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A Basic Course on Supernova Remnants

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- 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

- SN explosion
- Mechanical energy:
- Ejected mass:
- VELOCITY:

- Ambient medium
- Density:Mej~Mswept when:
- SIZE:
- AGE:

- Density:Mej~Mswept when:

Tycho – SN 1572

- 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

- Probably the “best” spectral range to observe
- Thermal:
- measurement of ambient density

- Non-Thermal:
- Synchrotron emission from electrons close to maximum energy (synchrotron cutoff)

- Thermal:

Cassiopeia A

- 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)

- Either fit with a thermal model
- 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

Cas A, with Chandra

SN 1006, with Chandra

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 Shock: into the CSM/ISM(fast)
- Reverse Shock: into the Ejecta (slow)

r

V

shock

Strong shock

If

- Hydrodynamic (MHD) discontinuities
- Quantities conserved across the shock
- Mass
- Momentum
- Energy
- Entropy

- Jump conditions(Rankine-Hugoniot)
- Independent of the detailed physics

- 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)

- Linear expansion only if ejecta behave as a “piston”
- Ejecta with and
(Valid for the outerpart of the ejecta)

- Ambient mediumwithand
(s=0 for ISM; s=2 for wind material)

(n > 5)

(s < 3)

- Dimensional parametersand
- Expansion law:

- VLBI mapping (SN 1993J)
- Decelerated shock
- For an r-2 ambient profileejecta profile is derived

(Chevalier 1982)

- Radial profiles
- Ambient medium
- Forward shock
- Contact discontinuity
- Reverse shock
- Expanding ejecta

P

P

S

S

UNSTAB

STABLE

RS

FS

- 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 viceversafor ns < 9Always unstable region

factor ~ 3

n=7, s=2

n=12, s=0

(Chevalier et al. 1992)

(Blondin & Ellison 2001)

1-D results, inspherical symmetry are not adequate

- 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)

- 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

- 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

- 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

- 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”

- Layer thickness
- Total energy
- Dynamics

Correct value:1.15 !!!

from spectral fits

… if in the Sedov phase

Deceleration parameter

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

SN 1006 Dec.Par. = 0.34

Required:

- RSNR/D(angular size)
- t(reliable only for historical SNRs)
- Vexp/D(expansion rate, measurable only in young SNRs)

- 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

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

Internal energy

Kinetic energy

- 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)

2/5

2/7=0.29

1/4=0.25

(Blondin et al 1998)

0.33

ttr

Blondin et al 1998

- 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

- 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

THE END