Relativistic Advection-Dominated Inflow-Outflow: Mass-loss rate variation of M87

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Radio-Loud AGN Model
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

• (Credit C.M. Urry and P. Padovani )

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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?
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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)
• 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
• 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.

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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
• 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 ?ii for ion-ion
  collisions is much longer than the disk height
  the gas is collisionless
• The mean free path ?mag for collisions with
  magnetic waves is much shorter than ?ii for the
  thermal particles, and much longer than ?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
• The maximum particle energy that can be produced
  in this model depends on the magnetic wave
  distribution via the recoil effect

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Isothermal shocks (TT_)

• 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 TT_, but elt e_ and KltK_
• 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 will show the gas is strongly bound in the
  post-shock region

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

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

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Disk-Jet Connection
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Flow structure with/without shock
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Results M87 Sgr A

• Our model then gives for the escape energy at the
  shock radius r r , which is the jet radius
  rjet 22 rg and rjet 16 rg 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.
• From observations, Biretta et al. (2002) suggest
  that the M87 jet forms in a region no larger than
  rjet lt 30 rg 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 rjet 16 rg
  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.

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The End