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Millimeter-to-submillimeter emission tells us much about these hidden galactic nuclei, for physical scales of several parsecs to several 100 pc in this work. First, these wavelengths contain various emission lines tracing the dominant (by mass) interstellar medium in these systems, that is, cold-to-warm molecular gas (∼10 to a few 100 K). The lines tell us the physical conditions and kinematics of the gas and thereby tell us about the fueling and feedback of the nuclear activities as well as the mass distribution in the nuclei. Second, the short millimeter and submillimeter continuum is usually dominated by thermal emission from dust. It is this dust continuum that carries the vast majority of the bolometric luminosity of these nuclei. Because of that, high-resolution information available at sub/millimeter wavelengths is very useful to characterize the nuclei, complementing spatially unresolved observations at the far-IR where the continuum spectrum peaks. Third, the dust in these nuclei is moderately opaque (the opacity is around the order of unity) at sub/millimeter wavelengths to produce bright emission, and yet it also makes the nuclei penetrable except at the very center in extreme cases. As a guide, τ
1 mm = 1 corresponds to 



NH2∼1025.5

 cm−2 for an environment similar to the Galactic disk (Planck Collaboration et al. 2014; Galliano et al. 2018). The structure of the nuclei can thus be probed more easily in the sub/millimeter than at far-IR and shorter wavelengths. At the same time, the continuum emission carries information about the dust opacity and hence the obscuring column density. Fourth, rotational lines from vibrationally excited HCN at sub/millimeter wavelengths can be an indicator and probe of the NGC 4418/Arp 220-type nuclei with significant obscuration (Sakamoto et al. 2009; Aalto et al. 2015, 2019; Imanishi et al. 2019). These nuclei are opaque enough to trap infrared photons to increase their inner temperature (i.e., the greenhouse effect), and the enhanced infrared radiation vibrationally excites molecules such as HCN (González-Alfonso & Sakamoto 2019). Their rotational lines in the sub/millimeter have a chance to leak out of the dusty nuclei and indicate their hot interior since dust opacity is lower at longer wavelengths. And finally, the Atacama Large Millimeter/submillimeter Array (ALMA) has dramatically enhanced our capability for high-resolution and high-sensitivity observations at sub/millimeter wavelengths. A characteristic ALMA resolution of 0.″1 is on the order of 10 pc at nearby hidden galactic nuclei at tens of megaparsecs. While the resolution does not match the accretion disks around supermassive black holes (r ≪ 1 pc), it is only an order of magnitude larger than that of young massive star clusters (Longmore et al. 2014) and corresponds to the outer radii of molecular tori around AGN (Combes et al. 2019). Therefore, ALMA observations are good at probing the obscuring interstellar medium around AGN (if any), circumnuclear star formation, and their effects on the circumnuclear material.
Citation: Galliano et al. 2018
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We should examine whether our picture is consistent with previous studies at a higher radio luminosity regime, 



logL1.4GHz>27

. It is natural to assume that the unification between radio galaxies (HzRGs) and RLQSOs works at this regime. Actually, observational evidence for the unification has been found in this luminosity regime (Wylezalek et al. 2013). Hyperluminous radio galaxies/RLQSOs with 



logL1.4GHz>27

 are expected to reside in the galaxy denser regions according to the L
jet − Σ relation,
16


16
The L
jet − Σ relation would break down in the extremely high-density regions, as a very large velocity dispersion of galaxies in the massive structures reduces the merger frequency; thus, SMBH spin and mass growth would be slow. as shown by arrow 



C

 in Figure 7. There is definitive evidence that hyperluminous radio galaxies exist in the rich galaxy overdense regions (Venemans et al. 2007; Falder et al. 2010; Wylezalek et al. 2013; Hatch et al. 2014; Husband et al. 2016). For instance, Venemans et al. (2007) examined the environments of eight radio galaxies with log L
1.4 GHz ≥ 27.3 at z ∼ 2−5 and found six of them in overdense regions. These radio galaxies with available optical spectra are classified as either HERGs, RLQSOs, or dust-obscured RLQSOs (Eales & Rawlings 1993; Venemans et al. 2007; Drouart et al. 2016; Nesvadba et al. 2017). Hatch et al. (2014) also found that radio-loud AGNs with log L
1.4 GHz > 27.2 are significantly more present in high-density regions than radio-quiet AGNs at z ∼ 1−3. Falder et al. (2010) found that there is a positive correlation between the radio luminosities and the ambient environments of HzRGs and RLQSOs with log L
1.4 GHz = 26.65–28.65 at z ∼ 1. A similar trend is also found for seven luminous radio galaxies at z ∼ 2.2 (Husband et al. 2016). The faintest radio galaxy with log L
1.4 GHz = 26.6 in Husband et al. (2016) resides in the lowest-density region, which is comparable to that of blank fields (Figure 3), and the others with log L
1.4 GHz > 27 reside in the denser regions. On the other hand, Zeballos et al. (2018) found that some of the HzRGs with log L
1.4 GHz > 27 do not reside in the overdense regions of SMGs. However, Zeballos et al. (2018) could not deny the possibility that the overdense regions around those radio galaxies are buried due to the sample variance. In future, we could assess hyperluminous radio galaxy environments at z ∼ 4; as the survey area of the HSC-SSP will reach ∼1000 deg2, about 10 hyperluminous radio galaxies are expected to be found, assuming the radio galaxy luminosity function of Dunlop & Peacock (1990).
Citation: Venemans et al. 2007
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The SFR of a gaseous clump with a density gradient is higher than if that same clump was made of uniform-density gas (Tan et al. 2006; Girichidis et al. 2011; Elmegreen 2011; Parmentier 2014, 2019). Centrally concentrated clumps actually process their gas into stars at a pace faster than expected based on their mean freefall time, because the density of their central regions is higher than the clump gas mean density. Parmentier (2019) refers to the ratio between the SFR of a clump with a density gradient, SFRclump, and the SFR of its top-hat equivalent, SFRTH, as the magnification factor ζ (see Equation (8) in Parmentier 2019):
1





The SFR of a clump can thus be written as (see Section 2 in Parmentier 2019, for a discussion)
2





In this equation, mgas is the gas mass hosted by the clump,1

1
The clump total mass mclump consists of the gas mass mgas and the mass mstars of the stars it has formed.
 and 





 is the mean freefall time of the clump gas:
3





The latter is defined based on the clump gas mean density
4





with rclump the radius containing the clump gas mass mgas. ζ is the magnification factor, which quantifies by how much the density gradient of a clump enhances its SFR compared with what is expected based on its mean freefall time 





. Equation (2) therefore allows one to disentangle the contribution of the density gradient, embodied by the ζ factor, from that of the star formation efficiency per freefall time itself. Parmentier (2019) coins 





 the intrinsic star formation efficiency per freefall time since it is independent of the clump density gradient.2

2
This is as opposed to the (globally) measured star formation efficiency per freefall time, defined as 





 (Parmentier 2019).
 For a top-hat profile, ζ = 1 and the SFR obeys
5





Note that the gas density of the top-hat equivalent is equal to the gas mean density 





 of the centrally concentrated clump (same gas mass mgas enclosed within the same clump radius rclump).
Citation: Parmentier; 2019
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With only 





 as a free parameter, different studies suggest that 





 = 10%–20% at z > 6 is necessary for galaxies to fully ionize the universe (Bolton & Haehnelt 2007b; Finkelstein et al. 2012; Kuhlen & Faucher-Giguère 2012; Bouwens et al. 2015a, 2015c; Mitra et al. 2015; Robertson et al. 2015; Khaire et al. 2016; Price et al. 2016). Simulations do not agree on 





 at high redshifts and find either very high (e.g., Sharma et al. 2016) or very low values (e.g., Gnedin et al. 2008; Ma et al. 2015). Furthermore, they predict a strong dependence on the mass of dark matter halos and star formation (e.g., Wise & Cen 2009; Razoumov & Sommer-Larsen 2010). Direct observational constraints on 





 in the EoR are not possible because of the increasing opacity of the IGM to LyC photons at z > 4 (e.g., Madau 1995; Inoue et al. 2014). Except for one strong LyC emitter at z = 3.2 with 





 > 50% (de Barros et al. 2016; Vanzella et al. 2016b), the handful of confirmed LyC emitters at z  3 all show consistently 





 ≲ 8% (Steidel et al. 2001; Leitet et al. 2013; Borthakur et al. 2014; Cooke et al. 2014; Siana et al. 2015; Izotov et al. 2016a, 2016b; Leitherer et al. 2016; Smith et al. 2016). The numerous non-detections listed in the literature show upper limits of 





 ∼ 2%–5% over large ranges of redshift (Vanzella et al. 2010; Sandberg et al. 2015; Grazian et al. 2016; Guaita et al. 2016; Rutkowski et al. 2016; Vasei et al. 2016). If galaxies are responsible for ionizing the universe at z > 6, then clearly their population-averaged LyC escape fraction needs to increase substantially with redshift by at least a factor of two (see also Inoue et al. 2006). What methods can we use to access 





 observationally in the EoR? Radiative transfer models suggest a correlation between the ratio 





/





 and 





 in density-bound H ii regions (e.g., Nakajima & Ouchi 2014), and a handful of recent observational studies verify this positive correlation (de Barros et al. 2016; Izotov et al. 2016a, 2016b; Vanzella et al. 2016a, 2016b). The increased 





/Hβ ratios found in z > 5 galaxies (e.g., Stanway et al. 2014; Roberts-Borsani et al. 2015; Faisst et al. 2016a) hint toward an increasing 





/





 ratio for the global population of galaxies at high redshifts and therefore could be the smoking gun for a strong evolution in 





(z). Currently, the 





 line cannot be measured spectroscopically at z > 4, and the use of broad-band photometry to determine 





 line strengths is degenerate with the 4000 Å Balmer break, which is a strong function of age and other galaxy parameters. However, local analogs of high-redshift galaxies can be used to probe the physical properties of these galaxies.
Citation: Izotov et al. 2016a
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To detect supernova neutrinos with the KamLAND data, a cluster of DC events is required: two DC events within a 10 s window. The very low DC rate enables us to use the minimum cluster condition (two DC events). An accidental DC event cluster is a background for supernova neutrinos. Based on the DC event studies, we evaluate the number of accidental cluster events (



≡nclusteraccidental

) via Monte-Carlo (MC) simulation. Accidental cluster rates and accumulation of 



nclusteraccidental

 are shown in Figure 1. Before distillation campaigns, the DC event is mainly caused by reactor -



ν¯e

, and 13C(α, n)16O interaction has a secondary contribution (Abe et al. 2008). After distillation campaigns, the DC event by 13C(α, n)16O interaction decreases but reactor -



ν¯e

 is still a dominant component (Gando et al. 2011). Japanese reactors were shut down after the Great East Japan Earthquake in 2011. In the reactor-off phase (Gando et al. 2013), the rate of reactor -



ν¯e

 events is decreased. These trends of DC event rate are also shown in Figure 1. In an energy region above 10 MeV, fast neutrons and atmospheric neutrinos have dominant contribution on the number of DC events (Abe et al. 2022b). Typically, the DC candidate rate is ∼1 day−1 in the reactor-on phase and 0.1 day−1 in the reactor-off phase. Usually, we call a KamLAND data set a “run,” which consists of typically 24 hr data. The number of expected DC events is estimated in run by run and the number of accidental clusters is calculated from that. Taking into account that time differences between each run are more than 10 s, there should be no accidental clusters that occur across two runs. As a result, the accumulated number of accidental clusters is 



nclusteraccidental=0.32−0.04+0.02

 clusters, and this rate is 0.023 cluster yr−1 on average. The error of 



nclusteraccidental

 includes systematic uncertainties of the number of expected DC events by reactor -



ν¯e

, atmospheric neutrino, and fast neutron.
Citation: Gando et al. 2013
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Citation: Gando et al. 2011
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One factor that we have not taken into account so far is that the strength of an AGN may affect how strong the corresponding emission from the NLR is. Thus, it may be the case that lower-luminosity or lower-accretion-rate AGNs are more easily overwhelmed by star formation. Therefore, we next explore whether correctly and incorrectly classified X-ray AGNs differ in their intrinsic AGN properties. One of the indicators of the accretion strength of an AGN in the optical regime is the luminosity of the forbidden [O iii] line, 





, which scales with the bolometric luminosity of the AGN (Mulchaey et al. 1994; Heckman et al. 2005; LaMassa et al. 2010; Azadi et al. 2017; Glikman et al. 2018). A related quantity, 





 divided by the fourth power of the stellar velocity dispersion, σ4, can provide an estimate of the Eddington ratio of the AGN (Kewley et al. 2006). Trump et al. (2015) suggested that higher sSFR galaxies must have more efficient AGNs in order to be classified as BPT–AGNs because of the relative contributions from star formation. We show 





 and 





 versus stellar mass in Figures 8 and 9, respectively, with the BPT star-forming galaxies from GSWLC-M1 composing the backgrounds in Figures 8(a) and 9(a) and the BPT–AGNs from GSWLC-M1 making up the backgrounds in Figures 8(b) and 9(b). In Figures 8 and 9, there appear to be two distinct sequences for the two BPT types when mass is included, where in Figure 8(a), the background BPT star-forming galaxies form one sequence where 





 appears to correlate with stellar mass, including galaxies with masses up to 





, while the star-forming galaxies in Figure 9(a) do not show a strong dependence of proxy Eddington ratio with stellar mass, which is expected because 





 from star-forming galaxies primarily comes from star formation. The BPT–AGNs form sequences in Figures 8(b) and 9(b) that have no apparent dependence on mass with masses ranging roughly from 





. The existence of these two sequences is apparently the case because of the different sources of [O iii] emission that are dominant in BPT star-forming galaxies versus BPT–AGNs. The majority of the BPT–H ii are more consistent with the background star-forming galaxies in Figures 8(a) and 9(a), whereas the BPT–AGNs all appear consistent with the background BPT–AGNs shown in Figures 8(b) and 9(b), which is to be expected if the NLR dominates [O iii] emission. Six BPT–H ii are more consistent with the background BPT–AGNs in Figures 8(b) and 9(b), and if the NLR is indeed the source of their [O iii] emission, their Eddington ratios are much lower than the average BPT–AGNs, suggesting that they have relatively inefficient accretion. We will return to these outliers in Section 3.2.3.
Citation: Azadi et al. 2017
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The disk-wind outflows that accompany highly super-Eddington accretion carry a total mass-loss rate 



Ṁw

, which nearly equals the entire mass-transfer rate, i.e., 



Ṁw∼Ṁ

 (e.g., Blandford & Begelman 1999; Hashizume et al. 2015), with only a small fraction making its way down to the BH/NS surface. Depending on the radial scale of their launching point in the disk or binary, the outflows can possess a range of speeds, from values similar to the binary orbital velocity, v
orb ≲ 100 km s−1, to the transrelativistic speeds v
j ≳ 0.3c that characterize jet-like outflows from the innermost radii of the disk (and similar to those observed in SS 433 and ULX; e.g., Jeffrey et al. 2016 and references therein). In ADIOS models for the radial disk structure (Blandford & Begelman 1999; Margalit & Metzger 2016), the mass accretion rate decreases as a power law with radius 



Ṁ∝rp

 for 



r∈[rin,rout≲Rtr]

, where r
out ≫ r
in. Assuming the outflows local to each annulus in the disk reach an asymptotic velocity equal to the local disk escape velocity, the kinetic energy-averaged wind velocity is given by (e.g., Metzger 2012)
6



vw≈p1−pGM•rinrinroutp≈0.05cM•10M⊙0.3rin6rg−0.2routR⊙−0.3,

where in the second equality we have normalized r
in to gravitational radius r
g = GM
•/c
2 and take p = 0.6 (as supported by hydrodynamical simulations of radiatively inefficient accretion flows; e.g., Yuan & Narayan 2014; Hu et al. 2022). In what follows, we take v
w ∼ 0.03c as a fiducial value, consistent with that expected for a main-sequence or moderately evolved donor star feeding a relatively compact accretion flow, r
out ∼ R
⊙. However, lower value v
w ≲ 0.01 c may be appropriate for a giant donor star (r
out ≳ 102
R
⊙) or for larger values of p. The kinetic luminosity of the wind is then
7



Lw≈12Ṁwvw2≈1042ergs−1Ṁw105ṀEdd×M•10M⊙vw,92ergs−1,

where v
w,9 = v
w/(109 cm s−1) and hereafter we adopt the short-hand notation Y
x ≡ Y/10x for quantities given in cgs units. In analytic estimates hereafter, we shall typically fix the value of M
• = 10M
⊙ and use L
w and 



Ṁw

 interchangeably.
Citation: Margalit & Metzger 2016
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In hydrodynamic and magnetohydrodynamic systems, different fluctuations interact with each other nonlinearly, generating turbulence (Matthaeus et al. 2015). One of the most important characteristics of turbulence is the existence of intermittency among various scales. Spatial intermittency manifests as coherent structures with large gradient at small scales. In ordinary fluids, coherent structures include a tangle of vortex filaments where vorticity is highly concentrated (Frisch 1995). In the turbulent plasma environments, examples of intermittent structures include current sheets, discontinuities, shock waves, and Alfvénic vortices (Veltri & Mangeney 1999; Sundkvist et al. 2007; Lion et al. 2016; Wang et al. 2019). The intermittency will influence the measured statistical properties of the fluctuating quantities. For example, the growth of flatness with decreasing scales indicates the existence of intermittency. Plenty of simulation works (Servidio et al. 2011; Karimabadi et al. 2013; Tenbarge & Howes 2013; Wan et al. 2015, 2016; Zhang et al. 2015) have indicated that dissipation, acceleration, and thermalization of turbulent plasmas mainly take place near intermittent structures on kinetic scale, while the actual physical mechanisms behind dissipation remain unclear. There are a variety of diagnostic approaches to measure intermittency. (1) Probability density functions (PDFs) of scale-dependent field increments develop heavy tails because of intermittency, and the tail is more enhanced with increasing intermittency (Marsch & Tu 1994). (2) The scale dependency of the normalized fourth-order moment, known as flatness, 





, where δv = v(t + τ)−v(t), is an alternative representation. This quantity increases as the intermittency becomes more significant along with decreasing scales. (3) The p-th order structure function, 





, will be larger than that for Gaussian PDF without intermittency and the scaling exponent, ζ(p), has a nonlinear form when intermittency presents. Based on such diagnostic approaches, the properties of intermittency in plasmas have been widely investigated in the solar atmosphere, magnetosheath, solar wind, termination shock, etc. (Burlaga 1991a, 1991b; Marsch & Liu 1993; Horbury et al. 1995; Macek et al. 2011, 2017; Chasapis et al. 2018). These observational analyses have revealed that intermittency is widely existing in the heliosphere and immensely influencing plasma dynamics.
Citation: Wang et al. 2019
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The distributions of separations at apoapsis and periapsis from our LSMC analysis shown in the left panel of Fig. 11 indicate a range at 68%∼18–57 au. If the companion is coplanar with the outer disk, a ∼0.25 M⊙ companion with a 50 au apoapsis and e ∼ 0.5 − 0.7 would in principle create a region of orbital instability extending out to ∼100 au (Holman & Wiegert 1999), which is the innermost possible location for the outer disk (e.g., Fukagawa et al. 2006; Casassus et al. 2012; Rameau et al. 2012; Rodigas et al. 2014; Avenhaus et al. 2017). Nevertheless, the inclination and longitude of node of HD 142527B disagree with those of the outer circumstellar disk (i = 28°, Ω = 160°, Verhoeff et al. 2011; Perez et al. 2015), as has been reported by Lacour et al. (2016). This result would at first sight rule out that HD 142527B is responsible for the outer disk truncation. However, recent hydrodynamical simulations have shown that for an eccentric companion with an almost polar inclination to the outer disk that approaches its periapsis passage, the interactions of companion and disk can reproduce several of the main observed disk features, such as its large cavity, and with the correct position angles, its spiral features and shadows (Price et al. 2018). This orbital configuration is broadly consistent with the results from our orbital analysis. On the other hand, the orbital plane of the companion is close to the plane of the inner circumstellar disk, as previously suggested by Lacour et al. (2016). The inner disk has a position angle of 110 ± 10° from CO(6-5) kinematics measured with ALMA (Casassus et al. 2015). Its mean radius is estimated to be about 10 au from near-infrared interferometric observations (Anthonioz et al., in prep.). From MIR imaging and SED modeling, Verhoeff et al. (2011) derived a maximum radial extension for the inner disk up to 30 au. However, Avenhaus et al. (2014) imaged the inner circumstellar environment down to ∼0.1″ (15 au) in polarized scattered light with NaCo, but did not detect traces of an inner disk. More recently, Avenhaus et al. (2017) imaged the disk in visible polarized light with SPHERE down to 25 mas (∼4 au) and found evidence for dust scattering close to the star, although it remains unclear if this scattering is related to the inner disk because of geometrical discrepancies with predictions from a modeling of the shadows projected onto the outer disk (Marino et al. 2015). Using our orbital analysis of the companion, we derived the distribution of its separation at periapsis (Fig. 11, right panel) and find a 68% confidence interval of ∼10 − 12 au. This results indicates that the shape of the inner disk is strongly affected by HD 142527B.
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Citation: Avenhaus et al. (2014)
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