Diffusive Particle Acceleration in Shocked, Viscous Accretion Disks: Green's Function Energy Distribution (original) (raw)
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The Astrophysical Journal, 2004
In this Letter, we suggest that the relativistic protons powering the outflows emanating from radio-loud systems containing black holes are accelerated at standing, centrifugally-supported shocks in hot, advection-dominated accretion disks. Such disks are ideal sites for first-order Fermi acceleration at shocks because the gas is tenuous, and consequently the mean free path for particleparticle collisions generally exceeds the thickness of the disk. The accelerated particles are therefore able to avoid thermalization, and as a result a small fraction of them achieve very high energies and escape from the disk. In our approach the hydrodynamics and the particle acceleration are coupled and the solutions are obtained self-consistently based on a rigorous mathematical treatment. The theoretical analysis of the particle transport parallels the early studies of cosmicray acceleration in supernova shock waves. We find that particle acceleration in the vicinity of the shock can extract enough energy to power a relativistic jet. Using physical parameters appropriate for M87 and Sgr A * , we confirm that the jet kinetic luminosities predicted by the theory agree with the observational estimates.
The Astrophysical Journal, 2008
In this Letter, we present a new self-consistent theory for the production of the relativistic outflows observed from radio-loud black hole candidates and active galaxies as a result of particle acceleration in hot, viscous accretion disks containing standing, centrifugally-supported isothermal shocks. This is the first work to obtain the structure of such disks for a relatively large value of the Shakura-Sunyaev viscosity parameter (α = 0.1), and to consider the implications of the shock for the acceleration of relativistic particles in viscous disks. In our approach, the hydrodynamics and the particle acceleration are coupled and the solutions are obtained self-consistently based on a rigorous mathematical method. We find that particle acceleration in the vicinity of the shock can provide enough energy to power the observed relativistic jet in M87.
Astrophysical Journal, 2005
Relativistic outflows ( jets) of matter are commonly observed from systems containing black holes. The strongest outflows occur in the radio-loud systems, in which the accretion disk is likely to have an advection-dominated structure. In these systems, it is clear that the binding energy of the accreting gas is emitted primarily in the form of particles rather than radiation. However, no comprehensive model for the disk structure and the associated outflows has yet been produced. In particular, none of the existing models establish a direct physical connection between the presence of the outflows and the action of a microphysical acceleration mechanism operating in the disk. In this paper we explore the possibility that the relativistic protons powering the jet are accelerated at a standing, centrifugally supported shock in the underlying accretion disk via the first-order Fermi mechanism. The theoretical analysis employed here parallels the early studies of cosmic-ray acceleration in supernova shock waves, and the particle acceleration and disk structure are treated in a coupled, self-consistent manner based on a rigorous mathematical approach. We find that first-order Fermi acceleration at standing shocks in advection-dominated disks proves to be a very efficient means for accelerating the jet particles. Using physical parameters appropriate for M87 and Sgr A Ã , we verify that the jet kinetic luminosities computed using our model agree with estimates based on observations of the sources.
Multitransonic Black Hole Accretion Disks with Isothermal Standing Shocks
The Astrophysical Journal, 2003
In this work we would like to address the issue of shock formation in black hole accretion discs. We provide a generalized two parameter solution scheme for multi-transonic, accretion and wind around Schwarzschild black holes, by mainly concentrating on accretion solutions which may contain steady, standing isothermal shocks. Such shocks conserve flow temperature by the dissipation of energy at the shock location. We use the vertically integrated 1.5 dimensional model to describe the disc structure, where the equations of motion apply to the equatorial plane of the central accretor, assuming the flow to be in hydrostatic equilibrium in the transverse direction. Unlike previous works in this field, our calculation is not restricted to any particular kind of post-Newtonian gravitational potentials, rather we use all available pseudo-Schwarzschild potentials to formulate and solve the equations governing the accretion and wind only in terms of flow temperature T and specific angular momentum λ of the flow. The accretion flow is assumed to be non-dissipative everywhere, except possibly at the shock location, if any. We observe that a significant region of parameter space spanned by {λ, T } allows shock formation. Our generalized formalism assures that the shock formation is not just an artifact of a particular type of gravitational potential, rather inclusion of all available black-hole potentials demonstrates a substantially extended zone of parameter space allowing for the possibility of shock formation. We thus arrive at the conclusion that the standing shocks are essential ingredients in rotating, advective accretion flows of isothermal fluid around a non-spinning astrophysical black hole. We identify all possible shock solutions which may be present in isothermal disc accretion and thoroughly study the dependence of various shock parameters on fundamental dynamical variables governing the accretion flow for all possible initial boundary conditions. Types of shocks discussed in this paper may appear to be 'bright' because of the huge amount of energy dissipation at shock, and the quick removal of such energy to maintain the isothermality may power the strong X-ray flares recently observed to be emerged from our Galactic centre. The results are discussed in connection to other astrophysical phenomena of related interest, such as the QPO behaviour of galactic black hole candidates.
DYNAMICAL STRUCTURE OF VISCOUS ACCRETION DISKS WITH SHOCKS
The Astrophysical Journal, 2009
We develop and discuss global accretion solutions for viscous advection-dominated accretion flow (ADAF) disks containing centrifugally supported isothermal shock waves. The fact that such shocks can exist at all in ADAF disks is a new result. Interestingly, we find that isothermal shocks can form even when the level of viscous dissipation is relatively high. In order to better understand this phenomenon, we explore all possible combinations of the fundamental flow parameters, such as specific energy, specific angular momentum, and viscosity, to obtain the complete family of global solutions. This procedure allows us to identify the region of the parameter space where isothermal shocks can exist in viscous ADAF disks. The allowed region is maximized in the inviscid case, and it shrinks as the level of viscous dissipation increases. Adopting the canonical value γ = 1.5 for the ratio of specific heats, we find that the shock region disappears completely when the Shakura-Sunyaev viscosity parameter α exceeds the critical value ∼0.27. This establishes for the first time that steady ADAF disks containing shocks can exist even for relatively high levels of viscous dissipation. If an isothermal shock is present in the disk, it would have important implications for the acceleration of energetic particles that can escape to power the relativistic jets commonly observed around underfed, radio-loud black holes. In two specific applications, we confirm that the kinetic luminosity lost from the disk at the isothermal shock location is sufficient to power the observed relativistic outflows in M87 and Sgr A * .
Steady state shocks in accretion disks around a Kerr black hole
Monthly Notices of the Royal Astronomical Society
Results of numerical simulations of shock solutions in a geometrical thin accretion disk around a Kerr black hole (BH) are presented. Using the smoothed particle hydrodynamics (SPH) technique, the influence of the central object is included by means of an effective potential, We first present the theory of standing shock formation in accretion disks around a Kerr black hole, and show that the results of our numerical simulation agree very well with the theoretical results. We find that the shocks in an inviscid flow are very stable. We also remove the ambiguity prevalent regarding the location and stability of shocks in adiabatic flows. Finally we sketch some of the astrophysical consequences of our findings in relation to accretion disks in Active Galactic Nuclei (AGN) and Quasars.
On the stability of isothermal shocks in black hole accretion disks
2021
Most black holes possess accretion disks. Models of such disks inform observations and constrain the properties of the black holes and their surrounding medium. Here, we study isothermal shocks in a thin black hole accretion flow. Modelling infinitesimal molecular viscosity allows the use of multiple-scales matched asymptotic methods. We thus derive the first explicit calculations of isothermal shock stability. We find that the inner shock is always unstable, and the outer shock is always stable. The growth/decay rates of perturbations depend only on an effective potential and the incoming–outgoing flow difference at the shock location. We give a prescription of accretion regimes in terms of angular momentum and black hole radius. Accounting for angular momentum dissipation implies unstable outer shocks in much of parameter space, even for realistic viscous Reynolds numbers of the order ≈ 1020.
We self-consistently study the properties of the dissipative standing shock waves in an accrertion flow around a stationary black hole. We use analytical method to achieve our goal and identify an effective area in the parameter space spanned by the specific energy and the specific an-gular momentum which allows accretion flow to pass through shock hav-ing some energy dissipation. As the dissipation is increased, the parameter space is reduced and finally disappears when the dissipation is reached its critical value. We show the variation of shock location and compression ratio as a function of the specific energy and study them in terms of energy dissipation across the shock.
On the stability of shocks in isothermal black hole accretion discs
Monthly Notices of the Royal Astronomical Society, 2022
Most black holes possess accretion discs. Models of such discs inform observations and constrain the properties of the black holes and their surrounding medium. Here, we study shocks in a thin isothermal black hole accretion flow. Modelling infinitesimal viscosity allows the use of multiple-scales matched asymptotic methods. We thus derive the first explicit calculations of isothermal shock stability. We find that the inner shock is al w ays unstable, and the outer shock is al w ays stable. The growth/decay rates of perturbations depend only on an ef fecti ve potential and the incoming-outgoing flo w dif ference at the shock location. We give a prescription of accretion regimes in terms of angular momentum and black hole radius. Accounting for viscous angular momentum dissipation implies unstable outer shocks in much of parameter space, even for realistic viscous Reynolds numbers of the order ≈10 20 .
Dynamically induced shock oscillation in the accretion disc around black holes
2015
We investigate the global accretion solution around a stati on ry black hole using the smooth particle hydrodynamics (SPH) me thod. With the suitable choice of the input parameters, accretion flow u ndergoes shock transition that are oscillatory in nature. Such unstable so lutions exhibit the modulation of the inner part of the disk, such as post-shock c rona (PSC) and perhaps be responsible as the source of Quasi Periodic Os cillations (QPOs) of emergent high energy radiation commonly observed in black hole sources.