1. High energy Astrophysics Mat Page Mullard Space Science Lab, UCL 4+5. Accretion and X-ray binaries

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 2

3. Chambers 20 th 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

4. 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

5. 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 m 1 m 2 r 12 E= Where G is the gravitational constant, m 1 and m 2 are the masses and r 12 is the distance between them. Note the ‘-’ sign Slide 5

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 GMm E= R Slide 6

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 7

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 8

9. So what happens when we accrete some material onto the surface of a white dwarf? Slide 9

10. Accretion onto white dwarfs Mass M ~ 1 solar mass = 2 x 10 30 kg Radius R ~ 10 7 m G=6.67 x 10 -11 m 3 kg -1 s -2 So energy released per kg is GM/R =1.4x10 13 J If this is converted completely to kinetic energy then what speed will the material reach? Slide 10

11. Start with Newtonian physics Equate energy to 0.5 mv 2 (= 0.5 v 2 ) v=5x10 6 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 m p : 0.5 (0.5 m p )v 2 = ( 3/2) x kT m p =1.67x10 -27 kg, so kT ~ 50 keV Slide 11

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 = c 2 So we can consider the ‘efficiency’ of accretion to be GM/(Rc 2 ) 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

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 13

14. Answer: a companion star Hence the term X-ray binary Slide 14

15. How will the accreting (‘primary’) star get material from the donor (‘secondary’) star? 2 possibilities… Slide 15

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 16

17. 2. Gravitational disruption of secondary star: This is the only way to get substantial material from a low mass, main sequence secondary Slide 17

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 18

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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 20

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 21

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 22

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. Slide 23

24. Picture by Mark Garlick (ex MSSL, now space artist) Cataclysmic variable Slide 24

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 25

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 26

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 27

28. Case 2: strong magnetic field White dwarfs can have fields of 10 3 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

29. –What will the emission mechanisms be? Slide 29

30. ASCA observation of Spinning magnetic white dwarf in AO Psc (2 day lightcurve) Slide 30

31. velocity only a few % of c moderate photon energy density strong magnetic field In the end the material crashes into white dwarf Slide 31

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 32

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34. What about accretion onto Neutron stars? Mass M ~ 1 solar mass = 4 x 10 30 kg Radius R ~ 10 4 m So energy released per kg is GM/R =1.4x10 16 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

35. Sco X-1 discovery observation Rocket flight by Giacconi et al 1962 Slide 35

36. Also: V -> half the speed of light – relativitistic effects important Magnetic field can be up to 10 8 T –(truly astronomical magnetic field!) Emission mechanisms? Slide 36

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 Slide 37

38. 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) R S =2GM/c 2 If E per unit mass = GM/R, E= 0.5 at R S So in principle might expect efficiency of ~0.5 Slide 38

39. 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 R S. Caution: Slide 39

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 R S 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

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 41

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/  -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

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) Slide 43