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Fund. Physics & Astrophysics of Supernova Remnants. Lecture #1 What SNRs are and how are they observed Hydrodynamic evolution on shell-type SNRs Microphysics in SNRs – electron-ion equ Lecture #2 Microphysics in SNRs - shock acceleration Statistical issues about SNRs Lecture #3

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fund physics astrophysics of supernova remnants
Fund. Physics & Astrophysicsof Supernova Remnants
  • Lecture #1
    • What SNRs are and how are they observed
    • Hydrodynamic evolution on shell-type SNRs
    • Microphysics in SNRs – electron-ion equ
  • Lecture #2
    • Microphysics in SNRs - shock acceleration
    • Statistical issues about SNRs
  • Lecture #3
    • Pulsar wind nebulae
order of magn estimates
Order-of magn. 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
    • comparedto optical
    • polarization
    • spectral index(~ – 0.5)


  • 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-emitting electrons are near the maximum energy (synchrotron cutoff)
x ray spectral analysis
X-ray spectral analysis
  • Low-res data
    • Overall fit with thermal models
  • High-res data
    • Abundances of elements
    • Single-line spectroscopy!
shell type snr evolution a classical and wrong scenario
Shell-type SNR evolutiona “classical” (and wrong) scenario

Isotropic explosion and further evolution

Homogeneous ambient medium

Three phases:

  • Linear expansion
  • Adiabatic expansion
  • Radiative expansion






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
forward and reverse shocks







Forward and reverse shocks
  • Forward Shock: into the CSM/ISM(fast)
  • Reverse Shock: into the Ejecta (slow)
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 evolution 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
  • Ambient medium with and
  • Dimensional parameters and
  • Expansion law:
a self similar model
A self-similar model

(Chevalier 1982)

  • Deviations from “linear” expansion
  • Radial profiles
    • Ambient medium
    • Forward shock
    • Contact discontinuity
    • Reverse shock
    • Expanding ejecta
evidence from sne
Evidence from SNe
  • VLBI mapping (SN 1993J)
  • Decelerated shock
  • For an r-2 ambient profileejecta profile is derived
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 negligible
  • Dimensional parameters of the problem
  • Evolution:
  • Self-similar, analytic solution (Sedov,1959)
the sedov profiles




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 sedov expansion

Deceleration parameter

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

SN 1006 Dec.Par. = 0.34

Testing 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 modelling the (thermal) X-ray spectrum
  • Modelling the Balmer line profile in non-radiative shocks (see below)
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

Bandiera & Petruk 2004

  • 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

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
collisionless shocks
Collisionless shocks
  • Coulomb mean free path
    • Collisional scale length (order of parsecs)
    • Larmor radius is much smaller (order of km)
  • High Mach numbers
    • Mach number of order of 100
  • MHD Shocks
    • B in the range 10-100 μG
  • Complex related microphysics
    • Electron-ion temperature equilibration
    • Diffusive particle acceleration
    • Magnetic field turbulent amplification
electron ion equilibration

(Cargill and Papadopoulos 1988)

(Spitzer 1978)

Electron & Ion equilibration
  • Naif prediction, for collisionless shocks
  • But plasma turbulence may lead electrons and ion to near-equilibrium conditions
  • Coulomb equilibration on much longer scales
optical emission in sn1006
Optical emission in SN1006
  • “Pure Balmer” emissionin SN 1006
  • Here metal lines are missing (while they dominate in recombination spectra)
    • Extremely metal deficient ?
non radiative emission
“Non-radiative” emission
  • Emission from a radiative shock:
    • Plasma is heated and strongly ionized
    • Then it efficiently cools and recombines
    • Lines from ions at various ionization levels
  • In a “non-radiative” shock:
    • Cooling times much longer than SNR age
    • Once a species is ionized, recombination is a very slow process
the role of neutral h
The role of neutral H

(Chevalier & Raymond 1978, Chevalier, Kirshner and Raymond 1980)

  • Scenario: shock in a partially neutral gas
  • Neutrals, not affected by the magnetic field, freely enter the downstream region
  • Neutrals are subject to:
    • Ionization (rad + coll)[LOST]
    • Excitation (rad + coll)Balmer narrow
    • Charge exchange (in excited lev.)Balmer broad
  • Charge-exchange cross section is larger at lower vrel
  • Fast neutral component more prominent in slower shocks
h alpha profiles

(Kirshner, Winkler and Chevalier 1987)

(Hester, Raymond and Blair 1994)

Cygnus Loop

H-alpha profiles
  • Intensity ratio
  • Displacement (not if edge-on)
  • FWHM of broad component (Ti !!)
  • FWHM of narrow component
  • (T 40,000 K – why not fully ionized?)
snr 1e 0102 2 7219




SNR 1E 0102.2-7219

(Hughes et al 2000, Gaetz et al 2000)

  • Very young and bright SNR in the SMC
  • Expansion velocity (6000 km s-1, if linear expansion)measured in optical (OIII spectra) and inX-rays (proper motions)
  • Electron temperature~ 0.4-1.0 keV, whileexpected ion T ~ 45 keV
  • Very smallTe/Ti, orTimuch less than expected?Missing energy in CRs?
lectures 2 3
Lectures #2 & #3
  • Shock acceleration
    • The prototype: SN 1006
    • Physics of shock acceleration
    • Efficient acceleration and modified shocks
  • Pulsar Wind Nebulae
    • The prototype: the Crab Nebula
    • Models of Pulsar Wind Nebulae
    • Morphology of PWN in theory and in practice
    • A tribute to ALMA
the strange case of sn1006

Tycho with ASCA

Hwang et al 1998

The “strange case” of SN1006

“Standard”X-ray spectrum

thermal non thermal
Thermal & non-thermal
  • Power-law spectrum at the rims
  • Thermal spectrum in the interior
diffusive shock acceleration


flow speed


Diffusive shock acceleration
  • Fermi acceleration
    • Converging flows
    • Particle diffusion(How possible, in acollisionless plasma?)
  • Particle momentum distributionwhere r is the compression ratio (s=2, if r = 4)
  • Synchrotron spectrum
  • For r = 4, power-law index of -0.5
  • Irrespectively of diffusion coefficient

(in the shock reference frame)

the diffusion coefficient
The diffusion coefficient
  • Diffusion mean free path(magnetic turbulence)(η > 1)
  • Diffusion coefficient
and its effects
…and its effects
  • Acceleration time
  • Maximum energy
  • Cut-off frequency
    • Naturally located near the X-ray range
    • Independent of B
basics of synchrotron emission
Basics of synchrotron emission
  • Emitted power
  • Characteristic frequency
  • Power-law particle distribution
  • If then
  • Synchrotron life time
sn 1006 spectrum
SN 1006 spectrum
  • Rather standard( -0.6)power-law spectrum in radio(-0.5 for a classical strong shock)
  • Synchrotron X-rays below radio extrapolationCommon effect in SNRs(Reynolds and Keohane 1999)
  • Electron energy distribution:
  • Fit power-law + cutoff to spectrum:

“Rolloff frequency”

measures of rolloff frequency
Measures of rolloff frequency
  • SN 1006 (Rothenflug et al 2004)
  • Azimuthal depencence of the breakChanges in tacc? or in tsyn? ηof order of unity?
dependence on b orientation
Dependence on B orientation?
  • Highly regular structure of SN 1006.Barrel-like shape suggested (Reynolds 1998)
  • Brighter where B is perpendicular to the shock velocity?

Direction of B ?

radio x ray comparison
Radio – X-ray comparison

(Rothenflug et al 2004)

  • Similar pattern (both synchrotron)
  • Much sharper limb in X-rays (synchrotron losses)

(Rothenflug et al 2004)

  • Evidence for synchrotron losses of X-ray emitting electrons
  • X-ray radial profile INCONSISTENT with barrel-shaped geometry (too faint at the center)
3 d geometry polar caps

Ordered magnetic field

(from radio polarization)

3-D Geometry. Polar Caps?

Polar cap geometry:

electrons accelerated

in regions with quasi-parallel field

(as expected from the theory)

statistical analysis
Statistical analysis

(Fulbright & Reynolds 1990)

Expected morphologies in radio

Polar cap SNR

(under variousorientations)

Barrel-like SNR

(under variousorientations)

the strength of b
The strength of B ?
  • Difficult to directly evaluate the value of the B in the acceleration zone.νrolloffis independent of it !
  • “Measurements” of B must rely on some model or assumption
b from limb sharpness
B from limb sharpness

(Bamba et al 2004)

Profiles of resolved non-thermal X-ray

filaments in the NE shell of SN 1006

Length scales 1” (0.01 pc) upstream20” (0.19 pc) downstream

Consistent withB ~ 30 μG

a diagnostic diagram


tsync> tacc

 > Bohm

A diagnostic diagram
  • Acceleration timetacc = 270 yr
  • Derivation of the diffusioncoefficients:u=8.9 1024 cm2s-1d=4.2 1025 cm2s-1(Us=2900 km s-1)to compare withBohm=(Emaxc/eB)/3
non linear shock acceleration
Non-linear shock acceleration
  • Such high values of B are not expected in the case of pure field compression(3-6 μG in the ISM, 10-20 μG in the shock – or even no compression in parallel shocks)
  • Turbulent amplification of the field?
  • Possible in the case of efficient shock acceleration scenario: particles, streaming upstream, excite turbulence

(e.g. Berezhko; Ellison; Blasi)

shock modification

Dynamical effects of theaccelerated particles ontothe shock structure(Drury and Voelk 1981)

Shock modification
  • Intrinsically non linear
  • Shock precursor
  • Discontinuity (subshock)
  • Larger overall compression factor
  • Accelerated particle distribution is no longer a power-law
deviations from power law

Blasi Solution


Deviations from Power-Law
  • In modified shocks,acc. particles withdifferent energiessee different shockcompression factors.Higher energy Longer mean free path Larger compress.factor Harder spectrum
  • Concavity in particledistribution.(also for electrons)

Standard PL

gamma ray emission







Gamma-ray emission
  • Measurement of gamma-ray emission, produced by the same electrons that emit X-ray synchrotron, would allow one to determine the value of B.

(Ellison et al 2000)

  • On the other hand, there is another mechanism giving Gamma-ray emission
    • accelerated ions
    • p-p collisions
    • pion production
    • pion decay (gamma)
  • Lower limit for B
  • Need for “targets”(molecular cloud?)
  • Efficiency in in accelerating ions?(The origin of Cosmic rays)
tev telescopes generation
TeV telescopes generation
  • H.E.S.S. Cherenkov telescopes
  • Observations :
  • RX J0852.0-4622(Aharonian et al 2005)
  • Upper limits on SN 1006(Aharonian et al 2005)
  • RX J1713.7-3946(Aharonian et al 2006)
observ of rx j0852 0 4622
Observ. of RX J0852.0-4622
  • Good matching between X-rays and gamma-rays
  • CO observation show the existence of a molecular cloud
  • Pion-decay scenario slightly favoured. Nothing proved as yet
indirect tests on the crs

(Blondin and Ellison 2001)

(Decourchelle et al 2000)

Indirect tests on the CRs
  • Some “model-dependent” side effects of efficient particle acceleration
  • Forward and reverse shock are closer, as effect of the energy sink
  • HD instabilities behavior depends on the value of eff
shock acceleration efficiency
Shock acceleration efficiency
  • Theory predicts (~ high) values of the efficiency of shock acceleration of ions.
  • Little is known for electrons
  • Main uncertainty is about the injection process for electrons
    • Shock thickness determined by the mfp of ions (scattering on magnetic turbulence)
    • Electrons, if with lower T, have shorter mfps
    • Therefore for them more difficult to be injected into the acceleration process
the d relationship
The Σ–D Relationship
  • Empirical relation
    • SNR surface brightness, in radio
    • SNR diameter
    • Any physicalreason forthis relation ?

(Case & Bhattacharya 1998)

a basic question
A basic question
  • Is the correlation representative of the evolution of a “typical object”?
  • Or is, instead, the convolution of the evolution of many different objects?
  • Theorists attempts to reproduce it.

Berezhko & Voelk 2004

dependence on ambient density
Dependence on ambient density

(Berkhuijsen 1986)

  • Primary correlations are D-n, and Σ-n
  • Diff. ISM conditions
the prototype
The Crab Nebula


Thermal filaments

Amorphous compon.


Filled-center nebula

No signs of shell


More compact neb.

Jet-torus structure


Crab Nebula - radio

Crab Nebula – Ha + cont

The “Prototype”
the crab nebula spectrum





The Crab Nebula spectrum

(apart from optical filaments and IR bump)

Synchrotron emission

  • Radio
  • Optical
  • Soft X-rays
  • Hard X-rays
some basic points
Some basic points
  • Synchrotron efficiency
    • 10-20% of pulsar spin-down power
  • Powered by the pulsar
  • High polarizations (ordered field)
  • No signs of any associated shell.
basics of synchrotron emission67
Basics of synchrotron emission
  • Emitted power
  • Characteristic frequency
  • Power-law particle distribution
  • If then
  • Synchrotron life time
simple modelling
Simple modelling

(Pacini & Salvati 1973)

  • Homogeneous models (no info on structure)
  • Magnetic field evolution
    • Early phases (constant pulsar input)
    • Later phases (most energy released)
Power-law injection

With upper energy cutoff

Continuum injection

link to the pulsar spin down

Particle evolution (adiabatic vs synchrotron losses)

Evolutionary break

Adiabatic regime

(-0.3 in radio)

Synchrotron-dominated regime

(-0.8 in optical)

kennel coroniti model 1984

Pulsar magnetosphere


Pulsar wind


Termination shock

Pulsar Wind Nebula

Kennel & Coroniti model (1984)

Basics of “Pulsar Wind Nebula” scenario

  • Pulsar magnetosphere
  • Pulsar wind
  • Termination shock
  • Pulsar Wind Nebula
  • Interface with theejecta (CD, FS)
  • Stellar ejecta
  • Interface with theambient medium(RS, CD, FS)
  • Ambient medium (either ISM or CSM)
the ingredients
The ingredients
  • Pulsar wind
    • super-relativistic
    • magnetized(toroidal field)
    • isotropic
  • Termination shock
    • mass conservation
    • magnetic flux cons.
    • momentum cons.
    • energy cons.

where (specific enthalpy)

large and small limits
Large and small σ limits
  • Large σ
    • weak shock
    • flow stays super-relativistic
    • neither field, nor density jump
    • inefficient in converting kinetic into thermal energy
  • Small σ
    • strong shock
    • flow braked to mildly relativistic speed
    • both field and density increase
    • kinetic energy efficienly converted
mhd evolution in the nebula
MHD evolution in the nebula
  • Steady solution (flow timescale << SNR age)
    • number flux cons. - magnetic flux cons.
    • momentum cons. - energy cons.
  • Asymptotic velocity !!!
    • no solution for V∞=0
    • outer expansion Vext~1500 km s-1 (for the Crab Nebula)
    • then σ~3 10-3
    • size of termination shock, from balance of wind ram pressure and nebular pressure

Rn~10 arcsec

(wisps region)

radial profiles
Radial profiles
  • Inner part with:
  • Outer part with:
  • Equipartition in the outer part:
do we expect what observed
Do we expect what observed?
  • Injected particles
    • power-law, between a min and a max energy
    • only 1 free parameter (n2 and p2 from the jump conditions at the termination shock)
    • plus wind parameters (L, σ and γ1 )
  • Energy evolution during radial advection
best fit solution
Best-fit solution
  • Parameters:
  • Fit to:
problems ia
Problems -Ia
  • The sigma paradox
    • A value is required, in order to get an effective slowing-down of the flow, and a high (10-20 %) synchrotron conversion efficiency
    • BUT the (magnetically driven) pulsar wind cannot have been produced with a low σ .
    • With a normal MHD evolution, the value of σ must keep constant from the acceleration region till the termination shock.
problems ib
Problems - Ib
    • A tilted pulsar generates a striped wind.
problems ic
Problems -Ic
  • Magnetic reconnection in the wind zone (if possible) would dissipate the field.(Coroniti 1990)
  • Reconnection in the wind zone does not efficiently destroy the field. Reconnection at the termination shock is more effective.

(Lyubarski & Kirk 1991)

problems iia
Problems - IIa
  • The unexpected radio emission
    • Predicted radio flux is far lower (a factor ~100) than observed.
    • No easy way to cure it. Little freedom on the particle number. Total power is fixed: more particles mean a lower γ1.
    • Radio emitting electrons as a relict. Was the Crab much more powerful in the past? Ad hoc. All PWNe are radio emitters.
problems iib
Problems IIb
  • Can it be “Diffusive synchrotron radiation”?(Fleishman & Bietenholz 2007)Turbulence spectral index ν.
  • Theory only for a fully turbulent field
    • Total spectrumis reproduced
    • But observedpolarization isnot explained
non spherical structure
Non-spherical structure

(Begelman & Li 1992)

  • Particle, moving passively along field lines (flow motion assumed to be irrotational)
  • Axisymmetric nebular field structure
  • Steady state solutions

pulsar axis

van der Swaluw 2003

3C 58

MHD simulations

elongated structures of pwne

pulsar spin

Elongated structures of PWNe

3C 58



Crab Nebula

details of the structure




inner ring


Details of the structure

Crab Nebula


jet sizes

4’ = 6 pc

40” =

0.4 pc

Crab Nebula (Weisskopf et al 2000)

PSR B1509-58 (Gaensler et al 2002)

13” = 0.2 pc

80” = 0.8 pc

3C 58 (Slane et al. 2004)

Vela Pulsar (Pavlov et al. 2003)

Jet sizes
simulating pwne
Simulating PWNe

(Komissarov, 2006; Del Zanna et al 2004, 2006)

  • Relativistic MHD codes
  • Modelling a PWN like the CrabVelocity Magnetization Max Energy
surface brightness maps
Surface brightness maps

Jet-Torus structure

  • Wind parameters
    • magnetization (still small, but not too much)σ~0.02 – 0.1aaa
    • wind anisotropy ( γeq~10 γpol )
    • “filling” the jets (since B = 0)
pwn ejecta interaction

Reverse Shock

PWN Shock

Forward Shock




Pulsar Wind

Unshocked Ejecta

Shocked Ejecta

Shocked ISM



PWN-ejecta interaction
  • PWNe are confined by the associated shell-like SNR
  • Not only the SNR is detectable (like in the Crab)
  • In the Crab NebulaUV emissionassociated with aslow shock (againstthe SN ejecta)
a tribute to alma
  • SNRs and PWNs are mostly non-thermal in that spectral range.
    • no use of spectral capabilities
    • use of high spatial resolution, + wide field, + photometric stability (extended sources)
  • Is mm-submm a “new band” for SNRs, or just an extension of the radio range?
  • A study of the Crab Nebula(extension of a former work, Bandiera et al 2002)
what has been done already



Spectral map

230 GHz map

What has been done already
  • Comparison of 1.3 mm (230 GHz) images (with IRAM 30-m telescope, 10” res) and radio (20 cm, VLA) maps
a further emission component
A further emission component
  • Radio spectral index: -0.27
  • Concave spectral index from radio to mmReal effector artifact?(absolutephotometry)
  • Evidence foran additionalemission component
component b
Component B
  • Image obtained optimizing the subtraction of amorphous part, and filaments, of radio image (PSF matched), with best-fit weights.
the subtracted components
The subtracted components
  • Amorphous component: consistent with an extension of the spectrum to mm, with the radio spectral index (-0.27).
  • Filaments: consistent with spectral bending (νb~80 GHz).
  • Morphologically, component B resembles more the Crab in the optical than in the radio (ALTHOUGH, in the mm range, electrons of Component B do not lose energy significantly by synchrotron).
the integrated spectrum
The integrated spectrum
  • Radio comp (A)
  • Component B,with low freqcutoff.
  • Evidence higherthan from theerror bar.
  • Components Aand B coexistin the optical.
physical scenario
Physical scenario
  • Number of particles in Component B:Ntot~ 2 1048.
  • Consistent with Kennel & Coroniti)
  • Filament magnetic fields ~6times higher than the rest AND particle do not diffuse in/out of filaments (κ<100 κB).
with alma
  • The same analysis, with a resolution 100 times higher.
  • Detailed mapping of Component B.
  • Separation of comp A and B also through differences in the polarization patterns.
  • Analysis of the spectral bending in individual filaments, and possibly even across the filament (B estimates).
  • Mapping B in filaments (aligned? ordered?)