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

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Order-of-magnitude estimates SN explosion –Mechanical energy: –Ejected mass: VELOCITY: Ambient medium –Density: M ej ~M swept when: SIZE: AGE:

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs “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 ? Tycho – SN 1572

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs 90cm Survey 4.5 < l < 22.0 deg (35 new SNRs found; Brogan et al ) Blue: VLA 90cm Green: Bonn 11cm Red: MSX 8  m Radio traces both thermal and non-thermal emission Mid-infrared traces primarily warm thermal dust emission A view of Galactic Plane

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Cassiopeia A 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)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs 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 the photoel. Absorption SNR N132D with BeppoSAX

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Higher resolution data –Abundances of elements –Line-ratio spectroscopy N132D as seen with XMM-Newton (Behar et al. 2001) –Plus mapping in individual lines

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Thermal vs. Non-Thermal Cas A, with Chandra SN 1006, with Chandra

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Shell-type SNR evolution a “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 Homogeneous Linear Adiabatic Radiative (but CSM)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Density Radius Forward shock Reverse shock Forward and reverse shocks Forward Shock: into the CSM/ISM (fast) Reverse Shock: into the Ejecta (slow)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs 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 shock  V If Strong shock

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Dimensional analysis and 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).

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Early evolution Linear expansion only if ejecta behave as a “piston” Ejecta with and (Valid for the outer part of the ejecta) Ambient medium withand (s=0 for ISM; s=2 for wind material) Log(r) Log(ρ) CORE ENVELOPE (n > 5) (s < 3)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Dimensional parameters and Expansion law: n=7n=12 s= s=

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Evidence of deceleration in SNe VLBI mapping (SN 1993J) Decelerated shock For an r -2 ambient profile ejecta profile is derived

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Self-similar models Radial profiles –Ambient medium –Forward shock –Contact discontinuity –Reverse shock –Expanding ejecta (Chevalier 1982)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Instabilities Approximation: pressure ~ equilibration Pressure increases outwards (deceleration) Conservation of entropy Stability criterion (against convection) P and S gradients must be opposite ns S FS, S RS decrease with time and viceversa for ns < 9 Always unstable region FSRS PP SS STABLEUNSTAB factor ~ 3

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs (Chevalier et al. 1992) (Blondin & Ellison 2001) 1-D results, in spherical symmetry are not adequate n=12, s=0 n=7, s=2 Linear analysis of the instabilities + numerical simulations

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs The case of SN 1006 Thermal + non-thermal emission in X-rays (Cassam-Chenai et al. 2008) FS from Ha + Non-thermal X-rays CD from keV Oxygen band (thermal emission from the ejecta) (Miceli et al. 2009)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Why is it so important? –R FS /R CD ratios in the range –Models instead require R FS /R CD > 1.16 –ARGUMENT TAKEN AS A PROOF FOR EFFICIENT PARTICLE ACCELERATION (Decouchelle et al. 2000; Ellison et al. 2004) Alternatively, effect due to mixing triggered by strong instabilities (Although Miceli et al. 3-D simulation seems still to find such discrepancy)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Acceleration as an energy sink Analysis of all the effects of efficient particle acceleration is a complex task Approximate models show that distance between RS, CD, FS become significantly lower (Decourchelle et al. 2000) Large compression factor - Low effective Lorentz factor

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs 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 reaches the center. See Truelove & McKee 1999 for a semi-analytic treatment of this phase RS FS Deceleration factor 1-D HD simulation by Blondin

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs 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)

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs 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” Shocked ISMISM Blast wave

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Thin-layer approximation Layer thickness Total energy Dynamics Correct value: 1.15 !!!

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs What can be measured (X-rays) from spectral fits … if in the Sedov phase

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs SN 1006 Dec.Par. = 0.34 Tycho SNR (SN 1572) Dec.Par. = 0.47 Testing the Sedov expansion Required: R SNR /D (angular size) t (reliable only for historical SNRs) V exp /D (expansion rate, measurable only in young SNRs) Deceleration parameter

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

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs End of the Sedov phase Sedov in numbers: When forward shock becomes radiative: with Numerically:

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Beyond the Sedov phase When t > t tr, energy no longer conserved. What is left? “Momentum-conserving snowplow” (Oort 1951) WRONG !! Rarefied gas in the inner regions “Pressure-driven snowplow” (McKee & Ostriker 1977) Kinetic energy Internal energy

Rino Bandiera, Arcetri Obs., Firenze, ItalyA Basic Course on SNRs Numerical results t tr Blondin et al / /7=0.291/4=0.25 (Blondin et al 1998)

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

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

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