A Basic Course on Supernova Remnants

1. A Basic Course onSupernova 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. r V shock 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=u1/u2): • 4, for a non relativistic fluid • 7, for a relativistic one

3. 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. Thermal and non-thermal particles • Naif view • Electrons & ions are shocked independently • Similar Vth, i.e. Te~(me/mp)Tp • 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. Even more striking, evidence fornon-thermal, relativistic particles • Radio synchrotron emission n SNRs • And even in X-rays, in a few of them

6. shock flow speed X Diffusive shock acceleration • Fermi acceleration • Converging flows • Particle diffusion(How possible, in acollisionless plasma?) • Scattering on MHD waves (in the shock reference frame)

7. v NR v+2U = v(1+2U/v) U p R p(1+2U/c) A test particle approach(Bell 1978) • Collision against a (N.R.) moving wall: • Momentum after N cycles: i.e. (averaged over directions)

8. Probability of having N cycles • Return probability • Probability of N cycles

9. 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. The convection-diffusion eq. • A different approach to the problem • Heuristic explanation: • Advected flow • Diffusive flow • Diffusion in momentum spaceprovided that

11. Solving the equation • Boundary conditions • Velocity profile: • Integrate between x=+∞ and x=- ∞(now x has disappeared) • Solution of linear equation:

12. A cosmic-ray precursor • In the unshocked medium • Accelerated particle may reach, in front of the shock, a distanceAny effect on the pre-shock fluid ?

13. Dimensional quantities • Parallel mean free path • Diffusion coefficient • Perpendicular diffusion(can be much lower than the parallel one)

14. Characteristic times • Acceleration time • Age • Synchrotron losses • Loss-dominated regime naturally located in the X-ray range Independent of B strength Diffusion must be efficientalso upstream !!

15. SN 1006 spectrum • Rather standard( -0.6)power-law spectrum in radio(-0.5 for a classical strong shock) • Synchrotron X-rays below radio extrapolationCommon effect in SNRs(Reynolds and Keohane 1999) • Electron energy distribution: • Fit power-law + cutoff to spectrum: “Rolloff frequency”

16. Measures of rolloff frequency • SN 1006 (Rothenflug et al 2004) • Azimuthal depencence of the breakTruly loss limited? Changes in tacc? Varying η?

17. Chandra ASCA Very sharp limbs in SN 1006

18. B from limb sharpness (Bamba et al 2004) Profiles of resolved non-thermal X-ray filaments in the NE shell of SN 1006 Length scales 1” (0.01 pc) upstream20” (0.19 pc) downstream Consistent withB ~ 30 μG

19. rolloff tsync> tacc  > Bohm A diagnostic diagram • Acceleration timetacc = 270 yr • Derivation of the diffusioncoefficients:u=8.9 1024 cm2s-1d=4.2 1025 cm2s-1(Us=2900 km s-1)to compare withBohm=(Emaxc/eB)/3

20. 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. 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. (Blondin and Ellison 2001) (Decourchelle et al 2000) 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

23. Optical X-rays Radio SNR 1E 0102.2-7219 (Hughes et al 2000, Gaetz et al 2000) • Very young and bright SNR in the SMC • Expansion velocity (6000 km s-1, if linear expansion)measured in optical (OIII spectra) and inX-rays (proper motions) • Electron temperature~ 0.4-1.0 keV, whileexpected ion T ~ 45 keV • Very smallTe/Ti, orTimuch less than expected?Missing energy in CRs?

24. Synchrotron νFν IC γ-ray Radio X-ray 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.

25. (Ellison et al 2000) • 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)

26. 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. Dynamical effects of theaccelerated particles ontothe shock structure(Drury and Voelk 1981) Shock modification • Intrinsically non linear • Shock precursor • Discontinuity (subshock) • Larger overall compression factor • Accelerated particle distribution is no longer a power-law

28. Blasi Solution Thermal Deviations from Power-Law • In modified shocks,acc. particles withdifferent energiessee different shockcompression factors.Higher energy Longer mean free path Larger compress.factor Harder spectrum • Concavity in particledistribution.(also for electrons) Standard PL

29. 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. Optical emission in SN1006 • “Pure Balmer” emissionin SN 1006 • Here metal lines are missing (while they dominate in recombination spectra) • Extremely metal deficient ?

31. “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. The role of neutral H (Chevalier & Raymond 1978, Chevalier, Kirshner and Raymond 1980) • 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 • Charge-exchange cross section is larger at lower vrel • Fast neutral component more prominent in slower shocks

33. (Kirshner, Winkler and Chevalier 1987) (Hester, Raymond and Blair 1994) Cygnus Loop H-alpha profiles • MEASURABLE QUANTITIES • Intensity ratio • Displacement (not if edge-on) • FWHM of broad component (Ti !!) • FWHM of narrow component • (T 40,000 K – why not fully ionized?)

34. THE END