**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, <sup>10</sup><sup>6</sup> 1010*M*⊙) 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 *λEdd* <0*:*01 [9]. The accretion flow in a quiescent state can be described as advectiondominated 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

#### **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.*

#### *The Unified Models for Black Hole Accretions DOI: http://dx.doi.org/10.5772/intechopen.105416*

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.

Several schemes are successful in unifying black hole accretion flows in active galactic nuclei (AGNs) and Galactic X-ray binaries (XRBs) [12–14], 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, 16–18]. 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.
