Particle Acceleration in Compact Objects

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Particle Acceleration in Compact Objects

• Demosthenes Kazanas
• NASA
• Goddard Space Flight Center

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• There is plenty of evidence for the presence of
  particle acceleration in compact objects
• High (and low) energy emission from pulsars.
• High (and low) energy emission from plerionic SN
  remnants.
• Emission from 109 1027 Hz in Active Galactic
  Nuclei.

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• Outline
• Direct particle acceleration by electric fields
  (in EM gaps).
• Bulk acceleration of particles in MHD flows.
• Stochastic Acceleration (shocks, turbulence).
• Dynamic Effects of accelerated particles (effects
  on accretion disks, outflows).

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The Seven Highest-Confidence Gamma-ray Pulsars
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Broad-band spectra

• Power peaked in g-rays
• No pulsed emission above 20 GeV
• Increase in hardness with age
• High-energy turnover
• Increase in hardness with age
• Thermal component appears in older pulsars

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• Must distinguish between acceleration of
  individual particles and acceleration in bulk.
• These two are generally distinct processes,
  however, there are cases in which they are
  intimately related.
• The most obvious evidence of the presence of
  acceleration of particles is that of pulsars.

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Rotating Magnetic Field
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Formation of an outflow

• The rotation of the highly conducting neutron
  star crust generates enormous potential
  differences over the surface
• above the surface gt very large
  outward-acting unbalanced electric stresses
• A charged magnetosphere is spontaneously built up
  in order to short-out the parallel component of
  the electric field (Goldreich-Julian 1969)

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The density of charge carriers can be easily
estimated

• This density co-rotates with the pulsar out to
• the light cylinder. Beyond that the magnetic
• stresses cannot confine the plasma and must
• open-up, i.e. the dipole is not a valid
• magnetospheric solution

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The flux of the open field lines at thelight
cylinder defines the polar cap of thepulsar, as
the region of the last open field line
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The pulsar slow down can then be worked out in a
simple way. It does not require the pulsar to be
misaligned the same slow down works out for a
purely aligned magnetosphere.
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Surface Fields and Currents
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• The presence of a sufficiently dense plasma
• cancels all parallel E. Discrepancy between
• the actual charge density from that of GJ
• leads to gaps (Polar Cap Outer Gap models).
• Particles can be accelerated at gaps and lead to
• the creation of photons. The resulting spectra
• depend on the ensuing interactions (A. Harding)
• The EM potentials available are of order of
• 1018 (P/ms) B15 eV. As such they
• could produce galactic cosmic rays up to the
• energy of ankle (Arons 02).

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• The problem of pulsar magnetospheric
• emission, as is the case with all problems
• that involve magnetic fields (which cannot
• be shorted out) is a global one. One has to
• solve for the currents and the resulting
• magnetic fields over all space before we can
• decide the dynamics and radiation emission
• from a pulsar.

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• The magnetosphere is determined by the
• balance between the current and electro-
• static forces in the magnetosphere. These
• are given by the Pulsar Equation

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The parameters involved are

• Poloidal electric current
• Magnetic flux
• Force-free
• Space charge density

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Contopoulos, Kazanas Fendt 1999 Gruzinov 2005
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• The solution is smooth, contains a return
• Current, it contains a zero charge line and
• it provides the wind asymptotic structure.
• Emission is expected at places where MHD is
  violated (polar cap, zero charge line, return
  current boundary, but not the Light Cylinder).

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Pulsar Winds/The s-Problem

• For the geometry of the magnetic lines beyond
• the Light Cylinder (split monopole) for which
• Bp 1/R2, Bf 1/ R , r 1/R2.
• Therefore their ratio, s 106 near the LC should
• be independent of the radius R .
• However, the spectra of the Crab nebula need a
• value s 3 10-3 to fit the observed spectrum and
• for Vela one needs s 1.

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• The asymptotic (split) monopole geometry
• of CKF allows a crack at this problem
• The energy conservation equation along a field
• line has the form
• While the flux freezing condition reads

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• Under force-free conditions
• the energy equation reads
• Leading eventually to
• (Contopoulos DK 2002)

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• Under conditions of a monopole geometry the
  Lorentz
• factor of the flow increases linearly with
  distance. This
• happens as long as the effects of inertia are
  negligible.
• Beyond this point the field geometry should
  deviate
• From monopolar and possibly part of it collimate
  and
• part form an equatorial wind. The wind terminates
  at a
• shock which is responsible for the nebular
  emission.
• (The extent of monopole geometry is debatable.
  It may
• extend only up to the fast magnetosonic point
  then the
• maximum g will be only s1/3 ).

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Plerion Components
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Vlahakis Konigl 2001

• Linearly increase in Lorentz factor is a property
  of general MHD flows of geometries different
  from monopolar (VlahakisKonigl 2001)

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The MHD outflow acceleration and the s-Problem
are related issues. They demand the simultaneous
solution of the conservation equations along with
the transverse force balanc.e

• First axisymmetric wind
• solutions by Blandford
• Payne extended to
• Relativistic case by Li,
• Chieuh, Begelman (92)
• and Contopoulos (94).
• Solutions known only for
• self-similar geometry.

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• Flow acceleration
• depends on assumptions
• used. LCB find logarithmic
• acceleration with height.
• Contopoulos (94) finds final
• velocity similar to that at
• the accretion disk at the
• base of the flow (Vlahakis
• Konigl 04 for a more
• recent study).

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The relativistic outflows produce shocks, which
accelerate particles and lead to radiation
emission. Blazaremission is thought to be
derived this way.

• The apparently thin
• photon spectra indicate
• emission from large
• distances and suggests
• association with jet
• flows (Mastichiadis
• Kirk 1997).

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Particle acceleration (in shocks, converging
flows, turbulence) is the result of an interplay
between particle energy gains in scattering and
particle transport. The exponentially small
probability of undergoing N interactions with
the plasma before escape, coupled with
exponentially increasing energy with the number
of scatterings lead to power law distributions.
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The geometry of particle transport across a plane
shock. The upstream velocity is u1 and the
downstream u2u. The particle velocity is v. The
shaded region shows the fraction of particles
that make it upstream and have a chance to
accelerate.
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Generic description of the acceleration process.
Application to plane parallel shocks (r is the
compres- sion ratio, P(p) is the integral
spectrum).
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Effects of acceleration on dynamics

• The presence of relativistic particles
• can affect the dynamics of the flow
• Relativistic particles reduce the fluid
• adiabatic index and increase the shock
• compression ratio r. This hardens the
• spectra most kinetic energy is
• converted to relativistic particles that
• dominate the pressure.
• Particle (relativistic) escape from the
• system also increases the compression
• ratio of the shock with similar effect.

• (Ellison et al 2000)

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• In the vicinity of a compact object, the strong
  gravitational
• field could separate the relativistic and the
  non-relativistic
• populations, provided that cooling does not
  this can cause
• outflows similar to those inferred in compact
  objects (DK
• Ellison 86) Subramanian et al (99), provided
  that the
• accelerated particles do not lose energy on time
  scales shorter
• than free-fall.
• Separation can also take place through the
  production of
• neutral particles (neutrons) that can increase
  the power of
• relativistic outflows (Contopoulos DK 94).

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Plasma production outside an Acc. Disk from n -gt
p e. For a large black hole, most neutron
produced protons are relativistic while for a
small one most are non-relativistic. The critical
value is M108 M_o
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The Radio Jets of GRS 1915105
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The Radio Jets of GRS 1915105
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The Radio Jets of GRS 1915105
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• Acceleration in Accretion Disks can
• result from particle-wave interactions
• (e.g. Dermer, Miller, Li 96). Acceler.
• Time scales are quite short and should
• Produce accelerated populations.

• Accretion Disks could accelerate
• particles by their shearing motion
• (Subramanian et al. 99). This leads
• to 2nd order acceleration.

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Slope and Maximum Energies

• The slope of accelerated population depends on
  the interplay between energy gain per interaction
  and escape probability (e.g. the Comptonization
  parameter t kT/mc2). For shocks this is 3/(r-1)
  (integral slope).
• The acceleration rate is hap-pening on the
  gyro-period at the given field E(eV)/B(G)

• Maximum energy is given by the balance between
  accele-ration and losses or escape from the
  system. For electrons this energy is TeV
  (blazars), while for protons it gets close to
  1020 eV.
• Eventually, the max.energy is roughly R (v/c)
  B, where R is the size of the system, v the
  velocity and B the magnetic field.

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Conclusions - Questions

• Particle Acceleration is a ubiquitous process in
  compact objects (spectra, superluminal motions).
• Particles can get accelerated in EM gaps
  (deviations from MHD conditions). Energy/particle
  Potential drop across gap.
• MHD acceleration in rotating magnetospheres.
  Conversion of magnetic to kinetic energy of high
  efficiency (depends on current distribution).
  Lorentz factors of 10 106 possible.
• Particle acceleration possible in turbulent,
  shocked plasmas. Conversion of KE to relativistic
  particles with high efficiency. Max. energy
  depends on particulars of system.
• Why dont we see prominent non-thermal emission
  in the spectra of accreting binary sources? Why
  are most AGN radio quiet?
• Does acceleration take place in the Acc. Disks of
  AGN, GBHC? If yes, do the accelerated particles
  play any role in the dynamics of these disks? Are
  observational tests to distinguish between these
  possibilities?

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The geometry of particle transport across a
shock. The upstream velocity is u1 and the
downstream u2u. The particle velocity is v. The
shaded region shows the fraction of particles
that make it upstream and have a chance to
accelerate.
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