Fund. Physics & Astrophysics of Supernova Remnants

1. Fund. Physics & Astrophysicsof Supernova Remnants • Lecture #1 • What SNRs are and how are they observed • Hydrodynamic evolution on shell-type SNRs • Microphysics in SNRs – electron-ion equ • Lecture #2 • Microphysics in SNRs - shock acceleration • Statistical issues about SNRs • Lecture #3 • Pulsar wind nebulae

2. Order-of magn. estimates • SN explosion • Mechanical energy: • Ejected mass: • VELOCITY: • Ambient medium • Density: Mej~Mswept when: • SIZE: • AGE:

3. Tycho – SN 1572 “Classical” Radio SNRs • Spectacular shell-like morphologies • comparedto optical • polarization • spectral index(~ – 0.5) BUT • Poor diagnostics on the physics • featureless spectra (synchrotron emission) • acceleration efficiencies ?

4. 90cm Survey4.5 < l < 22.0 deg(35 new SNRs found;Brogan et al. 2006) Blue: VLA 90cm Green: Bonn 11cmRed: MSX 8 mm • Radio traces both thermal and non-thermal emission • Mid-infrared traces primarily warm thermal dust emission A view of Galactic Plane

5. SNRs in the X-ray window • Probably the “best” spectral range to observe • Thermal: • measurement of ambient density • Non-Thermal: • synchrotron-emitting electrons are near the maximum energy (synchrotron cutoff)

6. X-ray spectral analysis • Low-res data • Overall fit with thermal models • High-res data • Abundances of elements • Single-line spectroscopy!

7. Shell-type SNR evolutiona “classical” (and wrong) scenario Isotropic explosion and further evolution Homogeneous ambient medium Three phases: • Linear expansion • Adiabatic expansion • Radiative expansion Isotropic Homogeneous Linear Adiabatic Radiative

8. r V shock Strong shock If Basic concepts of shocks • Hydrodynamic (MHD) discontinuities • Quantities conserved across the shock • Mass • Momentum • Energy • Entropy • Jump conditions(Rankine-Hugoniot) • Independent of the detailed physics

9. Forward shock Density Reverse shock Radius Forward and reverse shocks • Forward Shock: into the CSM/ISM(fast) • Reverse Shock: into the Ejecta (slow)

10. Dimensional analysisand Self-similar models • Dimensionality of a quantity: • Dimensional constants of a problem • If only two, such that M can be eliminated, THEN evolution law follows immediately! • Reduced, dimensionless diff. equations • Partial differential equations (in r and t) then transform into total differential equations (in a self-similar coordinate).

11. Early evolution • Linear expansion only if ejecta behave as a “piston” • Ejecta with and • Ambient medium with and • Dimensional parameters and • Expansion law:

12. A self-similar model (Chevalier 1982) • Deviations from “linear” expansion • Radial profiles • Ambient medium • Forward shock • Contact discontinuity • Reverse shock • Expanding ejecta

13. Evidence from SNe • VLBI mapping (SN 1993J) • Decelerated shock • For an r-2 ambient profileejecta profile is derived

14. The Sedov-Taylor solution • After the reverse shock has reached the center • Middle-age SNRs • swept-up mass >> mass of ejecta • radiative losses are negligible • Dimensional parameters of the problem • Evolution: • Self-similar, analytic solution (Sedov,1959)

15. Density Pressure Temperature The Sedov profiles • Most of the mass is confined in a “thin” shell • Kinetic energy is also confined in that shell • Most of the internal energy in the “cavity”

16. Thin-layer approximation • Layer thickness • Total energy • Dynamics Correct value:1.15 !!!

17. from spectral fits What can be measured (X-rays) … if in the Sedov phase

18. Deceleration parameter Tycho SNR (SN 1572) Dec.Par. = 0.47 SN 1006 Dec.Par. = 0.34 Testing Sedov expansion Required: • RSNR/D(angular size) • t(reliable only for historical SNRs) • Vexp/D(expansion rate, measurable only in young SNRs)

19. Other ways to “measure”the shock speed • Radial velocities from high-res spectra(in optical, but now feasible also in X-rays) • Electron temperature from modelling the (thermal) X-ray spectrum • Modelling the Balmer line profile in non-radiative shocks (see below)

20. End of the Sedov phase • Sedov in numbers: • When forward shock becomes radiative: with • Numerically:

21. Internal energy Kinetic energy Beyond the Sedov phase • When t>ttr, energy no longer conserved.What is left? • “Momentum-conservingsnowplow” (Oort 1951) • WRONG !! Rarefied gas in the inner regions • “Pressure-driven snowplow” (McKee & Ostriker 1977)

22. 2/5 2/7=0.29 1/4=0.25 Numerical results (Blondin et al 1998) 0.33 ttr Blondin et al 1998

23. An analytic model Bandiera & Petruk 2004 • Thin shell approximation • Analytic solution H either positive (fast branch) limit case: Oort or negative (slow branch) limit case: McKee & Ostriker H,K from initial conditions

24. Inhomogenous ambient medium • Circumstellar bubble (ρ~ r -2) • evacuated region around the star • SNR may look older than it really is • Large-scale inhomogeneities • ISM density gradients • Small-scale inhomogeneities • Quasi-stationary clumps (in optical) in young SNRs (engulfed by secondary shocks) • Thermal filled-center SNRs as possibly due to the presence of a clumpy medium

25. Collisionless shocks • Coulomb mean free path • Collisional scale length (order of parsecs) • Larmor radius is much smaller (order of km) • High Mach numbers • Mach number of order of 100 • MHD Shocks • B in the range 10-100 μG • Complex related microphysics • Electron-ion temperature equilibration • Diffusive particle acceleration • Magnetic field turbulent amplification

26. (Cargill and Papadopoulos 1988) (Spitzer 1978) Electron & Ion equilibration • Naif prediction, for collisionless shocks • But plasma turbulence may lead electrons and ion to near-equilibrium conditions • Coulomb equilibration on much longer scales

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

28. “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 ?

29. 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

30. (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?)

31. 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?

33. Lectures #2 & #3 • Shock acceleration • The prototype: SN 1006 • Physics of shock acceleration • Efficient acceleration and modified shocks • Pulsar Wind Nebulae • The prototype: the Crab Nebula • Models of Pulsar Wind Nebulae • Morphology of PWN in theory and in practice • A tribute to ALMA

34. Tycho with ASCA Hwang et al 1998 The “strange case” of SN1006 “Standard”X-ray spectrum

35. Thermal & non-thermal • Power-law spectrum at the rims • Thermal spectrum in the interior

36. shock flow speed X Diffusive shock acceleration • Fermi acceleration • Converging flows • Particle diffusion(How possible, in acollisionless plasma?) • Particle momentum distributionwhere r is the compression ratio (s=2, if r = 4) • Synchrotron spectrum • For r = 4, power-law index of -0.5 • Irrespectively of diffusion coefficient (in the shock reference frame)

37. The diffusion coefficient • Diffusion mean free path(magnetic turbulence)(η > 1) • Diffusion coefficient

38. …and its effects • Acceleration time • Maximum energy • Cut-off frequency • Naturally located near the X-ray range • Independent of B

39. Basics of synchrotron emission • Emitted power • Characteristic frequency • Power-law particle distribution • If then • Synchrotron life time

40. 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”

41. Measures of rolloff frequency • SN 1006 (Rothenflug et al 2004) • Azimuthal depencence of the breakChanges in tacc? or in tsyn? ηof order of unity?

42. Dependence on B orientation? • Highly regular structure of SN 1006.Barrel-like shape suggested (Reynolds 1998) • Brighter where B is perpendicular to the shock velocity? Direction of B ?

43. Radio – X-ray comparison (Rothenflug et al 2004) • Similar pattern (both synchrotron) • Much sharper limb in X-rays (synchrotron losses)

44. (Rothenflug et al 2004) • Evidence for synchrotron losses of X-ray emitting electrons • X-ray radial profile INCONSISTENT with barrel-shaped geometry (too faint at the center)

45. Ordered magnetic field (from radio polarization) 3-D Geometry. Polar Caps? Polar cap geometry: electrons accelerated in regions with quasi-parallel field (as expected from the theory)

46. Statistical analysis (Fulbright & Reynolds 1990) Expected morphologies in radio Polar cap SNR (under variousorientations) Barrel-like SNR (under variousorientations)

47. The strength of B ? • Difficult to directly evaluate the value of the B in the acceleration zone.νrolloffis independent of it ! • “Measurements” of B must rely on some model or assumption

48. Chandra ASCA Very sharp limbs in SN 1006

49. 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

50. 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