The 2D Disk Structure with Advective Transonic Inflow–Outflow Solutions around Black Holes

Abstract

We solved analytically viscous two-dimensional (2D) fluid equations for accretion and outflows in spherical polar coordinates (r, θ, φ) and obtained explicitly flow variables in r− and θ−directions around black holes (BHs). We investigated global transonic advection-dominated accretion flow (ADAF) solutions in r−direction on an equatorial plane with using Paczyński-Wiita potential. We used radial flow variables of ADAFs with symmetric conditions on the equatorial plane, as initial values for integration in θ−direction. In the study of 2D disk structure, we used twoazimuthal components of viscous stress tensors namely, τ rφ and τ θφ . Interestingly, we found that the whole advective disk is not participating in outflow generation and the outflows form close to the BHs. Normally, outflow strength increased with increasing viscosity parameter (α 1 ), mass-loss parameter (s) and decreasing gas pressure ratio (β). Outflow region increased with increasing s, α 1 for τ rφ and decreasing α 2 for τ θφ . The τ θφ is effective in angular momentum transportation at high latitude and outflows collimation along an axis of symmetry since it changes polar velocity (v θ ) of the flow. The outflow emission is also affected by the ADAF size and decreased with decreasing it. Transonic surfaces formed for both inflows (v r < 0, very close to BH) and outflows (v r > 0). We also explored no outflows, outflows and failed outflows regions, which mainly depend on the viscosity parameters.

Self-similar Solutions for Finite Size Advection-dominated Accretion Flows

“…We kept λ 0 in the E A because λ 0 becomes comparable to λ K , when r OB is close to the BH, otherwise λ 0 << λ K . The ADAF solutions with E A are also obtained in Kumar & Gu (2018). We calculated the size r OB of the ADAFs corresponding to E A for given λ 0 is represented in a panel (a) of Figure 1.…”

“…First, all the three flows can coexist with a possible configuration, in that the outer part is the cool KD flow (E K ) and the inner part is the hot sub-Keplerian ADAF (E A ) around the equatorial plane (like two-zone radial geometry), and both flows can be covered partially or fully (depends on the smooth/shocked solutions and also may depend on the sources of the hot accreting gas) with hot sub-Keplerian gas (E h ), because this flow has lowest λ distribution with higher the disk thickness from the flow with E A . For instance, Kumar & Gu (2018) have found that the supersonic and subsonic regions are formed above the equatorial plane in the inner part of some 2D disk structures, and both regions are connected with the shock like sharp transitions but close to the equatorial plane, the flow is always subsonic, before the inner CP. Second, the two flows can coexist as described in Wandel & Liang (1991), and any other flow is negligible, e.g., the outer part is the cool KD and the inner is the hot sub-Keplerian ADAF, which is referred to as the two-zone radial configuration geometry flow (Esin et al 1997), or the cool KD is covered with hot sub-Keplerian flow (E h ) with extending to the BH horizon, which is referred to as the sandwich geometry or two-component accretion flow (TCAF) (Chakrabarti & Titarchuk 1995).…”

“…where s is the mass loss parameter (Kumar & Gu 2018). Here r b is an outer radius of the outflowing disk, andṀ b is the mass-accretion rate at r b .…”

Stochastic Acceleration of ∼0.1–5 keV Pickup Ions in the Heliotail

“…For the purposes of this study, we focus on the transport of protons down the heliotail including charge-exchange, adiabatic heating, and stochastic acceleration based on a single initial proton distribution (Equation (9)). In future studies, other distributions will be tested, e.g., multiple Maxwell-Boltzmann or filled-shell distributions (e.g., Vasyliunas & Siscoe 1976;Zank et al 2010;Zirnstein et al 2014Zirnstein et al , 2017, distributions based on more complex variations of PUI transport and processing in the supersonic SW (e.g., Isenberg 1987;Chalov et al 1995Chalov et al , 1997Schwadron et al 1996;le Roux & Ptuskin 1998;Schwadron 1998;Fahr & Lay 2000;Fahr et al 2007;Wu et al 2016;Zank 2016), as well as distributions derived from particle-in-cell simulations of acceleration at the TS (e.g., Matsukiyo & Scholer 2014;Yang et al 2015;Kumar et al 2018). Models of PUI transport should also be compared directly with observations of PUIs in the supersonic SW made by New Horizons' Solar Wind Around Pluto (SWAP) instrument (McComas et al 2008(McComas et al , 2017bRandol et al 2012Randol et al , 2013, which are the only direct observations of PUI distributions beyond ∼5 au from the Sun.…”

“…McComas et al (2017b) analyzed the interstellar hydrogen and helium PUI distributions from ∼20 to 38 au from the Sun, and found that the functional form of the isotropic, filledshell distribution from Vasyliunas & Siscoe (1976) can be used to quantify the interstellar hydrogen and helium PUI distributions in the supersonic SW at ∼20-40 au from the Sun, but that the parameters of the distribution are not realistic most of the time in the vicinity of shocks or compressional waves. For the purposes of this paper, however, our model assumptions are reasonable based on our current knowledge of the proton distribution downstream of the TS at high energies from the Voyager spacecraft (e.g., Decker et al 2005) and the inference that PUIs are likely heated and accelerated to higher energies at the TS (e.g., Zank et al 1996Zank et al , 2010Richardson 2008;Yang et al 2015;Kumar et al 2018).…”