Radiation Processes

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

2. Absorption Processes So far, considered the production of X-rays. Now, will consider X-ray absorption. Emission processes Recombination Inverse Compton e-/p+ annihilation synchrotron emission Absorption process Photoionization electron scattering e-/p+ pair production synchrotron self absorption

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

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

5. 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

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

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

8. 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

9. Column density The column density is given by : 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...

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

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

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

13. 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.

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

15. 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

16. Compton scattering In Compton scattering, the photon wavelength increases, ie its energy decreases. electron q frequency change

17. Compton scattering cont. On average,

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

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

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

21. Total initial momentum, thus

22. But since , and -

23. 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

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

25. Minimum energy for mm-wave photon g-ray photon interacts with mm-wave First converting to eV : l=1.2mm corresponds to hn=10 eV -3

26. 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.

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

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

29. E logF n n logn Synchrotron Spectrum Flux emitted as a function of frequency:

30. Blackbody turnover max Assume power-law cut off, n , is given by: And assume each electron emits & absorbs only at this peak frequency. Then, we will replace this with the mean energy per particle for a thermal source, ~kT.

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

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

33. SSA logF n logn n a Optically-thick regime Optically-thin n lies at the point where the observed synchrotron flux equals the blackbody limit. a SSA spectrum

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

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

36. SSA in Compact X-ray sources 18 X-ray frequency, n=10 Hz Assume F ~ 10 J m s Hz 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

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

38. 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 • from , => B=6x10 Tesla To produce X-rays, -10

39. Inverse Compton Scattering Consider starlight: <hn> ~ 2eV (l~6000A) or 3K background photons, <hn> ~3x10 eV then = for stars = for the 3K background, to produce X-rays. We need cosmic rays!!! -4

40. Non-thermal process (cont.) Energy distribution of cosmic ray particles within a unit volume has the form: (over at least part of the energy range) We use this to determine the relative importance of synchrotron and IC processes

41. Power radiated in the two processes is about equal in the case of equipartition of energy ie when ie an electron with a given g loses energy equally rapidly by the two processes However, it does not mean that X-rays are produced at the same rate in the two cases.

42. Ratio of IC to Synchrotron Xrays For example: Galactic X-rays require (stars) (3K) but for synchrotron

43. Ratio IC to Synchrotron (cont.) Ratio = (no of electrons with ) (no of electrons with ) But:

44. Ratio IC to Synchrotron (cont.) Thus: So which is more important for producing X-rays via IC; starlight or 3K background?

45. X-rays from IC scattering (no. X-rays produced from starlight per ) (no. X-rays produced from 3K per )

46. IC - starlight versus 3K We know that and Thus ie 3K photons more important!

47. IC or synchrotron for X-rays? Remember assuming for : thus synchrotron dominates over IC in Galaxy

48. Synchrotron emission Synchrotron emission requires very high energy particles however - and electron energy distribution may well have tailed off if there is no continuous re-supply. Also 3K radiation extends outside our Galaxy. Extragalactic radiation depends on whether there are enough electrons to produce IC.