Transcript highen_04_05_binaries - Mullard Space Science Laboratory

High energy Astrophysics
Mat Page
Mullard Space Science Lab, UCL
4+5. Accretion and
X-ray binaries
Slide 2
1. Overview
• This pair of lectures:
• Accretion as a supply of energy
• Accretion onto white dwarfs, neutron stars
and black holes
• X-ray binaries
• Emission mechanisms
Slide 3
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
Slide 4
Why is this important in high energy
astrophysics?
• 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 any of the emission mechanisms discussed
last time, this energy can be radiated.
• Accretion is a means of getting energy from
gravity.
Why important at high energies?
Slide 5
• 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
Slide 6
For high energy astrophysics we need high
energy per particle. 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
Slide 7
• 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
• Accretion onto massive objects and/or
compact objects will be important in high
energy astrophysics
Slide 8
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 incredible.
Slide 9
So what happens
when we accrete
some material onto
the surface of a white
dwarf?
Slide 10
Accretion onto white dwarfs
•
•
•
•
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?
Slide 11
•
•
•
•
•
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, so kT ~ 50 keV
Slide 12
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%
Slide 13
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?
Slide 14
Answer: a companion star
Hence the term X-ray binary
Slide 15
How will the accreting (‘primary’) star
get material from the donor
(‘secondary’) star?
2 possibilities…
Slide 16
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
Slide 17
2. Gravitational disruption of
secondary star:
This is the only way to get substantial material
from a low mass, main sequence secondary
Slide 18
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.
Slide 19
Slide 20
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”.
Slide 21
Question: What happens to
the accreting material?
Will it fall straight onto the white dwarf?
Where and how will the kinetic energy be
dissipated?
Slide 22
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
Slide 23
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.
Cataclysmic variable
Slide 24
Picture by Mark Garlick (ex MSSL, now space artist)
Slide 25
• 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.
Slide 26
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.
• Viscosity mechanism not well understood!
Slide 27
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.
Slide 28
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.
Slide 29
– What will the emission mechanisms be?
Slide 30
ASCA observation of Spinning magnetic
white dwarf in AO Psc (2 day lightcurve)
Slide 31
•
•
•
•
velocity only a few % of c
moderate photon energy density
strong magnetic field
In the end the material crashes into
white dwarf
Slide 32
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.
Slide 33
Slide 34
What about accretion onto Neutron stars?
• Mass M ~ 1 solar mass = 4 x 1030 kg
• Radius R ~ 104 m
• So energy released per kg is GM/R
=1.4x1016 J
• This is an ‘efficiency’ of about ~15%
– So we expect neutron star X-ray binaries to
have much higher luminosities than
cataclysmic variables.
Slide 35
Sco X-1 discovery observation
• Rocket flight by Giacconi et al 1962
Slide 36
Also:
• V -> half the speed of light – relativitistic
effects important
• Magnetic field can be up to 108 T
– (truly astronomical magnetic field!)
• Emission mechanisms?
Slide 37
Emission mechanisms in neutron star
binaries
•
•
•
•
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
Black holes: energy from
throwing things into
bottomless pits?
Slide 38
• 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
Slide 39
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.
Slide 40
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?
Slide 41
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
Slide 42
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/g-ray surveys so far are the only way
we have successfully used to find stellar
mass black holes.
• Much of the work taking place is to find out if
their properties match theoretical predictions.
Slide 43
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 (~0.1)