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. Order-of-magnitude 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 • compared to optical • spectral index • polarization 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 emission from electrons close to maximum energy (synchrotron cutoff) Cassiopeia A

6. X-ray spectral analysis • Lower resolution data • Either fit with a thermal model • Temperature • Density • Possible deviations from ionization eq. • Possible lines • Or a non-thermal one (power-law) • Plus estimate of thephotoel. Absorption SNR N132D with BeppoSAX

7. Higher resolution data • Abundances of elements • Line-ratio spectroscopy N132D as seen with XMM-Newton(Behar et al. 2001) • Plus mapping in individual lines

8. Thermal vs. Non-Thermal Cas A, with Chandra SN 1006, with Chandra

9. Shell-type SNR evolutiona “classical” (and incorrect) scenario Isotropic explosion and further evolution Homogeneous ambient medium Three phases: • Linear expansion • Adiabatic expansion • Radiative expansion Goal: simple description of these phases Isotropic (but CSM) Homogeneous Linear Adiabatic Radiative

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

11. 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

12. Dimensional analysisand Self-similar models • Dimensionality of a quantity: • Dimensional constants of a problem • If only two, such that M can be eliminated, THEN expansion 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).

13. Log(ρ) CORE ENVELOPE Log(r) Early evolution • Linear expansion only if ejecta behave as a “piston” • Ejecta with and (Valid for the outerpart of the ejecta) • Ambient medium with and (s=0 for ISM; s=2 for wind material) (n > 5) (s < 3)

14. Dimensional parameters and • Expansion law:

15. Evidence of deceleration in SNe • VLBI mapping (SN 1993J) • Decelerated shock • For an r-2 ambient profileejecta profile is derived

16. Self-similar models (Chevalier 1982) • Radial profiles • Ambient medium • Forward shock • Contact discontinuity • Reverse shock • Expanding ejecta

17. P P S S UNSTAB STABLE RS FS Instabilities • Approximation: pressure ~ equilibration Pressure increases outwards (deceleration) • Conservation of entropy • Stability criterion (against convection) P and S gradients must be opposite ns < 9 -> SFS, SRS decrease with time and viceversa for ns < 9Always unstable region factor ~ 3

18. n=7, s=2 n=12, s=0 Linear analysis of the instabilities+ numerical simulations (Chevalier et al. 1992) (Blondin & Ellison 2001) 1-D results, inspherical symmetry are not adequate

19. The case of SN 1006 • Thermal + non-thermalemission in X-rays (Cassam-Chenai et al. 2008) FS from Ha + Non-thermal X-raysCD from 0.5-0.8 keV Oxygen band (thermal emission from the ejecta) (Miceli et al. 2009)

20. Why is it so important? • RFS/RCD ratios in the range 1.05-1.12 • Models instead require RFS/RCD > 1.16 • ARGUMENT TAKEN AS A PROOF FOR EFFICIENT PARTICLE ACCELERATION (Decouchelle et al. 2000; Ellison et al. 2004) • Alternatively, effectdue to mixing triggeredby strong instabilities (Although Miceli et al. 3-Dsimulation seems still tofind such discrepancy)

21. Acceleration as an energy sink • Analysis of all the effects of efficient particle acceleration is a complex task • Approximate modelsshow that distancebetween RS, CD, FSbecome significantlylower(Decourchelle et al. 2000) • Large compressionfactor - Low effectiveLorentz factor

22. FS Deceleration factor RS 1-D HD simulation by Blondin End of the self-similar phase • Reverse shock has reached the core region of the ejecta (constant density) • Reverse shock moves faster inwards and finally reachesthe center. See Truelove & McKee1999 for a semi-analytictreatment of this phase

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

24. Shocked ISM ISM Blast wave 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”

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

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

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

28. 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 modeling the (thermal) X-ray spectrum • Modeling the Balmer line profile in non-radiative shocks

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

30. 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)

31. 2/5 2/7=0.29 1/4=0.25 Numerical results (Blondin et al 1998) 0.33 ttr Blondin et al 1998

32. An analytic model • 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 Bandiera & Petruk 2004

33. 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

34. THE END