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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 on supernova remnants
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

Order of magnitude estimates
Order-of-magnitude estimates

  • SN explosion

    • Mechanical energy:

    • Ejected mass:

      • VELOCITY:

  • Ambient medium

    • Density: Mej~Mswept when:

      • SIZE:

      • AGE:

Classical radio snrs

Tycho – SN 1572

“Classical” Radio SNRs

  • Spectacular shell-like morphologies

    • compared to optical

    • spectral index

    • polarization


  • Poor 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 mm

  • Radio traces both thermal and non-thermal emission

  • Mid-infrared traces primarily warm thermal dust emission

A view of Galactic Plane

Snrs in the x ray window
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

X ray spectral analysis
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

  • Higher resolution data

    • Abundances of elements

    • Line-ratio spectroscopy

      N132D as seen with

      XMM-Newton(Behar et al. 2001)

    • Plus mapping in individual lines

Thermal vs non thermal
Thermal vs. Non-Thermal

Cas A, with Chandra

SN 1006, with Chandra

Shell type snr evolution a classical and incorrect scenario
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


(but CSM)





Forward and reverse shocks







Forward and reverse shocks

  • Forward Shock: into the CSM/ISM(fast)

  • Reverse Shock: into the Ejecta (slow)

Basic concepts of shocks




Strong shock


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

Dimensional analysis and self similar models
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).

Early evolution





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)

Evidence of deceleration in sne
Evidence of deceleration in SNe

  • VLBI mapping (SN 1993J)

  • Decelerated shock

  • For an r-2 ambient profileejecta profile is derived

Self similar models
Self-similar models

(Chevalier 1982)

  • Radial profiles

    • Ambient medium

    • Forward shock

    • Contact discontinuity

    • Reverse shock

    • Expanding ejecta











  • 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

Linear analysis of the instabilities numerical simulations

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

The case of sn 1006
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)

  • 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 sink
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

End of the self similar phase


Deceleration factor


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

The sedov taylor solution
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)

The sedov profiles

Shocked 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”

Thin layer approximation
Thin-layer approximation

  • Layer thickness

  • Total energy

  • Dynamics

Correct value:1.15 !!!

What can be measured x rays

from spectral fits

What can be measured (X-rays)

… if in the Sedov phase

Testing the sedov expansion

Deceleration parameter

Tycho SNR (SN 1572) Dec.Par. = 0.47

SN 1006 Dec.Par. = 0.34

Testing the Sedov expansion


  • 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 speed
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

End of the sedov phase
End of the Sedov phase

  • Sedov in numbers:

  • When forward shock becomes radiative: with

  • Numerically:

Beyond the sedov phase

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)

Numerical results




Numerical results

(Blondin et al 1998)



Blondin et al 1998

An analytic model
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

Inhomogenous ambient medium
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