shock

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
Order-of magn. estimates
• SN explosion
– Mechanical energy:
ESN  1051 erg
– Ejected mass: M ej  1033 g
 5M Sun
• VELOCITY: Vej  ESN / M ej  109 cm s 1
• Ambient medium
– Density:
nISM  0.1cm 3
Mej~Mswept when:
1/ 3
 1019 cm  3 pc
• SIZE: RSNR  3M ej / 4nISM 
• AGE:
Rino Bandiera, OAA
tSNR  RSNR / Vej
 1010 s  300 yr
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
“Classical” Radio SNRs
• Spectacular shell-like morphologies
– compared
to optical
– polarization
– spectral index
(~ – 0.5)
BUT
• Poor diagnostics on the physics
Tycho – SN 1572
– featureless spectra (synchrotron emission)
– acceleration efficiencies ?
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
A view of Galactic Plane
90cm Survey
Blue: VLA 90cm
Green: Bonn 11cm
Red: MSX 8 m
4.5 < l < 22.0 deg (35 new SNRs found; Brogan et al. 2006)
• Radio traces both thermal and non-thermal emission
• Mid-infrared traces primarily warm thermal dust emission
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
SNRs in the X-ray window
• Probably the “best”
spectral range to
observe
kTe  meVej2
 1keV
– Thermal:
• measurement of
ambient density
EM   nH ne dV
– 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
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
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
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Basic concepts of shocks
• Hydrodynamic (MHD)
discontinuities
• Quantities conserved
across the shock
–
–
–
–

V
Mass
2V2  1V1
2
2
Momentum 2V2  p2  1V1  p1
2
2
Energy 2V2 V2 / 2  w2   1V1 V1 / 2  w1 
Entropy s2  s1
• Jump conditions
Strong shock
2 
(Rankine-Hugoniot)
• Independent of the
detailed physics
Rino Bandiera, OAA
If
p2 , 2 , V2 p1 , 1 , V1
shock
p1  1V12
 1
 1
2
1; V2 
V1; p2 
1V12
 1
 1
 1
  5/3
2  41; V2  V1 / 4; p2  31V12 / 4
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Forward and reverse shocks
Density
Forward
shock
Reverse
shock
Radius
• 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
Dimensional analysis
and Self-similar models
• Dimensionality of a quantity:
• Dimensional constants of a problem
A  M p LqT r
– 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
Early evolution
• Linear expansion only if ejecta behave
as a “piston”
3
n


g
t
(
r
/
t
)
• Ejecta with V  r / t
and ej
• Ambient medium
s


qr
V

0
with
and amb
• Dimensional parameters
g   ML( n3)T ( n3) and q  ML( s3)
• Expansion law: R  g / q 1/(n s ) t ( n3) /(ns )
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
A self-similar model
(Chevalier 1982)
• Deviations from
“linear” expansion
s  2, n  7 : R  t 0.60
s  2, n  12 : R  t 0.90
• Radial profiles
–
–
–
–
–
Ambient medium
Forward shock
Contact discontinuity
Reverse shock
Expanding ejecta
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Evidence from SNe
• VLBI mapping (SN 1993J)
• Decelerated shock
• For an r -2 ambient profile
ejecta profile is derived
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
 ISM :
 ISM   ML3
ESN :
ESN   ML2T 2
R (t )   ( E /  ) t
• Evolution:
• Self-similar, analytic solution
1/ 5 2 / 5
SNR
Rino Bandiera, OAA
SN
ISM
Fundamental Physics & Astrophysics of SNRs
(Sedov,1959)
SNA07, May 20-26, 2007
The Sedov profiles
Density
Pressure
Temperature
• 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
Thin-layer approximation
• Layer thickness
• Total energy
• Dynamics
4 R 2 r 2 
4 3
R 1 R
R 1  r 

3
3  2 12
4 3 pc
u22
4 3
E
R
M ; M 
R 1;
3
 1
2
3
d
Mu 2   4 R 2 pc
dt
R  tq
 

d 1 3 
2 2
 R R    R R
dt  3

4q  1
2
1
; q
 
3q
5
2
2
2
 2   1
4 3 1  2 R  
2
R5
  5 1 2
E
R 1 
 


3
2  5 t   (  1)(  1)    1   
t
Rino Bandiera, OAA
pc   p2
Fundamental Physics & Astrophysics of SNRs

5
   1.12
3
Correct value: 1.15 !!!
SNA07, May 20-26, 2007
What can be measured (X-rays)
EM   nH ne dV
Tx  1.28Tshock
from spectral fits
1 / 5 1 / 5 2 / 5
RSed  12.5 E51
n0 t 4 pc
 EM / d 2

R / d
kT  V
 x

Rino Bandiera, OAA
E
n
 0

t
d
… if in the Sedov phase
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Testing Sedov expansion
Deceleration parameter
Vexp t / RSNR  2 / 5
Required:
• RSNR/D (angular size)
• t (reliable only for
historical SNRs)
• Vexp/D (expansion rate,
measurable only in
young SNRs)
Rino Bandiera, OAA
SN 1006
Tycho
SNR (SN 1572)
Fundamental Physics & Astrophysics of SNRs
Dec.Par.==0.47
0.34
Dec.Par.
SNA07, May 20-26, 2007
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 nonradiative shocks (see below)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
End of the Sedov phase
• Sedov in numbers:
1 / 5 1 / 5 2 / 5
RSed  12.5 E51
n0 t 4 pc
• When forward shock becomes radiative:
with
1
(T )  10 T erg cm s
t : t t 
16
tr
age
cool
1
3 1
 n0
• Numerically:
4 / 17 9 / 17
t tr  2.9 10 4 E51
n0
yr
1 / 17 2 / 17
1

V

260
E
n
km
s

51
0
5 / 17  7 / 17
 Rtr 
19 E51
n0
pc
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Beyond the Sedov phase
• When t>ttr, energy no longer conserved.
What is left?
  ISM R 3V  const
 R  t 1/ 4
• “Momentum-conserving 
 ISM  const

snowplow” (Oort 1951)
• WRONG !! Rarefied gas in the inner regions
• “Pressure-driven snowplow” (McKee & Ostriker 1977)
Internal energy
Kinetic energy
Rino Bandiera, OAA

 Eint / R 3  Pinn   inn
 R 3
2 /(3 3 )

R

t

 Ekin / R 3   ISMV 2
R  t 2 / 7 for   5 / 3
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Numerical results
(Blondin et al 1998)
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
An analytic model
Bandiera & Petruk 2004
• Thin shell approximation
dM
 40 R 2 R ;
dt
d ( MR )
 4 pc R 2 ;
dt
d pc
R
 3 pc
dt
R
• Analytic solution
  3R  3(2   ) KR 3 1
R
R
2

R 2  K R 3  HR 6

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
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
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
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Electron & Ion equilibration
• Naif prediction, for collisionless shocks
kTe kTi
3

 Vsh2
me
mi 16
 Te 
me
Ti
mi
• But plasma turbulence may lead electrons and
ion to near-equilibrium conditions
m
Te  e Ti
mi
(Cargill and Papadopoulos 1988)
• Coulomb equilibration on much longer scales
 Te 
Leq  2.4  
T 
 p
5/ 2
 n0 


3 
1
cm


1
4


Vsh

 pc
1 
1000
km
s


(Spitzer 1978)
Tp  Te
dTe
 0.13 ne 3 / 2
dt
Te
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
c.g.s.
SNA07, May 20-26, 2007
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
“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
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
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
H-alpha profiles
(Kirshner, Winkler and Chevalier 1987)
(Hester, Raymond and Blair 1994)
Cygnus Loop
MEASURABLE QUANTITIES
•FWHM of broad component (Ti !!)
•Intensity ratio
•FWHM of narrow component
•Displacement (not if edge-on)
• (T  40,000 K – why not fully ionized?)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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 in
X-rays (proper motions)
Optical
• Electron temperature
X-rays
~ 0.4-1.0 keV, while
Radio
expected ion T ~ 45 keV
• Very small Te/Ti, or Ti
much less than expected?
Missing energy in CRs?
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
The “strange case” of SN1006
“Standard”
X-ray spectrum
Tycho with ASCA
Hwang et al 1998
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
Diffusive shock acceleration
shock
flow speed
• Fermi acceleration
– Converging flows
– Particle diffusion
(How possible, in a
collisionless plasma?)
X
(in the shock reference frame)
• Particle momentum distribution
where r is the compression ratio (s=2, if r = 4)

• Synchrotron spectrum S ( ) 
• For r = 4, power-law index of -0.5
• Irrespectively of diffusion coefficient
F ( p)  p ( r  2) /(r 1)  p  s
 ( s 1) / 2
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
3 / 2 /(r 1)
SNA07, May 20-26, 2007
The diffusion coefficient
• Diffusion mean free path
(magnetic turbulence)
   rg
with   (B / B)
2
res
(η > 1)
mc2
rg 

eB
• Diffusion coefficient
v
mc3
  


3
3eB
Rino Bandiera, OAA
Fdiff  
Fundamental Physics & Astrophysics of SNRs
f
 udiff f
x
SNA07, May 20-26, 2007
…and its effects
• Acceleration time t
• Maximum energy
acc
3 1 1
r (r  1) mc3
    


u1  u2  u1 u2 
(r  1) eBu sh2

  
1 
2
 tacc 




t




u
syn
max
sh / B
2 
2 

Bu sh  
B

• Cut-off frequency
 cutoff  B
2
max

ush2

2
 cutoff

u
0.11 
 3 sh 1  keV

  10 km s 
– Naturally located near the X-ray range
– Independent of B
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Basics of synchrotron emission
•
•
•
•
•
Emitted power
Characteristic frequency
Power-law particle distribution
If F ( p)  p then S ( ) 
Synchrotron life time
2e 4
2 2
2
2 2


Wsyn 
B
sin



(
mc
)
c
B

1

2 3
3m c
0.29 3eB sin  2
 syn 
  c2 B 2
2
2mc
 ( s 1) / 2
s
Wsyn
d
 (mc )
dt
Rino Bandiera, OAA
2
tsyn 
1
c1 B
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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:
N e ( E )  E  s exp(  E / Emax )
• Fit power-law + cutoff to spectrum:
“Rolloff frequency”
Rino Bandiera, OAA
S ( )    exp( ( / rolloff )1/ 2 )
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Measures of rolloff frequency
• SN 1006
(Rothenflug et al 2004)
• Azimuthal depencence of the break
Changes in tacc?
or in tsyn?
Rino Bandiera, OAA
η of order of unity?
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Dependence on B orientation?
• Highly regular structure of SN 1006.
Barrel-like shape suggested (Reynolds 1998)
Direction of B ?
• Brighter where B is perpendicular to
the shock velocity?
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
(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
3-D Geometry. Polar Caps?
Ordered magnetic field
Polar cap geometry:
(from radio polarization)
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
Statistical analysis
(
F
u
l
b
r
i
g
h
t
&
R
e
y
n
o
l
d
s
1
9
9
0
)
Expected morphologies in radio
Barrel-like SNR
(under various
orientations)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
Polar cap SNR
(under various
orientations)
SNA07, May 20-26, 2007
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
Very sharp limbs in SN 1006
Chandra
ASCA
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
B from limb sharpness
Profiles of resolved non
(Bamba et al 2004)
filaments in the NE shell of SN 1006
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
Length scales
 1” (0.01 pc)
upstream
 20” (0.19 pc)
downstream
SNA07, May 20-26, 2007
A diagnostic diagram
• Acceleration time
tacc = 270 yr
• Derivation of
the diffusion
coefficients:
u=8.9 1024 cm2s-1
d=4.2 1025 cm2s-1
(Us=2900 km s-1)
to compare with
Bohm=(Emaxc/eB)/3
Rino Bandiera, OAA
rolloff
tsync> tacc
 > Bohm
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
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
Blasi Solution
Thermal
• Concavity in particle
distribution.
Standard PL
(also for electrons)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Gamma-ray emission
νFν
• 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
Rino Bandiera, OAA
X-ray
γ-ray
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
• 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?)
(Ellison et al 2000)
• Efficiency in in accelerating ions?
(The origin of Cosmic rays)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
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
(Blondin and Ellison 2001)
(Decourchelle et al 2000)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
The Σ–D Relationship
• Empirical relation
 2.38 without Cas A
 2.64 with Cas A
 
– 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
• Is the correlation
representative of
t
“
h
t
e
y
e
p
v
i
c
o
a
l
l
u
t
o
i
b
o
n
j
o
e
c
f
t
a
”
?
Rino Bandiera, OAA
Berezhko & Voelk 2004
n
•
Rino Bandiera, OAA
T
h
e
“
P
r
o
t
o
t
y
p
The Crab Nebula
•
Thermal filaments
Optical
X
Amorphous compon.
C
r
a
b
N
e
b
u
l
a
-
Crab Nebula – H

R
i
n
o
B
a
n
d
i
e
r
a
,
O
A
A
F
u
n
d
a
m
e
n
t
a
l
P
h
y
s
i
c
s
&
A
s
t
r
o
p
h
y
s
i
c
s
o
f
S
N
R
s
S
N
A
0
7
,
M
a
y
2
0

-
cont
26, 2007
e
”
T
h
e
C
r
a
b
N
e
b
u
l
a
s
p
e
c
t
r
u
m
(apart from optical filaments an
Synchrotron emission
-0.8
-1.1
• Radio
•Optical
( Bneb  0.3 mG )
R
i
n
o
B
a
n
d
i
e
r
a
,
O
A
A
•Soft X-rays
-0.3
F
u
n
d
a
m
e
n
t
a
l
P
h
y
s
i
c
s
&
A
s
t
-1.5
•Hard X-rays
r
o
p
h
y
s
i
c
s
o
f
S
N
R
s
SNA07, May 20-26, 2007
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.
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Basics of synchrotron emission
•
•
•
•
•
Emitted power
Characteristic frequency
Power-law particle distribution
If F ( p)  p then S ( ) 
Synchrotron life time
2e 4
2 2
2
2 2


Wsyn 
B
sin



(
mc
)
c
B

1

2 3
3m c
0.29 3eB sin  2
 syn 
  c2 B 2
2
2mc
 ( s 1) / 2
s
Wsyn
d
 (mc )
dt
Rino Bandiera, OAA
2
tsyn 
1
c1 B
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Simple modelling(Pacini & Salvati 1973)
• Homogeneous models (no info on structure)
• Magnetic field evolution
– Early phases (constant pulsar input)
3
B2R
Lt
t   ; WB 

6
2
 B
Lt
 t 1
3
R
– Later phases (most energy released)
t   ; BR 2  6WB ( ) R( )
Rino Bandiera, OAA
 B
Fundamental Physics & Astrophysics of SNRs
L R( )
2

t
R2
SNA07, May 20-26, 2007
• Power-law injection
s  1  2  1.5
– With upper energy cutoff
– Continuum injection
• link to the pulsar spin down
• Particle evolution (adiabatic vs synchrotron losses)
• Evolutionary break
tsyn  t   br 
1
c1 B(t ) 2 t
  br  c2 B(t ) br2 
c2
c12 B(t )3 t 2
• Adiabatic regime
N ( , t )   j ( , t ) dt    s
S ( )    ( s 1) / 2 (-0.3 in radio)
• Synchrotron-dominated regime
N ( , t )  j ( , t ) tsyn    s 1 S ( )    s / 2
Rino Bandiera, OAA
(-0.8 in optical)
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Kennel & Coroniti model (1984)
Basics of “Pulsar Wind Nebula” scenario
•
•
•
•
•
Pulsar magnetosphere
ISM
Pulsar wind
Termination shock
Pulsar Wind Nebula
Interface with the
ejecta (CD, FS)
• Stellar ejecta
Stellar
ejecta
• Interface with the
ambient medium
Pulsar Wind Nebula
(RS, CD, FS)
• Ambient medium (either ISM or CSM)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
Pulsar magnetosphere
Pulsar wind
Termination shock
SNA07, May 20-26, 2007
The ingredients
• Pulsar wind
– super-relativistic
– magnetized
(toroidal field)
– isotropic
n  proper density
u  radial comp 4 - speed

FPoynting
Fparticle
B2

4 nu mc 2
• Termination shock
–
–
–
–
n1u1  n2u2
mass conservation
magnetic flux cons. B1u1 /  1  B2u2 /  2  E
2
2
2
2
momentum cons. 1n1u1  p1  B1 / 8  2n2u2  p2  B2 / 8
1n1u1 1  EB1 / 4  2n2u2 2  EB2 / 4
energy cons.
where   mc2   p (specific enthalpy)
 1 n
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
–
–
–
–
 2   , B2  B1 , n2 /  2  n1 /  1 , kT2  mc2u1 / 8 
 2  9 / 8 , B2  3B1 , n2 /  2  3n1 /  1 , kT2  mc2u1 / 18
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
MHD evolution in the nebula
• Steady solution (flow timescale << SNR age)
– number flux cons.
– momentum cons.
• Asymptotic velocity
–
–
–
–
- magnetic flux cons.
- energy cons.
V  c
u



1 
!!!
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
LRn / Vext
Rs
Vext
L
Rn~10 arcsec



 
2
3
4 Rs c 4 Rn / 3
Rn
c
(wisps region)
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Radial profiles
• Inner part with: u  r , n  const , B  r
• Outer part with: u  const , n  r , B  r
• Equipartition in the outer part:
2
2
1
B2
4
0

r

r
4 nu mc 2
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Do we expect what observed?
• Injected particles
– power-law, between a min and a max energy
f 2 ( )  A 2( 2 1) ;  2   2   2
– 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
u
d
 dn
 u
 c1 B 2 2
dr 3n dr
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Best-fit solution
• Parameters:
L  5 1038 erg s 1 , rs  3 1017 cm,  1  3 106 ,   0.6,   0.003
• Fit to:
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Problems -Ia
• The sigma paradox
– A value   1 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
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
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
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
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
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
3C 58
pulsar axis
MHD simulations
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
van der Swaluw 2003
SNA07, May 20-26, 2007
Elongated structures of PWNe
3C 58
G5.4-0.1
pulsar spin
G11.2-0.3
Crab Nebula
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Details of the structure
counter-jet
torus
knot
inner ring
jet
Crab Nebula
Vela
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Jet sizes
40” =
0.4 pc
4’ = 6 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)
Rino Bandiera, OAA
Vela Pulsar (Pavlov et al. 2003)
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
Simulating PWNe
(Komissarov, 2006; Del Zanna et al 2004, 2006)
• Relativistic MHD codes
• Modelling a PWN like the Crab
Velocity
Rino Bandiera, OAA
Magnetization
Fundamental Physics & Astrophysics of SNRs
Max Energy
SNA07, May 20-26, 2007
Surface brightness maps
Jet-Torus structure
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
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)
Reverse Shock
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
ISM
Shocked Ejecta
Shocked ISM
Forward Shock
Unshocked Ejecta
Pulsar
Termination
Shock
PWN
Pulsar Wind
PWN Shock
SNA07, May 20-26, 2007
Rino Bandiera, OAA
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
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
-0.28
-0.20
230 GHz map
Rino Bandiera, OAA
Spectral map
Fundamental Physics & Astrophysics of SNRs
SNA07, May 20-26, 2007
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
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
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
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
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
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