High energy Astrophysics

Mat Page

Mullard Space Science Lab, UCL

4+5. Accretion and X-ray binaries

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 2

• 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

What is accretion:

Slide 3

• 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 is this important in high energy astrophysics?

Slide 4

Why important at high energies?

• Gravity is a very weak force: – the gravitational attraction between individual

particles is very small (c.f. electrostatic forces)– The gravitational potential energy is:

-G m1m2

r12

E=

Where G is the gravitational constant, m1 and m2 are the masses and r12 is the distance between them. Note the ‘-’ sign

Slide 5

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

GMmE=

R

Slide 6

• 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 7

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 8

So what happens when we accrete some material onto the surface of a white dwarf?

Slide 9

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 10

• 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 11

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 12

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 13

Answer: a companion star

Hence the term X-ray binary

Slide 14

How will the accreting (‘primary’) star get material from the donor

(‘secondary’) star?

2 possibilities…

Slide 15

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 16

2. Gravitational disruption of secondary star:

This is the only way to get substantial material from a low mass, main sequence secondary

Slide 17

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 18

Slide 19

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 20

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 21

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 22

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.

Slide 23

Picture by Mark Garlick (ex MSSL, now space artist)

Cataclysmic variable Slide 24

• 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 25

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 26

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 27

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 28

– What will the emission mechanisms be?

Slide 29

ASCA observation of Spinning magnetic white dwarf in AO Psc (2 day lightcurve)

Slide 30

• velocity only a few % of c

• moderate photon energy density

• strong magnetic field

• In the end the material crashes into white dwarf

Slide 31

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 32

Slide 33

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 34

Sco X-1 discovery observation

• Rocket flight by Giacconi et al 1962

Slide 35

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 36

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

Slide 37

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

Slide 38

• 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.

Caution:Slide 39

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 40

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 41

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/-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 42

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)

Slide 43