1. Kunihito Ioka & Mihoko M. Nojiri (KEK, Japan)
Continuous Injection of High Energy Positrons from an Astrophysical Object: Can a Pulsar Account for the Cosmic Ray Electron/Positron Data?
Norita Kawanaka
Kunihito Ioka & Mihoko M. Nojiri
(KEK, Japan)
Rencontres de Moriond 04/02/09

2. Positron Excess: PAMELA
Observed positron flux seems to exceed that expected in the context of secondary positron production.
Similar trend had been observed (AMS, HEAT etc.)
Some primary sources are needed!
~1-100GeV
(Adriani et al. 2008)

3. ATIC/PPB-BETS ~10GeV-3TeV (Chang et al. 2008)
Sharp spectral cutoff around ~600GeV
m~600GeV dark matter annihilation/decay?

4. H.E.S.S. ~1-10TeV (H.E.S.S. collaboration 2008)
Sharp drop-off above 1TeV
(H.E.S.S. collaboration 2008)

5. Astrophysical source(s)?
Electrons/Positrons are cooled via synchrotron & inverse Compton scattering during the propagation.
electron energy~10GeV-1TeV  Sources should be within Rd~kpc (< Galactic disk~10kpc)
diffusion time~Rd2/K ~107yr (~birth rate of the source)
Etot ~1050 erg is needed.
(Lavalle et al. 2007)

6. Candidates Pulsars Gamma-Ray Bursts
e± pairs are produced in the magnetosphere and accelerated by the electric fields and/or the pulsar wind. (Chi+ 1996; Zhang & Cheng 2001; Grimani 2007; Hooper+ 2008; Profumo 2008 etc.)
Gamma-Ray Bursts
Pair creations between TeV photons and soft photons (~eV) far outside the GRB remnant (Ioka 2008)
Microquasars
Pair creations in the internal shock in the jet? (Heinz & Sunyaev 2002 etc.)
and so on…
GRB model (proposed by one of my collaborators Ioka), GRB occurred ~10^5 years ago in our Galaxy.

7. e± propagation Diffusion equation
injection
cooling (synchrotron, IC)
 Green’s function with respect to r and t (Atoyan+ 1995)
This is just the observed spectrum in the case of a transient point source (e.g. GRB)

8. The case of transient source (e.g. GRB)
t=5.6x105yr … age
r=1kpc
Etot=1x1050erg
a=1.8 ?
Epeak~1/bt~600GeV

9. Continuous injection (expected in pulsars, MQs, etc.)
The spectral peak around Ee~1/bt will be broadened!
Case 1: pulsar-type decay
cf.)
In the context of pulsars, long tau0 corresponds to the weak B field.
Case 2: exponential decay

10. Results: Electron/Positron Flux
solid line :exponential decay (t0~105yr)
thick: total (source+2nd)
DE: effect of finite t0
pure secondary
t=5.6x105yr
r=1kpc
Etot=2x1050erg
a=1.4
Emax=3TeV
K0=3.2x1028cm2s-1
d=0.6
transient source
Epeak~1/bt~600GeV
pure source
(NK, Ioka and Nojiri in prep.)

11. Spin down time should not be too long?
* A significant fraction of observed electrons are emitted recently.
pulsar type: t0=105yr
t=5.6x105yr
r=1kpc
Etot=2x1050erg
a=1.4
Emax=3TeV
K0=3.2x1028cm2s-1
d=0.6
H.E.S.S.
From ATIC data, the model with long spin down time may be favored.
pulsar type: t0=104yr
pure source
(NK, Ioka and Nojiri in prep.)

12. Young pulsars should not have any contribution?
Why so rare?
Local birth rate is intrinsically low?
HE pairs are confined in the pulsar wind nebula?
Most pulsars have lower Etot (<2×1050 erg)? (= P0 >~10msec)
Only the pulsars with low B (=long tau0) and low Emax (avoiding HE tail) should contribute?
H.E.S.S.
t=3.0x104 yr
r=1 kpc
Etot=6x1047 erg
a=1.4
(NK, Ioka and Nojiri in prep.)

13. Results: Positron Fraction
Total contribution from old pulsars (birth rate~1 per 5x105yr)
thin solid lines: old pulsars with a=1.4
thin dashed lines: a=1.6
(NK, Ioka and Nojiri in prep.)

14. Summary
We investigate the effects of continuous electron/positron injection from astrophysical objects on the observed electron/positron spectrum.
Epeak  tage of the source
Epeak  the duration of electron injection
Assuming pulsar spin down type injection, high energy tail in the electron spectrum would be enhanced if t0 is long.  H.E.S.S. has already put serious constraints on pulsar models?
High resolution spectra will be obtained by Fermi, CALET etc., and we may be able to discriminate models.