Radiation Processes

1. Radiation Processes High Energy Astrophysics jlc@mssl.ucl.ac.uk http://www.mssl.ucl.ac.uk/

2. Interaction of radiation with matter: Photoelectric absorption and the ISM; Thomson and Compton scattering; Pair production; Synchrotron self-absorption; Inverse Compton scattering [2]

3. Absorption Processes Photon emission processes have corresponding absorption processes We will consider X-ray absorption. Emission processes Recombination Inverse Compton e-/e+ annihilation synchrotron emission Absorption process Photoionization electron scattering e-/e+ pair production synchrotron self absorption

4. Photon Absorption Process Cross Sections Z E (MeV) → • Absorption coefficients are plotted • against photon energy for the three • processes: • - Photoelectric absorption • - Compton effect • - Pair production • Absorber is lead – plots shift • up and down in energy with • Z increasing or decreasing • Photoelectric absorption is • dominant at low energies • and pair production at high • energies (E > 2moc2) while • the Compton effect is • dominant at intermediate • energies

5. Photoionization e- Atom absorbs photon Atom, ion or molecule Cross-section (s) characterized by edges corresponding to ionization edges.

6. Photoelectric Absorption Cross-section The photoelectric absorption cross-section for photons with En > EI and hn << mec2 is given by - sK = 4√2 sTa4 Z5 (moc2/n)7/2 where EI is the electron binding energy, a is the fine structure constant and sT is the Thomson cross-section Note dependence on Z5 and on n-7/2

7. Example of photoelectric absorption eg. soft X-rays from a star absorbed by ISM interstellar cloud star observer I I n n

8. How much passes through? Take a path of length dl (metres) is the number density ( ) of element Z. Cross-section offered by element Z at energy E is given by: dl (m) dV

9. The fraction of volume dV which is blocked by the presence of element Z is : Thus fraction of flux F lost in volume dV is: or :

10. Integrating over length from source... Including all elements in the line of sight:

11. Optical depth This becomes: This is ‘t’, the optical depth, which has no dimensions This is the effective cross-section, weighted over the abundance of elements with respect to hydrogen

12. Interstellar Medium Absorption Cross-section The effective photoelectric absorption cross-section, seff, is plotted against wavelength in Å for the interstellar medium for an assumed set of interstellar element abundances (Morison and McCammon, 1983, Ap.J., 270, 119)

13. Column density The column density given by : is the number of H – atoms per m2 column Column density is measured from the 21cm atomic hydrogen line - but not foolproof. There is a factor of 2 uncertainty, wide beams, molecular hydrogen contamination...

14. Clumping of the ISM Take an example at low energies, e.g. at At a distance, d=100 pc Average ISM density

15. Smooth versus clumpy observer star smooth clumpy Hot medium Cold dense clouds

16. Numerical example • Through the smooth medium - • Through the clumpy medium -

17. Electron scattering • Thomson scattering - the scattering of a photon by an electron where the photon energy is much less than the rest mass of the electron. • Compton scattering - photons have a much higher energy in this case and lose some of their energy in the scattering process.

18. Thomson Scattering low-E photon scattered by electron - Thomson cross-section is given by - electron , where

19. Thomson scattering cont. then fraction of area blocked by a square metre of path = If N = number of particles per 1m 1m If R is the extent of the absorbing region along the line of sight, ( = optical depth) and

20. Compton scattering In Compton scattering, wavelength increases and frequency decreases i.e. photon energy decreases electron q frequency change

21. Compton scattering (cont.) On average,

22. e- g-ray y q x e+ photon Electron-positron pair production Two photons, one of which must be a g-ray with E > 2mec2, collide and create an electron-positron (e-/e+) pair. This is therefore a form of g-ray absorption

23. Minimum g-ray energy required Must first demonstrate that is a relativistic invariant. Rest energy of particle,

24. Thus, from and , And this is a relativistic invariant

25. Total initial momentum, thus

26. But since , and -

27. Calculating the minimum energy Assuming e+ and e- have no momentum… and since , Which gives us this expression for the energy of the g-ray photon

28. And this is... found by simply making the denominator as large as possible, ie when cos(q)= -1, or when q=180 degrees. g-ray e-/e+ photon And the minimum g-ray energy is given by:

29. Photon-nucleus pair production • In the laboratory, it is more usual to consider photon-nucleus production. So why do we ignore it in space? • Photons and nuclei have a similar cross-section, and the g-ray does not differentiate much between another photon or a nucleus. • Then we must compare the photon density with the particle density in space.

30. Photon versus particle density e.g. for 3 K m-wave background photons - 9 3 Corresponding to about 10 photons / m 6 3 No of nuclei in space is about 10 / m

31. Synchrotron Self-Absorption e- e- Relativistic electrons moving in a magnetic field

32. logF n logn Synchrotron Emission Electrons, mainly responsible for emission at frequency n, have energy, E, given by: and for a power law electron spectrum

33. Blackbody turnover Assume Synchrotron power-law cut off, nmax, is given by: and assume each electron emits and absorbs only at this peak frequency. Then, we will replace this with the mean energy per particle for a thermal source or E ~ kT

34. impossible logF blackbody synchrotron R-J logn On the Rayleigh-Jeans side... n Rayleigh-Jeans approximation to blackbody...

35. W R d Source distance For d=source distance and R=source size,

36. Total flux at Earth... So total energy flux at Earth is given by:

37. SSA log F n log n n a Optically-thick regime Optically-thin n lies at the point where the observed synchrotron flux equals the blackbody limit. a SSA spectrum

38. … and SSA frequency Substituting for W then: and

39. SSA in Compact X-ray sources 18 X-ray frequency, n=10 Hz If F ~ 10 J m s Hz - typical X-ray source value d = 10 kpc and B = 10 Tesla (the field for a neutron star) This gives a maximum for R of ~1 km for SSA of X-rays to occur (ie for n to be observable in the X-ray band). but a neutron star diameter is 10 to 20km -29 -2 -1 n 8 a

40. Radiation processes (summary) • Thermal - Bremsstrahlung electron energies ~ photon energies to produce X-rays, b = v/c ~ 0.1 • Non-thermal - Synchrotron and Inverse Compton

41. Synchrotron Emission For an electron spiralling in a magnetic field B with energy E, the peak radiated frequency, nm is nm = g2 B e/2 p mo • = E2 B e/2 p mo3 c4 But E = g mo c2 - for a relativistic electron Hence g2 = 2 p mo nm/B e

42. Electron energies required • Synchrotron emission depends on the magnetic field strength. Assuming equipartition of energy - starlight, cosmic rays + magnetic fields have all the same energy density in Galaxy and from , => B=6x10 Tesla To produce X-rays of nm ~ 1018 Hz, we need -10

43. -4 Inverse Compton Scattering For a relativistic electron colliding with a low energy photon, gIC2≈ hnfinal/hninitial For X-ray production consider: - starlight: <hn> ~ 2eV (l~6000A) - 3K background: <hn> ~3x10 eV then = for stars = for the 3K background We need cosmic rays!!!

44. RADIATION PROCESSES END OF TOPIC