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Radiation Processes High Energy Astrophysics jlc@mssl.ucl.ac.uk http://www.mssl.ucl.ac.uk/ 1. Interaction of radiation with matter: Photoelectric absorption and the ISM; Thomson and Compton scattering; Pair production; Synchrotron self-absorption; Inverse Compton scattering [2] 2 Absorption Processes Photon emission processes have corresponding absorption processes We will consider X-ray absorption. Emission processes Absorption process Recombination Photoionization Inverse Compton electron scattering e-/e+ annihilation e-/e+ pair production synchrotron emission synchrotron self absorption 3 Photon Absorption Process Cross Sections • 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 Z energies (E > 2moc2) while the Compton effect is dominant at intermediate 4 E (MeV) → energies Photoionization e- Atom absorbs photon ( EI ) Atom, ion or molecule h 3.5 Cross-section () characterized by edges corresponding to h ionization edges. 5 Photoelectric Absorption Cross-section The photoelectric absorption cross-section for photons with E > EI and h << mec2 is given by - K = 4√2 T a4 Z5 (moc2/)7/2 where EI is the electron binding energy, a is the fine structure constant and T is the Thomson cross-section Note dependence on Z5 and on -7/2 6 Example of photoelectric absorption eg. soft X-rays from a star absorbed by ISM star interstellar cloud observer I I 7 How much passes through? Take a path of length dl (metres) nZ is the number density (m 3 ) of element Z. Cross-section offered by element Z at energy E is given by: Z ( E )( m 2 ) dl (m) dV 8 The fraction of volume dV which is blocked by the presence of element Z is : nZ Z ( E )dl Thus fraction of flux F lost in volume dV is: dF FnZ Z ( E )dl or : dF nZ Z ( E )dl F 9 Integrating over length from source... dF F nZ Z ( E)dl Z ( E ) nZ dl F F0 exp( Z ( E ) nZ dl ) Including all elements in the line of sight: nH F F0 exp Z ( E ) nZ dl Z nH 10 Optical depth This becomes: F0 exp ( eff ( E ). N H ) This is ‘t’, the optical depth, which has no dimensions nZ eff ( E ) Z ( E ) This is the effective cross-section, Z nH weighted over the abundance of elements with respect to hydrogen 11 Interstellar Medium Absorption Cross-section The effective photoelectric absorption cross-section, eff, 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) 12 Column density The column density given by : N H nH dl 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... 13 Clumping of the ISM Take an example at low energies, e.g. at h 0.1keV , eff 10 m 24 2 Average ISM density At a distance, d=100 pc H 10 m 6 3 310 m 18 14 Smooth versus clumpy star observer smooth 6 3 10 / m clumpy Hot medium Cold dense clouds 0.110 / m 6 3 4 10 / m 6 3 15 Numerical example • Through the smooth medium - N H H d 3 10 / m 24 2 F F0 exp( 3 10 10 ) 24 F0 24 0.05F0 20 • Through the clumpy medium - N H 3 10 0.110 0.3 10 / m 18 6 24 2 ( F F0 exp 0.3 10 10 24 24 ) 0.75 F 0 16 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. 17 Thomson Scattering low-E photon scattered by electron - electron h h Thomson cross-section is given by - 8 re , where re 2.82 10 15 m 2 3 6.65 10 e 29 2 m 18 Thomson scattering cont. 3 If N = number of particles per m then fraction of area 1m blocked by a square metre of path = 29 6.65 10 N /m 1m If R is the extent of the absorbing region t 6.65 10 29 NR ( = optical depth) F F0 exp ( t ) along the line of sight, and 19 Compton scattering In Compton scattering, wavelength increases and frequency decreases i.e. photon energy decreases electron h h 0 q frequency 1 h 1 (1 cosq ) change 0 mo c 2 20 Compton scattering (cont.) 0 h On average, 0 mo c 2 h 0 mo c 2 21 Electron-positron pair production e- g-ray y q x photon e+ 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 22 Minimum g-ray energy required Must first demonstrate that E ( pc ) 2 2 is a relativistic invariant. Rest energy of particle, E mo c 2 1 m gm0 g v 2 1 2 c 23 Thus, from E mc and pc mvc, 2 (m c ) 2 2 (m0vc) 2 m c c v 2 2 ( 2 2 ) (1 v ) (1 v ) ( ) 0 0 2 /c 2 2 /c 2 1 v / c 2 2 m c c v 2 0 2 m0 c ( 2 4 2 2 ) c v 2 2 2 And this is a c relativistic invariant 24 Total initial momentum, p pg p p ( pc) ( px c ) ( p y c ) 2 2 2 thus ( pg c p p c cosq ) ( p p c sin q ) 2 2 pg c p c cos q 2 2 2 2 p 2 2 pg p p c cosq p pc sin q 2 2 2 2 pg c p c 2 pg p pc cosq 2 2 2 2 p 2 25 But since pg c Eg , ( pc)2 Eg E 2Eg E p cosq 2 2 p and - [ E ( pc) ]initial (Eg E p ) 2 2 2 (Eg E 2Eg E p cosq ) 2 2 p 2 Eg E p (1 cosq ) 26 Calculating the minimum energy Assuming e+ and e- have no momentum… [ E ( pc) ] final 2mo c 2 2 ( ) 2 2 and since 2 Eg E p (1 cosq ) , (2m c ) Which gives us 2 2 this expression Eg o 2 E p (1 cosq ) for the energy of the g-ray photon 27 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 Eg min (m c ) o 2 2 given by: Ep 28 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. 29 Photon versus particle density e.g. for 3 K m-wave background photons - E h 3 10 eV 4 14 3 3 U ph 5 10 Jm 310 eVm 5 Corresponding to about 109 photons / m 3 6 No of nuclei in space is about 10 / m3 30 Synchrotron Self-Absorption e- e- Relativistic electrons moving in a magnetic field 31 Synchrotron Emission Electrons, mainly responsible for emission at frequency , have energy, E, given by: 1 2 mo c 2 1 2 E~ mo c . eB c and for a power law electron spectrum logF log 32 Blackbody turnover Assume Synchrotron power-law cut off, max, is given by: 2 E eB max 2mo c 3 4 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 33 On the Rayleigh-Jeans side... impossible logF blackbody R-J synchrotron log Rayleigh-Jeans approximation to blackbody... I ( )d 2 d 2kT 2 c 34 Source distance For d=source distance and R=source size, R d 2 R 2 d 35 Total flux at Earth... So total energy flux at Earth is given by: F I ( ) 2 2E 2 c 1 8m 3 5 2 o Be 36 SSA spectrum SSA log F log a Optically-thick regime Optically-thin a lies at the point where the observed synchrotron flux equals the blackbody limit. 37 … and SSA frequency Substituting for then: 1/ 2 8m 3 5 R 2 F Be o 2 d and R 3 10 F B d 17 1/ 2 1/ 4 5 / 4 38 SSA in Compact X-ray sources X-ray frequency, =1018 Hz -29 If F ~ 10 J m-2 s -1 Hz - typical X-ray source value d = 10 kpc and B = 108 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 a to be observable in the X-ray band). but a neutron star diameter is 10 to 20km 39 Radiation processes (summary) • Thermal - Bremsstrahlung electron energies ~ photon energies to produce X-rays, b = v/c ~ 0.1 • Non-thermal - Synchrotron and Inverse Compton 40 Synchrotron Emission For an electron spiralling in a magnetic field B with energy E, the peak radiated frequency, m is m = g2 B e/2 mo = E2 B e/2 mo3 c4 But E = g mo c2 - for a relativistic electron Hence g2 = 2 mo m/B e 41 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 2 B -10 and from U PH , => B=6x10 Tesla 2m 0 To produce X-rays of m ~ 1018 Hz, we need g S ~ 5 10 16 2 42 Inverse Compton Scattering For a relativistic electron colliding with a low energy photon, gIC2 ≈ hfinal/hinitial For X-ray production consider: - starlight: <h> ~ 2eV (l~6000A) -4 - 3K background: <h> ~3x10 eV 8keV then g 2 h IC 3 = 410 for stars 7 = 310 for the 3K background We need cosmic rays!!! 43 RADIATION PROCESSES END OF TOPIC 44

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