Radio-Loud AGN Model (Credit: C.M. Urry and P. Padovani ) These objects also have hot, ADAF-type accretion flows, where the radiative cooling is very inefficient These objects also have hot, ADAF-type accretion flows, where the radiative cooling is very inefficient and most of the dissipated energy is advected into the black hole Hot, tenuous disks are favorable sites for relativistic particle acceleration because the gas is collisionless Up to the present date, the precise nature of the mechanism responsible for transferring the gravitational potential energy from the infalling matter to the small population of nonthermal particles that escape to form the jet is not yet clear

Blandford-Znajek Mechanism –Rotation of black hole drags the inertial frame –This results in twisting of the magnetic field lines supported by the surrounding disk –The resulting magnetic stress is then released as a Poynting flux away from the hole –In this mechanism, the power of the jets is provided by the rotating hole Is it possible to explain the outflows in terms of well-understood microphysical processes operating in the hot, tenuous disk, such as the possible acceleration of the jet particles at a standing accretion shock?

Connection with cosmic-ray acceleration The discovery of the high-energy cosmic-ray spectrum prompted work on the acceleration of cosmic rays in SN shock waves via the first-order Fermi mechanism (Krymsky 1977; Bell 1978; Blandford and Ostriker 1978) The discovery of the high-energy cosmic-ray spectrum prompted work on the acceleration of cosmic rays in SN shock waves via the first-order Fermi mechanism (Krymsky 1977; Bell 1978; Blandford and Ostriker 1978) These models were developed in the test-particle approximation (this must be abandoned if the compression ratio equals or exceeds 4) These models were developed in the test-particle approximation (this must be abandoned if the compression ratio equals or exceeds 4) We apply the same picture to understand particle acceleration in We apply the same picture to understand particle acceleration in accretion disks containing standing, centrifugally-supported shocks In our disk/outflow model the liberated energy and entropy are thought to be lost from the disk in the vicinity of the shock via the escape of high-energy particles in ADAFs disks. In our disk/outflow model the liberated energy and entropy are thought to be lost from the disk in the vicinity of the shock via the escape of high-energy particles in ADAFs disks. Shock UpstreamDownstream B.H. Shock Outflows

Particle acceleration in accretion disks In this case there are two groups of particles: the thermally-distributed background particles, and the higher-energy, relativistic “test particles” In this case there are two groups of particles: the thermally-distributed background particles, and the higher-energy, relativistic “test particles” Since we are employing the test particle approximation, the pressure of the accelerated particles is not included in the dynamics Since we are employing the test particle approximation, the pressure of the accelerated particles is not included in the dynamics In ADAF disks, the mean free path λ ii for ion-ion collisions is much longer than the disk height – the gas is collisionless In ADAF disks, the mean free path λ ii for ion-ion collisions is much longer than the disk height – the gas is collisionless The mean free path λ mag for collisions with magnetic waves is much shorter than λ ii for the thermal particles, and much longer than λ ii for the relativistic particles – we assume collective processes thermalize the background The mean free path λ mag for collisions with magnetic waves is much shorter than λ ii for the thermal particles, and much longer than λ ii for the relativistic particles – we assume collective processes thermalize the background Therefore the background particles cross the shock ONCE, and the relativistic test particles cross the shock MULTIPLE times Therefore the background particles cross the shock ONCE, and the relativistic test particles cross the shock MULTIPLE times The maximum particle energy that can be produced in this model depends on the magnetic wave distribution via the recoil effect The maximum particle energy that can be produced in this model depends on the magnetic wave distribution via the recoil effect

Isothermal shocks (T + =T_) In isothermal shocks radiative cooling is very efficient In isothermal shocks radiative cooling is very efficient –More energy is lost than in the isentropic or RH shocks –The entropy decreases as the gas crosses the shock –This implies that the sound speed and the thickness of the flow remain unchanged through the shock –This type of shock T + =T_, but ε + < ε _ and K + <K_ The compression ratio is maximized for a given Mach number, enhancing particle acceleration The compression ratio is maximized for a given Mach number, enhancing particle acceleration We focus on isothermal shocks here and therefore we assume that particles escape from the disk only at the shock location We focus on isothermal shocks here and therefore we assume that particles escape from the disk only at the shock location We will show the gas is strongly bound in the post-shock region We will show the gas is strongly bound in the post-shock region

Equations describing structure of adiabatic, inviscid accretion flows with isothermal shocks Equations describing structure of adiabatic, inviscid accretion flows with isothermal shocks Sonic Point Analysis Sonic Point Analysis Shock Point Analysis Shock Point Analysis

Transport equation that governs the relativistic particle energy/space distribution Transport equation that governs the relativistic particle energy/space distribution Assumption about Spatial Diffusion Coefficient Assumption about Spatial Diffusion Coefficient Assumption about Vertical Escape Assumption about Vertical Escape Solutions for the Relativistic Number & Energy Densities Solutions for the Relativistic Number & Energy Densities

Disk-Jet Connection Constrain Γ esc Assume E 0 Minimize E esc Constrain κ 0 Constrain A 0 Powering the jet from the disk Heating the seed particles Constrain N 0.

Flow structure with/without shock shock-free profile shocked profile

shock-free profile shocked profile

Results: M87 & Sgr A* Our model then gives for the escape energy at the shock radius r = r *, which is the jet radius r jet ~ 22 r g and r jet ~ 16 r g for M87 and Sgr A*, respectively. Our model then gives for the escape energy at the shock radius r = r *, which is the jet radius r jet ~ 22 r g and r jet ~ 16 r g for M87 and Sgr A*, respectively. Our results indicate that the shock acceleration mechanism can produce relativistic outflows with terminal Lorentz factor of ~ 8 (M87) and ~ 7 (Sgr A*), and the total powers comparable to those estimated in M87 and Sgr A*. Our results indicate that the shock acceleration mechanism can produce relativistic outflows with terminal Lorentz factor of ~ 8 (M87) and ~ 7 (Sgr A*), and the total powers comparable to those estimated in M87 and Sgr A*. From observations, Biretta et al. (2002) suggest that the M87 jet forms in a region no larger than r jet < 30 r g ; Biretta et al. (1999) estimate for the bulk flow in the jet of M87. From observations, Biretta et al. (2002) suggest that the M87 jet forms in a region no larger than r jet < 30 r g ; Biretta et al. (1999) estimate for the bulk flow in the jet of M87. In the case of Sgr A*, our disk-jet model indicates that the jet forms at r jet ~ 16 r g which is fairly close to the value suggested by Yuan (2000) model. However, future observational work will be needed to test our prediction for the asymptotic Lorentz factor of Sgr A*, since no reliable observational estimate for that quantity is currently available. In the case of Sgr A*, our disk-jet model indicates that the jet forms at r jet ~ 16 r g which is fairly close to the value suggested by Yuan (2000) model. However, future observational work will be needed to test our prediction for the asymptotic Lorentz factor of Sgr A*, since no reliable observational estimate for that quantity is currently available.

The End