1. 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
Pulsar wind nebulae
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

2. Order-of magn. estimates
SN explosion
Mechanical energy:
Ejected mass:
VELOCITY:
Ambient medium
Density: Mej~Mswept when:
SIZE:
AGE:
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

3. “Classical” Radio SNRs
Spectacular shell-like morphologies
compared to optical
polarization
spectral index (~ – 0.5)
BUT
Poor diagnostics on the physics
featureless spectra (synchrotron emission)
acceleration efficiencies ?
Tycho – SN 1572
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

4. A view of Galactic Plane
90cm Survey 4.5 < l < 22.0 deg (35 new SNRs found; Brogan et al. 2006)
Blue: VLA 90cm Green: Bonn 11cm Red: MSX 8 mm
Radio traces both thermal and non-thermal emission
Mid-infrared traces primarily warm thermal dust emission
Brogan et al 2006, ApJ 639, L25
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

5. 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

6. X-ray spectral analysis
Low-res data
Overall fit with thermal models
High-res data
Abundances of elements
Single-line spectroscopy!
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

7. Shell-type SNR evolution a “classical” (and wrong) scenario
Isotropic explosion and further evolution
Homogeneous ambient medium
Three phases:
Linear expansion
Adiabatic expansion
Radiative expansion
Isotropic
Homogeneous
Linear
Adiabatic
Radiative
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

8. 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
shock r V
Strong shock If
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

9. Forward and reverse shocks
Density
Radius
Reverse
shock
Forward Shock: into the CSM/ISM (fast)
Reverse Shock: into the Ejecta (slow)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

10. Dimensional analysis and 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).
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

11. Early evolution Linear expansion only if ejecta behave as a “piston”
Ejecta with and
Ambient medium with and
Dimensional parameters and
Expansion law:
Chevalier 1982, ApJ 258, 790
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

12. A self-similar model Deviations from “linear” expansion
(Chevalier 1982)
Deviations from “linear” expansion
Radial profiles
Ambient medium
Forward shock
Contact discontinuity
Reverse shock
Expanding ejecta
Chevalier 1982, ApJ 258, 790
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

13. Evidence from SNe VLBI mapping (SN 1993J) Decelerated shock
For an r -2 ambient profile ejecta profile is derived
Bartel et al 2002, ApJ 581, 404 (SN1993J)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

14. 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

15. The Sedov profiles Most of the mass is confined in a “thin” shell
Density
Temperature
Pressure
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”
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

16. Thin-layer approximation
Layer thickness
Total energy
Dynamics
Correct value: 1.15 !!!
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

17. What can be measured (X-rays)
from spectral fits
… if in the Sedov phase
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

18. Testing Sedov expansion
Tycho SNR (SN 1572) Dec.Par. = 0.47
Deceleration parameter
SN Dec.Par. = 0.34
Required:
RSNR/D (angular size)
t (reliable only for historical SNRs)
Vexp/D (expansion rate, measurable only in young SNRs)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

19. 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

20. End of the Sedov phase Sedov in numbers:
When forward shock becomes radiative: with
Numerically:
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

21. Beyond the Sedov phase
When t>ttr, energy no longer conserved. What is left?
“Momentum-conserving snowplow” (Oort 1951)
WRONG !! Rarefied gas in the inner regions
“Pressure-driven snowplow” (McKee & Ostriker 1977)
Kinetic energy
Internal energy
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

22. Numerical results 2/5 0.33 2/7=0.29 1/4=0.25 ttr (Blondin et al 1998)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

23. An analytic model Thin shell approximation Analytic solution
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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

24. 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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

25. Collisionless shocks Coulomb mean free path High Mach numbers
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 μG
Complex related microphysics
Electron-ion temperature equilibration
Diffusive particle acceleration
Magnetic field turbulent amplification
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

26. 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
(Cargill and Papadopoulos 1988)
(Spitzer 1978)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

27. Optical emission in SN1006 “Pure Balmer” emission in SN 1006
Here metal lines are missing (while they dominate in recombination spectra)
Extremely metal deficient ?
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

28. “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
WHY BALMER LINES ARE PRESENT ?
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

29. The role of neutral H Scenario: shock in a partially neutral gas
(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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

30. H-alpha profiles MEASURABLE QUANTITIES Intensity ratio
(Hester, Raymond and Blair 1994)
(Kirshner, Winkler and Chevalier 1987)
Cygnus Loop
MEASURABLE QUANTITIES
Intensity ratio
Displacement (not if edge-on)
FWHM of broad component (Ti !!)
FWHM of narrow component
(T  40,000 K – why not fully ionized?)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

31. SNR 1E 0102.2-7219 Very young and bright SNR in the SMC
(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 in X-rays (proper motions)
Electron temperature ~ keV, while expected ion T ~ 45 keV
Very small Te/Ti, or Ti much less than expected? Missing energy in CRs?
Optical
Radio
X-rays
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

32. Rino Bandiera, OAA. Fundamental Physics & Astrophysics of SNRs
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

33. Lectures #2 & #3 Shock acceleration Pulsar Wind Nebulae
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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

34. The “strange case” of SN1006
Tycho with ASCA
Hwang et al 1998
“Standard” X-ray spectrum
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

35. Thermal & non-thermal Power-law spectrum at the rims
Thermal spectrum in the interior
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

36. Diffusive shock accelerationX
flow speed
Fermi acceleration
Converging flows
Particle diffusion (How possible, in a collisionless plasma?)
Particle momentum distribution where 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

37. The diffusion coefficient
Diffusion mean free path (magnetic turbulence) (η > 1)
Diffusion coefficient
Reynolds 1998
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

38. …and its effects Acceleration time Maximum energy Cut-off frequency
Naturally located near the X-ray range
Independent of B
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

39. Basics of synchrotron emission
Emitted power
Characteristic frequency
Power-law particle distribution
If then
Synchrotron life time
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

40. SN 1006 spectrum
Rather standard ( -0.6) power-law spectrum in radio (-0.5 for a classical strong shock)
Synchrotron X-rays below radio extrapolation Common effect in SNRs (Reynolds and Keohane 1999)
Electron energy distribution:
Fit power-law + cutoff to spectrum:
“Rolloff frequency”
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

41. Measures of rolloff frequency
SN (Rothenflug et al 2004)
Azimuthal depencence of the break Changes in tacc? or in tsyn? η of order of unity?
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

42. Dependence on B orientation?
Highly regular structure of SN Barrel-like shape suggested (Reynolds 1998)
Brighter where B is perpendicular to the shock velocity?
Direction of B ?
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

43. Radio – X-ray comparison
(Rothenflug et al 2004)
Similar pattern (both synchrotron)
Much sharper limb in X-rays (synchrotron losses)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

44. Evidence for synchrotron losses of X-ray emitting electrons
(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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

45. 3-D Geometry. Polar Caps? Polar cap geometry: electrons accelerated
Ordered magnetic field
(from radio polarization)
Polar cap geometry:
electrons accelerated
in regions with quasi-parallel field
(as expected from the theory)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

46. Statistical analysis Expected morphologies in radio Polar cap SNR
(Fulbright & Reynolds 1990)
Expected morphologies in radio
Barrel-like SNR
(under various orientations)
Polar cap SNR
(under various orientations)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

47. The strength of B ?
Difficult to directly evaluate the value of the B in the acceleration zone. νrolloff is independent of it !
“Measurements” of B must rely on some model or assumption
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

48. Very sharp limbs in SN 1006 Chandra ASCA
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

49. B from limb sharpness Profiles of resolved non-thermal X-ray
(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 with B ~ 30 μG
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

50. A diagnostic diagram Acceleration time tacc = 270 yr
Derivation of the diffusion coefficients: u= cm2s-1 d= cm2s-1 (Us=2900 km s-1) to compare with Bohm=(Emaxc/eB)/3
rolloff
tsync> tacc
 > Bohm
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

51. 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, 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

52. Shock modification
Dynamical effects of the accelerated particles onto the shock structure (Drury and Voelk 1981)
Intrinsically non linear
Shock precursor
Discontinuity (subshock)
Larger overall compression factor
Accelerated particle distribution is no longer a power-law
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

53. Deviations from Power-Law
In modified shocks, acc. particles with different energies see different shock compression factors. Higher energy Longer mean free path Larger compress.factor Harder spectrum
Concavity in particle distribution. (also for electrons)
Thermal
Blasi Solution
Standard PL
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

54. 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.
Synchrotron IC
Radio
X-ray
γ-ray
νFν
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

55. Need for “targets” (molecular cloud?)
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)
(Ellison et al 2000)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

56. TeV telescopes generation
H.E.S.S. Cherenkov telescopes
Observations :
RX J (Aharonian et al 2005)
Upper limits on SN 1006 (Aharonian et al 2005)
RX J (Aharonian et al 2006)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

57. 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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

58. 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
(Decourchelle et al 2000)
(Blondin and Ellison 2001)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

59. 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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

60. The Σ–D Relationship Empirical relation
SNR surface brightness, in radio
SNR diameter
Any physical reason for this relation ?
(Case & Bhattacharya 1998)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

61. 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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

62. Dependence on ambient density
(Berkhuijsen 1986)
Primary correlations are D-n, and Σ-n
Diff. ISM conditions
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

63. Rino Bandiera, OAA. Fundamental Physics & Astrophysics of SNRs
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

64. The “Prototype” The Crab Nebula Optical Radio X-rays Thermal filaments
Crab Nebula - radio
The Crab Nebula
Optical
Thermal filaments
Amorphous compon.
Radio
Filled-center nebula
No signs of shell
X-rays
More compact neb.
Jet-torus structure
Crab Nebula – Ha + cont
X-rays
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

65. The Crab Nebula spectrum
(apart from optical filaments and IR bump)
Synchrotron emission
-0.8
-1.1
-0.3
-1.5
Radio
Optical
Soft X-rays
Hard X-rays
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

66. Some basic points Synchrotron efficiency Powered by the pulsar
10-20% of pulsar spin-down power
Powered by the pulsar
High polarizations (ordered field)
No signs of any associated shell.
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

67. Basics of synchrotron emission
Emitted power
Characteristic frequency
Power-law particle distribution
If then
Synchrotron life time
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

68. Simple modelling Homogeneous models (no info on structure)
(Pacini & Salvati 1973)
Homogeneous models (no info on structure)
Magnetic field evolution
Early phases (constant pulsar input)
Later phases (most energy released)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

69. Particle evolution (adiabatic vs synchrotron losses)
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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

70. Kennel & Coroniti model (1984)
Basics of “Pulsar Wind Nebula” scenario
Pulsar magnetosphere
Pulsar wind
Termination shock
Pulsar Wind Nebula
Interface with the ejecta (CD, FS)
Stellar ejecta
Interface with the ambient medium (RS, CD, FS)
Ambient medium (either ISM or CSM)
Pulsar magnetosphere
Pulsar wind
Termination shock
Pulsar Wind Nebula
Stellar ejecta
ISM
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

71. The ingredients Pulsar wind Termination shock super-relativistic
magnetized (toroidal field)
isotropic
Termination shock
mass conservation
magnetic flux cons.
momentum cons.
energy cons.
where (specific enthalpy)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

72. Large and small σ limits
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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

73. 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

74. Radial profiles Inner part with: Outer part with:
Equipartition in the outer part:
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

75. 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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

76. Best-fit solution Parameters: Fit to:
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

77. Rino Bandiera, OAA. Fundamental Physics & Astrophysics of SNRs
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

78. 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.
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

79. Problems - Ib A POSSIBLE WAY OUT
A tilted pulsar generates a striped wind.
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

80. 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

81. 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.
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

82. Problems IIb
Can it be “Diffusive synchrotron radiation”? (Fleishman & Bietenholz 2007) Turbulence spectral index ν.
Theory only for a fully turbulent field
Total spectrum is reproduced
But observed polarization is not explained
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

83. 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
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

84. 3C 58 MHD simulations van der Swaluw 2003 pulsar axis
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

85. Elongated structures of PWNe
pulsar spin G G
Crab Nebula
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

86. Details of the structure
knot
jet
inner ring
torus
counter-jet
Crab Nebula
Vela
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

87. Crab Nebula (Weisskopf et al 2000)
Jet sizes
Crab Nebula (Weisskopf et al 2000)
40” =
0.4 pc
PSR B (Gaensler et al 2002)
4’ = 6 pc
3C 58 (Slane et al. 2004)
13” = 0.2 pc
80” = 0.8 pc
Vela Pulsar (Pavlov et al. 2003)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

88. Simulating PWNe Relativistic MHD codes
(Komissarov, 2006; Del Zanna et al 2004, 2006)
Relativistic MHD codes
Modelling a PWN like the Crab Velocity Magnetization Max Energy
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

89. Surface brightness maps
Jet-Torus structure
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

90. Ingredients Wind parameters
magnetization (still small, but not too much) σ~0.02 – 0.1 aaa
wind anisotropy ( γeq~10 γpol )
“filling” the jets (since B = 0)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

91. 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 Nebula UV emission associated with a slow shock (against the SN ejecta) 
ISM
Shocked ISM
Shocked Ejecta
Unshocked Ejecta
PWN
Pulsar Wind
Forward Shock
Reverse Shock
PWN Shock
Pulsar
Termination
Shock
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

92. Rino Bandiera, OAA. Fundamental Physics & Astrophysics of SNRs
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

93. 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)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

94. 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
Spectral map
230 GHz map
-0.28
-0.20
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

95. A further emission component
Radio spectral index: -0.27
Concave spectral index from radio to mm Real effect or artifact? (absolute photometry)
Evidence for an additional emission component
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

96. Component B
Image obtained optimizing the subtraction of amorphous part, and filaments, of radio image (PSF matched), with best-fit weights.
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

97. 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).
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

98. The integrated spectrum
Radio comp (A)
Component B, with low freq cutoff.
Evidence higher than from the error bar.
Components A and B coexist in the optical.
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

99. Physical scenario Number of particles in Component B: Ntot ~ 2 1048.
Consistent with Kennel & Coroniti)
Filament magnetic fields ~6 times higher than the rest AND particle do not diffuse in/out of filaments (κ<100 κB).
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007

100. 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?)
Rino Bandiera, OAA Fundamental Physics & Astrophysics of SNRs SNA07, May 20-26, 2007