A Uniformly Selected Sample of Low-mass Black Holes in Seyfert 1 Galaxies. II. The SDSS DR7 Sample

Compared with H ii galaxies, AGNs can emit a harder continuum which results in a distinct ionization condition in surrounding gas. Specific emission-line ratios can help distinguish the central radiating sources that ionize the circumnuclear medium. In practice, two-dimensional diagrams of certain narrow-line ratios have been widely applied to discriminate between H ii galaxies and type 2 AGNs (e.g., Baldwin et al. 1981; Veilleux & Osterbrock 1987; Ho et al. 1997a; Kewley et al. 2001, 2006; Kauffmann et al. 2003a). The so-called BPT diagrams involving the narrow-line ratios of Hα, Hβ, [O iii], [N ii], [S ii], and [O i] are shown in Figure 5. In general, the distributions of our LMBHs are consistent with those of Dong et al. (2012b). On the [O iii] λ5007/Hβ versus [N ii] λ6583/Hα diagram (panel (a)), the vast majority of these LMBHs are located in the region of either Seyfert galaxies or composite objects, and only a few sources (∼10) fall into the pure star-forming region. On the [O iii] λ5007/Hβ versus [S ii] λλ6716,6731/Hα and [O i] λ6300/Hα diagrams (panels (b) and (c)), about two-thirds of these objects are found in the AGN region, while the rest are located in the H ii region.

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These results confirm the AGN nature for the vast majority of our sample, though a few objects have narrow-line spectra similar to those of star-forming galaxies. Regarding those objects located in the pure H ii portion, their broad Hα fluxes, FWHMs, and luminosities are all similar to those of the whole parent sample, with chance probabilities >0.1 according to the Kolmogorov–Smirnov test (KS test). Visual checks of their SDSS spectra and the statistics (broad Hα flux with S/N > 5) both demonstrate that the broad Hα components of these objects are significant and reliable. A probable explanation is that the spectra of these objects are strongly contaminated by starlight from those star formation regions in the host galaxies, given the relatively large aperture of the fiber of 3''.

We note that about two dozen objects fall into the region of LINERs (Heckman 1980) according to the Seyfert–LINER demarcation lines of either [O iii] λ5007/Hβ = 3 in panel (a) or Kewley et al. (2006) in panels (b) and (c). LINERs are commonly found in early-type galaxies with classical bulges containing supermassive BHs especially with old stellar populations (Ho et al. 1997b). LMBHs tend to reside in late-type disk-dominated galaxies often harboring pseudobulges just on the opposite side. Therefore, such LMBH LINERs are of great interest in the study of LINERs as a population, though it is not a surprise that only a small number of low-mass AGNs show LINER-like spectra. Mostly manifesting themselves as low-luminosity AGNs, LINERs are thought to have relatively low accretion rates, and their accretion flows are dominated by ADAF (advection-dominated accretion flow; see, e.g., Narayan & Yi 1995; Kewley et al. 2006; Ho 2009). The combination of low BH mass and low accretion rate makes it even difficult to identify LINERs with LMBHs in the presence of host galaxy light. These may explain the low incidence of LINERs in the LMBH sample.

X-ray is an important bandpass to study BH accretion. A number of LMBH AGNs in the GH07 sample have been observed in X-ray with Chandra (e.g., Greene & Ho 2007c; Desroches et al. 2009; Dong et al. 2012a) which gave a snapshot of the X-ray properties of LMBHs. Focusing on low-mass AGNs with very low Eddington ratios (L_bol/L_Edd ∼ 0.01), i.e., the faintest AGN population known, Yuan et al. (2014) studied the X-ray properties of four objects observed by Chandra in the Dong et al. (2012b) sample, and suggested there should exist a large population of underluminous LMBHs in the nearby universe. Plotkin et al. (2016) performed a similar analysis on seven LMBHs with low Eddington ratios from GH07 using Chandra observations. The two well-studied LMBHs, NGC 4395 and POX 52, were found to show rapid and strong X-ray variabilities (e.g., Iwasawa et al. 2000; Moran et al. 2005; Dewangan et al. 2008; Thornton et al. 2008). Their spectral characteristics resemble those of classical Seyfert 1 galaxies. Miniutti et al. (2009) performed a detailed analysis of four LMBHs from Greene & Ho (2004) using XMM-Newton observations, finding that they are extremely variable, and three out of the four objects show soft excess in their spectra. Similarly, Ludlam et al. (2015) followed up a study with 14 LMBHs from GH07 with XMM-Newton, eight of which show soft excess emissions. In addition, LMBHs also present diverse timing properties. In general, LMBHs tend to show a larger X-ray variability amplitude than their more massive cousins. Pan et al. (2015) and Ludlam et al. (2015) showed the previously known inverse correlation between M_BH and the normalized excess variance of X-ray variability, which flattens at M_BH ∼ 10⁶ M_⊙ and thus vanishes for LMBH AGNs.

In this study, we briefly investigate the statistical X-ray properties of the total sample of 513 sources based on the ROSAT All-Sky Survey (RASS; Boller et al. 2016) and pointed observations (2RXP). Detailed X-ray spectral and timing analyses using XMM-Newton are deferred to later work.

4.2.1. X-Ray Detection

Of the 513 sources, 85 were detected by RASS and 32 in pointed observations, with 15 detected in both (for these sources, the data from the pointed observations are adopted). Thus, a total of 102 objects have X-ray detections with the ROSAT Position-Sensitive Proportional Counter (PSPC). Their X-ray fluxes and spectral indices in the 0.1–2.4 keV band are estimated following Schartel et al. (1996) and Yuan et al. (1998, 2008), assuming an absorbed power-law spectral shape. As the first step, the photon index Γ is calculated from the two hardness ratios,¹³ if available. The absorption column density N_H is fixed at the Galactic value (Dickey & Lockman 1990) or set to a free parameter if no meaningful Γ is obtained using the Galactic N_H. For those sources without meaningful hardness ratios, the mean value (Γ = 2.36) is adopted. Next, we estimate the X-ray fluxes in the 0.1–2.4 keV band from the count rates using the energy-to-counts conversion factor (ECF; ROSAT AO-2 technical appendix, 1991), which is calculated from the ROSAT PSPC effective area for each source, for the given power-law spectrum with Γ and N_H obtained above. The X-ray fluxes in the band of 0.5–2.0 keV are tabulated in Table 4, which range from 1.8 × 10⁻¹⁴ to 2.9 × 10⁻¹² erg s⁻¹ cm⁻². The corresponding luminosities span a range from 8.0 × 10³⁹ to 1.1 × 10⁴⁴ erg s⁻¹, comparable to 9.3 × 10³⁹–6.9 × 10⁴³ erg s⁻¹ for the GH07 sample. This indicates that the X-ray emission is mostly dominated by AGN radiation, since the X-ray luminosities of normal galaxies are generally below this level.

Table 4.  ROSAT Detections

ID	Count Rate	NH	Γ	f0.5–2.0 keV	log L0.5–2.0 keV	L2500 Å	αOX
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Our new sample
6	0.074 ± 0.014	4.40	${2.71}_{-0.23}^{+0.22}$	−12.24 ± 0.08	42.31 ± 0.08	27.57	−1.27
27	0.058 ± 0.014	3.10	${2.14}_{-0.31}^{+0.28}$	−12.35 ± 0.11	43.94 ± 0.11	28.57	−0.92
34	0.043 ± 0.014	3.50	⋯	−12.49 ± 0.14	42.76 ± 0.14	27.96	−1.19
37	0.116 ± 0.019	3.60	${2.49}_{-0.22}^{+0.20}$	−12.08 ± 0.07	42.88 ± 0.07	27.92	−1.15
39	0.174 ± 0.022	1.70	${2.89}_{-1.33}^{+1.42}$	−12.32 ± 0.06	42.34 ± 0.06	27.63	−1.30
45	0.031 ± 0.012	1.50	${1.56}_{-0.67}^{+0.49}$	−12.63 ± 0.16	43.29 ± 0.16	28.16	−0.96
47	0.061 ± 0.013	2.60	${2.25}_{-0.34}^{+0.33}$	−12.40 ± 0.10	42.63 ± 0.10	27.64	−1.11
59	0.049 ± 0.014	1.60	⋯	−12.67 ± 0.12	42.77 ± 0.12	27.78	−1.12
75	0.005 ± 0.001	2.10	${2.31}_{-0.33}^{+0.29}$	−13.59 ± 0.05	40.86 ± 0.05	26.43	−1.33
82	0.040 ± 0.012	1.80	⋯	−12.72 ± 0.12	42.92 ± 0.12	28.00	−1.14
87	0.072 ± 0.015	1.70	⋯	−12.49 ± 0.09	43.68 ± 0.09	28.60	−1.06
96	0.014 ± 0.002	1.40	1.73 ± 0.16	−13.05 ± 0.05	41.84 ± 0.05	26.87	−1.06
99	0.058 ± 0.000	1.60	⋯	−12.60 ± 0.00	43.29 ± 0.00	28.08	−1.02
100	0.176 ± 0.023	2.30	${1.71}_{-0.17}^{+0.15}$	−11.84 ± 0.06	43.27 ± 0.06	27.88	−0.89
103	0.072 ± 0.014	1.40	${2.94}_{-0.28}^{+0.23}$	−12.79 ± 0.09	43.31 ± 0.09	28.13	−1.11
104	0.051 ± 0.013	1.20	⋯	−12.73 ± 0.11	43.45 ± 0.11	28.41	−1.08
110	0.007 ± 0.002	2.60	2.39 ± 0.35	−13.39 ± 0.10	42.63 ± 0.10	28.35	−1.38
117	0.060 ± 0.013	1.30	2.04 ± 0.16	−12.52 ± 0.09	41.71 ± 0.09	27.06	−1.22
118	0.022 ± 0.009	1.10	⋯	−13.12 ± 0.18	42.66 ± 0.18	27.84	−1.18
121	0.027 ± 0.011	1.10	⋯	−13.04 ± 0.17	41.93 ± 0.17	27.51	−1.34
123	0.698 ± 0.038	1.20	${2.83}_{-0.76}^{+0.79}$	−11.81 ± 0.02	43.55 ± 0.02	28.37	−1.11
124	0.098 ± 0.016	1.10	${1.57}_{-0.22}^{+0.20}$	−12.19 ± 0.07	43.48 ± 0.07	28.10	−0.87
125	0.052 ± 0.012	1.10	⋯	−12.74 ± 0.10	42.59 ± 0.10	28.19	−1.35
126	0.062 ± 0.013	1.20	${1.26}_{-0.21}^{+0.20}$	−12.30 ± 0.09	42.79 ± 0.09	28.15	−1.13
130	0.297 ± 0.023	1.20	${2.43}_{-1.01}^{+1.02}$	−12.00 ± 0.03	42.74 ± 0.03	27.69	−1.11
132	0.053 ± 0.012	0.90	⋯	−12.79 ± 0.10	43.36 ± 0.10	28.26	−1.06
135	0.052 ± 0.000	1.10	${2.88}_{-0.75}^{+0.77}$	−12.99 ± 0.00	42.03 ± 0.00	28.01	−1.56
138	0.083 ± 0.023	2.00	⋯	−12.38 ± 0.12	42.83 ± 0.12	28.00	−1.18
144	0.029 ± 0.010	1.40	${1.93}_{-0.27}^{+0.26}$	−12.78 ± 0.15	43.06 ± 0.15	28.05	−1.05
150	0.028 ± 0.004	1.60	1.78 ± 0.18	−12.73 ± 0.06	42.97 ± 0.06	28.05	−1.07
155	0.098 ± 0.015	1.00	⋯	−12.49 ± 0.07	43.25 ± 0.07	28.14	−1.06
165	0.036 ± 0.014	1.90	⋯	−12.75 ± 0.17	43.30 ± 0.17	28.34	−1.11
166	0.095 ± 0.005	2.40	2.05 ± 0.11	−12.18 ± 0.02	42.74 ± 0.02	27.35	−0.93
176	0.023 ± 0.010	3.80	⋯	−12.73 ± 0.18	42.45 ± 0.18	27.49	−1.13
177	0.116 ± 0.022	3.90	${2.37}_{-0.33}^{+0.29}$	−12.03 ± 0.08	42.55 ± 0.08	27.32	−1.04
186	0.047 ± 0.012	5.50	⋯	−12.32 ± 0.11	42.38 ± 0.11	27.62	−1.21
190	0.015 ± 0.001	3.50	${1.27}_{-0.23}^{+0.18}$	−12.78 ± 0.04	41.56 ± 0.04	26.35	−0.92
192	0.111 ± 0.015	1.70	${1.65}_{-0.18}^{+0.17}$	−12.09 ± 0.06	43.46 ± 0.06	28.15	−0.91
Dong et al. (2012b)
10	0.050 ± 0.013	3.9	${2.53}_{-0.29}^{+0.27}$	−12.42 ± 0.11	42.76 ± 0.11	27.86	−1.18
15	0.030 ± 0.014	5.3	${2.56}_{-0.44}^{+0.37}$	−12.55 ± 0.20	43.31 ± 0.20	27.94	−0.99
18	0.024 ± 0.004	3.6	${1.55}_{-0.19}^{+0.16}$	−12.61 ± 0.13	42.48 ± 0.13	27.15	−0.90
21	0.067 ± 0.019	7.2	${2.42}_{-0.16}^{+0.17}$	−12.11 ± 0.19	42.57 ± 0.19	27.82	−1.23
24	0.026 ± 0.011	8.1	⋯	−12.49 ± 0.16	43.16 ± 0.16	28.30	−1.16
27	0.026 ± 0.010	6.2	⋯	−12.54 ± 0.08	42.21 ± 0.08	27.55	−1.25
67	0.145 ± 0.025	2.8	${2.91}_{-0.32}^{+0.31}$	−12.20 ± 0.13	42.83 ± 0.13	27.43	−1.04
68	0.046 ± 0.014	3.0	${2.39}_{-0.29}^{+0.17}$	−12.52 ± 0.11	43.19 ± 0.11	28.03	−1.05
74	0.061 ± 0.015	4.9	${3.83}_{-0.28}^{+0.27}$	−12.55 ± 0.08	42.75 ± 0.08	27.84	−1.36
78	0.105 ± 0.019	4.3	${3.06}_{-0.45}^{+0.63}$	−12.18 ± 0.12	43.60 ± 0.12	28.11	−1.01
79	0.053 ± 0.014	3.7	${3.96}_{-0.27}^{+0.34}$	−12.86 ± 0.08	43.98 ± 0.08	28.76	−1.23
87	0.113 ± 0.022	1.7	${3.24}_{-0.87}^{+1.27}$	−12.66 ± 0.16	42.26 ± 0.16	27.69	−1.40
98	0.034 ± 0.013	1.6	⋯	−12.83 ± 0.07	42.23 ± 0.07	27.95	−1.39
99	0.107 ± 0.016	0.9	⋯	−12.48 ± 0.13	44.03 ± 0.13	28.40	−0.84
101	0.072 ± 0.000	0.7	⋯	−12.60 ± 0.20	42.17 ± 0.20	26.95	−1.01
102	0.040 ± 0.012	1.3	⋯	−12.82 ± 0.14	42.68 ± 0.14	27.89	−1.19
103	0.017 ± 0.008	2.5	⋯	−13.01 ± 0.14	43.09 ± 0.14	28.24	−1.16
105	0.033 ± 0.011	3.5	⋯	−12.60 ± 0.06	42.76 ± 0.06	27.53	−1.03
110	0.019 ± 0.002	3.0	${2.61}_{-0.30}^{+0.31}$	−12.95 ± 0.12	42.47 ± 0.12	27.18	−1.03
112	0.029 ± 0.009	1.3	⋯	−12.96 ± 0.10	39.90 ± 0.10	25.45	−1.34
115	0.127 ± 0.017	0.7	${2.53}_{-0.14}^{+0.15}$	−12.55 ± 0.05	42.54 ± 0.05	27.01	−0.93
117	0.002 ± 0.001	4.3	2.28 ± 0.05	−13.75 ± 0.06	41.79 ± 0.06	28.04	−1.58
123	0.046 ± 0.013	3.0	${2.57}_{-0.22}^{+0.27}$	−12.56 ± 0.15	43.96 ± 0.15	28.85	−1.07
125	0.067 ± 0.016	1.4	${2.37}_{-0.36}^{+0.42}$	−12.57 ± 0.12	43.23 ± 0.12	28.41	−1.18
135	0.005 ± 0.002	0.8	${1.51}_{-0.06}^{+0.05}$	−13.50 ± 0.08	41.57 ± 0.08	27.09	−1.22
138	0.099 ± 0.000	1.9	${1.46}_{-0.28}^{+0.33}$	−12.52 ± 0.15	43.62 ± 0.15	27.76	−0.84
149	0.032 ± 0.003	1.1	1.21 ± 0.13	−13.12 ± 0.12	42.43 ± 0.12	27.71	−1.26
153	0.115 ± 0.000	2.4	${1.96}_{-0.41}^{+0.30}$	−12.19 ± 0.09	43.03 ± 0.09	27.89	−1.07
163	0.176 ± 0.021	1.1	${2.52}_{-0.44}^{+0.52}$	−12.29 ± 0.17	42.51 ± 0.17	27.48	−1.13
164	0.226 ± 0.029	2.0	${2.10}_{-0.12}^{+0.11}$	−11.86 ± 0.03	42.27 ± 0.03	27.77	−1.28
169	0.041 ± 0.014	1.9	⋯	−12.70 ± 0.13	42.40 ± 0.13	27.56	−1.18
174	0.044 ± 0.012	1.2	⋯	−12.72 ± 0.06	40.95 ± 0.06	26.84	−1.44
175	0.101 ± 0.019	1.6	1.56 ± 0.16	−12.12 ± 0.05	43.01 ± 0.05	27.60	−0.87
183	0.030 ± 0.011	1.0	⋯	−13.01 ± 0.09	42.46 ± 0.09	27.37	−1.08
184	0.045 ± 0.012	1.4	⋯	−12.75 ± 0.13	43.50 ± 0.13	28.54	−1.11
196	0.101 ± 0.022	2.0	${1.44}_{-0.32}^{+0.30}$	−12.06 ± 0.14	42.23 ± 0.14	27.33	−1.06
203	0.021 ± 0.008	1.2	${2.06}_{-0.96}^{+0.77}$	−13.01 ± 0.09	42.03 ± 0.09	27.67	−1.33
212	0.396 ± 0.027	0.9	⋯	−11.91 ± 0.07	43.67 ± 0.07	27.98	−0.85
214	0.032 ± 0.010	1.7	⋯	−12.81 ± 0.13	42.52 ± 0.13	27.98	−1.28
217	0.125 ± 0.016	1.8	${2.36}_{-0.33}^{+0.31}$	−12.23 ± 0.16	42.77 ± 0.16	27.69	−1.08
221	0.121 ± 0.015	2.0	${2.24}_{-0.16}^{+0.17}$	−12.17 ± 0.06	43.30 ± 0.06	28.12	−1.03
229	0.041 ± 0.008	1.6	⋯	−12.75 ± 0.07	42.97 ± 0.07	27.88	−1.07
230	0.027 ± 0.008	1.8	⋯	−12.89 ± 0.05	42.81 ± 0.05	27.98	−1.17
232	0.043 ± 0.014	2.8	${2.28}_{-0.28}^{+0.37}$	−12.54 ± 0.08	42.95 ± 0.08	27.99	−1.12
235	0.055 ± 0.011	1.4	⋯	−11.90 ± 0.09	43.62 ± 0.09	27.64	−0.73
237	0.098 ± 0.016	1.5	${2.89}_{-0.24}^{+0.29}$	−12.61 ± 0.07	43.04 ± 0.07	28.18	−1.23
239	0.047 ± 0.014	2.6	${2.17}_{-0.41}^{+0.37}$	−12.55 ± 0.12	41.72 ± 0.12	26.70	−1.12
244	0.052 ± 0.005	1.3	${1.69}_{-0.06}^{+0.05}$	−12.58 ± 0.02	42.76 ± 0.02	27.96	−1.15
246	0.024 ± 0.009	1.0	1.63 ± 0.15	−12.83 ± 0.06	42.35 ± 0.06	27.45	−1.07
249	0.095 ± 0.013	1.4	${2.20}_{-0.46}^{+0.52}$	−12.36 ± 0.08	43.10 ± 0.08	28.14	−1.11
252	0.073 ± 0.012	1.4	${2.49}_{-0.18}^{+0.16}$	−12.59 ± 0.12	42.72 ± 0.12	27.95	−1.22
253	0.107 ± 0.013	1.7	${1.96}_{-0.42}^{+0.37}$	−12.18 ± 0.10	42.95 ± 0.10	28.04	−1.10
256	0.103 ± 0.018	1.5	${2.87}_{-0.38}^{+0.39}$	−12.58 ± 0.14	42.67 ± 0.14	27.88	−1.26
259	0.038 ± 0.008	1.3	${2.61}_{-0.45}^{+0.46}$	−12.95 ± 0.18	42.93 ± 0.18	27.73	−1.06
263	0.185 ± 0.028	2.4	${3.37}_{-0.45}^{+0.40}$	−12.34 ± 0.14	42.76 ± 0.14	27.77	−1.26
269	0.042 ± 0.011	6.6	3.36 ± 0.10	−12.44 ± 0.06	42.99 ± 0.06	28.02	−1.26
271	0.895 ± 0.035	1.3	2.55 ± 1.21	−11.55 ± 0.00	42.89 ± 0.00	27.57	−1.03
276	0.088 ± 0.013	1.3	⋯	−12.40 ± 0.04	42.03 ± 0.04	27.10	−1.12
284	0.017 ± 0.003	2.5	${2.65}_{-1.06}^{+0.78}$	−13.09 ± 0.15	42.24 ± 0.15	27.77	−1.36
286	0.017 ± 0.005	2.8	${1.51}_{-0.61}^{+0.52}$	−12.81 ± 0.19	42.84 ± 0.19	27.68	−0.95
287	0.022 ± 0.005	3.1	${2.20}_{-0.52}^{+0.53}$	−12.79 ± 0.00	42.62 ± 0.00	27.73	−1.14
289	0.034 ± 0.011	5.0	${3.34}_{-1.18}^{+1.23}$	−12.66 ± 0.03	42.51 ± 0.03	27.98	−1.43
297	0.021 ± 0.009	4.9	${3.20}_{-0.73}^{+0.75}$	−12.85 ± 0.00	43.05 ± 0.00	28.27	−1.30
301	0.045 ± 0.014	2.9	${2.20}_{-0.88}^{+0.89}$	−12.49 ± 0.04	43.76 ± 0.04	27.79	−0.70

Note. Column (1): identification number assigned in this paper and Dong et al. (2012b), respectively. Column (2): ROSAT count rate (count s⁻¹). Column (3): Galactic column density ${N}_{{\rm{H}}}$ (10²⁰ cm⁻²). Column (4): photon index of X-ray spectrum. Column (5): X-ray flux in the 0.5–2.0 keV in log-scale (erg s⁻¹ cm⁻²). Column (6): X-ray luminosity in the 0.5–2.0 keV in log-scale (erg s⁻¹). Column (7): monochromatic luminosity at 2500 Å (erg s⁻¹ Hz⁻¹). Column (8): optical-to-X-ray effective spectral index α_OX.

A machine-readable version of the table is available.

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For those undetected by the ROSAT, upper limits on the X-ray fluxes are estimated using the method in Yuan et al. (2008). An upper limit of 12 source counts is adopted for each undetected object, and thus the count rate upper limit is calculated using the corresponding effective exposure time from the RASS exposure map. Then, the flux upper limits are estimated using the method described above assuming the Galactic N_H and the mean Γ of 2.36.

4.2.2. X-Ray versus [O iii] λ5007 Luminosity

The soft X-ray emission is susceptible to absorption, while the [O iii] luminosity is suggested to be an isotropic indicator of the intrinsic AGN power since the [O iii] line originates from the narrow-line region and should be unaffected by obscuration. A strong correlation between the X-ray and [O iii] λ5007 luminosity has been found in unobscured AGNs (e.g., Panessa et al. 2006). This can help to discriminate whether our low-mass AGNs are heavily obscured.

The relation between the 2--10 keV luminosity and the [O iii] λ5007 luminosity for the X-ray-detected sources is shown in Figure 6; overplotted are the low-mass AGN sample with ROSAT detections from GH07, LMBHs observed by Chandra from Dong et al. (2012a), more massive AGNs in Jin et al. (2012), and low-mass AGNs with log (L_bol/L_Edd) < −1.5 observed using Chandra in Yuan et al. (2014) and Plotkin et al. (2016). Luminosities in the 2–10 keV band are calculated by extrapolating the spectra of ROSAT to 10 keV assuming a photon index of 2.5. The ROSAT-detected sources in our total sample are roughly consistent with the correlation between the X-ray and [O iii] λ5007 luminosity derived by more massive AGNs (Panessa et al. 2006). It indicates that our low-mass AGNs with X-ray detections suffer little or no obscuration in X-rays.

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4.2.3. Optical–X-Ray Spectral Index

The optical/X-ray effective spectral index, α_OX ≡ −0.384 log(f_{2500 Å}/f_{2 keV}), where f_{2500 Å} and f_{2 keV} are the rest-frame flux densities at 2500 Å and 2 keV, respectively, is commonly used to describe the relative dominance of the optical and X-ray emission (Tananbaum et al. 1979).¹⁴ The statistical properties of α_OX have been well-studied for the classical AGNs (e.g., Avni & Tananbaum 1986; Yuan et al. 1998; Vignali et al. 2003; Steffen et al. 2006). Recently, Dong et al. (2012a) studied the α_OX properties of 49 low-mass AGNs in the GH07 sample with Chandra observations. In this work, we briefly investigate the α_OX properties of LMBHs based on ROSAT observations.

The α_OX indices are calculated as follows. f_{2 keV} is derived from the ROSAT observations as described in Section 4.2.1, and ${f}_{2500\mathring{\rm A} }$ is calculated from ${L}_{{\rm{H}}{\alpha }^{{\rm{B}}}}$ using the relation between ${L}_{{\rm{H}}{\alpha }^{{\rm{B}}}}$ and λL_λ(5100 Å) given by Greene & Ho (2005) assuming a spectral index of 1.56 (f_λ ∝ λ^−1.56; Vanden Berk et al. 2001). The α_OX values are listed in Table 4, and their distribution is shown in Figure 7. The α_OX distribution has a large scatter, ranging from −1.58 to −0.70, with a median of $\langle {\alpha }_{\mathrm{OX}}\rangle =-1.12$, which is systematically flatter than those of AGNs with more massive BHs (e.g., α_OX ∼ −1.5; Yuan et al. 1998). The α_OX distribution of our low-mass BHs is similar to that of the ROSAT-detected sources in GH07, but slightly flatter than that of LMBHs with Chandra observations in Dong et al. (2012a). These LMBHs are roughly in accordance with the relation between α_OX and the monochromatic luminosity at 2500 Å defined by those more massive AGNs (Steffen et al. 2006), albeit with a large scatter (see Figure 8). In addition, Figure 8 shows that low-mass AGNs have systematically flatter α_OX and a larger scatter compared to those of more massive BHs, which is consistent with Dong et al. (2012a).

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As can be seen from Figure 8, although the distribution of our LMBH AGNs are mostly confined within the 1σ scatter of the α_OX–L_{2500 Å} relationship, there is a much larger scatter when the Chandra samples of Dong et al. (2012a) and Yuan et al. (2014) are taken into account, which contains some ;X-ray-weak objects detected by Chandra owing to its high sensitivity. To explore further the large scatter of α_OX for LMBH AGNs, we plot in Figure 9 α_OX versus the Eddington ratio and BH mass for our sample as well as for the other AGN samples as in Figure 8. No significant correlation is found between α_OX and L_bol/L_Edd over a wide range for the LMBHs spanning nearly two orders of magnitudes. This is consistent with previous results for LMBH AGNs (e.g., Greene & Ho 2007c; Dong et al. 2012a). Regarding the α_OX–M_BH relationship, no correlation is found for LMBHs only given the narrow dynamic range of M_BH; however, a weak correlation (Spearman's rank correlation coefficient is −0.25 with a null probability of ∼10⁻⁷) appears to be present when taking into account AGNs with more massive BHs from the other samples, albeit with a large dispersion for the LMBHs. A similar weak correlation was also suggested by Dong et al. (2012a). Thus, the wide α_OX distribution for LMBH AGNs is not caused by the distributions of the Eddington ratio or BH mass.

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Three possibilities might account for the large scatter in the α_OX distribution. The first is X-ray variability. It has been demonstrated that the amplitude of short-timescale X-ray variability is anticorrelated with the BH mass for AGNs with M_BH > 10⁶ M_⊙ (e.g., Ponti et al. 2012; Kelly et al. 2013), below which the relation flattens (Pan et al. 2015; Ludlam et al. 2015). This means that LMBH AGNs show the largest amplitude of X-ray variability among all AGNs. Moreover, LMBH AGNs appear to show strong variations in the X-ray spectral shape, as manifested by their wide range of spectral indices (Γ = 1.2–4.0). A typical example is NGC 4395, which was found to exhibit rapid and strong X-ray variability (Iwasawa et al. 2000; Dewangan et al. 2008), and its X-ray spectral slope varied from Γ < 1.25 to Γ > 1.7 over about one year (Moran et al. 2005). Similar behavior was also found in POX 52 (Thornton et al. 2008).

Second, LMBHs may have a wide distribution in the intrinsic X-ray luminosities. As commonly believed, the X-ray emission is mainly produced in the hot corona by inverse-Compton scattering of optical/UV photons from the disk. The relative dominance of the optical/UV and X-ray emission is determined by the fraction of energy deposited into the hot corona out of the total viscous energy produced in the accretion disk. For instance, in models where the corona is heated by magnetic reconnection (Liu et al. 2003), the fraction is mainly determined by the magnetic field strength in the corona, which may vary from one object to another.

Third, X-ray absorption may play a role as well. Although no strong effect of X-ray obscuration is present for most of the objects as suggested by the L_{2–10 keV}–L_{[O iii]} relation above, moderate absorption cannot be ruled out in some of the objects. It is probable that the environment of LMBHs may be more gas-rich compared to normal AGNs powered by more massive BHs, whose stronger radiation makes it easier to expel circumnuclear materials.

We explore the radio properties for our total LMBH sample using radio data at 20 cm from the VLA FIRST survey¹⁵ (Becker et al. 1995). There are 26 objects detected, leading to a low detection fraction of 5%. The low incidence of radio activity is consistent with the result in GH07. The radio powers at 20 cm of these sources range from 2 × 10²¹ to 4 × 10²³ W Hz⁻¹, with a median of 4 × 10²² W Hz⁻¹ (see Table 5). Figure 10 shows their radio power versus the [O iii] luminosity, which appears broadly consistent with that found in GH07.

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Table 5.  FIRST Detections

ID	${S}_{20\mathrm{cm}}$	log P20 cm	log R
(1)	(2)	(3)	(4)
Our new sample
23	1.14 ± 0.16	22.80 ± 0.06	1.36
28	0.85 ± 0.15	22.15 ± 0.07	1.22
55	2.86 ± 0.19	22.32 ± 0.03	1.49
89	1.22 ± 0.16	22.89 ± 0.06	1.51
95	16.75 ± 0.86	23.59 ± 0.02	2.49
123	2.72 ± 0.19	22.76 ± 0.03	1.05
143	1.97 ± 0.17	22.20 ± 0.04	1.51
199	2.67 ± 0.18	22.27 ± 0.03	0.80
201	1.79 ± 0.16	23.07 ± 0.04	1.34
Dong et al. (2012b)
22	1.82 ± 0.14	22.32 ± 0.03	1.57
30	3.18 ± 0.27	23.12 ± 0.04	2.03
36	4.53 ± 0.26	23.32 ± 0.03	2.06
54	2.07 ± 0.18	22.75 ± 0.04	1.43
78	1.44 ± 0.17	22.88 ± 0.05	1.44
118	1.04 ± 0.14	21.87 ± 0.06	0.84
140	2.38 ± 0.19	22.05 ± 0.03	1.57
141	2.55 ± 0.18	21.83 ± 0.03	1.58
170	1.03 ± 0.16	21.95 ± 0.07	1.58
181	1.29 ± 0.16	22.32 ± 0.06	0.91
206	2.33 ± 0.18	21.39 ± 0.03	1.49
208	8.81 ± 0.46	23.20 ± 0.02	2.21
222	2.69 ± 0.20	21.58 ± 0.03	1.15
257	2.52 ± 0.19	22.56 ± 0.03	1.50
273	1.43 ± 0.16	22.53 ± 0.05	1.09
277	0.68 ± 0.14	23.02 ± 0.09	1.36
305	3.78 ± 0.23	22.79 ± 0.03	1.98

Note. Column (1): identification number assigned in this paper and Dong et al. (2012b), respectively. Column (2): flux density at 20 cm from FIRST (mJy). Uncertainties include the 5% systematic uncertainty recommended by White et al. (1997). Column (3): corresponding radio power (W Hz⁻¹) at 20 cm. Column (4): radio loudness in log-scale. R $\equiv \,{f}_{6\mathrm{cm}}/{f}_{4400\mathring{\rm A} }$ assuming a spectral index of α_r  = 0.46 (radio; Ulvestad & Ho 2001) and α_o = 0.44 (optical; Vanden Berk et al. 2001), where ${f}_{\nu }\propto {\nu }^{-{\alpha }_{o}}$.

A machine-readable version of the table is available.

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As a common practice, the radio-loudness parameter, defined as the radio to optical flux ratio (R ≡ f_{6 cm}/f_{4400 Å}), is used to separate radio-loud AGNs from radio-quiet ones, with an operational dividing value of 10. The radio loudness is calculated for the radio-detected sources as follows: f_{6 cm} is derived assuming a radio spectral index of α_r = 0.46 (${f}_{\nu }\propto {\nu }^{-{\alpha }_{r}};$ Ulvestad & Ho 2001) from the flux density at 20 cm, while f_{4400 Å} is estimated in the same way as f_{2500 Å}. Among the 26 sources with FIRST detections, 23 are radio-loud, corresponding to a radio-loud fraction of 4%. For those sources undetected in FIRST,¹⁶ upper limits on radio loudness are estimated assuming a radio flux density of 1 mJy at 20 cm, which is the detection limit of the FIRST survey (see Figure 11).

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The radio-loud fraction in the LMBH AGN sample is lower than that in classical AGNs (∼15%; Ivezić et al. 2002). This seems to be consistent with the finding that radio sources may prefer to reside in more massive galaxies (Best et al. 2005). For our LMBHs, their host galaxies are indeed at the lower stellar mass end of the parent sample from SDSS DR7 (see Section 5.3 for details). However, it should be noted that the above radio-loud fraction should only be considered as a lower limit, since the FIRST flux sensitivity is not deep enough to give stringent constraints on the radio loudness. Further deep and high spatial resolution radio surveys are needed to determine the true radio-loud fraction for LMBHs.

As a natural interpretation, the radio emission of an active galaxy is a mixture of contribution from nuclear AGNs and star formation in the host galaxy. This may be particularly true for the fluxes listed in the FIRST catalog we used here, which were obtained by fitting the sources usually as extended radio sources (cf., the "Deconv.MajAx" column in the catalog). However, it is difficult to seek clues from the radio morphology since most of these sources have very weak radio emissions (S_{20 cm} < ∼5 mJy, close to the detection limit of 1 mJy), and their FIRST images are unresolved. Only one brighter object (S_{20 cm} > 10 mJy), SDSS J122412.51+160012.1, probably shows marginally extended structure with integrated to peak flux ratio of 1.5 and deconvolved major axis = 545. On the other hand, radio luminosities at 6 GHz may provide some information on the radio origins. It is suggested that for AGNs at low redshifts, low-luminosity radio emission with L_{6 GHz} < 10²³ W Hz⁻¹ seems to be powered by star formation, while that with L_{6 GHz} ≥ 10²³ W Hz⁻¹ is more likely AGN-dominated (e.g., Kimball et al. 2011; Condon et al. 2013; Kellermann et al. 2016). The luminosity at 6 GHz is derived assuming a spectral slope of 0.46. All the objects except one (SDSS J122412.51+160012.1) have 6 GHz luminosities located in the range of 10²¹ W Hz⁻¹ ≤ L_{6 GHz} ≤ 10²³ W Hz⁻¹, and thus their radio fluxes may also be contributed by host stellar processes.

Most low-mass AGNs tend to have broad-line widths (FWHMs) narrower than ∼2000 km s⁻¹, which is the conventional criterion for narrow-line Seyfert 1 galaxies (NLS1s; Osterbrock & Pogge 1985). It is thus interesting to compare these two AGN subclasses. In fact, some objects in our total sample have also been classified as NLS1s in a comprehensive study of NLS1 AGNs from SDSS DR3 by Zhou et al. (2006). NLS1s are characterized by some peculiar properties, including strong Fe ii lines, weak [O iii]/Hβ line ratios, high Eddington ratios, low radio-loud fraction, significant soft X-ray excess (in some), strong X-ray variability, and steep X-ray spectra (see, e.g., Laor 2000; Komossa 2008 for reviews). Based simply on the BH mass estimation method from the line width and luminosity, a relatively narrow broad-line width can result from either a low BH mass, or/and a high Eddington ratio. With their peculiar multiwavelength properties, NLS1s are found to cluster at one end of the so-called EV1, and are suggested to be driven by high accretion rates (Boroson & Green 1992). Thus, NLS1s are generally suggested to harbor relatively less massive BHs radiating near their Eddington limits.

However, LMBHs are selected only from BH masses regardless of the Eddington ratios. They are simply the low-BH-mass counterparts of classical Seyfert galaxies, and are expected to exhibit diverse properties depending on the Eddington ratios, which span a wide dynamical range. Greene & Ho (2004) found that their low-mass AGNs span a larger range in both the Fe ii and the [O iii] strengths relative to Hβ than classical NLS1s. There is a wide distribution of Eddington ratios in our sample, some as low as two orders of magnitudes below their Eddington limits. LMBHs show diverse properties in X-ray, with a wide range of X-ray photon indices (e.g., Γ = 1.0–2.7 in Desroches et al. 2009; Γ = 1.5–2.8 in Dong et al. (2012b), and Γ = 1.2–4.0 in the soft X-ray band for our sample). Moreover, some LMBHs, especially those with low Eddington ratios, do not show a soft X-ray excess, as found in the spectrum of NGC 4395. On the other hand, some typical NLS1s, such as those with extremely narrow widths of the broad lines as studied by Ai et al. (2011), do have BH masses as low as 10⁶ M_BH or lower.

It is clear that NLS1s, when solely selected from the line width, are a heterogeneous class of AGNs, which may include ordinary Seyfert galaxies having simply LMBHs, regardless of the Eddington ratios. Classical NLS1s were selected by also considering the strong Fe ii and weak [O iii] emissions. These tend to select objects with high Eddington ratios given the observed eigenvector i correlations. We thus suggest that a simple criterion based solely on the line width may not be a good approach for the selection of NLS1s and other criteria have to be incorporated. Similar remarks can also be found in Ai et al. (2011).

One interesting feature is that both types have relatively low fractions of radio-loud objects. This might be related to the suggested observed statistical relations among radio loudness, BH mass, and Eddington ratio. However, the underlying physical mechanisms driving these relations are not known.

The host galaxy luminosities are calculated following Dong et al. (2012b) and GH07. First, the AGN luminosities are estimated from the broad Hα luminosities¹⁷ that are free from starlight contamination, and are then subtracted from the SDSS photometric Petrosian g-band magnitude. The host galaxy luminosities are then derived after K-corrections using the routine of Blanton & Roweis (2007). The distributions of the g-band absolute magnitudes of the AGN, host, and the total are shown in Figure 12, with those from Dong et al. (2012b) and GH07 plotted for comparison. The distributions of these luminosities for the DR7 LMBH sample are similar to those of Dong et al. (2012b). The current sample has a median AGN luminosity of M_g = −17.80 mag and a median host galaxy luminosity of M_g = −20.14 mag (these values are −17.70 and −20.22, respectively, in Dong et al. 2012b). The median host galaxy luminosity is slightly brighter than the characteristic luminosity of ${M}_{g}^{* }=-20.1\,\mathrm{mag}$ at z = 0.1 (Blanton et al. 2003). Only six objects have host galaxy luminosities falling into the dwarf galaxy of M_g > −18.0 mag. It indicates that although LMBHs usually indeed reside in small stellar systems, their hosts may not necessarily be dominantly dwarf galaxies. Note that the host galaxy luminosities are possibly overestimated in our AGN-host separation method since fiber loss may result in the underestimation of the nuclear luminosity, though the systematic overestimation is smaller than 0.3 mag according to GH07. Furthermore, the AGN luminosities estimated from the Hα luminosities assuming a power-law continuum may be subject to an uncertainty of about 0.1 mag (Dong et al. 2012b).

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In general, it is not practical to visually classify the galaxy morphology for most of our sample objects using the SDSS images due to their limited depth and spatial resolution. Instead, we try to gain information on the morphologies from the host galaxy colors. The u − g colors are found to have a mean value of 1.28 mag with a standard deviation of 0.38 mag, and the g − r colors have a mean of 0.61 mag and a standard deviation of 0.16 mag. They correspond to the typical colors of Sbc galaxies according to Fukugita et al. (1995).

Two stellar indices, the 4000 Å break strength (D₄₀₀₀) and Balmer absorption line index (Hδ_A), are used to infer the stellar populations of the host galaxies. In general, D₄₀₀₀ is small for young stellar populations (D₄₀₀₀ < 1.5 for ages < 1 Gyr) and large for old, metal-rich galaxies. On the other hand, galaxies that experienced starburst activity that has ended ∼0.1–1 Gyr ago tend to show strong Hδ absorption lines (Kauffmann et al. 2003b). Hence, these two indices can be used to constrain the mean stellar ages of the host galaxies of LMBHs and to diagnose the star formation history over the past few gigayears.

The two indices are calculated from the decomposed stellar component as described in Section 2.1 based on the definition and calculation method in Kauffmann et al. (2003b). Note that only 157 objects with AGN contribution less than 75% at 4000 Å in the SDSS spectra are used. The resulting typical errors (1σ) of the two indices for the LMBH sample are 0.1 and 1.6 Å, respectively (see Section 4.2.3 in Dong et al. 2012b for the details of error estimation).

The distribution of 419 low-mass AGNs (262 objects from Dong et al. 2012b also included) on the D₄₀₀₀–Hδ_A plane is shown in Figure 13, and the distribution of ∼492,000 inactive galaxies is plotted as contours for comparison. These inactive galaxies are derived from SDSS DR7 spectra classified as "galaxies" by the SDSS pipeline and with S/N > 5 pixel⁻¹ around 4000 Å in their spectra. In addition, broad-line AGNs and those Seyfert 2 galaxies defined by the BPT diagram are excluded. Note that the negative values of Hδ_A are due to the definition and corresponding calculation method of the line index (Worthey & Ottaviani 1997; Kauffmann et al. 2003b). Most of our LMBH hosts (112 out of 157) have D₄₀₀₀ < 1.5, indicating that their mean stellar ages tend to be less than 1 Gyr. In general, for those galaxies with D₄₀₀₀ < 1.5, if they have experienced an instantaneous burst of star formation in the last few gigayears, they tend to have Hδ_A > 5 Å. However, most objects with D₄₀₀₀ < 1.5 in our LMBH sample do not follow this tendency. It indicates that the distribution of our LMBHs on the D₄₀₀₀–Hδ_A plane is more likely overlapping the locus of continuous star formation, which is in broad agreement with that of normal galaxies.

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Studies of optical images and spectra indicated that there are two distinct populations of host galaxies of the LMBHs (Greene et al. 2008; Jiang et al. 2011). The majority are gas-rich, late-type galaxies similar to the prototype NGC 4395. The rest are spheroidal galaxies like POX 52, which are gas-deficient and have red color. Kormendy & Bender (2012) suggested that such spheroidal galaxies were transformed from irregular and late-type disk galaxies at an early epoch by both internal and secular processes. The low fraction of LMBH host galaxies with nearby companions also imply that these galaxies mainly evolve through secular processes (Jiang et al. 2011). This is also supported by the above finding that most of the host galaxies of our LMBHs have undergone continuous star formation in the past few gigayears.

The stellar masses of the host galaxies are estimated using three methods. The first is by using near-infrared (NIR) photometry, which can be considered as a tracer of stellar mass. In the NIR band, the luminosities of the LMBH AGNs are dominated by host galaxies, and AGNs have negligible contribution (∼7%).¹⁸ Moreover, the mass-to-light ratio in the NIR band is sensitive neither to dust absorption nor to star formation history. Of the total sample, 180 objects are detected in the Two Micron All-Sky Survey (2MASS¹⁹ ) and among the rest, 129 objects are detected in the UKIRT Infrared Deep Sky Surveys (UKIDSS; Lawrence et al. 2007). Here we adopt the mass-to-light ratios provided by Into & Portinari (2013; the scatter is about 0.1 dex), which are dependent on the galaxy colors r − i,

$$\begin{eqnarray}&&\mathrm{log}({M}_{* }/{L}_{{Ks}})=2.843(r-i)-1.093,\end{eqnarray} \tag{ 3 }$$

where L_Ks is the Ks-band luminosity from 2MASS in units of L_⊙, and r − i is the color derived from the SDSS Petrosian magnitudes after K-correction and subtraction of the AGN continuum. The K-correction is calculated following Blanton & Roweis (2007). The K-band magnitudes of the UKIDSS-detected sources are transformed to the 2MASS Ks band using the color equations given by Hewett et al. (2006). For the sources not detected in 2MASS and UKIDSS, we derive their stellar masses from the MPA–JHU catalog²⁰ (Kauffmann et al. 2003a; Brinchmann et al. 2004; Tremonti et al. 2004; Salim et al. 2007) if available, or otherwise using the relation between M_* and the 3.4 μm luminosity from the Wide-field Infrared Survey Explorer (WISE) All-Sky survey calibrated using the MPA–JHU catalog (Wen et al. 2013). We compare the stellar masses given by the MPA–JHU catalog with those derived from the NIR luminosities and r − i colors for those objects detected in both surveys, and found that the two estimators are statistically in good agreement. The stellar masses for the total sample range from 6.0 × 10⁸ M_⊙ to 2.5 × 10¹² M_⊙, with a median of 3.7 × 10¹⁰ M_⊙, slightly lower than that of the MPA–JHU sample (5.7 × 10¹⁰ M_⊙; see Figure 14 for their distributions). The stellar masses are mostly greater than 10^9.5 M_⊙, which is the mass of the Large Magellanic Cloud (LMC), indicating again that LMBHs do not necessarily reside in dwarf galaxies.

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The 512 sources with reliable stellar mass estimations are plotted on the color–mass diagram (see Figure 15). The green lines indicate the location of the so-called green valley defined by Schawinski et al. (2014), which is a superposition of red and blue galaxies with the same intermediate optical colors. It has been suggested to be a special stage in the evolution of massive galaxies after star formation is quenched, and perhaps as evidence of AGN feedback. Our LMBH sources span almost the entire u − r color range, while most are located in the green valley or blue sequence, which is consistent with the suggestion that most low-mass AGNs in GH07 reside in gas-rich, disk galaxies (Jiang et al. 2011).

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We note that there still exist about 11% of our sample objects in the red sequence. An interesting question arises: how were these LMBH AGNs triggered and fueled in such red and presumably gas-deficient galaxies? We know that AGN activity requires both available feeding fuel (gas or stars) and a process to get out of their angular momentum. As discussed in Kormendy & Ho (2013), the feeding rates of low-mass AGNs are very modest. Assuming these LMBHs accrete at their Eddington limits, the mass accretion rate, $\dot{M}=2.2\times {10}^{-8}(\eta /0.1)({M}_{\mathrm{BH}}/{M}_{\odot }){M}_{\odot }$, is only ∼0.02 M_⊙ yr⁻¹ for BHs with M_BH ∼ 10⁶ M_⊙ (Kormendy & Ho 2013). These values are tiny even for red galaxies, and hence there may always be enough gas to feed the nuclear low-mass AGNs. On the other hand, various physical process may break the "angular momentum barrier" and push the gas into the nuclear regions of galaxies, such as wet major and minor mergers of the galaxies (e.g., Silk & Rees 1998; Hopkins et al. 2008), inflow along spiral arms or bar (for instance, NGC 1097; e.g., Fathi et al. 2006; Davies et al. 2009), and disk instabilities (e.g., cold flows; Dekel et al. 2009; Bournaud et al. 2011). Current observations give evidence that the triggering of low-mass AGNs are indeed dominated by secular processes. For instance, about 90% of LMBH AGNs in the low-redshift universe reside in galaxies with so-called pseudobulges, which are formed mainly by slow process without major mergers involved (Jiang et al. 2011). Our result on the D₄₀₀₀–Hδ_A distribution also support this idea. The other processes, however, may not be completely ruled out. For example, SDSS J083803.68+540642.0, a red and gas-poor LINER in the sample of Dong et al. 2012b, shows a peculiar circumgalactic ring, which may be caused by collision with a gas-rich galaxy, suggesting a history of violent galaxy interaction (Liu et al. 2017). Such a process may also play a role in triggering low-mass AGNs. As discussed in Liu et al. (2017), major mergers of low-mass galaxies in the local universe may be more common than massive galaxies. Further studies are needed to fully understand this question.

As discussed above, LMBHs seem to evolve with secular processes and have not experienced major mergers. Thus, they can be used to trace the initial stage of evolution of BHs and their host galaxies. We briefly investigate the co-evolution of BHs and host galaxies in the low-mass regime by using the relation between BH mass accretion rates and host star formation rates (SFRs). The mass accretion rates are derived from the bolometric luminosities assuming the efficiency factor η = 0.1, while the SFRs are given by the MPA–JHU catalog with no aperture corrections. Figure 16 shows the distribution of 282 low-mass AGNs with both quantities available on the diagram of mass accretion rates versus SFRs, revealing a strong correlation between them.

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This suggests that there may exist a connection between AGN activity and star formation. However, more compelling and direct evidence is still needed to support the co-evolution of LMBHs and their hosts. In fact, there is no strong evidence that LMBHs have direct feedback on their host galaxies in the local universe. Furthermore, the link between BH accretion and star formation may also be explained by the fact that they both depend on the gas from the same reservoir (Kormendy & Kennicutt 2004). Nevertheless, our result hints at a possible co-evolution scenario between LMBHs and their host galaxies.