Models of Pulsars

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Models of Pulsars

• Electrodynamics Radiative Process
• Moumita Aich
• IUCAA

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History

• The first pulsar was discovered in 1967, by
  Jocelyn Bell Burnell and Antony Hewish of the
  University of Cambridge, UK. (PSR 191921).
• The suggestion that pulsars were rotating neutron
  stars was put forth independently by Thomas Gold
  and Franco Pacini in 1968, and was soon proven
  beyond doubt by the discovery of a pulsar with a
  very short 33-millisecond pulse period in the
  Crab nebula.
• In 1974, Joseph Taylor and Russell Hulse (1993
  the Nobel prize ) discovered for the first time
  a pulsar in a binary system, PSR B191316. This
  pulsar orbits another neutron star with an
  orbital period of just eight hours.
• In 1982, a pulsar with a rotation period of just
  1.6 milliseconds was discovered, by Shri Kulkarni
  and Don Backer. Observations soon revealed that
  its magnetic field was much weaker than ordinary
  pulsars, while further discoveries cemented the
  idea that a new class of object, the "millisecond
  pulsars" (MSPs) had been found.

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Classes of pulsars

• Rotation-powered pulsars, where the loss of
  rotational energy of the star powers the
  radiation.

Composite Optical/X-ray image of the Crab Nebula
pulsar, showing surrounding nebular gases stirred
by the pulsar's magnetic field and radiation.
The Vela Pulsar, a neutron star corpse left from
a titanic stellar supernova explosion, shoots
through space powered by a jet emitted from one
of the neutron star's rotational poles.
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Accretion-powered pulsar (accounting for most
but not all X-ray pulsars)The gravitational
potential energy of accreted matter is the energy
source (producing X-rays that are observable from
Earth)
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MagnetarsThe decay of an extremely strong
magnetic field powers the radiation causes
emission of copious amounts of high-energy
electromagnetic radiation, particularly X-rays
and gamma rays.
Location of the magnetar SGR 1806-20
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Magnetic Dipole Model for Pulsar
Using Larmors formula for a magnetic dipole

Rotational K.E.
A pure magnetic dipole field at the magnetic pole
of the star, BP, is related to m by
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Energetics of Crab Pulsar (Gunn Ostiker -
1969)

• BP 5.2 x 1012 G
  (sina 1)

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Non-vacuum Pulsar Models The Aligned rotator
(Goldreich Julian - 1969)
Goldreich Julian model(1969) model of pulsar
magnetosphere with parallel magnetic rotation
axes.
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• Particles attached to closed magnetic-field lines
  corotate with the star form corotating
  magnetosphere.
• Magnetic field lines that pass through the light
  cylinder are open are deflected back to form a
  toroidal field component. Charged particles
  stream out along these lines.
• The critical filed line is at the same electric
  potential as the exterior interstellar medium.
  This line divides regions of positive and
  negative current flow from the star and the plus
  and minus signs indicate the charge of particular
  regions of space.
• The diagonal dashed line is the locus of BP 0,
  where the space charge changes sign.
• The angle subtended by the polar cap region
  containing open field lines is ?P.

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Magnetic filed is largely dipolar in the near
zone i.e. at distances lt vacuum wavelength of
the radiation emitted, r lt ? c/O Rc

• BP is the field strength at the magnetic
  pole and R is the stellar radius.

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• Particles are torn off the surface create a
  region of plasma around the star the
  magnetosphere. A vacuum solution for the region
  surrounding a rotating neutron star is unstable.
• Inside the light cylinder, the plasma corotates
  with the star because of strong magnetic field.
• The magnetosphere acts as an extension of the
  perfectly conducting interior, so that E.B 0
  remain valid. The filed where the filed lines
  close beyond the light cylinder, receives
  particles which are permanently lost to the star
  satisfies E.B ? 0.
• In this model, a spinning neutron star has an
  aligned dipole external magnetic field. Since
  such an axisymmetric configuration will not
  pulse, some obliquity must be imagined to explain
  the pulsed emission. (Ref 3)

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Discussions
Crab pulsar's jets. The jets present evidence
that the magnetic and rotational axes of the
pulsars are aligned. Charged particles can only
escape through the magnetic field in the polar
regions, so if the magnetic and rotational axes
were not aligned then the jets would be cone
shaped. The images argue against the validity of
the conventional rotational pulsar model, since a
rotating pulsar becomes disabled when the axes
are aligned.
The magnetic force between the poles of a
magnetized sphere is attractive. The force at the
equator is repulsive, so the magnetic field
causes an equatorial bulge. Centrifugal force
also causes an equatorial bulge. The
energetically preferred orientation of the
magnetic field is therefore parallel to the spin
axis.
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• The oscillatory power calculation is based only
  on basic energy relationships, so the energy
  discrepancy in this model may be due to mass
  ejection. In this model the pulsar has an intense
  E field so that when in falling material becomes
  ionized half the particles are ejected from the
  system. The other half collides with the pulsar,
  creating more charged particles. At high energies
  a relatively small mass flow could account for
  the computed energy transfer, but a more likely
  explanation is that the equation badly
  overestimates the actual power output if the
  pulsar ejects its own mass, which can happen in
  an electrostatic field. The computed power output
  must therefore be taken as only an upper limit
  until observational data on the pulsar's mass
  flow become available. Infrared observations show
  that the pulsar is surrounded by a dust cloud,
  which may be relevant to the energy flow
  equation.
• Outer-gap model proposed by Zhang (2004).
• High-energy photons emitted by relativistic
  charged particles produce e  pairs through
  magnetic-pair production on their way from the
  outer gap to the neutron-star surface, and these
  pairs produce the bulk of pulsed X-rays by the
  synchrotron radiation.

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References

• Black Holes, White dwarfs and neutron stars
  Shapiro Teukolsky
• Pulsars Manchester Taylor
• The non-aligned pulsar magnetosphere An
  illustrative model for small obliquity L.
  Mestel Y.M. Wang