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        Chapter 14
Neutron Stars and Black Holes
The preceding chapters have traced the story of stars from
their birth as clouds of gas in the interstellar medium to their
final collapse. This chapter finishes the story by discussing
the kinds of objects that remain after a massive star dies.
How strange and wonderful that we humans can talk about
places in the universe where gravity is so strong it bends
space, slows time, and curves light back on itself! To carry
on these discussions, astronomers have learned to use the
language of relativity. Throughout this chapter, remember
that our generalized discussions are made possible by
astronomers studying general relativity in all its
mathematical sophistication. That is, our understanding
rests on a rich foundation of theory.
This chapter ends the story of individual stars. The next
three chapters, however, extend that story to include the
giant communities in which stars live— the galaxies.
I. Neutron Stars
    A. Theoretical Prediction of Neutron Stars
    B. The Discovery of Pulsars
    C. A Model Pulsar
    D. The Evolution of Pulsars
    E. Binary Pulsars
    F. The Fastest Pulsars
    G. Pulsar Planets

II. Black Holes
     A. Escape Velocity
     B. Schwarzschild Black Holes
     C. Black Holes Have No Hair
     D. A Leap into a Black Hole
     E. The Search for Black Holes
Outline (continued)
III. Compact Objects with Disks and Jets
     A. X-Ray Bursters
     B. Accretion Disk Observations
     C. Jets of Energy from Compact Objects
     D. Gamma-Ray Bursts
Formation of Neutron Stars
     A supernova explosion of a M > 8 Msun
        star blows away its outer layers.
  The central core           Compact objects more
 will collapse into a           massive than the
 compact object of            Chandrasekhar Limit
    ~ a few Msun.              (1.4 Msun) collapse
                             beyond the formation of
                                 a white dwarf.
                          Pressure  becomes so high
                          that electrons and protons
                            combine to form stable
                        neutrons throughout the object:
                                p + e-  n + ne
                              Neutron    Star
Formation of Neutron Stars (2)
Properties of Neutron Stars
Typical size: R ~ 10 km    a piece of neutron star
                            matter of the size of a
Mass: M ~ 1.4 – 3 Msun
                          sugar cube has a mass of
Density: r ~ 1014 g/cm3      ~ 100 million tons!!!

                                    A neutron star
                                    (more than the
                                     mass of the
                                      sun) would
                                    comfortably fit
                                       within the
Discovery of Pulsars
                          Angular momentum conservation
                          => Collapsing stellar core spins
                             up to periods of ~ a few
                          Magnetic fields are amplified up to
                                 B ~ 109 – 1015 G.

                          (up to 1012 times the average
                            magnetic field of the sun)

=> Rapidly pulsed (optical and radio) emission from
some objects interpreted as spin period of neutron stars
Pulsars / Neutron Stars
 Neutron star surface has a temperature of
               ~ 1 million K.
                         Cas A in X-rays

          Wien’s displacement law,
         lmax = 3,000,000 nm / T[K]
 gives a maximum wavelength of lmax = 3 nm,
         which corresponds to X-rays.
Pulsar Periods

                 Over time, pulsars
                  lose energy and
                 angular momentum

                 => Pulsar rotation
                    is gradually
                  slowing down.
Pulsar Winds
   Pulsars are emitting winds and jets
      of highly energetic particles.

   These winds carry away about 99.9 % of the
  energy released from the slowing-down of the
                pulsar’s rotation.
Lighthouse Model of Pulsars

           A Pulsar’s
           magnetic field
           has a dipole
           structure, just
           like Earth.

                is emitted
                 along the
Images of Pulsars and Other Neutron Stars

The vela Pulsar moving
through interstellar space

                                  The Crab
                                 nebula and
The Crab Pulsar

                             Pulsar wind + jets

  Remnant of a supernova observed in A.D. 1054
The Crab Pulsar (2)

Visual image

               X-ray image
Light Curves of the Crab Pulsar
Proper Motion of Neutron Stars

                                Some neutron
                              stars are moving
                               rapidly through
                             interstellar space.

 This might be a result of
  anisotropies during the
   supernova explosion
 forming the neutron star
Binary Pulsars
Some pulsars form binaries with other neutron stars (or black holes).

  Radial velocities resulting from
  the orbital motion lengthen the
   pulsar period when the pulsar
   is moving away from Earth...

   …and shorten the pulsar
 period when it is approaching
Neutron Stars in Binary Systems:
X-ray Binaries
                 Example: Her X-1             Star eclipses neutron
                                               star and accretion
                      2 Msun (F-type) star
                                                disk periodically

           Neutron star    Orbital period =
                           1.7 days
   Accretion disk material heats to
  several million K => X-ray emission
Pulsar Planets
Some pulsars have
planets orbiting
around them.

Just like in binary pulsars,
this can be discovered
through variations of the
pulsar period.

As the planets orbit
around the pulsar, they
cause it to wobble
around, resulting in
slight changes of the
observed pulsar period.
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun),
         there is a mass limit for neutron stars:

          Neutron stars can not exist
            with masses > 3 Msun

   We know of no mechanism to halt the collapse
        of a compact object with > 3 Msun.

   It will collapse into a single point – a singularity:

                 => A Black Hole!
Escape Velocity
                       Velocity needed
                      to escape Earth’s
                       gravity from the
                        surface: vesc ≈
                          11.6 km/s.
                      Now, gravitational
                       force decreases            vesc
                       with distance (~
                       1/d2) => Starting
                      out high above the
                       surface => lower
                       escape velocity.
If you could compress Earth to a smaller radius
   => higher escape velocity from the surface.
The Schwarzschild Radius
   => There is a limiting radius
    where the escape velocity
  reaches the speed of light, c:

           Rs = ____
                                    Vesc = c

  G = Universal const. of gravity
  M = Mass

      Rs is called the
   Schwarzschild Radius.
Schwarzschild Radius and Event Horizon
                             No object can
                           travel faster than
                           the speed of light
                             => nothing (not
                             even light) can
                           escape from inside
                           the Schwarzschild
                            • We have no way
                           of finding out what’s
                             happening inside
                            the Schwarzschild

            ―Event horizon‖
Black Holes in Supernova Remnants

                       remnants with
                         no pulsar /
                      neutron star in
                      the center may
                        contain black
Schwarzschild Radii
―Black Holes Have No Hair‖
    Matter forming a black hole is losing
        almost all of its properties.

        Black Holes are completely
        determined by 3 quantities:

         Angular Momentum
           (Electric Charge)
General Relativity Effects
Near Black Holes (1)

      At a distance, the
gravitational fields of a black
hole and a star of the same
 mass are virtually identical.
At small distances, the much
deeper gravitational potential
   will become noticeable.
General Relativity Effects
Near Black Holes (2)
                An astronaut descending
                down towards the event
                horizon of the BH will be
                stretched vertically (tidal
                 effects) and squeezed

                   This effect is called
General Relativity Effects
Near Black Holes (3)
                Time dilation
   Clocks starting at
  12:00 at each point.
  After 3 hours (for an
   observer far away                 Clocks closer to the
     from the BH):                   BH run more slowly.

                                    Time dilation
                                 becomes infinite at
                                 the event horizon.
                          Event Horizon
General Relativity Effects
Near Black Holes (4)

      Gravitational Red Shift

   All wavelengths of emissions
   from near the event horizon
    are stretched (red shifted).
    Frequencies are lowered.

                       Event Horizon
Observing Black Holes
   No light can escape a black hole
=> Black holes can not be observed directly.

                                        If an invisible
                                    compact object is
                                      part of a binary,
                                     we can estimate
                                    its mass from the
                                    orbital period and
                                       radial velocity.

                                   Mass > 3 Msun
                                   => Black hole!
Candidates for Black Hole

                Compact object with
                 > 3 Msun must be a
                     black hole!
Compact Objects with Disks and Jets

      Black holes and neutron stars can be
             part of a binary system.

                                     Matter gets
                                   pulled off from
                                   the companion
                                    star, forming
                                    an accretion
       => Strong X-ray source!

         Heats up to a few million K.
X-Ray Bursters
 Several bursting X-ray
  sources have been
      observed:           Rapid outburst
                           followed by
                          gradual decay

                                     The longer
                                    the interval,
                                    the stronger
                                      the burst
The X-Ray Burster 4U 1820-30
          In the cluster NGC 6624

Optical                             Ultraviolet
Black-Hole vs. Neutron-Star Binaries
                   Black Holes: Accreted matter
                   disappears beyond the event
                        horizon without a trace.

   Neutron Stars: Accreted
   matter produces an X-ray
   flash as it impacts on the
   neutron star surface.
Black Hole X-Ray Binaries
       Accretion disks around black holes

                Strong X-ray sources
   Rapidly, erratically variable (with flickering on
        time scales of less than a second)
  Sometimes: Quasi-periodic oscillations (QPOs)
          Sometimes: Radio-emitting jets
Model of the X-Ray Binary SS 433
 Optical spectrum shows
spectral lines from material
          in the jet.

    Two sets of lines:
    one blue-shifted,
     one red-shifted

   Line systems shift
  back and forth across
  each other due to jet
 Gamma-Ray Bursts (GRBs)

GRB a few hours       Same field,      Short (~ a few s),
 after the GRB                          bright bursts of
                    13 years earlier

Later discovered with X-ray and
optical afterglows lasting several
       hours – a few days

 Many have now been associated
   with host galaxies at large
   (cosmological) distances.
A model for Gamma-Ray Bursts
    At least some GRBs are
probably related to the deaths of
 very massive (> 25 Msun) stars.

In a supernova-like explosion of
   stars this massive, the core
 might collapse not to a neutron
star, but directly to a black hole.

   Such stellar explosions are

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