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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

- SN explosion
- Mechanical energy:
- Ejected mass:
- VELOCITY:
- Ambient medium
- Density: Mej~Mswept when:
- SIZE:
- AGE:

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 ?

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

- 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

- 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

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

shock

Density

Reverse

shock

Radius

Forward and reverse shocks- Forward Shock: into the CSM/ISM(fast)
- Reverse Shock: into the Ejecta (slow)

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 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).

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)

Dimensional parameters and

- Expansion law:

Evidence of deceleration in SNe

- VLBI 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

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

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

- 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

- 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

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

- 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)

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”

Deceleration parameter

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

SN 1006 Dec.Par. = 0.34

Testing 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 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

- Sedov in numbers:
- When forward shock becomes radiative: with
- Numerically:

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)

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

- 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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