Supernova Remnants as Cosmic Rays Accelerators

Vladimir S. Ptuskin

Institute for Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences

(IZMIRAN), Troitsk, Moscow region 142190, Russia

cosmic ray halo

Sun

bubble

GC close binary

Galactic disk

pulsar SNR

stellar wind

M87

GRB

interacting galaxies

ulsar

Ncr ~ 10-10 cm-3 - total number density

wcr ~ 1.5 eV/cm3 - energy density

Emax ~ 3×1020 eV - max. observed energy

Lcr ~ 5×1040 erg/s - Galactic luminosity in

CR

δcr ~ 10-3 at 1012 - 1014 eV - anisotropy

rg ~ 1E/(Z×3×1015 eV) pc - Larmor radius

source spectrum

Ncr

TQcr

E-2.7

cosmic ray densityescape time E-(0.3 … 0.6)

source spectrum E-(2.0 … 2.4)

two power laws: source spectrum + propagation

secondary species: Qcr,2 =

nvσ21N1 d, 3He, Li, Be, B … p, e+

escape length: X = ρvT

~ 10 g/cm2 at 1 GeV/nucleon

SNRSun

cosmic-ray halo

galactic disk

r

2H

flat-halo diffusion model

D

HX

2

v

Ginzburg & Ptuskin 1976 Berezinskii et al 1990 Strong & Moskalenko 1998

surface gas density 2.4 mg/cm2

GV5 s,/cm102 254.05

28 RRHD

km/s40s,/cm109.5 23.05

28 aVRHD

rigidity magnetic,v

kpc,5 5 Ze

cpR

cHH

pure diffusion

diffusion + distributed reaccele- ration in ISMJones et al 2001

Alfven velocity

Energy balance

local galactic CRenergy density 1.5 eV/cm3

needed source power 3×1038 erg/s kpc2

SN kinetic energy 2×1039 erg/s kpc2

(Wsn=1051 erg, 50 Myr-1 kpc-2)

~ 15% efficiency of CR acceleration

+ pulsars 2×1050 (10 ms/τ)2 erg+ stellar winds 2×1038 erg/s kpc2

+ Galactic GRBs 1051 erg/105 yr+ Galactic Center

SNR blast waves• SN II, SN Ib/c –core collapse of massive stars• SN Ia – thermonuclear explosion of white dwarf in binary

system Mechanical energy Wsn ~ 1051 erg (1053 for hypernova)

- Free expansion (ejecta-dominated stage): t < 300 yr, ush = 5×108 – 3×109 cm/s, R < 2 pc- Adiabatic deceleration (Sedov stage): t = 103 - 3×104 yr, ush ~ (Wsn/nism)1/5t-3/5

- Radiation cooling: t > 105 yr, R > 20 pc

Acceleration by external shock: a) “normal” composition after correction on atomic properties (FIP, volatility)

b) delay between nuclear synthesis and acceleration

yr 101.1

Co,Ni

5

59EC59

high obs. 59Co/56Fe – δt > 105 yrSoutoul et al. 1978, Leske 1993

Diffusive shock acceleration

pdt

dp sh

3

u

SNR

Fermi 1949, Krymsky 1977, Bell 1978

ush

D(p)

shock

-average gain of momentum

2

20

2

2

41

3

3

/)(

)()(

)(

res

g

sha

r

r

B

BvrD

upDt

pfpEI

pppf

distributionfunction(test particles)

time ofacceleration

CR intensity

resonantdiffusion kres~1/rg

Larmor radius

Maximum energy

10)(

pD

Ru shshcondition of acceleration,critical Pecklet number(parameter of modulation)

SNRWsn=1051erg

ismn0=1cm-3

scmPD

scmnWRu

GVism

shsh

/106

/10

23.028

25/2

05128

-maximum value

-typical in interstellar medium

diffusion should be anomalously slow near the shock

(upstream and downstream)

cosmic ray streaming instability in shock precursorBell 1978, Lagage & Cesarsky 1983, McKenzie & Vőlk 1982, Achterberg 1983,Vőlk et al. 1988, Fedorenko 1990, Bell & Lucek 2001, VSP & Zirakashvili 2003

Nagano & Watson 2000

Bohm limit

galacticextra-galactic?

knee

standard assumption δB ~ Bism

Bohm diffusion

5/1max

14max

221

10

/106

3

tE

eVZE

scmP

vrD

GV

gB

might be better for SNexplosion in progenitor windVőlk & Biermann 1988

x

u(x)

ush

ush/r

D(p)/u

precursorsubshock

upstream downstream

-∇Pcr

Nonlinear shock modification by CR pressure

nonmodified shock

xsh

cosmic ray density

Berezhko &Elliison 1999

not power law spectrum for high Mach number shocks

Axford 1977, 1981Eichler 1984Berezhko et al. 1996Malkov et al. 2000

mcp

apppf

uP

a

crshcrcr

,5.00,)(

5.0,

4

2

overall CR spectrum

Berezhko &Völk 2000

Cassiopeia A is bright at all energies of the electromagnetic spectrum. This composite image shows Cassiopeia A at many different wavelengths: radio polarization in red (VLA), X-rays in green (CHANDRA) and optical in blue (HST). Notice the outer shock, visible only in X-rays, as the thin green rim most visible at the top of the image. Also notice the bright ring which is visible at all three wavelengths, and the many different filamentary structures seen at each wavelength. The compact remains of the exploded star are visible only in X-rays, as the bright green spot slightly below and to the left of the geometric center of the bright ring.

observationsradio emissionνMHz = 4.6 BμGEe,GeV

2

E = 50 MeV – 30

GeV

(100 GeV for IR)

γ = 1.9 – 2.5

We = 1048 – 1049 erg

Ginzburg &

Syrovatskii 1964

Shklovsky 1976

nonthermal X-raysεkeV = 1 BμG(Ee/120 TeV)2

εmax ~ 100 TeV

SN1006 Koyama et al. 1995Cas A Allen et al. 1997RX J1713-39 Koyama et al. 1997RX J0852-46 (“Vela jr”) Slane et al 2001

γ-rays (π0)Ε = 30-3000 MeVγ Cygni, IC443Esposito et al. 1996Sturner & Dermer 1996

TeV γ – rayselectrons/protonsεmax ~ 100 TeV

SN1006 Tanimori et al 1998RX J1713 Muraishi et al. 2000Cas A Aharonian et al. 2001

Only upper limits on TeV γ-rays from many SNRs with

ages > 3×103 yr Buckley et al. 1998, Aharonian et al. 2002

e

γsynchrotron

e

γ inverse Comptonεγ = ε0(Ee/mec2)2p

π0

γ

SNR

SN1006

Tanimori et al. 2001

Problems:

- Galactic sources should work up to (1-3)×1018 eV (Fe ?) (reacceleration may help: Axford 1994, Bell 1992,

Bykov & Toptygin 2001, Vőlk & Zirakashvili 2004;dispersion of SN parameters: Sveshnikova 2003)

- no VHE gamma-rays from not very young SNRs tsnr ≥ 3×103 yr

(Buckley et al. 1998, Aharonian et al. 2002)

- cosmic ray source spectrum γs = 2.0 - 2.4 (depends on propagation model)

VSP & Zirakashvili 2003

Wsn = 1051 erg, Bism = 5 μG, n0 = 0.4 cm-3 ξcr = 0.5, κ = 0.04, a = 0.3

strong streaming instability and non-linear wave interactions in shock precursor:

under extreme conditions:

Emax ≈ 1017Z(ush/3×104km/s)2

×(κ/0.1)(ξcr/0.5)Mej1/3n1/6 eV

δBmax≈ 10-3 (ush/3×104km/s)n1/2 G

maximum momentum of accelerated particles:abandonment of Bohm limit hypotheses

Random field produced by cosmic-ray streaming instability

in shock precursor

22

,4

, shcrcrcr

ash uPB

wx

PV

x

wu

0,0

00,0 ,

4,

a

shcr

a

V

u

B

B

BVBB

0,0

,0 ,4

,

a

shcr

efa

V

u

B

B

BVBB

Alfven velocity

cosmic-ray pressure

wave energy density

weak random field: strong random field:

characteristic velocity of waves

Bell & Lucek 2001VSP & Zirakashvili 2003

Average source spectrum

spectrum atthe shock instantaneousSNR luminosityin run-awaycosmic rays

averagecosmic-raysourcespectrum

adiabatic stage Q ~ ξcrνsnWsnp-4 (Sedov) - universal spectrum !

ejecta-dominated stageSNII in RSG wind: Q ~ p-6.5 at ρstar~ r -10

SNI in uniform medium: Q ~ p-7

(Chevalier – Nadyozhin)

))((~

))((~

maxmax4

max32

max4

max2

ptpdt

dppRuq

ptpHppuf

shshcr

aashcr

SN rate

hot bubble0.013 cm-3, 3μG

ism R=60pc

n=1cm-3

RSG wind

Weaver et al. 1977Chevalier & Liang 1989

KASCADE

SNII

Roth et al. 2003

·Eknee ≈ 7×1015 Z eV, ~ ξcrWsnM1/2(Mejuw)-1

Emax ≈ 4×1016 Z eV at tmin = 7 days

ρstar~ r-10

∙M=10-5

uw=10km/sRw=2pc

Wsn= 1051 erg, ξcr= 0.5

VSP & Zirakashvili 2004

Other proposals on acceleration beyond the knee:

• Reacceleration by multiple shocks

• Reacceleration in plerions

SNRSNR

SNR

pulsar wind

SNR

ΩδΦ

δΦ = 4×1015Z eV – 1019Z eV

Bell 1991, 2000, Berezhko 1993

uＥ θ= Bφur/c

OBassociationu=3×103 km/sB=10-5 GR=30 pc

f ~ 1/p3

ta ~ R/(Fshu) at Di < uR ~ D/(Fshu2) at Di > uR

R u

Emax ~ 1017Z eV

Axford & Ip 1991, Bykov & Toptygin 1990, 2001Klepach et al. 2000

terminationshock

Crab pulsar few msec pulsar

•Galactic wind

u

R acceleration at terminationshock Jokipii & Morfill 1985, 1991

R = 300 kpc, u = 400 km/s

Emax = 3×1018Z eV

galactic disk

SNRacceleration by travelingshocks and interactionregions Völk & Zirakashvili 2004

Nagano & Watson 2000 galacticextra-galactic?

knee