Upload
amice-kelley
View
223
Download
0
Embed Size (px)
Citation preview
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
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)
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
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
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
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
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 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) !
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)
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
<>
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
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
Nagano & Watson 2000
galacticextra-galactic?
knee
dispersion of SNs? reacceleration?early transition to extragalactic CRs?
2nd 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
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
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.
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
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:
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