A Basic Course on Supernova Remnants

Rino Bandiera, Arcetri Obs., Firenze, Italy A Basic Course on SNRs

A Basic Course onSupernova Remnants

• Lecture #1– How do they look and how are observed?– Hydrodynamic evolution on shell-type SNRs

• Lecture #2– Microphysics in SNRs - shock acceleration– Non-thermal emission from SNRs


Basic concepts of shocks• Quantities conserved across

the shock discontinuity– Mass– Momentum– Energy

• For a strong shock, i.e.the jump conditions are:

• Compression ratio (r=u1/u2):– 4, for a non relativistic fluid– 7, for a relativistic one

12

1122

22 pVpV 1

21112

2222 2/2/ wVVwVV

1122 VV

shock111 ,, up 222 ,, up

V

2111 Vp

21121212 1

2;

1

1;

1

1VpVV


More complex than this

• Collisionless shocks– Coulomb equilibration scale (order of parsecs)

But shocks are much sharper than that

– Even tiny magnetic fields are more effective(gyration radius)

– Free to escape along the field lines? Not in the presence fluctuations(e.g. MHD waves)

pcskm000,1cm1

4.24

1sh

1

30

2/5

Vn

T

TL

p

eeq

1

3 μG10km/s10km000,10U

BU

m

m

eB

mcr

pG

2

res||

2

/

cyclesafterradians1

1in/,If

BBr

N

rBBBB

G

G


Thermal and non-thermal particles

• Naif view– Electrons & ions are shocked

independently

– Similar Vth, i.e. Te~(me/mp)Tp

• Anomalous electron heating, mediated by MHD waves?(Cargill & Papadopoulos 1988, + … )

• Possibly observed? (Ghavamian et a. 2007)

Using Balmer line profile,

Te & Tp derived independently


Even more striking, evidence fornon-thermal, relativistic particles

• Radio synchrotron emission n SNRs• And even in X-rays, in a few of them


shock

X

flow speed

(in the shock reference frame)

Diffusive shock acceleration

• Fermi acceleration– Converging flows– Particle diffusion

(How possible, in acollisionless plasma?)

• Scattering on MHD waves


A test particle approach (Bell 1978) • Collision against a (N.R.) moving wall:

• Momentum after N cycles:

i.e.

213

2uu

v

pp

R

NRvv+2U = v(1+2U/v)

U

pp(1+2U/c)

0

1

21

3

21)( p

v

uuNp

N

i i

N

i ivuu

p

Np

121

0

1

3

2)(ln

(averaged over directions)


Probability of having N cycles

• Return probability

• Probability of N cycles

222 2

12

vudvvu x

u

v

x

222 2

1

2

uvdvuv x

v

u

x

222 2

12

uvdvuv x

u

v

x

2

2

2ret /1

/1

vu

vu

flow

flowP

down

up

2

1 2

2

/1

/1

N

i i

i

vu

vuNP

N

i i

N

i i

i

vu

vu

vuNP

12

1 2

2 14

/1

/1ln2ln


Compare the two formulas

from which

and finally the distribution

For r=4, σ=2. Spectral index 0.5 (as in radio!)

Diffusivity is fundamental for the process to take place, but does not appear explicitly

N

i ivuu

p

Np

121

0

1

3

2)(ln

N

i i

N

i i

i

vu

vu

vuNP

12

1 2

2 14

/1

/1ln2ln

pppp

Ppf rruuuu )1/()2()/()2( 2121)(

)/(3

0021

2

212

..ln3

lnuuu

p

ppPei

p

p

uu

upP


The convection-diffusion eq. • A different approach to the problem

• Heuristic explanation:– Advected flow– Diffusive flow

– Diffusion in momentum space

provided that

),()(

3

1),(),(),()( pxpf

px

xu

x

pxfpxpxfxu

x

),()( pxfxu

x

pxfpx

),(

),(

),(),()(

3

1),(

)(

3

1pxfp

ppxpf

x

xu

ppxpf

px

xu

px

xup

)(

3

1


Solving the equation

• Boundary conditions

• Velocity profile:• Integrate between x=+∞ and x=- ∞

(now x has disappeared)

• Solution of linear equation:

),()(

3

1),(),(),()( pxpf

px

xu

x

pxfpxpxfxu

x

0;:0at

0;:at

22

11

x

fffx

x

fffx

xuux

u 21:jump

)()()( 21231

1122 ppfuupfupfu p

Bppfppdppfp

p

)()2()( 11

2

0


A cosmic-ray precursor

• In the unshocked medium

• Accelerated particle may reach, in front of the shock, a distance

Any effect on the pre-shock fluid ?

),()(

3

1),(),(),()( pxpf

px

xu

x

pxfpxpxfxu

x

0),(

),(),()(

x

pxfpxpxfxu

x

)(

),(

xu

px


Dimensional quantities• Parallel mean free path

• Diffusion coefficient

• Perpendicular diffusion

(can be much lower than the parallel one)

Gr || 1;/)( -2res BBp

1

72

μG10pc10

B

m

m

eB

mcr

pG

eBmcv 3/3/ 3||||

2||

2|||| 1//1/ Gr


Characteristic times• Acceleration time• Age• Synchrotron losses

• Loss-dominated regimenaturally locatedin the X-ray range

Independent of B strength

p

p p

pd

uuuu 02

2

1

1

21acc

3 22acc u

c

u

2/12/3

2

31

2

2

3

2/12/3

2

21

2

2

acc

mc

eB

e

mc

mc

eB

e

mc

mc

eB

u

c

mc

eB

u

c

syn

1

2

12

2cutoff km/s1000keV1.0

uu

e

mc

Diffusion must be efficientalso upstream !!


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”

)/exp()( maxEEEEN se

))/(exp()( 2/1rolloff S


Measures of rolloff frequency

• SN 1006 (Rothenflug et al 2004)

• Azimuthal depencence of the break

Truly loss limited? Changes in tacc? Varying η?


Very sharp limbs in SN 1006

ASCA

Chandra


B from limb sharpness

Profiles of resolved non-thermal X-rayfilaments in the NE shell of SN 1006

(Bamba et al 2004)

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

Consistent withB ~ 30 μG


A diagnostic diagram• Acceleration time

tacc = 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 withBohm=(Emaxc/eB)/3

rolloff

tsync> tacc

> Bohm


Acceleration times & energies

• (Theoretical) need for large fields

• The case of a perpendicular field

• BUT how to inject particles?(mean free path has tobe comparable with the shock width)

1

2

2

2acc

mc

eB

u

c

u

2||

2|||| 1//1/ Gr

1

2

2

22acc 1

mc

eB

u

c

u


Not just test particles ?• (Indirect) evidences that cosmic-ray

component is dynamically relevant (ions)– Large magnetic field

• If synchrotron-losses regime• If interpretation of narrow filaments is correct

– Deviations from predicted fluid behaviour• RS closer to FS• Too low post-shock (ion) temperature

– Effects of a shock precursor


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)


SNR 1E 0102.2-7219• 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 small Te/Ti, or Timuch less than expected?Missing energy in CRs?

(Hughes et al 2000, Gaetz et al 2000)

Optical

Radio

X-rays


Gamma-ray emissionA definitive way to measure the field?

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

SynchrotronIC

Radio X-ray γ-ray

νFν


• 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)


A self-regulating model• If acceleration is efficient, cosmic-ray

precursor upstream• Generation of MHD waves, by streaming

instabilities• Turbulent amplification of upstream field• Effects on the diffusion coefficient• A smaller diffusion coefficient makes

further acceleration more efficientCLOSING THE LOOP


Shock modificationDynamical effects of the

accelerated particles ontothe 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


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

Thermal

Blasi Solution


The injection of electrons ?• 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


Optical emission in SN1006• “Pure Balmer” emission

in SN 1006

• Here metal lines are missing (while they dominate in recombination spectra)– Extremely metal deficient ?


“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 ?


The role of neutral H• 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

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

•Charge-exchange cross section is larger at lower vrel

•Fast neutral component more prominent in slower shocks


H-alpha profiles

(Hester, Raymond and Blair 1994)

(Kirshner, Winkler and Chevalier 1987)

Cygnus Loop

•FWHM of broad component (Ti !!)

•FWHM of narrow component

• (T 40,000 K – why not fully ionized?)

MEASURABLE QUANTITIES

•Intensity ratio

•Displacement (not if edge-on)


THE END

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A Basic Course on Supernova Remnants