Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

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Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia

Transcript of Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

Page 1: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

Cosmic Ray Acceleration in Supernova Remanants

Vladimir Ptuskin

IZMIRAN, Russia

Page 2: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, 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 ~ 3x1020 eV - max. observed

energy

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

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

Page 3: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

energy balance Ginzburg & Syrovatskii 1964

•required source power 3×1038 erg/(s kpc2)•SN kinetic energy 2×1039 erg/(s kpc2)(Wsn=1051 erg, νGal = 0.03 yr-1

local SN rate 50 Myr-1kpc-2)

~ 15% - efficiency of CR acceleration in SNRs

other Galactic accelerators: pulsars [2×1050 (10 ms/τ)2 erg], stellar winds [2×1038 erg/s kpc2], Galactic GRBs [1051 erg/105 yr], micro quasars, Galactic Center …

acceleration by external shock: a) “normal” composition after correction on atomic properties (FIP, volatility) b) delay between nuclear synthesis and acceleration (Soutoul test: 59Ni 59Co, high obs. 59Co/56Fe gives δt > 105yr Leske 1993)

Page 4: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

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

distribution

function(test particles)

time ofacceleration

CR intensity

resonantdiffusion kres~1/rg

Larmor radius

Page 5: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

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 2000, 2001

Page 6: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

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

Page 7: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

Berezhko &Elliison 1999

nonlinear shock modification by cosmic ray pressure for high Mach shocks

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

not power law spectrum at the shock

mcp

apppf

uP

a

crshcrcr

,5.00,)(

5.0,

4

2

Page 8: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

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.

Page 9: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

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 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. 2000 Aharonian et al. 2004Cas A Aharonian et al. 2001RX J0852-46 (“Vela jr”)G338.3-0.0; G23.3-0.3; G8.7-0.1 Aharonian et al. 2005

e

γsynchrotron

e

γ inverse Comptonεγ = ε0(Ee/mec2)2

pπ0

γ

SNR

not confirmedby HESS (2004) !

Page 10: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

confrontation with observations

problems:- Galactic sources should work up to (1-3)×1018 eV (Fe ?)

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

- average cosmic ray source

spectrumγs = 2.1 - 2.4 (depending on propagation

model)

Page 11: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

Ptuskin & Zirakashvili 2003

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

under extreme

conditions:

Emax ≈ 1017Z(ush/3×104km/s)2

×(ξcr/0.5)Mej1/3n1/6 eV

δBmax ≈ 103(ush/3×104km/s)n1/2 μG

-strong cosmic-ray streaming instability (δB B0), Bell & Lucek 2000, 2001

- non-linear wave interactions of Kolmogorov type in shock precursorPtuskin & Zirakashvili 2003, 2005

δB > B0

δB < B0

maximum momentum of accelerated protons

abandonment of Bohm limit hypotheses

<>

Page 12: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

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-7.0 (Chevalier – Nadyozhin)

))((~

))((~

maxmax4

max32

max4

max2

ptpdt

dppRuq

ptpHppuf

shshcr

aashcr

SN rate

step function

delta function

Page 13: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

hot bubble0.013 cm-3, 3μG

ism R=60pc

n=1cm-3

denseRSG wind

Weaver et al. 1977Chevalier & Liang 1989

KASCADE

SNII

Roth et al. 2003

·Eknee ≈ 6×1015 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

Ptuskin & Zirakashvili 2004

expected break of all particle spectrum δγ = 0.5

Page 14: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

Nagano & Watson 2000

galacticextra-galactic?

knee

dispersion of SNs? reacceleration?early transition to extragalactic CRs?

2nd knee

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• 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

OB association: u=3×103 km/s, B=10-5 G, R=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

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SummaryMaximum energy of accelerated particles strongly depends on SNR age in the presence of cosmic-ray streaming instability accompanied by non-linear wave dissipation. Emax can reach 1017Z eV in very young SNRs (with corresponding

increase of random magnetic field to up to 10-3 G) and may fall down to less than 1011Z eV at the end of Sedov stage. Standard estimate of Emax based on the

Bohm limit calculated for interstellar magnetic filed strength is not justified.This gives a clue to understanding why SNRs are not bright in very high energy γ-rays at t > 3×103 yr.

Average source spectrum ~ p-4 up to ~ 6×1015Z eV is formed during adiabatic (Sedov) stage of SNR evolution provided constant fraction of incoming gas momentum flux goes to cosmic ray pressure at the shock. Steep power-law spectrum above this energy is produced at the preceding ejecta-dominated stage. The knee observed at 4×1015 eV may mark the transition from ejecta-dominated to adiabatic evolution of SNR shocks which accelerate cosmic rays.

Page 17: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

strong streaming instability and non-linear wave interactions in shock precursor ( ):abandonment of Bohm limit hypotheses

0)(

x

fu

x

fpD

x

knllcrk wx

wu

2

BismB

Ptuskin & Zirakashvili 2003

eq. for cosmic rays(1D, u=const)

eq. for mhd waves(wk is spectral energy density)

supersonicconvection

growth rate…D f∇in agreement withBell & Lucek 2001

lineardamping

nonlinear waveinteractions ofKolmogorov type~ kδB(>k)/(4πρ)1/2

Verma et al. 1996

1.0~,max )( shshRupD eq. for maximummomentum

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12/122

2/12

)1( ,)(3

)1(

gtotresg

res

tot rAkvrkA

AD

x

fD

p

kpdpp

kc

AVeZk

kp

restotacr

res

)(

2

2

2/12222 )(1

)1(12)(

diffusion coefficient:

growth rate:

Page 19: Cosmic Ray Acceleration in Supernova Remanants Vladimir Ptuskin IZMIRAN, Russia.

streaming instability in shock precursor(no damping)

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

~ 0.5 for very strong shock