Transcript Document

Energy spectra of electrons and positrons,
produced in supernova remnants (SNRs)
E.G.Berezhko, L.T. Ksenofontov
Yu.G.Shafer Institute of Cosmophysical Research and Aeronomy
Yakutsk, Russia
Do we need except SNRs some extra,
“positron rich” CR sources
in order to explain the observed
energy spectra of electrons and positrons?
Standard picture for secondary CR generation
Galactic halo
Secondary CR
Galactic disk
CR source
Gas atom
Primary CR
Secondary
Primary
Energy
Positron/electron ratio

p + p → π+ + … → μ+ + … → e+ + …
e
e
Fermi
Evidence for
positron rich sources?
Pamela
10 GeV
100 GeV
Energy
SN
shock
Production of primary and secondary (Li, Be, B, e+, p, …) CRs in SNRs
Injection of primaries from thermal pool
CR
Berezhko, Ksenofontov, Ptuskin,
Völk, Zirakashvili (2003)
Reacceleration of
primary and secondary CRs
Effect is proportional to the volume
sweep up by SN shock
Efficient in the case
of diluted ISM
Primary CR
Acceleration of secondaries,
created in nuclear collisions
of accelerating primary CRs
with gas atoms
Effect is proportional
to the number of collisions
Efficient in the dense ISM
Energy spectrum of secondary CRs produced in SNR
is harder then produced in ISM
Secondary CR
s/p ratio flattens with energy
Computational details
ε2I, MeV cm-2 sr-1 s-1
Moskalenko & Strong (1998)
e¯
εinj = 300 MeV
10
1
effective energy of injected
CR electrons and positrons
Ninj = (4π/c) I(ε > εinj)
+
e
number density of
injected particles
0.1
10
102
103
B0 = BISM = 5 μG
104
upstream (unamplified) magnetic field
Kep = 10-4
for
t << 104 yr
Kep = 10-2
for
t >~ 104 yr
ESN = 1051 erg
Mej = 1.4 MSun
ε, MeV
electron to proton ratio
supernova explosion parameters
Nonlinear kinetic (time-dependent) theory
of
CR acceleration in SNRs
Kang & Jones 2006,
Ptuskin & Zirakashvili 2008
•Gas dynamic equations
•CR transport equation
•Suprathermal particle injection
•Gas heating due to wave dissipation
•Time-dependent (amplified)
magnetic field
Applied to any individual SNR theory gives at any evolutionary phase t>0 :
nuclear Np(p,r), NHe(p,r), …, electron Ne(p,r) and positron Ne+(p,r) momentum
and spatial distributions
Energy spectra of electrons and positrons, produced in SNRs
J(ε) ~ τlossJSNR(ε) ~ ε-1JSNR(ε)
ρ = 1.4 NH mp
ISM density
At ε > 10 GeV positron spectrum
is dominated by component
created in p-p collisions (ppSNR)
(roughly consistent with
previous estimate (Blasi 2009))
Energy spectra of electrons and positrons, produced in SNRs
At lower ISM density
reaccelerated positron
component (reSNR)
becomes more relevant
Conclusions
• Energy spectrum of positrons, produced in SNRs, are expected to be
flatter at 10 – 100 GeV compared with electron spectrum due to
acceleration of background CRs and secondary particles, created in
p-p collisions
• Electron and positron spectra expected from SNRs are qualitatively
consistent with the experiment.
Remark
Since electron/positron spectra are very sensitive to the actual
distribution of SNRs in solar vicinity (e.g. Pohl & Esposito 1998),
which is not well known,
it is hardly possible to make reliable prediction of their spectra