15'6 THE SPINUP OF NEUTRON STARS BY ACCRETION

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15.6 THE SPIN-UP OF NEUTRON STARS BY ACCRETION
The angular momentum comes from the inner point
of the accretion disk. This inner point may be
defined as the point where the ram pressure of
the infalling gas just balances the magnetic
field pressure of the neutron star The Alfen
Radius.
The ram pressure is the rate at which momentum is
transported inwards per unit area
For a dipole field of intensity BS at the surface
of the neutron star (radius R) the magnetic
pressure is
where rA is the Alfen radius
Since the accretion rate
and
By substitution we can obtain an expression for
the Alfen radius
Thus for the innermost region of the accretion
disk at the Alfen radius, we have
The rate of angular momentum transfer by
accretion is
Since it is this which causes the neutron star to
spin up then
2
Now since
where P is the period
and the luminosity due to accretion is
we can obtain
by substitution for rA and dm/dt in equation (1).
I 2/5 MR2 is the moment of inertia of the
neutron star
The adjacent figure demonstrates that the
theoretical model provides a good representation
of the spin-up process, in which the spin-up rate
is related to the luminosity of the source. i.e.
that the accretion of matter provides the
spin-up. L30 is the luminosity measured in units
of 1030 J s-1
.
Log (PL306/7)
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15.7 MILLISECOND PULSARS
Millisecond radio pulsars have been discovered,
many of which are members of a binary system.
They are found to be slowing in the same way as
ordinary radio pulsars at a rate which is
consistent with the neutron stars having weak
(105 T) magnetic fields. The most likely scenario
is that these objects were spun-up by accretion
in the past as an X-ray binary source, and now
the accretion process has stopped leaving the
neutron star to radiate as a radio pulsar.
Substitution of expression for rA
Now since
we see that a higher accretion rate leads to a
shorter period, and also that the stronger the
magnetic field BS the longer this eventual period
will be.
If we assume the accretion to take place at the
maximum level possible, i.e. the Eddington level
then for a M M0 and R 104 m neutron star we
can estimate the minimum attainable period Pmin
so that, if the surface magnetic field is 105
Tesla, then we can just spin-up a neutron star to
become a 2 ms pulsar. Note that it is not
possible, on the basis of this theory, to
generate millisecond pulsars from neutron stars
with the strong (108 T) magnetic fields which are
found to be associated with ordinary radio
pulsars.
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15.8 ERRATICALLY VARIABLE X/g EMISSION FROM XRB
SOURCES
The above X-ray signal from Cygnus X-1 shows
that it is extremely variable on just about all
timescales down to milliseconds, and with no
measurable periodicity. An optical search of the
sky region at the location of the X-ray source
revealed the existence of a 5.6 day
spectroscopic binary HDE 226868 which is a
supergiant star which has a mass of around 20 M0.
Velocity km s-1
Orbital Phase
The optical spectroscopy revealed that it had a
large projected radial velocity of at least 50
km s-1 and no visible binary companion. If the
x-ray object is the companion then its mass would
be somewhere in the region of 15 M0, much too
high to be a neutron star. Cyg X-1 is the
archetypal black hole candidate.

• NOTE some caution as to the exact mass value
  must be considered since
• With a luminous X/g emitter so close is it
  really an OB type?
• Cyg X-1 is not an eclipsing binary and hence the
  inclination is not sure

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15.9 OBSERVATIONAL CHARACTERISTICS OF BLACK
HOLE CANDIDATES
One of the key goals in the studies associated
with black hole physics is to find a set of
observational criteria which can be used to
identify and define the existence of black holes
in binary systems. So far, apart from the dynamic
mass function, this has not been conclusive and
the process is on-going. Let us briefly review
some of these aspects.

• The Dynamic Mass Function. This is currently the
  crucial factor, but as noted above has some
  problems. However for objects in e.g. the
  galactic centre the obscuration due to gas and
  dust makes it impossible to study any optical
  companion.

• Rapid Variability of the X/g Signal. To do this
  well requires a bright source in order to get
  good statistics. However some NS binaries also
  exhibit the same characteristic. However Quasi
  Periodic Oscillation (QPO) characteristics have
  been observed in both BH and NS systems

• Transient Emission. Most of the black hole
  candidate sources exhibit dramatic changes in
  intensity. This transient nature of their
  emission appears to be a strong clue as to the
  existence of a black hole in a close binary
  system.

The adjacent figure illustrates the observed
characteristics of a typical transient outburst
from black hole candidate sources. The emission
rises many orders of magnitude in intensity over
a very short time period (lt day) to a level which
is consistent with the Eddington limit for a mass
of typically 1 - 10 M0. The emission subsequently
dies away over some day to months, often
exhibiting secondary smaller outbursts
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• X/g-ray Emission Spectra. The emission spectra
  demonstrate a number of factors which appear to
  be largely restricted to BH binary systems.

Broad red shifted 511 annihilation line?
Fe Line
In the so-called high state the spectrum is
dominated by an intense soft X-ray excess,
thought to be emission from the hot accretion
disk.
Soft X-ray excess
Log IX/g
In the so-called low state (transient HE
outburst) the emission becomes dominated by
g-rays in the 100 keV to 1 MeV range. Often
visible is a broad line, thought to be due to
electron-positron annihilation close to the black
hole. There is also evidence for Compton
backscatter peaks.
Backscatter?
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101
102
103
Photon Energy keV
This bimodal nature of the high energy spectral
emission seems to be a characteristic of black
hole binary systems. The 6 keV iron line
spectral structure has been interpreted as due to
the spiral motion of the material as it funnels
down the potential well in the accretion disk.
Likewise the backscatter peaks are thought to be
related to related to 511 keV g-rays which
interact with the surrounding accretion and are
Compton scattered in the direction of the earth.
Red shifted 511 keV e e- annihilation line
170 keV Compton backscattered g-rays
Accretion disk
Source
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• Relativistic Jets - Galactic Micro-Quasars

Radio images of the transient g-ray sources have
discovered vast radio jets which emerge from the
object and extend several light years into the
surrounding interstellar medium. Just like
quasars there is a forward and 1800 backward jet,
they are also superluminal. The adjacent picture
shows the 6 cm radio jets associated with the
g-ray transient source 1E 1740.7 which is
situated close to the galactic centre.
Site of the g-ray source

Expanding superluminal radio blob
The g-ray transient events appear to be
correlated with the production of the
superluminal radio emitting blobs. The amount of
energy associated with the bulk motion of the
radio clouds is quite phenomenal. The mass of the
clouds are typically gt1022 kg, and the associated
kinetic energy
Where g is the Lorenz factor associated with the
bulk motion. It is interesting to note that if
the actual ejection took place within a timescale
of about one minute then these objects become as
powerful as an AGN during this short time.