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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

BUT

  • Poor diagnostics on the physics
    • featureless spectra (synchrotron emission)
    • acceleration efficiencies ?
slide4
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

slide7
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

Isotropic

(but CSM)

Homogeneous

Linear

Adiabatic

Radiative

forward and reverse shocks
Forward

shock

Density

Reverse

shock

Radius

Forward and reverse shocks
  • Forward Shock: into the CSM/ISM(fast)
  • Reverse Shock: into the Ejecta (slow)
basic concepts of shocks
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
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
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)

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
instabilities
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

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)

slide20
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
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

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

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 !!!

testing the sedov expansion
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)
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
2/5

2/7=0.29

1/4=0.25

Numerical results

(Blondin et al 1998)

0.33

ttr

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
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