Supernova Remnants as Cosmic Rays Accelerators

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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

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Ncr 10-10 cm-3 - total number density wcr
1.5 eV/cm3 - energy density Emax 31020 eV -
max. observed energy Lcr 51040 erg/s -
Galactic luminosity in CR dcr 10-3 at 1012 -
1014 eV - anisotropy rg 1E/(Z31015 eV) pc
- Larmor radius

ulsar
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source spectrum
E-2.7 cosmic ray density
Ncr T
Qcr
source spectrum E-(2.0 2.4)
escape time E-(0.3 0.6)
two power laws source spectrum propagation
secondary species Qcr,2 nvs21N1 d, 3He, Li,
Be, B p, e
escape length X ?vT
10 g/cm2 at 1 GeV/nucleon
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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
r
pure diffusion
diffusion distributed reaccele- ration in ISM
Alfven velocity
Jones et al 2001
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Energy balance
local galactic CR energy density
1.5 eV/cm3 needed source power 31038
erg/s kpc2 SN kinetic energy
21039 erg/s kpc2

(Wsn1051 erg, 50 Myr-1 kpc-2)
15 efficiency of CR acceleration
pulsars 21050 (10 ms/t)2 erg
stellar winds 21038 erg/s kpc2
Galactic GRBs 1051 erg/105 yr
Galactic Center
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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 lt 300 yr, ush 5108 3109
  cm/s, R lt 2 pc
• - Adiabatic deceleration (Sedov stage)
• t 103 - 3104 yr, ush
  (Wsn/nism)1/5t-3/5
• - Radiation cooling
• t gt 105 yr, R gt 20 pc
• Acceleration by external shock a) normal
  composition after correction on atomic properties
  (FIP, volatility)
• b) delay between nuclear synthesis and
  acceleration

high obs. 59Co/56Fe dt gt 105 yr Soutoul et
al. 1978, Leske 1993
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Diffusive shock acceleration
Fermi 1949, Krymsky 1977, Bell 1978

• average gain
• of momentum

D(p)
SNR
ush
distribution function (test particles)
shock
CR intensity
time of acceleration
resonant diffusion kres1/rg
Larmor radius
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Maximum energy
condition of acceleration, critical Pecklet
number (parameter of modulation)
SNR Wsn1051erg

• maximum value

-typical in interstellar medium
ism n01cm-3
diffusion should be anomalously slow near the
shock (upstream and downstream) cosmic ray
streaming instability in shock precursor
Bell 1978, Lagage Cesarsky 1983, McKenzie
Volk 1982, Achterberg 1983, Volk et al. 1988,
Fedorenko 1990, Bell Lucek 2001, VSP
Zirakashvili 2003
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Bohm limit
standard assumption dB Bism Bohm
diffusion
Nagano Watson 2000
extra- galactic?
galactic
knee
might be better for SN explosion in progenitor
wind Volk Biermann 1988
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Nonlinear shock modification by CR pressure
upstream
downstream
u(x)
D(p)/u
nonmodified shock
ush
cosmic ray density
-?Pcr
precursor
subshock
ush/r
x
xsh
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not power law spectrum for high Mach number
shocks
Berezhko Elliison 1999
Axford 1977, 1981 Eichler 1984 Berezhko et al.
1996 Malkov et al. 2000
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overall CR spectrum
Berezhko Völk 2000
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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.
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observations
radio emission ?MHz 4.6 BµGEe,GeV2 E 50 MeV
30 GeV (100 GeV for IR) ? 1.9
2.5 We 1048 1049 erg Ginzburg Syrovatskii
1964 Shklovsky 1976
nonthermal X-rays ekeV 1 BµG(Ee/120 TeV)2 emax
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
synchrotron
?
e
SNR
?
inverse Compton e? e0(Ee/mec2)2
p
e
p0
TeV ? rays electrons/protons emax 100
TeV SN1006 Tanimori et al 1998 RX
J1713 Muraishi et al. 2000 Cas A
Aharonian et al. 2001
?
?-rays (p0) ? 30-3000 MeV ? Cygni,
IC443 Esposito et al. 1996 Sturner Dermer 1996
Only upper limits on TeV ?-rays from many SNRs
with ages gt 3103 yr Buckley et al. 1998,
Aharonian et al. 2002
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SN1006
Tanimori et al. 2001
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• Problems
• - Galactic sources should work up to
• (1-3)1018 eV (Fe ?)
• (reacceleration
  may help Axford 1994, Bell 1992,
  Bykov Toptygin
  2001, Volk Zirakashvili 2004
• dispersion of SN parameters Sveshnikova 2003)
• no VHE gamma-rays from not very young SNRs tsnr
  3103 yr
• (Buckley et al. 1998,
  Aharonian et al. 2002)
• cosmic ray source spectrum ?s 2.0 - 2.4
• (depends on propagation model)

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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/3104km/s)2
(?/0.1)(?cr/0.5)Mej1/3n1/6 eV dBmax 10-3
(ush/3104km/s)n1/2 G
Wsn 1051 erg, Bism 5 µG, n0 0.4 cm-3 ?cr
0.5, ? 0.04, a 0.3
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Random field produced by cosmic-ray streaming
instability in shock precursor
Bell Lucek 2001 VSP Zirakashvili 2003
cosmic-ray pressure
Alfven velocity
wave energy density
weak random field
strong random field
characteristic velocity of waves
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Average source spectrum
spectrum at the shock
instantaneous SNR luminosity in run-away cosmic
rays
SN rate
adiabatic stage Q ?cr?snWsnp-4
(Sedov) - universal
spectrum !
average cosmic-ray source spectrum
ejecta-dominated stage SNII in RSG wind Q
p-6.5 at ?star r -10 SNI in uniform medium
Q p-7 (Chevalier Nadyozhin)
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Weaver et al. 1977 Chevalier Liang 1989
ism R60pc n1cm-3
Wsn 1051 erg, ?cr 0.5
?star r-10 M10-5 uw10km/s Rw2pc
RSG wind

Eknee 71015 Z eV, ?crWsnM1/2(Mejuw)-1 Ema
x 41016 Z eV at tmin 7 days
SNII
hot bubble 0.013 cm-3, 3µG
Roth et al. 2003
KASCADE
VSP Zirakashvili 2004
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Other proposals on acceleration beyond the knee

• Reacceleration by multiple shocks

R u
f 1/p3 ta R/(Fshu) at Di lt uR
D/(Fshu2) at Di gt uR
SNR
SNR
OB association u3103 km/s B10-5 G R30 pc
Emax 1017Z eV Axford Ip 1991, Bykov
Toptygin 1990, 2001 Klepach et al. 2000
SNR

• Reacceleration in plerions

O
Crab pulsar
few msec pulsar
dF
E? Bfur/c
pulsar wind
u
dF 41015Z eV 1019Z eV Bell 1991, 2000,
Berezhko 1993
SNR
termination shock
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• Galactic wind

acceleration at termination shock Jokipii
Morfill 1985, 1991 R 300 kpc, u 400
km/s Emax 31018Z eV
R
u
SNR
acceleration by traveling shocks and
interaction regions Völk Zirakashvili 2004
galactic disk
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extra- galactic?
Nagano Watson 2000
galactic
knee