The Unified Models for Black Hole Accretions

Abstract

Decades of observations and theoretical studies present intriguing results about black hole accretions: supermassive black holes (SMBHs), located in the centers of galaxies, are accreting similar to Galactic stellar-mass black hole systems (GBHs). This is the unified model of black hole accretion, which indicates active galactic nuclei (AGNs, the accreting SMBHs) are only the scaled-up version of galactic X-ray binaries (XRBs, the accreting GBHs). The analogy between AGNs and XRBs ensures us to determine AGN evolutions on cosmological timescales by simply studying the quick-playing Galactic systems, which is much easy in observation and modeling. X-ray emission is produced by the inner region of the accretion disk and corona, which is close to the black holes and provides the diagnostics of accretion strength. Meanwhile, radio emission is an indicator of the ejection process, which is another fundamental part of accreting black holes. Furthermore, accreting flows are also regulated by black hole masses and accretion rates/Eddington ratios. Therefore, the unified model of black hole accretion is the correlation between accretion and ejection process and black hole masses. In this chapter, we will review models concerning the unified model of black hole accretions and present recent updates in this area.

1. Introduction

Stellar-mass black holes, formed from the direct collapses of massive stars [1], are widely observed in the Universe. In contrast, supermassive black holes (SMBHs, ${10}^6-{10}^{10}{M}_{\odot }$) are also common in the centers of galaxies with bulges [2]. The accretion process is found in both stellar-mass black holes and supermassive black holes. Stellar-mass black holes accrete matters from a companion star and form X-ray binaries (XRBs). While, the accreting supermassive black holes at the centers of galaxies are observed as active galactic nuclei (AGNs), and they accrete matters from their host environment. Observations show that the structure of accretion flows around both XRBs and AGNs are similar and depend primarily on the accretion rates in terms of Eddington ratios. The accretion state transitions are associated with the evolution of Eddington ratios. With the evolution of Eddington ratios, the accretion flow or disk geometry will also change, meanwhile, resulting in multiband spectral features.

Galactic X-ray binaries (XRBs) can be well described with several distinct X-ray states, some of them being associated with jet launching [3]. A full evolution cycle of the state transition can be observed with convenient timescales (months to years), which was well explained as the evolution of accretion disk and jet-disk coupling [4]. It is now thought that the structure of 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]. The current observational picture of state/disk-jet correlation is: (a) in the “hard” state, which exists typically below a few percent of the Eddington luminosity, there is a compact and steady jet; (b) subsequently, the transition from “hard” to “soft” state always associated with a transient/episodic jet, which corresponds to a “very high state” with near/super-Eddington rates; (b) in steady “soft” states with Eddington ratio lower than the very high state, the jet production is strongly suppressed. It was noted that with the accretion rate increasing to near and moderately super-Eddington ratios, the standard disk cannot maintain its geometry and will inevitably evolve into a “slim disk” [6], the corresponding state in observation was named as “ultraluminous state” [7]. The study of jet-disk coupling in “ultraluminous state” is limited to a few XRBs that can temporarily transit to super-Eddington accretion and the long-lived super-Eddington source SS 433.

The theoretical understanding of the state transition is explained as the evolution of the accretion disk. Figure 1 shows the geometry of the disk in different accretion states. The quiescent state XRBs host low accretion flow with Eddington ratio ${\lambda }_{\mathit{Edd}}<0.01$ [9]. The accretion flow in a quiescent state can be described as advection-dominated accretion flows (ADAFs, Narayan and Yi [10]). The advection-dominated accretion flows are radiatively inefficient (Shapiro et al. 1976). With the increase in accretion rates, the accretion flow of X-ray binaries transit to a geometrically thin accretion disk, i.e., the so-called standard accretion disk or Shakura-Sunyaev disk [11]. During this state, the X-ray spectrum becomes dominated by comptonized hard X-rays. With further increase of Eddington ratio, the accretion flow becomes hot and luminous, it emits soft-X-ray emission with a thermal spectrum, the spectra are characteristics as soft state. Between the low/hard state and high/soft state, there is sometimes an intermediate state, corresponding to an unstable accretion flow. In the intermediate state, the accretion will have an extremely high or super-Eddington accretion rate, its accretion disk is described as a slim disk. For this reason, the intermediate state is also called the very high state. Despite the success of this general picture for accretion state transitions in stellar-mass black holes, it remains unclear if supermassive black hole accretion flows undergo similar processes.

Figure 1.

Illustration of the spectral states of black hole accretion disks from [8]. The accretion rate is given in terms of the Eddington ratios.

Several schemes are successful in unifying black hole accretion flows in active galactic nuclei (AGNs) and Galactic X-ray binaries (XRBs) [12, 13, 14], it is now widely accepted that supermassive and stellar-mass black holes have similar physics in accretion, i.e., AGNs and XRBs have similar accretion states and associated ejection (especially in low/hard state). Over several years, observations have built kinds of universal correlation between XRBs and AGNs: (1) the fundamental plane of black hole activity reveals a correlation among radio luminosities, X-ray luminosities, and black hole masses [12, 15]. The correlation can be well applied to both low and moderate accretion rates (in Eddington units) XRBs and AGNs. The fundamental plane correlation of black hole activity suggests that both the accretion and ejection process are regulated by black hole masses; (2) similarly, a more universal correlation is found between radio loudness and the Eddington ratio, which hints at the suppression of the ejection process with the increase of accretion rates in units of black hole masses [13, 16, 17, 18]. The correlation has a broader application as it covers from low to super-Eddington rates; (3) another fundamental correlation of black hole accretion is among the characteristic timescales of X-ray variability, bolometric luminosities, and black hole masses [19]. The correlation links the accretion process and black hole mass in both XRBs and AGNs, which indicates accreting black holes have mass regulated disk geometry; (4) The most fruitful result in studying accretion states and transitions in XRBs is the hardness intensity diagram, while in applying the scheme to AGNs, it has big problem primarily due to the extremely long timescale in evolution cycle of AGNs. Therefore, the disk-fraction luminosity diagrams [14, 20] are taken as an alternative scheme in AGNs.

However, none of the above correlations are applicable to all accretion states or Eddington ratios. Furthermore, some extreme accretion states, for example, the extremely low accretion flow, the very high/intermediate state, and the super-Eddington state, are not fully understood in studying XRBs. Especially the models for the ultraluminous/super-Eddington state are not established yet due to the short timescales in XRBs. Furthermore, for example, it’s not clear whether the accretion of intermediate-mass black holes can follow the fundamental plane of black hole activity. It is thus questionable when applying the fundamental plane of black hole activity to constrain the black hole mass of AGNs in dwarf galaxies.

2. The universal correlations among accretion systems

2.1 X-ray variability

X-ray emission, produced from the inner region of the accretion disk and corona, served as a proxy of accretion properties. X-ray emissions from accreting black holes have strong variability, the timing properties of X-ray emission can be explored with the power spectral densities (PSDs), $P\left(\nu \right)\propto {\nu }^{-\alpha }$, which is a function of timescales $1/\nu$ of the variability. In both XRBs and AGNs, the PSD has a power-law spectrum. The spectral index $\alpha \approx 1$ on long timescales, while it is transient to a steep spectral index $\alpha >2$ on short timescales. The characteristic timescale, $T_{\mathrm{B}}$, on where the PSD break or transitions, is a common feature in both XRBs and AGNs. Using the timescale, $T_{\mathrm{B}}$, as a representation of black hole accretion was established with the finding of a correlation between $T_{\mathrm{B}}$ and black hole mass $M_{\mathit{BH}}$ was established by [19].

Again, it was strengthened as the break timescale is also correlated with spectral states or luminosities of both XRBs and AGNs, i.e., the low and high accretion states have different PSD profiles. Therefore, $T_{\mathrm{B}}$ is a good reflector of black hole masses and accretion states (in terms of bolometric luminosity $T_{\mathit{bol}}$). The correlation among the critical timescale $T_{\mathrm{B}}$, black hole mass $M_{\mathit{BH}}$, and bolometric luminosity $L_{\mathit{bol}}$ is fitted by [19] (see Figure 2) as Eq. (1)

Figure 2.

The predicted break timescales, $T_{\mathit{\text{predicted}}}$, derived by inserting the observed bolometric luminosities and masses into the best fit relationship (Eq. 1) to the combined sample of AGNs and GBHs [19]. Where GRS 1915$+$1105 is presented as a filled maroon star, Cyg X-1 as blue crosses, and the 10 AGN as red circles. The low-luminosity AGN (LLAGN), NGC 4395, is shown as an open crossed red circle; the other nine AGN are filled red circles. The filled green squares are NGC 5548, and Fairall 9 and the LLAGN NGC 4258.

$$log{T}_B=\left(2.10\pm 0.15\right)log{M}_{\mathrm{BH}}-\left(0.98\pm 0.15\right)log{L}_{\mathit{bol}}-\left(2.32\pm 0.2\right)$$E1

They have included 10 AGNs and 2 XRBs and with a wide range of accretion rates.

Assuming ${\dot{m}}_{\mathrm{E}}\approx {\lambda }_{\mathrm{Edd}}$, then $T_{\mathrm{B}}\approx M_{\mathrm{BH}}^{1.12}/{\dot{m}}_{\mathrm{E}}^{0.98}$, where ${\lambda }_{\mathrm{Edd}}=L_{\mathrm{bol}}/L_{\mathrm{E}}$. If the break timescale is proportional to a thermal or viscous timescale associated with the inner radius of the accretion disk, $R_{\text{disk}}$, then from the above empirical correlation, it can be deduced $R_{\text{disk}}\propto {\dot{m}}_{\mathrm{E}}^{-2/3}$. Models based on evaporation of the inner accretion disk predict $R_{\text{disk}}\propto {\dot{m}}_{\mathrm{E}}^{-0.85}$ and $T_{\mathrm{B}}\propto M_{\mathrm{BH}}^{1.2}$, which are roughly consistent with the empirical correlation.

Strong support or enhancement for this linkage, among characteristic timescale $T_{\mathrm{B}}$, black hole masses, and luminosities, comes from the correlation between $T_{\mathrm{B}}$ and emission line region in the circumnuclear region of black holes (see Figure 3). As the emission line width, the full width at the half maximum $\mathit{\text{FWHM}}$ is regulated by black hole masses and accretion rates. Therefore, the correlation between $\mathit{\text{FWHM}}$ and $T_{\mathrm{B}}$ is a straightforward product. The correlation is explored as the permitted optical emission lines in AGN whose widths (in both broad-line AGN and narrow-emission-line Seyfert 1 galaxies) correlate strongly with the characteristic X-ray timescale (see Figure 3),

Figure 3.

Correlation of optical emission linewidth $\mathit{\text{FWHM}}$ with PSD break timescale $T_{\mathrm{B}}$ from [19]. The LLAGN NGC 4395 is shown as an open crossed red circle and the other eight AGNs are filled red circles. Filled green squares are Fairall 9 and NGC 5548, their linewidths are available but whose upper break timescales are only lower limits.

$$log{T}_B=\left({4.20}_{-0.56}^{+0.71}\right)log\mathit{\text{FWHM}}-14.3$$E2

2.2 The fundamental plane of black hole activity

The fundamental plane relation among nuclear radio luminosity, nuclear X-ray luminosity, and black hole mass unified the accretion and ejection process in the compact system. The existence of such a relationship is based on the radio emission produced in a jet/outflow and the X-ray emission produced in a disk-corona system. Both radio and X-ray power are related to black hole mass and accretion rate. Therefore, the fundamental plane relation is thought to work in any accretion system, which is in quiescent and low/hard accretion state (associated with a steady ejection, see [9, 12]).

The fundamental plane of black hole activity explored by [12] is

$$log{L}_R=\left({0.60}_{-0.11}^{+0.11}\right)log{L}_X+\left({0.78}_{-0.09}^{+0.11}\right)log{M}_{\mathrm{BH}}+{7.33}_{-4.07}^{+4.05},$$E3

While the Merloni’s fundamental plane has a large dispersion when uses it to estimate black hole masses from radio and X-ray luminosities. The recent updates include correlation from [21]

$$log{L}_R=\left({0.60}_{-0.11}^{+0.11}\right)log{L}_X+\left({0.78}_{-0.09}^{+0.11}\right)log{M}_{\mathrm{BH}}+{7.33}_{-4.07}^{+4.05},$$E4

and the most recent version [22]

$$log\left(\frac{M_{\mathrm{BH}}}{{10}^8{M}_{\odot }}\right)=\begin{array}{l}\left(1.09\pm 0.10\right)log\left(\frac{L_R}{{10}^{38}\mathrm{erg}{\mathrm{s}}^{-1}}\right)\\ +\left(-{0.59}_{-0.15}^{+0.16}\right)log\left(\frac{L_X}{{10}^{40}\mathrm{erg}{\mathrm{s}}^{-1}}\right)\\ +\left(0.55\pm 0.22\right)\end{array}$$E5

Additionally, the very high/intermediate state may also produce radio ejection that can follow the same trend [see 4, they also include transient sources]. However, including sources with a very high/intermediate state induces a dispersion in the fundamental plane relation. This is primarily due to the evolution of individual radio blobs, as the radio ejecting process is episodic in this state. Compact symmetric objects (CSOs) are thought the episodic ejection produced by AGNs in a very high/transient state. There are two types of known contamination in the fundamental plane of black hole activity: (1) radio emissions from lobes will be enhanced when they propagate through a dense medium [23]; (2) X-ray emission contains a contribution from the jet, e.g., through synchrotron or inverse Compton mechanisms [24]. Furthermore, taking the radio emissions from lobes of CSOs is unmatched by the X-ray observations, because the radio emissions from lobes are substantially produced in different epochs from the core X-ray emission.

There are several works exploring the fundamental plane relation on CSOs [25, 26, 27]. Most of the results suggest CSOs do deviate from the classical trends. To be specific, an exploration of fundamental plane relation on a sample of CSOs (with radio flux density from lobes) indicates that they can follow the trend, while their radio luminosity is $\sim$1 dex higher than the original fitting of the fundamental plane relation [see 26], which is consistent with the transient state in XRBs. Another point is the vacuum region between stellar-mass black holes and supermassive black holes in the fundamental plane of black hole activity. This region can be filled by either intermediate-mass black holes or extremely low luminosity AGNs. We will discuss it in the following sections.

2.3 The inverse correlation between radio loudness and Eddington ratio

The persistent jets are ubiquitous at low accretion rates (the low/hard state) in XRBs but intermittent or entirely absent at high accretion rates (the high/soft state and the intermittent/very high state; e.g., [3, 28, 29]). Resembling the inverse correlation between the radio luminosity of jets and X-ray luminosity in XRBs, Ho [16] found a similar inverse correlation between radio-loudness ($\mathrm{ℛ}=L_{\nu 5}/L_{\mathit{\nu B}}$) and the Eddington ratio (${\lambda }_{\mathit{Edd}}=L_{\mathit{bol}}/L_{\mathit{Edd}}$) in AGNs. In this scheme, radio-loud AGNs with powerful relativistic jets often have low Eddington ratios and vice versa. In contrast to the fundamental plane relation only being valid for certain conditions, the inverse correlation between $\mathrm{ℛ}$ and ${\lambda }_{\mathit{Edd}}$ is ubiquitous in both AGNs and XRBs [18] although with a large scatter. A global analogy between stellar-mass black holes and SMBHs has been established in the $\mathrm{ℛ}$ and ${\lambda }_{\mathit{Edd}}$ correlation: low-luminosity AGNs are similar to XRBs in the low/hard state, and with the high- or super-Eddington accreting AGNs (e.g., NLS1s) being an analogy of XRBs in the high/soft and the very high state. It should be noted here that only a few XRBs experience transitions from classical spectral states to the super-Eddington regime [30]. The super-Eddington accretion state is poorly understood primarily because of the extremely short timescales of the spectral state transition in XRBs. Therefore, the study of the production and quenching of AGN jets in super-Eddington accretion systems will shed light on the physical properties of AGNs during this short-lived spectral state (Figure 4).

Figure 4.

Radio loudness $\mathrm{ℛ}$ vs Eddington ratio ${\lambda }_{\mathit{Edd}}$. The markers are designated in the left-bottom corner and the error bars in some extremely high Eddington ratio accreting SMBHs come from the uncertainty of the BH spin. The vertical dotted line is ${\lambda }_{\mathit{Edd}}=1$ and the horizontal dotted line at $\mathrm{ℛ}=10$ represents the division between radio-loud (above) and radio-quiet (below) sources.

In the work by Yang et al. [13], the inverse correlation between radio loudness and the Eddington ratio has been extended to the super-Eddington regime. It was shown that the correlation is even more fundamental than between radio and X-ray luminosity and black hole mass, as the correlation works among extremely low-power accreting black holes. However, the radio loudness-Eddington ratio correlation has a large dispersion, and it suggests there is an additional parameter at work.

2.4 X-ray loudness versus Eddington ratio

It is impossible to observe a whole state transition in AGNs due to their extremely long evolutionary timescales. While, fortunately, an unbiased sample of AGNs will naturally have a mixture of AGNs in various accretion states, e.g., an AGN sample includes low-luminosity AGNs (LLAGNs), low-excitation emission line regions (LINERs), and narrow line Seyfert I galaxies (NLS1s). The properties/structures of the accretion disk and corona are represented by the X-ray loudness or UV to X-ray spectral index ${\alpha }_{\mathrm{ox}}$, which is defined, for example [31], as

$${\alpha }_{\mathrm{ox}}=-\frac{log{\left(\nu L_{\nu }\right)}_{\mathrm{o}}-log{\left(\nu L_{\nu }\right)}_{\mathrm{x}}}{log{\nu }_{\mathrm{o}}-log{\nu }_{\mathrm{x}}}+1,$$E6

Where ${\left(\nu L_{\nu }\right)}_{\mathrm{o}}$ and ${\left(\nu L_{\nu }\right)}_{\mathrm{x}}$ are monochromatic immensities at the rest-frame optical/UV and X-ray energies, ${\lambda }_{\mathrm{o}}=c/{\nu }_{\mathrm{o}}=2500\AA$ and $E_{\mathrm{x}}=h{\nu }_{\mathrm{x}}=2\mathrm{keV}$, respectively; correlates primarily with $L_{\nu ,x}$; and that there is a strong correlation between $L_{\nu ,\mathrm{o}}$ and $L_{\nu ,\mathrm{x}}$ (Figure 5).

Figure 5.

The transition behavior along X-ray loudness ${\alpha }_{\mathrm{ox}}$ versus Eddington ratio $L/L_{\mathrm{Edd}}$ [31]. A change of the sign of the ${\alpha }_{\mathrm{ox}}$ can be observed for $L/L_{\mathrm{Edd}}=0.01$. The transition behavior is free of black hole masses. The dotted and dashed lines correspond to the correlations found by Lusso et al. [32] and Grupe et al. [33], respectively.

A characteristic spectral behavior was found by taking the typical galactic X-ray binary GRO J1655$-$40 as a template, which drives a complete state transition within 1 year. The X-ray loudness versus Eddington ratio distribution has a “V”-shaped morphology, i.e., in low Eddington ratios of $L_{\mathrm{bol}}/L_{\mathrm{Edd}}<0.01$, the X-ray loudness has an inverse correlation with Eddington ratio, while in higher Eddington ratios of $L_{\mathrm{bol}}/L_{\mathrm{Edd}}>0.01$, XRBs show a positive correlation between X-ray loudness and Eddington ratio.

The correlation between X-ray loudness and Eddington ratio can be explained as the evolution of accretion flow along with accretion state transition. In the quiescent state, $L_{\mathrm{bol}}/L_{\mathrm{Edd}}<0.01$, the accretion disk is described as the radiatively inefficient advection-dominated accretion flow (ADAF) and drives a compact jet, where ADAF dominates the UV emission and corona dominate X-ray emission. Furthermore, the jet may also contribute to UV and X-ray emissions in this state. With the increase of Eddington ratios in this state, (1) the inner ADAF will progressively fall to touch with the outer thin disk (SSD), leading to a decrease in UV emission; (2) the corona will extend upward from the accretion disk and enhance the X-ray emission. Eventually, the increase of the Eddington ratio in this state leads to the hardening of the UV to X-ray spectrum. With the further increase of Eddington ratios from $L_{\mathrm{bol}}/L_{\mathrm{Edd}}=0.01$ to $1$, the hot accretion flow of the thin disk produces strong thermal UV emission and the corona will be suppressed into small scale. This leads to a signature that with the increase of Eddington ratios the UV to X-ray spectrum will gradually soften and result in the positive correlation between ${\alpha }_{\mathrm{ox}}$ and $L_{\mathrm{bol}}/L_{\mathrm{Edd}}$.

It should be expected that XRBs and AGNs have a similar accretion flow and evolution scheme, which corresponds to the straightforward XRB/AGN analogy. The correlation between ${\alpha }_{\mathrm{ox}}$ and $L_{\mathrm{bol}}/L_{\mathrm{Edd}}$ was found in a large unbiased sample of AGNs [34, 35, 36, 37, 38, 39, 40], indicating that the different types of AGNs have an evolutionary connection with each other and the AGN accretion flow may evolve similarly with XRBs. Recently, a fascinating finding is that the changing-look AGNs evolve along the ${\alpha }_{\mathrm{ox}}$ vs. $L_{\mathrm{bol}}/L_{\mathrm{Edd}}$ trend, which hints at the state transition in individual AGN.

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, 43, 44, 45, 46, 47, 48, 49, 50, 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 jet-disk 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, 43, 44, 46, 47, 48, 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, 56, 57, 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, 59, 60, 61, 62]. In particular, unambiguous detection of both powerful radio jets and radio-emitting winds was reported only in the Galactic microquasar SS 433 [63, 64, 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., $M_{\mathrm{BH}}={10}^7{M}_{\odot }$) would last ${10}^6$ times longer than in $10M_{\odot }$ stellar-mass 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, $M_{\mathrm{BH}}={10}^2-{10}^6{M}_{\odot }$) 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, $M_{\mathrm{BH}}={10}^6-{10}^{10}{M}_{\odot }$) 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 ${10}^{10}{M}_{\odot }$ [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, $M_{\mathrm{BH}}={10}^2-{10}^6{M}_{\odot }$ 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$$M_{\odot }$) originate from the end stages of the evolution of massive stars, as has been inferred from studies of X-ray binaries (BH actively accreting from a companion star) in our Galaxy. Supermassive BHs (SMBHs; $\ge {10}^6$$M_{\odot }$) on the other hand are resident at the centers of most massive galaxies. These have been mainly inferred through their role in the evolution of the host galaxy (through the correlations of the SMBH mass with the galactic bulge properties, including the dispersion velocity, luminosity, and mass). As there have been deductions of SMBH hosts even in the early Universe (less than a Gyr) through their observational signatures (accretion power and nuclear activity), modes of growth to such large masses (${10}^6-{10}^{10}$$M_{\odot }$) remain debatable. Possibilities include mergers and accretion activity. These scenarios require a rapid progression involving lower mass seed BHs, which are plausible. The presence of intermediate-mass BHs (IMBHs; ${10}^2-{10}^6$$M_{\odot }$) can help realize these scenarios more efficiently than lower mass seed BHs.

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 $\mathit{\text{Chandra}}$ observation [72].

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${}^{\ast }$ are from Merloni, Heinz, and di Matteo [12]. Note that the radio luminosities for NGC 3628, NGC 4293, and J1115$-$0004 are only upper limits.

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 low-power 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, 76, 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 $\sim {10}^{-8.5}$ [81]. The X-ray emission of M32’s AGN is detected by $\mathit{\text{Chandra}}$ [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 $\sim 4$ and $\sim 1.5$ parsec, respectively. Again, the IMBHs NGC 404 and NGC 4395 are both low-luminosity AGNs, they have Eddington ratio ${\lambda }_{\mathrm{Edd}}=1.5\times {10}^{-6}$ [72] and $1.2\times {10}^{-3}$ [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 $\sim 1$ 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 $\sim$1 and $\sim$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 ($z=0.017$), 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 wide-angled/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 $\sim {10}^{-5}$ 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 $\sim$ 30 years; (3) recently, we have successfully detected an increase of radio flux density, which is $\sim$ 700 and $\sim$ 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).

4. Conclusion and future directions

Accretion is an essential process to drive black hole growth, and it is thought to work in different types of accreting black hole systems from stellar-mass galactic black holes to supermassive black holes located in the centers of galaxies. Now, we are near to reaching a consensus that the physics in controlling the accretion and the associated ejecting process is exactly same in various kinds of accreting systems. In this chapter, we explored the correlations concerning the universal evolution among various accreting systems: (1) the correlation among X-ray variability, the black hole mass, and bolometric luminosity; (2) the fundamental plane of black hole activity, i.e., the correlation among core X-ray and radio luminosity and black hole mass; (3) the inverse correlation between radio loudness and Eddington ratio; (4) the correlation between X-ray loudness and Eddington ratio. These evidences ensure us to apply the theory to study the accretion process in, e.g., high red-shift quasars, the evolutionary connection between FRI and FRII radio galaxies, and the accretion signatures of low luminosity AGNs, and so on. However, the unified models for black hole accretions still face challenges in a few types of cases in practical applications: (1) the extremely high and super-Eddington accreting systems are poorly understood in both XRBs and AGNs; (2) the intermediate region between stellar-mass black holes and supermassive black holes in the fundamental plane of black hole activity is still unfilled; (3) the intermediate-mass black holes are absent; (4) the lack of evidence of state transition in individual AGNs still throws doubt on the unified scheme in AGNs. Furthermore, the unified models for black hole accretion have weak constraints and well understanding of the ejection process. Especially, in radio-quiet AGNs, corona and wind-like outflows are the two primary radio-emitters except for the jets, while it is unclear how the three processes interplay with each other and which one is in holding the dominance with the accretion flow evolves. Future high-resolution observations are essential to identify the radio origin. Additionally, it may shed light on how jet bases connect with accretion disk and how jet forms. Again, the high-resolution radio observations of intermediate-mass black holes and super-Eddington AGNs are equally important in filling the break between XRBs and AGNs in the fundamental plane of black hole activity and extending it to the super-Eddington regime.