little has been reported on
physical property of low-metallicity AGNs. 
In this section, we present some basic properties of BPT-valley objects which are expected 
to be low-metallicity AGNs.



 §.§ Stellar mass

Naively it is expected that the stellar mass of low-metallicity AGNs is expected to be 
relatively low, as suggested by the mass-metallicity relation seen in star-forming galaxies 
<cit.>.
Accordingly <cit.> introduced a mass criterion 
(i.e., M_* < 10^10  M_⊙) to select low-metallicity AGNs. 
However, it is not clarified whether low-metallicity AGNs should be always found in 
a sample of AGNs with a low-mass host galaxy. 
Therefore, in this paper, we select low-metallicity AGNs without stellar-mass cut and 
investigate the mass distribution of host galaxies of low-metallicity AGNs. 
Here the stellar mass has been measured and given in the MPA-JHU DR7 catalog 
<cit.>.
Among the 43 BPT-valley AGNs and 70 BPT-valley objects, the host mass is 
available for 39 and 64 objects, respectively. 
Figure <ref> shows the histogram of the stellar mass of the 39 BPT-valley AGNs, 
64 BPT-valley objects and 13,662 Seyferts.
The median of the stellar mass of the BPT-valley AGNs, BPT-valley objects 
and Seyferts are 10^10.15  M_⊙, 10^10.07  M_⊙ and 
10^10.77  M_⊙, respectively. 
This result clearly shows that the stellar mass of the BPT-valley AGNs is systematically lower 
than that of Seyferts. 
However, interestingly, a substantial fraction of the BPT-valley AGN (23 among 39 objects) 
are actually hosted by galaxies with M_* > 10^10  M_⊙, 
suggesting that low-metallicity AGNs are not necessarily hosted by low-mass galaxies. 
Note that such low-metallicity AGNs with a relatively massive host galaxy cannot be selected 
by the criteria of <cit.> due to the mass criterion of 
M_* < 10^10  M_⊙. 
Such low-metallicity AGNs hosted by a relatively massive host galaxy may be realized by 
taking into account of the inflow of low-metallicity gas from the surrounding environment  
<cit.>. 









 §.§ Electron temperature

Considering the effect of the metal cooling, 
low-metallicity AGNs are expected to be characterized by the higher electron temperature.
Hence we investigate the [O iii]λλ(4959+5007)/[O iii]λ4363 line 
ratio which is very sensitive to the gas temperature.
Here it should be mentioned that, [O iii]λλ(4959+5007)/[O iii]λ4363 line 
ratio also depends on the electron density <cit.>. 
Therefore we investigate the  [O iii]λλ(4959+5007)/[O iii]λ4363 and 
[S ii]λ6717/[S ii]λ6731 line ratios simultaneously in Figure <ref>. 
Here this figure shows the emission-line flux ratios of BPT-valley objects and Seyferts but only for 
objects with a significant detection of the [O iii]λ4363 line (S/N > 3).
As described in Section 4.2, only objects with log ([O iii]λ5007/Hβ) > 0.5 are used 
(that results in 9,043 Seyferts and 70 BPT-valley objects).
Note that [O iii]λλ(4959+5007)/[O iii]λ4363 line ratio is corrected 
for the reddening effect in the same way as Section 4.2.
The median values of log ([S ii]λ6717/[S ii]λ6731) of the BPT-valley AGNs, 
BPT-valley objects and Seyferts with a [O iii]λ4363 detection are 0.088, 0.088 and 0.055, 
respectively.
Therefore the electron density of the BPT-valley sample is slightly higher than that of Seyferts 
as already mentioned in Section 4.1. 
The median of log ([O iii]λλ(4959+5007)/[O iii]λ4363) of 
the BPT-valley AGN, BPT-valley objects and Seyferts are 1.77, 1.77 and 1.79, respectively.
This result suggests that the electron temperature of the BPT-valley objects is not significantly higher 
than that of Seyferts. 
However, the fraction of objects showing a significant (S/N > 3) [O iii]λ4363 emission 
is very different between the Seyferts and BPT-valley objects. 
More specifically, 44 among the 70 BPT-valley objects (∼ 63 %) show the [O ii]λ4363 
emission while only 1,516 among 9,043 Seyferts (∼ 17 %) show the [O iii]λ4363 line. 
This difference infers that generally the gas temperature of the NLR in BPT-velley objects tends to be 
so high that the [O iii] λ4363 line is detected in most cases, 
while the typical gas temperature of the NLR in Seyferts may be lower than that in BPT-valley objects 
and only highly biased objects with a relatively high temperature in the Seyfert sample show the 
[O iii]λ4363 line. 
This result is consistent to our expectation that the BPT-valley objects is actually characterized by a 
relatively high gas temperature, due to the low gas metallicity. 







§ CONCLUSIONS


In this paper, we focus on low-metallicity AGNs (Z_ NLR ≲ 1 Z_⊙) 
which are very rare but important since they are in the early phase of the galaxy-SMBH co-evolution.
Specifically, in this work it is examined whether the BPT-valley selection is an effective and reliable 
way to identify low-metallicity AGNs, as proposed by <cit.>. 
The main results are as follows:

 
  * We select 70 BPT valley sample which expected low metallicity AGN from 
14,253 Seyfert galaxies of MPA-JHU SDSS DR7 galaxy catalog.
 
  * Out of 70 BPT-valley objects, 43 objects show clear evidence of the AGN based on 
 the detection of the broad Hα component and/or He iiλ4686 emission.
  
  * The typical gas density of the BPT-valley sample (∼210 cm^-3) is not higher than that of 
  the Seyfert sample (∼270 cm^-3), suggesting that the lower 
  [N ii]λ6584/Hαλ6563 ratio in the BPT-valley AGNs with respect to 
  the Seyfert sample is not caused by the collisional de-excitation effect. 
  
  * The higher [O iii]λ5007/[O ii]λ3727 ratio in the BPT-valley sample 
  (∼4.5) with respect to that in the Seyfert sample (∼2.9) suggests a typically higher 
  ionization parameter of the BPT-valley sample; however, photoionization models suggest that 
  the inferred difference in the ionization parameter between the BPT-valley sample and 
  Seyfert sample is not enough to explain the observed lower 
  [N ii]λ6584/Hαλ6563 ratio of the BPT-valley sample.  
  
  * The BPT-valley selection for identifying low-metallicity AGNs is thus confirmed to be a useful method; 
  in our analysis, more than 60% of the BPT-valley sample are low-metallicity AGNs 
  (Z_ NLR ≲ 1 Z_⊙). 






We would like to thank the anonymous referee for her/his
careful reading this paper and useful suggestions, and also
Masaru Kajisawa and Kazuyuki Ogura for their useful comments.
TN is financially supported by JSPS grants Nos. 25707010, 16H01101, and 16H03958. 
KM is also supported by JSPS grant No. 14J01811. 
Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/.
The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.






