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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. Order-of-magnitude estimates. SN explosion Mechanical energy:

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A Basic Course onSupernova RemnantsLecture #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 Order-of-magnitude estimatesSN explosion Mechanical energy: Ejected mass: VELOCITY: Ambient medium Density: Mej~Mswept when: SIZE: AGE: Tycho – SN 1572“Classical” Radio SNRsSpectacular shell-like morphologies compared to optical spectral index polarization BUTPoor diagnostics on the physics featureless spectra (synchrotron emission) acceleration efficiencies ? 90cm Survey4.5 < l < 22.0 deg(35 new SNRs found;Brogan et al. 2006)Blue: VLA 90cm Green: Bonn 11cmRed: MSX 8 mmRadio traces both thermal and non-thermal emission Mid-infrared traces primarily warm thermal dust emission A view of Galactic PlaneSNRs in the X-ray windowProbably the “best” spectral range to observe Thermal: measurement of ambient density Non-Thermal: Synchrotron emission from electrons close to maximum energy (synchrotron cutoff) Cassiopeia AX-ray spectral analysisLower 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 BeppoSAXHigher resolution dataAbundances of elements Line-ratio spectroscopy N132D as seen with XMM-Newton(Behar et al. 2001)Plus mapping in individual lines Thermal vs. Non-ThermalCas A, with ChandraSN 1006, with ChandraShell-type SNR evolutiona “classical” (and incorrect) scenarioIsotropic explosion and further evolutionHomogeneous ambient mediumThree phases:Linear expansion Adiabatic expansion Radiative expansion Goal: simple description of these phasesIsotropic(but CSM)HomogeneousLinearAdiabaticRadiativeForward shockDensityReverse shockRadiusForward and reverse shocksForward Shock: into the CSM/ISM(fast) Reverse Shock: into the Ejecta (slow) rVshockStrong shockIfBasic concepts of shocksHydrodynamic (MHD) discontinuities Quantities conserved across the shock Mass Momentum Energy Entropy Jump conditions(Rankine-Hugoniot) Independent of the detailed physics Dimensional analysisand Self-similar modelsDimensionality 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). Log(ρ)COREENVELOPELog(r)Early evolutionLinear 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)Dimensional parameters andExpansion law: Evidence of deceleration in SNeVLBI mapping (SN 1993J) Decelerated shock For an r-2 ambient profileejecta profile is derived Self-similar models(Chevalier 1982)Radial profiles Ambient medium Forward shock Contact discontinuity Reverse shock Expanding ejecta PPSSUNSTABSTABLERSFSInstabilitiesApproximation: 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 timeand viceversa for ns < 9Always unstable regionfactor ~ 3n=7, s=2n=12, s=0Linear analysis of the instabilities+ numerical simulations(Chevalier et al. 1992) (Blondin & Ellison 2001) 1-D results, inspherical symmetry are not adequateThe case of SN 1006Thermal + 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)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)Acceleration as an energy sinkAnalysis 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 FSDeceleration factorRS1-D HD simulation by BlondinEnd of the self-similar phaseReverse 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 phaseThe Sedov-Taylor solutionAfter 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) Shocked ISMISMBlast waveThe Sedov profilesMost 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” Thin-layer approximationLayer thickness Total energy Dynamics Correct value:1.15 !!!from spectral fitsWhat can be measured (X-rays)… if in the Sedov phaseDeceleration parameterTycho SNR (SN 1572) Dec.Par. = 0.47SN 1006 Dec.Par. = 0.34Testing the Sedov expansionRequired:RSNR/D(angular size) t(reliable only for historical SNRs) Vexp/D(expansion rate, measurable only in young SNRs) Other ways to “measure”the shock speedRadial 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 End of the Sedov phaseSedov in numbers: When forward shock becomes radiative: with Numerically: Internal energyKinetic energyBeyond the Sedov phaseWhen 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) 2/52/7=0.291/4=0.25Numerical results(Blondin et al 1998)0.33ttrBlondin et al 1998An analytic modelThin shell approximation Analytic solution H either positive (fast branch) limit case: Oort or negative (slow branch) limit case: McKee & OstrikerH,K from initial conditionsBandiera & Petruk 2004Inhomogenous ambient mediumCircumstellar 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 THE END

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