1. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs A Basic Course on Supernova Remnants Lecture #1 –How do they look and how are observed? –Hydrodynamic evolution on shell-type SNRs Lecture #2 –Microphysics in SNRs - shock acceleration –Non-thermal emission from SNRs

2. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Basic concepts of shocks Quantities conserved across the shock discontinuity –Mass –Momentum –Energy For a strong shock, i.e. the jump conditions are: Compression ratio (r=u 1 /u 2 ): –4, for a non relativistic fluid –7, for a relativistic one shock  V

3. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs More complex than this Collisionless shocks –Coulomb equilibration scale (order of parsecs) But shocks are much sharper than that –Even tiny magnetic fields are more effective (gyration radius) –Free to escape along the field lines? Not in the presence fluctuations (e.g. MHD waves)

4. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Thermal and non-thermal particles Naif view –Electrons & ions are shocked independently –Similar V th, i.e. T e ~(m e /m p )T p Anomalous electron heating, mediated by MHD waves? (Cargill & Papadopoulos 1988, + … ) Possibly observed? (Ghavamian et a. 2007) Using Balmer line profile, Te & Tp derived independently

5. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Even more striking, evidence for non-thermal, relativistic particles Radio synchrotron emission n SNRs And even in X-rays, in a few of them

6. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs shock X flow speed (in the shock reference frame) Diffusive shock acceleration Fermi acceleration –Converging flows –Particle diffusion (How possible, in a collisionless plasma?) Scattering on MHD waves

7. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs A test particle approach (Bell 1978) Collision against a (N.R.) moving wall: Momentum after N cycles: i.e. R NR v v+2U = v(1+2U/v) U p p(1+2U/c) (averaged over directions)

8. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Probability of having N cycles Return probability Probability of N cycles

9. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Compare the two formulas from which and finally the distribution For r=4, σ=2. Spectral index 0.5 (as in radio!) Diffusivity is fundamental for the process to take place, but does not appear explicitly

10. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs The convection-diffusion eq. A different approach to the problem Heuristic explanation: –Advected flow –Diffusive flow –Diffusion in momentum space provided that

11. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Solving the equation Boundary conditions Velocity profile: Integrate between x=+∞ and x=- ∞ (now x has disappeared) Solution of linear equation:

12. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs A cosmic-ray precursor In the unshocked medium Accelerated particle may reach, in front of the shock, a distance Any effect on the pre-shock fluid ?

13. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Dimensional quantities Parallel mean free path Diffusion coefficient Perpendicular diffusion (can be much lower than the parallel one)

14. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Characteristic times Acceleration time Age Synchrotron losses Loss-dominated regime naturally located in the X-ray range Independent of B strength Diffusion must be efficient also upstream !!

15. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs SN 1006 spectrum Rather standard (  -0.6 ) power-law spectrum in radio (-0.5 for a classical strong shock) Synchrotron X-rays below radio extrapolation Common effect in SNRs (Reynolds and Keohane 1999) Electron energy distribution: Fit power-law + cutoff to spectrum: “Rolloff frequency”

16. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Measures of rolloff frequency SN 1006 (Rothenflug et al 2004) Azimuthal depencence of the break Truly loss limited? Changes in t acc ? Varying η ?

17. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Very sharp limbs in SN 1006 ASCA Chandra

18. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs B from limb sharpness Profiles of resolved non-thermal X-ray filaments in the NE shell of SN 1006 (Bamba et al 2004) Length scales  1” (0.01 pc) upstream  20” (0.19 pc) downstream Consistent with B ~ 30 μG

19. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs A diagnostic diagram Acceleration time t acc = 270 yr Derivation of the diffusion coefficients:  u =8.9 10 24 cm 2 s -1  d =4.2 10 25 cm 2 s -1 (U s =2900 km s -1 ) to compare with  Bohm =(E max c/eB)/3 rolloff t sync > t acc  >  Bohm

20. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Acceleration times & energies (Theoretical) need for large fields The case of a perpendicular field BUT how to inject particles? (mean free path has tobe comparable with the shock width)

21. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Not just test particles ? (Indirect) evidences that cosmic-ray component is dynamically relevant (ions) –Large magnetic field If synchrotron-losses regime If interpretation of narrow filaments is correct –Deviations from predicted fluid behaviour RS closer to FS Too low post-shock (ion) temperature –Effects of a shock precursor

22. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Indirect tests on the CRs Some “model-dependent” side effects of efficient particle acceleration Forward and reverse shock are closer, as effect of the energy sink HD instabilities behavior depends on the value of  eff (Decourchelle et al 2000) (Blondin and Ellison 2001)

23. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs SNR 1E 0102.2-7219 Very young and bright SNR in the SMC Expansion velocity (  6000 km s -1, if linear expansion) measured in optical (OIII spectra) and in X-rays (proper motions) Electron temperature ~ 0.4-1.0 keV, while expected ion T ~ 45 keV Very small T e /T i, or T i much less than expected? Missing energy in CRs? (Hughes et al 2000, Gaetz et al 2000) Optical Radio X-rays

24. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Gamma-ray emission A definitive way to measure the field? Measurement of gamma-ray emission, produced by the same electrons that emit X-ray synchrotron, would allow one to determine the value of B. Synchrotron IC Radio X-ray γ-ray νFννFν

25. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs On the other hand, there is another mechanism giving Gamma-ray emission –accelerated ions –p-p collisions –pion production –pion decay (gamma) Lower limit for B Need for “targets” (molecular cloud?) Efficiency in in accelerating ions? (The origin of Cosmic rays) (Ellison et al 2000)

26. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs A self-regulating model If acceleration is efficient, cosmic-ray precursor upstream Generation of MHD waves, by streaming instabilities Turbulent amplification of upstream field Effects on the diffusion coefficient A smaller diffusion coefficient makes further acceleration more efficient CLOSING THE LOOP

27. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Shock modification Dynamical effects of the accelerated particles onto the shock structure (Drury and Voelk 1981) Intrinsically non linear Shock precursor Discontinuity (subshock) Larger overall compression factor Accelerated particle distribution is no longer a power-law

28. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Deviations from Power-Law In modified shocks, acc. particles with different energies see different shock compression factors. Higher energy Longer mean free path Larger compress.factor Harder spectrum Concavity in particle distribution. (also for electrons) Standard PL Thermal Blasi Solution

29. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs The injection of electrons ? Theory predicts (~ high) values of the efficiency of shock acceleration of ions. Little is known for electrons Main uncertainty is about the injection process for electrons –Shock thickness determined by the mfp of ions (scattering on magnetic turbulence) –Electrons, if with lower T, have shorter mfps –Therefore for them more difficult to be injected into the acceleration process

30. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Optical emission in SN1006 “Pure Balmer” emission in SN 1006 Here metal lines are missing (while they dominate in recombination spectra) –Extremely metal deficient ?

31. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs “Non-radiative” emission Emission from a radiative shock: –Plasma is heated and strongly ionized –Then it efficiently cools and recombines –Lines from ions at various ionization levels In a “non-radiative” shock: –Cooling times much longer than SNR age –Once a species is ionized, recombination is a very slow process WHY BALMER LINES ARE PRESENT ?

32. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs The role of neutral H Scenario: shock in a partially neutral gas Neutrals, not affected by the magnetic field, freely enter the downstream region Neutrals are subject to: –Ionization (rad + coll) [LOST] –Excitation (rad + coll) Balmer narrow –Charge exchange (in excited lev.) Balmer broad (Chevalier & Raymond 1978, Chevalier, Kirshner and Raymond 1980) Charge-exchange cross section is larger at lower v rel Fast neutral component more prominent in slower shocks

33. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs H-alpha profiles (Hester, Raymond and Blair 1994) (Kirshner, Winkler and Chevalier 1987) Cygnus Loop FWHM of broad component ( T i !!) FWHM of narrow component ( T  40,000 K – why not fully ionized?) MEASURABLE QUANTITIES Intensity ratio Displacement (not if edge-on)

34. Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs THE END