Supernova Remnants
Luke Drury
Dublin Institute for Advanced Studies
Barcelona 6 July 2006
Supernovae
Identified by Baade and Zwicky in 1934
(in this paper they already speculated
about a possible link to the origin of CRs)
A few per century per galaxy (about 1 per
second in observable universe)
Barcelona 6 July 2006
Taxonomy
Original astronomical classification
Strong hydrogen lines - type II
Weak or no hydrogen lines - type I
More fundamental distinction
Core-collapse - type II and Ib
Thermonuclear deflagration - type Ia
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Core-collapse
Endpoint of stellar evolution for stars of
more than several solar masses
solar mass Iron core supported by
electron degeneracy
Inverse beta decay sets in
catastrophic collapse to neutron star or
black hole
Barcelona 6 July 2006
Neutron star gravitational binding energy is about
53
10% rest mass energy or about 3x10
erg.
Radiated mainly in neutrinos and gravitational
waves.
Energy deposition in uncollapsed mantle of about
51
10 erg - not well understood!
MHD jet production?
Nice review by Burrows, Walder, Ott and Livne in
astro-ph/0409035
Barcelona 6 July 2006
White dwarf
deflagration
End point of few solar mass stellar evolution
All hydrogen burnt mainly to carbon
Carbon ignites and combustion front
transforms all material to Iron
Releases about 10
-3
rest mass, also 10
51
erg!
Barcelona 6 July 2006
Remarkable coincidence!
Two quite distinct mechanisms
51
Both deposit about 10
solar mass of material!
erg in about one
Good evidence for a rare class of
hypernovae where something approaching
54
the full 10
erg is available.
Barcelona 6 July 2006
Circumstantial link to CR
origin....
SN mechanical energy input to Galaxy is
enough to power the GCR accelerator.
But adiabatic loss problem means SNRs, not
SNe....
Theoretical mechanism (DSA).
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Environments
Core-collapse
Massive stars, rapid evolution, clouds etc
Winds, mass-loss
Disturbed environment
Deflagration
Old passive precursors
Undisturbed ISM
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Shells and Plerions
Plerion = filled centre remnant, PWN
powered by spin-down of pulsar.
Shell = dynamic structure produced by
explosion itself.
Will only consider shell SNRs in rest of talk...
Barcelona 6 July 2006
Simple theory (toy model)
Exact spherical symmetry
Uniform ejecta
Uniform and stationary ambient medium of
low pressure and density.
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Ballistic phase
Ejecta expand almost freely and barely
notice tenous external medium.
Drive strong shock into ambient medium
Pressure of shock heated ambient medium
produces a weak reverse shock in the
ejecta.
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Zeroth order
approximation
Uniformly expanding sphere in vacuo
3Me j
ρe j =
0 < r < V0t
3 3
4πV0 t
Z V0t
!
"
r 2
3
21
4πr ρe j
ESN =
dr = Me jV02.
2
t
10
0
r
V (r) = ,
t
Note that for SNRs initial velocity is about
0.03c!
Barcelona 6 July 2006
First order
approximation
Ejecta sweep up ambient medium through
a strong forward shock and compress it to
at least four times the ambient density
(NB ideal gas EOS).
Pressure of shocked amient medium drives
a weak reverse shock back into the ejecta.
Barcelona 6 July 2006
"
4π 3
4π ! 3
3
R F ρ0 ≈
RF − RCD 4ρ0,
3 # $ 3
1/3
4
RCD ≈ 1.1006RCD
RF ≈
3
2
ρe jVR
2
ρ0VF
≈
! "32
t
VR ≈ 1.1
V0
tSW
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Energy flows
Directed Bulk Motion
Kinetic Energy
Expansion
PdV work
Shocks!
Random Micro Motion
Internal Energy
Pressure
SN Explosion
Radiative losses
SNR = cosmic heat engine
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Time scales are initially
very different!
Shocks
Directed Bulk Motion
Kinetic Energy
!
"−1
MV 2 1
τ≈
ρ04πR2V 3
2
2
ρint R
≈
ρ0 V
Expansion
Random Micro Motion
Internal Energy
Pressure
Fast
SN Explosion
τ≈texp
R
=
V
Slow
Radiative losses
Multi-messenger signals
Barcelona 6 July 2006
Initially almost all energy converts to
kinetic energy - ballistic expansion
Once swept up mass roughly equals initial
ejecta mass conversion from kinetic to
“thermal” can compete with the PdV
conversion the other way
Dynamic equilibrium established
Barcelona 6 July 2006
Sedov-Taylor-von Neumann solution for the
strong point explosion in a cold gas.
Roughly constant fraction of energy in
form of KE implies
ρ0R V = const
3/2 dR
R
= const,
dt
5/2
2/5
R ∝ t, R ∝ t .
3 2
Barcelona 6 July 2006
Internal pressure roughly constant (subsonic
region behind shock).
Mass concentrated in thin shell behind shock
of thickness no more than about 10% radius
(even less if shock more compressive than 4).
Barcelona 6 July 2006
Flux of energy through the forward shock
#
$
!
"
1
2
3
ρ0V
ΦF = 4πR
2
2
∝t ,
t ! tSW
−1
∝t ,
t # tSW
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Power of the forward and reverse
shocks
ΦF
ΦR
tSW
t
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Sweep-up time is typically a few hundred
years.
Useful approximate formula for Forward
shock radius valid in both Sedov and freeexpansion phases is
!
R(t) ≈ 1.1V0t 1 +
"
t
tSW
#3/2$−2/5
Barcelona 6 July 2006
At late times radiative losses become
important and/or the external pressure
5
becomes significant, typically at 10 years
or so.
Cooling is quite complex and can lead to
instabilities and secondary shocks.
Another instability is important at
transition from ballistic expansion to Sedov
phase.
Barcelona 6 July 2006
Expansion decelerates as remnant evolves
from ballistic to Sedov phase.
Deceleration is equivalent to a local
gravitational field directed radially
outwards.
Contact discontinuity between dense ejecta
and light ambient material is RT unstable.
Barcelona 6 July 2006
Leads to mixing of ejecta and swept-up
material.
“Fingers” and “blobs” of dense ejecta form.
Complex small-scale structure (seen in
hydro simulations)
May locally increase magnetic field....
Barcelona 6 July 2006
Caveats
Ejecta are not uniform!
radial structure (sharp edge most
unlikely!)
angular structure (polarization seen at
early stages of SN-II)
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Environment is not uniform!
interaction with progenitor
wind blown cavities, shells etc
Galactic structure
Molecular clouds
Density gradients
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Why so spherical?
Well not always!
Interior is in approximate pressure
equilibrium
Basically just bubbles of very hot gas (and
cosmic rays..?) expanding because of their
overpressure relative to the environment.
Barcelona 6 July 2006
Shock front propagation tends to smooth
out any severe departures from sphericity.
Large scale gradients in ambient density to
first order just lead to an off-centre, but
still roughly spherical structure.
(NB implosion of reverse shock can be very
asymmetric).
Barcelona 6 July 2006
Particle Acceleration
Little effect on bulk dynamics
Significant impact on compression of main shock can be order ten rather than four - more
concentration of mass in thin shell behind shock.
Magnetic field amplification - exciting new idea
for acceleration, but probably little impact on bulk
dynamics (NB not RT effect).
Barcelona 6 July 2006
Diffusive Shock
Acceleration
Mesoscopic theory on intermediate length
and time scales. In reality:
no sharp distinction between thermal
plasma and accelerated particles,
nor between outer dynamics and shock
structure.
But useful simplifying approximations.
Barcelona 6 July 2006
Outer scale of
bulk dynamics, eg solar
wind, SNR, jet, etc
shock formation
Precursor
Intermediate scales
Shock acceleration theory
shock
structure
Subshock
Inner scale
Plasma physics
Injection!
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Very wide scale separation is a numerical
nightmare, but useful for analytic
approaches. Can distinguish two extreme
scales..
Outer scale of macroscopic system and
maximum energies
Inner scale of injection processes and kinetic
effects
Aim of theory should be to bridge the gap
between these two regimes, but not to try to
be a complete theory.
Barcelona 6 July 2006
Simplest test particle theory gives the well
known result (Krymsky, 1977; Bell, 1978;
Blandford and Ostriker, 1978; Axford, Leer and
Skadron, 1978);
f (p) ∝ p
U1
−3U −U
1 2
the intermediate asymptotic form of the
distribution function is a simple power-law
with an exponent determined purely by the
shock compression!
Barcelona 6 July 2006
But easy to show that accelerated particle
pressure can be significant, so must worry about
reaction effects. Also, if process is to work with
high efficiency, as appears to be required, eg, to
explain the Galactic cosmic ray origin, we need a
nonlinear theory.
In principle easy - we just have to solve the
diffusive transport equation and the usual
hydrodynamic equations with an additional
cosmic ray pressure in the momentum equation!
Z
3
PC(x) =
4πp v
f (p, x) d p
3
In practice very hard!
Barcelona 6 July 2006
Possible approaches
Throw it at the computer (Dorfi, Duffy,
Jones, Kang....)
Monte-Carlo approach (Ellison and coworkers)
Two-fluid approximation (largely historical)
Semi-analytic theories (Eichler, Malkov, Blasi)
Good general agreement
now between all
approaches!
From P. Blasi, 2002
Barcelona 6 July 2006
Bad news
All these approaches assume that the
shock structure can be treated as steady
on intermediate scales
But there are strong arguments for
generic mesoscopic instabilities
Good news
Can significantly amplify magnetic fields
Accelerate to higher energies
Seems to be required by observations
Basic physics of acceleration is very
robust.
The Instability Zoo
Streaming excitation of Alfven waves (eg
Wentzel, 1974; Skilling 1975)
Acoustic instability (Drury and Falle, 1986)
Parker instability (1966, 1967)
McKenzie and Voelk, 1981 - wave heating or
“plastic deformation of field”.
Bell and Lucek, 2000, 2001; Bell 2004, 2005
Generic Weibel-type instabilities
Bulk CRs should fill interior of remnant in
Sedov phase (roughly constant pressure)
Highest energy particles probably escape,
but rest are stored inside - push shock
and are adiabatically decelerated.
Release into ISM when shock dies
Implies low energy composition dominated
by last batch accelerated....
Barcelona 6 July 2006
Expect detectable levels of TeV gammas
from hadronic (DAV, 1994) and leptonic
channels.
In general hadronic emission should have
more spatial structure (gas target is highly
structured, CMB is flat), but radiative
losses for the high energy electrons
complicate the picture.
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Ten years later!
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RXJ1713-3946
1.5 × 10−11 cm−2 s−1
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Over to Marianne and Leonid!
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