Transcript Supernova Remnants as Accelerators of the Cosmic Rays

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
M87
interacting
galaxies
GRB
cosmic ray halo
bubble
close
binary
GC
Sun
SN
R
pulsar
stellar
wind
Galactic
disk
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 ~ 10-3ul at 1012 - 1014 eV - anisotropy
s
15 eV) pc - Larmor radius
a
rg ~ 1E/(Z×3×10
r
source spectrum
E-2.7
cosmic ray density
escape time
E-(0.3 … 0.6)
Ncr
T
Qcr
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
flat-halo diffusion model
Ginzburg & Ptuskin 1976
Berezinskii et al 1990 Strong & Moskalenko 1998
surface gas density 2.4 mg/cm2
cosmic-ray halo
Sun
SNR
2H
galactic disk
vH
X
2D
r
D  2 1028 H5 R0.54 cm2 / s, R  5 GV
D  5.9 10 H5 R
28
0.3
cm / s, Va  40km/s
2
Alfven velocity
pure diffusion
diffusion +
distributed reacceleration in ISM
Jones et al 2001
H  5  H 5 kpc,  
v
cp
, R
 magnetic rigidity
c
Ze
Energy balance
local galactic CR
energy density
needed source power
SN kinetic energy
1.5 eV/cm3
3×1038 erg/s kpc2
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
59
EC
Ni 
 59 Co,
  1.1 105 yr
high obs. 59Co/56Fe – δt > 105 yr
Soutoul et al. 1978, Leske 1993
Diffusive shock acceleration
Fermi 1949, Krymsky 1977, Bell 1978
u sh
dp

p
dt
3
D(p)
SNR
shock
ush
distribution
function
(test particles)
CR intensity
time of
acceleration
resonant
diffusion
kres~1/rg
-average gain
of momentum
3r
f ( p )  p r 1  p  4

I ( E )  p 2 f ( p)
2
t a  D ( p ) / u sh
Larmor radius
D
vrg
B02
2
3 Bres
Maximum energy
condition of acceleration,
critical Pecklet number
(parameter of modulation)
28 W51
SNR
Wsn=1051erg
ism
n0=1cm-3
u sh Rsh  10 

u sh Rsh
 10
D( p)

n0 
2/5
cm 2 / s
0.3
Dism  6  1028 PGV
cm 2 / s
-maximum value
-typical in
interstellar medium
diffusion should be anomalously slow near the shock
(upstream and downstream)
cosmic ray streaming instability in shock precursor
Bell 1978, Lagage & Cesarsky 1983, McKenzie & Vőlk 1982, Achterberg 1983,
Vőlk et al. 1988, Fedorenko 1990, Bell & Lucek 2001, VSP & Zirakashvili 2003
Bohm limit
standard assumption
δB ~ Bism
Bohm diffusion
DB 
3
 6  1021 PGV cm 2 / s
Nagano & Watson 2000
galactic
knee
vrg
extragalactic?
Emax  1014 Z eV
Emax  t 1/ 5
might be better for SN
explosion in progenitor wind
Vőlk & Biermann 1988
Nonlinear shock modification by CR pressure
u(x)
upstream
D(p)/u
downstream
nonmodified shock
ush
cosmic ray density
precursor
-∇Pcr
subshock
ush/r
xsh
x
not power law spectrum for high Mach number
shocks
2
Pcr  cr u sh
, cr  0.5
f ( p) p 4  p a , 0  a  0.5,
p  mc
Berezhko &
Elliison 1999
Axford 1977, 1981
Eichler 1984
Berezhko et al. 1996
Malkov et al. 2000
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), Xrays 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.
observations
radio emission
nonthermal X-rays
νMHz = 4.6
E = 50 MeV – 30 GeV
(100 GeV for IR)
γ = 1.9 – 2.5
We = 1048 – 1049 erg
Ginzburg &
Syrovatskii 1964
Shklovsky 1976
BμGEe,GeV2
synchrotron
γ
e
SNR
π0
γ-rays (π0)
γ
Ε = 30-3000 MeV
γ Cygni, IC443
Esposito et al. 1996
Sturner & Dermer 1996
p
εkeV = 1 BμG(Ee/120 TeV)2
εmax ~ 100 TeV
SN1006
Koyama et al. 1995
Cas A
Allen et al. 1997
RX J1713-39
Koyama et al. 1997
RX J0852-46 (“Vela jr”) Slane et al 2001
γ inverse Compton
εγ = ε0(Ee/mec2)2
e
TeV γ – rays
electrons/protons
εmax ~ 100 TeV
SN1006
RX J1713
Cas A
Tanimori et al 1998
Muraishi et al. 2000
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
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)
maximum momentum of accelerated particles:
abandonment of Bohm limit hypotheses
VSP & Zirakashvili 2003
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
Wsn = 1051 erg, Bism = 5 μG, n0 = 0.4 cm-3
ξcr = 0.5, κ = 0.04, a = 0.3
Random field produced by cosmic-ray
streaming instability in shock precursor
Bell & Lucek 2001
VSP & Zirakashvili 2003
cosmic-ray pressure
Pcr
w
ush
 Va
,
x
x
Alfven velocity
wave energy density
weak random field:
B  B0 , Va,0 
B
2
w
, Pcr  cr ush
4
2
B0
4
strong random field:
,
B  B0 , Va,ef 
B
,
4
characteristic velocity of waves
B
u sh
  cr
B0
Va,0
B
u sh
  cr
B0
Va ,0
Average source spectrum
spectrum at
the shock
2 a 4 a
f ~ cr ush
pmax p
H ( pmax (t )  p)
instantaneous
SNR luminosity
in run-away
cosmic rays
2 3 4  dpmax 
q ~ cr ush Rsh pmax 
 ( pmax (t )  p)
dt
average
cosmic-ray
source
spectrum


SN rate
adiabatic stage
(Sedov)
Q ~ ξcrνsnWsnp-4
- universal spectrum !
ejecta-dominated stage
SNII in RSG wind:
Q ~ p-6.5 at ρstar~ r -10
SNI in uniform medium: Q ~ p-7
(Chevalier – Nadyozhin)
Weaver et al. 1977
Chevalier & Liang 1989
ρstar~
∙
M=10-5
uw=10km/s
Rw=2pc
ism
r-10
RSG wind
SNII
hot bubble
0.013 cm-3, 3μG
R=60pc
n=1cm-3
Wsn= 1051 erg, ξcr= 0.5
Eknee ≈ 7×1015 Z eV, ~ ξcrWsnM· 1/2(Mejuw)-1
Emax ≈ 4×1016 Z eV at tmin = 7 days
Roth et al. 2003
VSP & Zirakashvili 2004
KASCADE
Other proposals on acceleration beyond the knee:
• Reacceleration by multiple shocks
SNR
SNR
OB
association
u=3×103 km/s
B=10-5 G
R=30 pc
R
u
f ~ 1/p3
ta ~ R/(Fshu) at Di < uR
~ D/(Fshu2) at Di > uR
Emax ~ 1017Z eV
SNR
Axford & Ip 1991, Bykov & Toptygin 1990, 2001
Klepach et al. 2000
• Reacceleration in plerions
Ω
δΦ
u
Ｅθ= Bφur/c
Crab pulsar
few msec pulsar
pulsar wind
δΦ = 4×1015Z eV – 1019Z eV
SNR
termination
shock
Bell 1991, 2000, Berezhko 1993
•Galactic wind
R
acceleration at termination
shock Jokipii & Morfill 1985, 1991
R = 300 kpc, u = 400 km/s
u
SNR
galactic disk
Emax = 3×1018Z eV
acceleration by traveling
shocks and interaction
regions Völk & Zirakashvili 2004
Nagano & Watson 2000
galactic
knee
extragalactic?