**3. In extreme cases**

### **3.1 Extremely high and super-Eddington accretion**

Accretion of black holes at near-Eddington or super-Eddington rates is the most powerful episode in nursing black hole growth [41], and it may work in several types of objects [13, 42–51]. It is still unclear whether the AGN/XRB analogy holds in the "ultraluminous state," and whether the geometry of the disk-corona system and jetdisk coupling are similar. Since it is impossible to observe the whole burst cycle of an individual AGN as the timescale is proportional to the black hole mass [13, 14], the previous studies rely on a large enough unbiased sample of AGNs, which naturally contains a mixture of objects in different spectral states. While near/super-Eddington AGNs provide an opportunity that it has a longer timescale than the short-lived "ultraluminous state" in XRBs and potentially connect with long-lived super-Eddington sources (SS 433 and ultraluminous X-ray sources). On the other hand, the jet is a long-lived emitter that saved long timescale information of an accretion state. Observationally confirming jet properties of the less explored "ultraluminous state" in AGNs would enhance the AGN/XRB analogy, as it enables us to eventually apply our understanding of X-ray binaries to explain AGN phenomenology (and vice versa). On the other hand, the study of near/super Eddington AGNs will shed light on our understanding of the physics to sustain a near/super-Eddington accretion and how the episodic jet works in this state.

The physics of accretion and jet-disk coupling in such a state remains unclear [52], mainly because the associated jets are not easily detectable due to the extremely weak or episodic nature of the jets. Although a few near/super Eddington objects have demonstrated jet activity [42–44, 46–49, 51, 53, 54], in most of these systems, such as super-Eddington active galactic nuclei (AGNs) [13] and ultraluminous X-ray sources [45], it remains doubtful whether there is jet emission. Recent observations [13, 55–58] suggest that the radio emission in near/super-Eddington AGNs comes from the nuclear region, with possible contributions from hot corona, accretion disk winds, fossil radio jet, or a combination of all above [13, 55, 58–62]. In particular, unambiguous detection of both powerful radio jets and radio-emitting winds was reported only in the Galactic microquasar SS 433 [63–65], while accretion disk wind is believed to be ubiquitous in the near/super-Eddington accretion mode.

It is now thought that the structure of the accretion flows and jet production depends primarily on the Eddington ratio. As the Eddington ratio fluctuates, the accretion flow transitions dramatically into different states, each with distinct geometries and multiwavelength spectral characteristics [5]. As the accretion rate increases to near or super-Eddington ratios, the standard disk geometry cannot be maintained and the accretion flow will inevitably evolve into a "slim disk" [6]. The corresponding state is sometimes called the "ultraluminous state" [7]. Studies of jet-disk coupling in "ultraluminous state" have been limited to a few XRBs that can temporarily transit to super-Eddington accretion and to the long-lived super-Eddington source SS 433. It is also widely accepted that supermassive and stellar-mass black holes have similarities in accretion physics, i.e., AGNs and XRBs have similar accretion state transitions and

associated jet ejection. However, it is still unclear whether the AGN/XRB analogy holds in the "ultraluminous state" and whether the geometry of the disk-corona system and jet-disk coupling are similar. Here, our interest is the connection between the short-lived canonical "very high state" in XRBs with the long-standing super-Eddington accretion in the microquasar SS 433 and ULXs, to determine which parameters are driving the long-lived super-Eddington accretion. As the time scale of state transition is proportional to the black hole mass [13, 14], a "very high state" in SMBHs (e.g., *<sup>M</sup>*BH <sup>¼</sup> <sup>10</sup><sup>7</sup> *<sup>M</sup>*⊙) would last 10<sup>6</sup> times longer than in 10*M*<sup>⊙</sup> stellarmass black holes found in XRBs. Therefore, the study of near/super-Eddington AGNs provides an opportunity to understand the ejection process in a quasi-steady "very high state" and may shed light on the physics to sustain a near/super-Eddington accretion.

#### **3.2 Intermediate mass black holes**

Directly connecting stellar-mass and supermassive black holes requires intermediate-mass black holes [66]. In the unified model of black hole accretion, filling intermediate-mass black holes will build a continuous distribution of accretion parameters. It is now widely accepted that the existence (or not) of intermediate-mass black holes (IMBHs, *<sup>M</sup>*BH <sup>¼</sup> <sup>10</sup><sup>2</sup> � <sup>10</sup><sup>6</sup>*M*⊙) is an even more fundamental question, and it has an essential impact on our theoretical deduction of black hole formation and evolution [see 18, and references therein]. It is believed that stellar-mass black holes are formed from the direct collapse of massive stars [1]. Such black holes are known to be abundant in our Galaxy. On the other hand, supermassive black holes (SMBHs, *<sup>M</sup>*BH <sup>¼</sup> <sup>10</sup><sup>6</sup> � <sup>10</sup><sup>10</sup>*M*⊙) are universally found in the centers of massive galaxies with bulges [2]. Mergers and accretion are known as the primary and effective ways to drive black hole growth. Observations indicate SMBHs with masses up to 10<sup>10</sup>*M*<sup>⊙</sup> [67, 68] have already existed when the Universe was only 5% of its current age. However, to assemble SMBHs through accretion would require dramatic feeding, which poses a severe challenge to the formation of SMBHs [see 18]. Seed black holes with intermediate-mass [IMBHs, *<sup>M</sup>*BH <sup>¼</sup> <sup>10</sup><sup>2</sup> � <sup>10</sup><sup>6</sup> *<sup>M</sup>*<sup>⊙</sup> are needed in the very early Universe when the first-generation SMBHs have not formed.

Astrophysical black holes (BHs), inferred through their observational signatures (electromagnetic, gravitational waves), are currently understood to fall into two categories based on their mass. Stellar-mass BHs (3 � 100 *M*⊙) originate from the end stages of the evolution of massive stars, as has been inferred from studies of X-ray binaries (BH actively accreting from a companion star) in our Galaxy. Supermassive BHs (SMBHs; ≥10<sup>6</sup> *M*⊙) on the other hand are resident at the centers of most massive galaxies. These have been mainly inferred through their role in the evolution of the host galaxy (through the correlations of the SMBH mass with the galactic bulge properties, including the dispersion velocity, luminosity, and mass). As there have been deductions of SMBH hosts even in the early Universe (less than a Gyr) through their observational signatures (accretion power and nuclear activity), modes of growth to such large masses (10<sup>6</sup> � <sup>10</sup><sup>10</sup> *<sup>M</sup>*⊙) remain debatable. Possibilities include mergers and accretion activity. These scenarios require a rapid progression involving lower mass seed BHs, which are plausible. The presence of intermediate-mass BHs (IMBHs; 102 � <sup>10</sup><sup>6</sup> *<sup>M</sup>*⊙) can help realize these scenarios more efficiently than lower mass seed BHs.

**Figure 6.**

*The fundamental plane relation of black hole activity based on [12]. The references in the legend show where the radio luminosity was taken. The black open squares and data for Sgr A*<sup>∗</sup> *are from Merloni, Heinz, and di Matteo [12]. Note that the radio luminosities for NGC 3628, NGC 4293, and J11150004 are only upper limits.*

IMBHs can follow the fundamental plane of black hole activity. This indicates that an outflow-disk-corona system still exists and is tightly related even in these systems. In **Figure 6**, we also include two well-studied IMBHs NGC 4395 and NGC 404. Especially, we take recently measured black hole mass of NGC 4395 [69] and NGC 404 [70]. Again, we take radio luminosity of NGC 404 from VLA A-array 5 GHz observation [71], which captured radio emission from the nuclear 7 parsec scale region; we take 5 GHz radio luminosity of NGC 4395 transferred from VLA A-array 15 GHz observation [21], which captured radio emission from the nuclear 4 parsec scale region. Because of low redshift, the VLA observation of NGC 4395 and NGC 404 obtained a resolution of parsec scale, which is comparable with VLBI observations on slightly high red-shift AGNs. We take the X-ray luminosity of NGC 404 from *Chandra* observation [72].

#### **3.3 Low-luminosity AGNs**

In addition to the requirement of IMBHs, low-luminosity AGNs will touch the most luminous stellar-mass black holes in the fundamental plane of black hole activity. In quiescent state XRBs, there exist compact radio emissions and are thought to be short and steady jets, while the nature is unclear. However, in low-luminosity AGNs, radio emissions from the core region are consistent with wind-like outflows or lowpower jets. Synchrotron emission as the result of propagating shocks produced and sustained by the injection of new material at the base of the outflow accelerated electrons downstream to relativistic energies. Low luminosity sub-Eddington emitting sources could host advection dominated accretion flows [ADAFs, 73] that are radiatively inefficient in the inner region [e.g., 16]. This can include nearby dwarf

galaxies (low mass low luminosity systems) hosting an inner truncated region, with the outer thin disk accretion [optically thick, geometrically thin, e.g., 31] transitioning into an ADAF [74]. Radio emission in these systems can be contributed to by the ADAF but is likely to be dominated by the jet or outflow [75–77], with observable signatures including shock ionization of the gas in the nuclear region [e.g., 78, 79].

It was shown that such low accretion flow deviates from the plane [80]. While in exploring the universal correlation between XRBs and AGNs, one should obtain radio emissions from the same radius, i.e., with regard to the Schwarzschild radius. Therefore, a moderate resolution is enough in a few nearby AGNs. M32 is one of the prominent low-luminosity AGNs with an Eddington ratio of only � <sup>10</sup>�8*:*<sup>5</sup> [81]. The X-ray emission of M32's AGN is detected by *Chandra* [81]. The radio luminosity was obtained from VLA B-array 6.6 GHz [82] and VLA A-array 6 GHz [83] observations. The two VLA observations of M32 obtained a resolution of � 4 and � 1*:*5 parsec, respectively. Again, the IMBHs NGC 404 and NGC 4395 are both low-luminosity AGNs, they have Eddington ratio *<sup>λ</sup>*Edd <sup>¼</sup> <sup>1</sup>*:*<sup>5</sup> � <sup>10</sup>�<sup>6</sup> [72] and 1*:*<sup>2</sup> � <sup>10</sup>�<sup>3</sup> [84], respectively. We note that these low-luminosity and low (or intermediate)-mass AGNs tend to have steep radio spectra and diffuse radio emissions. The radio emissions fall below the detection threshold with the resolution higher than � 1 parsec scale (Yang et al. In preparation) [72, 83], which results in underestimation of radio luminosity in the fundamental plane. Therefore, the radio emission can be explained as wind-like outflows driven by weakly accreting AGNs [85]. As the fundamental plane of black hole activity looks reliable for most low-mass AGNs, which suggests that a moderate resolution, as well as high sensitivity, should be taken to fully collect wind-like radio emission produced by the central engine but avoid contamination from hosts, i.e., between �1 and �10 parsec scale region. In exploring the fundamental plane relation of black hole activity for both XRBs and AGNs, it is reasonable to constrain radio emission from a similar region with regard to Schwarzschild radius. Meanwhile, it's still possible that low-luminosity AGNs deviate from the fundamental plane relation [e.g., 80].

#### **3.4 Capturing the state transition in AGNs**

Changing-look AGNs (CLAGNs) are a subclass of AGNs, they change the spectral type from type 1 to type 2 (disappearance of the broad emission line) or vice versa (emergence of the broad emission line) on timescales shorter than a few years [86]. The spectral-type changes in CLAGNs are commonly associated with multiband continuum behaviors [86]. The changing look of AGNs challenges the unified model of AGN [87, 88]; however, it provides a chance to explore the dramatic state transition in AGNs.

Directly capturing the changing-look events when it is in the act is essential to explore the accretion state transition in AGNs. The chance comes from 2018, a rapid spectral-type change was observed in the Seyfert 2 AGN 1ES 1927 + 654 (*z* ¼ 0*:*017), which was followed up with multiband observations, including in the X-ray, optical, and radio wavelengths. The All-Sky Automated Survey for SuperNovae (ASAS-SN) first reported an optical flare from the nuclear region of 1ES 1927 + 654 on 2018-2103- 03 [ATel #11391, 89]; this was accompanied by the emergence of broad Balmer lines in the optical spectrum [90] with the consequent classification as a changing-look AGN (from Type 2 to Type 1). The Neutron star Interior Composition Explorer (NICER) observations of 1ES 1927 + 654 (on 2018-2105-22) found an extremely soft

X-ray spectrum and a continued decrease in the X-ray luminosity [ATel #12169, 91] compared with archival data. This is followed by the NICER detection of an increase in the X-ray luminosity beyond 1st July [ATel #12169, 91], 4 months after the optical outburst. The dense optical/UV and X-ray monitoring observations [90, 92] confirm the changing-look nature of 1ES 1927 + 654.

1ES 1927 + 654 has been reported to show unusual timing and spectroscopic properties. The nuclear region is relatively unobscured based on a low neutral gas column density from X-ray observations (lack of sufficient absorbing gas along the line of sight); this and timing properties are reminiscent of a Seyfert type 1 [93]. However, optical spectroscopic observations reveal a Seyfert type 2 nuclear region [93, 94]. These pose challenges for the line-of-sight-based AGN unification model [e.g., 63]. A previous lack of broad optical emission lines typical of Seyfert type 2 galaxies with their prominent appearance post the changing-look event [90], accompanied by a relatively unobscured X-ray emission [95], suggests an origin (of the emission lines and the changing-look event) associated with physical processes in the accretion flow. The studies of [92, 95] find an X-ray spectrum dominated by the soft (black-body, disk) continuum with the disappearance of the hard power-law component following the optical/UV outburst. The disappearance and subsequent reappearance of the power-law component (with an accompanying increase in luminosity) are interpreted as the destruction and recreation of the accretion disk. One of the promising models for the changing look in 1ES 1927 + 654 is the consequent evolution of the jet/outflow and radiative properties [96].

The radio emission can originate from an outflow (collimated/relativistic or wideangled/nonrelativistic). Propagating shocks either internal to the outflow [injection events from accretion – outflow activity, e.g., 97] or as a consequence of its interaction with the surrounding medium [e.g., 98] can accelerate electrons downstream with the consequent emission of synchrotron radiation. 1ES 1927 + 654 has been studied in the radio bands, with successful VLBI observations conducted in epochs prior to, covering, and post the changing-look event. Very long baseline interferometric observations of 1ES 1927 + 654 revealed exciting results, which provide further constraint on the quick accretion state changing in this source [99]: (1) The European VLBI Network (EVN) observation during 2013–2014 yields a radio to X-ray luminosity ratio 10<sup>5</sup> and a steep radio spectrum, suggesting that the radio emission likely originates from an outflow; (2) a long-time decline in radio flux density is similar to that in the optical and X-rays, which confirms a multiband decay over past 30 years; (3) recently, we have successfully detected an increase of radio flux density, which is 700 and 450 days delayed since the optical and X-ray flare (Yang et al. ATel), respectively; (4) from the VLBA X-band observation in 2020, we have resolved for the first time the innermost structure of this source. A continued monitoring observation of radio emission is still ongoing, we are expecting to see further intriguing evidence to constrain properties of the outflow (proper motion, radiative evolution, and association with the accretion, total energy, and magnetic field strength) and surrounding environment (number density, density contrast).
