Accretion power for beginners
Overview
•  This lecture:
•  Accretion as a supply of energy
•  Accretion onto white dwarfs, neutron stars and
black holes
•  X-ray binaries
•  Emission mechanisms
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Context
•  This lecture has a high-energy astrophysics motivation.
•  The basic ideas about accretion power apply equally to
lower-energy scenarios, e.g. the formation of the solar
system.
•  But the specific examples I give here will be high energy.
•  MSSL’s astrophysics group started with X-ray astronomy,
and high-energy astrophysics is still a key strength of
MSSL.
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What is accretion:
•  Chambers 20th Century dictionary* says:
– to accrete: to unite, to form or gather
round itself
– accretion: continued growth
•  My definition of accretion:
– growth by accumulating material
* The dictionary that used to be in office 158
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Why is this important as a source of
energy?
•  There is an attraction between any two bodies
due to gravity.
•  The two bodies have gravitational potential
energy.
•  As two bodies fall together this potential energy
is converted into kinetic energy.
•  By a number of emission mechanisms, this
energy can be radiated.
•  Accretion is a means of getting energy from
gravity.
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How much energy can you get?
•  Gravity is a very weak force:
–  the gravitational attraction between individual particles
is very small (c.f. electrostatic forces)
–  The gravitational potential energy is:
E=
-G m1m2
r12
Where G is the gravitational constant, m1 and m2 are the masses and
r12 is the distance between them. Note the ‘-’ sign
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Lets think of an individual particle of mass m being
accreted onto a body of mass M and radius R from
an infinite distance.
The potential energy lost by the particle is
Initial potential energy – final potential energy
E=
GMm
R
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•  Remember the potential energy lost is the
kinetic energy gained by the particle.
•  Particle mass m is fixed. Gravitational
constant G is fixed. So, to get high energy
particles we need:
Large mass M
and/or
Small radius R
•  Even though gravity is a weak force,
accretion onto massive objects and/or
compact objects is important in high
energy astrophysics.
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Accretion onto compact stars
•  We know of 3 types of compact stars: white
dwarfs, neutron stars and black holes.
•  Start with the least extreme case, and work
through to the most remarkable.
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So what happens when we accrete
some material onto the surface of a
white dwarf?
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Accretion onto white dwarfs
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Mass M ~ 1 solar mass = 2 x 1030 kg
Radius R ~ 107 m
G=6.67 x 10-11 m3 kg-1 s-2
So energy released per kg is GM/R =1.4x1013 J
If this is converted completely to kinetic energy
then what speed will the material reach?
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Start with Newtonian physics
Equate energy to 0.5 mv2 (= 0.5 v2)
v=5x106 m s-1
Few % of c
If all the energy is thermalised (i.e. the
velocities are randomised) and assuming gas
of protons and electrons, so mean particle
mass = 0.5 mp:
•  0.5 (0.5 mp)v2= (3/2)
x kT
•  mp=1.67x10-27 kg, K =1.38x10-23 m2 kg s-2 K-1
•  so kT ~ 50 keV
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Important concept: accretion efficiency
•  How much energy can we get from accretion
compared to fusion?
•  Energy released per unit mass of material accreted =
GM/R
•  Energy equivalent per unit rest mass = c2
•  So we can consider the ‘efficiency’ of accretion to be
GM/(Rc2)
•  For a white dwarf this is ~ 1.5 x 10-4
•  Fusion of hydrogen converts 0.007 of rest mass to
energy so we could say this has an efficiency of
0.7%
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What actually will happen?
•  Accretion onto a white dwarf not very efficient
–  50 times less efficient than fusion
–  Need to accrete rapidly to be luminous source
•  Question: where can a white dwarf get enough
material to be a luminous accretion powered
source?
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Answer: a companion star
Hence the term X-ray binary
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How will the accreting (‘primary’) star
get material from the donor
(‘secondary’) star?
2 possibilities…
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1.
Stellar wind or extended
atmosphere
Massive stars have strong
dense winds, and eject
large amounts of material:
up to 10-6 solar masses per
year for O stars
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2. Gravitational disruption of
secondary star:
This is the only way to get substantial material from a low mass,
main sequence secondary
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Roche Lobes
•  Geometry considered by French
mathematician Edouard Roche
•  Imagine the two stars as point masses
rotating about their centre of mass. If we work
out the force on a test particle at any place in
the systems we can work out surfaces of
constant potential. Close to the individual
stars the potential surfaces will be spheres
around the individual stars. Far away there
will be one circle enclosing both stars. For
some potential there will be two regions in
contact. These regions are called the Roche
Lobes.
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If one of the stars fills its Roche lobe (it won’t be the compact star!)
material can be transferred through the inner Lagrangian point. This is
called “Roche lobe overflow”.
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Question: What happens to the accreting
material?
Will it fall straight onto the white dwarf?
Where and how will the kinetic energy be dissipated?
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Answer
•  Because the binary is rotating, the material will
not fall directly towards the primary.
•  How it gets to the white dwarf depends on the
magnetic field of the white dwarf
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Case 1: no magnetic field
•  The material leaving the secondary has angular
momentum, so it cannot fall directly onto the
primary. Instead it will form a disc.
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Cataclysmic variable
Picture by Dr Mark Garlick
(ex-MSSL, now space artist and author)
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•  Angular momentum must be lost
–  Must be some friction or viscosity in the disk to
allow material to move from the outside to the
inside.
–  Inner parts of the disk will have higher velocities
than outer parts, just like the Keplerian orbits of
planets.
–  The viscosity will cause the material to radiate.
–  The disk will relatively flat but also dense, because
it is constrained to lie in the orbital plane.
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Viscosity:
Imagine dividing the disk up into little pieces as shown.
The inner piece is moving faster than the outer piece.
Any drag between the two pieces will slow the inner
piece and accelerate the outer piece – this transfers
angular momentum. The outer piece will move
outward, the inner piece will move inward.
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Radiation emitted by the disc?
•  Up to half the available energy can be
extracted by viscosity in the disc.
–  Proof: assume the material ends in a circular orbit
at the W.D. surface
–  Accretion disc should be bright.
•  Flat but dense structure; optically thick.
•  The rest of the energy comes out when the
material reaches white dwarf surface –
thermal emission, may be optically thick or
optically thin.
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Case 2: strong magnetic field
•  White dwarfs can have fields of 103 T
•  Force on charged particles crossing magnetic
field lines is proportional to magnetic field B.
–  If B is large, particles cannot cross!
–  Material will be channeled directly along the
magnetic field lines onto the white dwarf.
–  No disc.
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Slide 9
Charged particle in a magnetic field
F=q x v⊥ x B
Slide 10
Charged particle in a magnetic field
•  F=q x v⊥ x B
•  circular motion in the plane of the sky
perpendicular to B
•  no acceleration parallel to B
•  gyro frequency is
qB
2πm
•  ‘cyclotron radiation’
–  What will the emission mechanisms be?
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ASCA observation of Spinning magnetic white dwarf in AO Psc
(2 day lightcurve)
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velocity only a few % of c
moderate photon energy density
strong magnetic field
In the end the material crashes into white
dwarf
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2 emission mechanisms
•  Cyclotron emission
•  Thermal emission
•  Both come from “Accretion column”.
–  Optically thin at the top where there is a shock.
–  Optically thick at the bottom where the density is high.
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What about accretion onto Neutron stars?
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Mass M ~ 1.5 solar mass = 3 x 1030 kg
Radius R ~ 1.3 x 104 m
So energy released per kg is GM/R =1.5x1016 J
This is an ‘efficiency’ of about ~15%
–  So we expect neutron star X-ray binaries to have
much higher luminosities than cataclysmic variables.
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Sco X-1 discovery observation
•  Rocket flight by Giacconi et al 1962
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Also:
•  V -> half the speed of light – relativistic effects
important
•  Magnetic field can be up to 108 T
–  (truly astronomical magnetic field!)
•  Emission mechanisms?
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Emission mechanisms in neutron star
binaries
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Large magnetic field – high energy cyclotron
v->c, and large magnetic field – synchrotron
v->c, photon density large – inverse Compton
Particles interactions in the disk, and on
collision with neutron star surface – thermal
emission
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Black holes: energy from throwing
things into bottomless pits?
•  Important difference from other stars:
•  Black holes do not have a solid surface
•  Nothing can escape from within the Schwarzschild
radius (non-rotating hole)
•  RS=2GM/c2
•  If E per unit mass = GM/R, E= 0.5 at RS
•  So in principle might expect efficiency of ~0.5
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Caution:
•  In Newtonian mechanics material dropped
into the hole will reach the speed of light.
Need special relativity to deal with it properly.
•  Actually need general relativity to deal with
such strong gravity.
•  However, basic features of accretion onto a
black hole can be gleaned just remembering
that nothing, not even light, escapes from
within RS.
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Getting the energy out
•  No physical surface -> no impact!
–  (c.f. NS, WD, 50% of energy released at surface)
–  The energy can be “advected” into the hole.
–  So any energy that is going to come out has to
escape before the material gets to RS
•  This means that the accretion disk will be an
extremely important source of radiation in an
accreting black hole
•  Efficiency will be < 50% (probably ~10%)
•  Emission mechanisms?
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Emission mechanisms
•  Similar to the neutron star binaries, but without the
extraordinarily strong magnetic fields.
•  Thermal emission from the disc
•  v->c, photon density large – inverse Compton
•  v->c, and magnetic field -- synchrotron
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Finding black holes
•  Black holes are not science fiction, we have found
them as X-ray sources in our own galaxy and in
the LMC.
•  X-ray/γ-ray surveys so far are the only way we
have successfully found stellar mass black holes.
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Key points:
•  Accretion can be a significant source of energy
provided:
–  It is onto a compact and/or massive object
–  There is a sufficient supply of fuel
•  X-ray binaries satisfy both these criteria
•  Accretion onto a WD has lower efficiency than
fusion (~10-4)
•  Accretion onto a NS or BH has higher efficiency
than fusion (~0.15)
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