Cosmic-Ray Electron Excess from Pulsars is SCosmic-Ray Electron Excess from Pulsars is Spiky or Smooth?: Continuous and Multiple Elepiky or Smooth?: Continuous and Multiple Ele

ctron/Positron Injectionsctron/Positron Injections

(arXiv:0903.3782, submitted to ApJ)

Norita Kawanaka (KEK)

Kunihito Ioka (KEK)

Mihoko M. Nojiri (KEK/IPMU)

KEK Theory Center Cosmophysics Group Workshop on High Energy Astrophysics

Nov. 12, 2009

Positron Excess: PAMELA

• Observed cosmic-ray 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!

(Adriani et al. 2008)

~1-100GeV

Electron+Positron Flux

ATIC/PPB-BETS

(Chang et al. 2008)

e~100-600GeV

bump+sharp cutoff

H.E.S.S.

(H.E.S.S. collaboration 2008)

~1-5TeV

spectral drop

Recent Results

Abdo et al. (arXiv:0905.0025)Aharonian et al. (arXiv:0905.0105)

Fermi LAT H.E.S.S. (340GeV~)

ATIC/PPB-BETS peak has not been confirmed.

What is the Origin of e± Excess?• Dark Matter Particles　 annihilation/decay e±

　 Cutoff ~600GeV in the ATIC/PPB-BETS corresponds to the mass of DM particles

　 annihilation: <>required~O(10-23)cm3s-1 >> <>thermal

Overproductions of anti-proton should be avoided.

• Astrophysical Sources　 Compact objects in our Galaxy (NS, SNR, BH…) Cutoff ~600GeV in the ATIC/PPB-BETS corresponds t

o the cooling time for e±

Required energy ~ 10-3x1050erg/SN ~ 1047erg/SN

~ CR nucleon energy

Astrophysical Origin•　 PulsarShen 70; Aharonian+ 95; Atoyan et al. 95; Chi+ 96; Zhang & Cheng 01; Grimani 07; Yuksel+ 08; Buesching+ 08; Hooper+ 08; Profumo 08; Malyshev+ 09; Grasso+ 09; NK+ 09

•　 Supernova RemnantShen & Berkey 68; Pohl & Esposito 98; Kobayashi+ 04; Shaviv+ 09; Hu+ 09; Fujita, Kohri, Yamazaki & Ioka 09; Blasi 09; Blasi & Serpico 09; Mertsch&Sarkar 09; Biermann+ 09; Ahlers, Mertsch & Sarkar 09

•　 Microquasar (Galactic BH)Heinz & Sunyaev 02

•　 Gamma-Ray Burst Ioka 08

•　 Propagation Effect

Delahaye+ 08; Cowsik & Burch 09; Stawarz+09; Schlickeiser & Ruppel 09

• Effects of continuous e± injections on the spectrum• Effects of multiple sources• Constraints in >TeV range by H.E.S.S.

• Astrophysical Sources? Or Dark Matter?

　 Can We Discriminate them from the Spectrum?

Any characteristic features in the e± spectrum from astrophysical sources?

Can we give any constraints on models by the future missions?

e± propagation in ISM

e

e

d

dn

e

1. Random walk due to the Galactic magnetic field diffusion approx.

2. Synchrotron + inverse Compton scattering energy loss

e

e

e

d

dn

e？

Propagation effects

e±

CR Propagation Equation and Solution

),,()()(),,( 2ee

eee rtQfBfKrtf

t

161-1-2

-122800

10 ,sGeV)(

3/1 ,scm108.5 ,GeV3/1)(

bbB

KKK

ee

ee

2

22

32/30 exp1),,(

diffe

diff

ee r

rbt

r

QrtG

• diffusion equation

injection

Spectrum from instantaneous injection from a point source (Atoyan+ 1995)

energy loss (synchrotron, inverse Compton scattering)

diffusion

tKr ediff )(2

eQ

cutoff energy:e~1/btage

： diffusion length

Galactic Magnetic Fields & Radiation Fields

B/C ratio

The case of transient source: e+ fraction

d=1kpc

(a)E=0.9x1050ergage=2x105yr=2.5

(b)E=0.8x1050ergage=5.6x105yr=1.8

(c)E=3x1050ergage=3x106yr=1.8

The cutoff energy corresponds to the age of the source.

Ioka 2008

The case of transient source: e± spectrum

(a)E=0.9x1050ergage=2x105yr=2.5

(b)E=0.8x1050ergage=5.6x105yr=1.8

(c)E=3x1050ergage=3x106yr=1.8

d=1kpc

The cutoff energy corresponds to the age of the source.

Ioka 2008

Continuous injection (expected in pulsars, SNRs, etc.)

200

spindown0/1

)( t

ELtQ tot

000

4ln exp

4ln )(

tE

tQ tot

2

2

0

2

32/30 exp1

)(),(

diff

t

ediff

ee r

rtb

r

ttQtdtF

Case 1: pulsar-type decay

Case 2: exponential decay

0

0

The spectral peak around Ee~1/bt will be broadened!

cf.) years G10/104.7 210ms

21230 PB

Continuous Injection (e++e-)

background

Burst-like event (e.g. GRB)

Flux without background

t=5.6x105yrr=1kpc

Ee+ ~Ee-~1050erg=1.7

Emax=5TeV Epeak~1/bt~600GeV

exponential decay,　 0~105yr

NK+ 2009

Constraints on pulsar-type decay time

pulsar type: 0=105yr

pulsar type: 0=104yr

* A significant fraction of observed electrons are emitted recently.

H.E.S.S.

e± Injection from Multiple Sources• Total injection energy required to account for the

peak of ATIC/PPB-BETS ~ 1050erg

~ Rotation energy of a pulsar with P0~10msec

　　 Too efficient?• Local pulsar birth rate ~10-5 yr-1 kpc-2 　 (Narayan 1985;

Lorimer+1994)

　　 Pulsars which have not observed (e.g. off-beam) should contribute significantly.

Young pulsars (age<5x105yr) should exist.• The peak might be made by a pulsar with an extr

aordinary large amount of energy.

• Then, what is the spectrum like on average?

Average e± Spectrum and Its Dispersion

Average flux from nearby sources with a birth rate of R:

Number of sources which contribute to the energy bin of e

NK+ 2009

Assuming the Poisson statistics of the source distribution,

Flux per source

215

3/5

20

)(

0

kpcyr)105.1/(1TeV6~

)(

)(2~2)(

diff1

R

b

RKrRdrdtN

e

e

e

db

e

e

e+ fraction

e±spectrum

solid lines ： fave(e)

dashed lines ： fave(e) ±fave

R~1/(1.5x105)/yr/kpc2

Ee+=Ee-~1048erg

~1.9

1.1. Average spectra are consistent Average spectra are consistent with PAMELA, Fermi & H.E.with PAMELA, Fermi & H.E.S.S.S.S.

2.2. ATIC/PPB-BETS peak is largATIC/PPB-BETS peak is largely separated from the averagely separated from the average flux to the 10e flux to the 10 level. level. Suc Such a peak is hardly to produce h a peak is hardly to produce by the sum of multiple pulsarby the sum of multiple pulsars.s.

3.3. Large dispersion in the TeV rLarge dispersion in the TeV range due to the small ange due to the small NN((ee) )

possible explanation for the cpossible explanation for the cutoff inferred by H.E.S.Sutoff inferred by H.E.S.S.

CALorimetric Electron Telescope

(Torii-san’s talk)

CALET

With the high energy resolution and statistics of the CALET observations, we will be able to discriminate models of injection.

(duration, the functional form of Q0(t), etc.)

A Dedicated Detector for Electron Observation in 1GeV – 20,000 GeV

Red points/errorbars:

expected from 5yr obs. by CALET

Energy resolution: ~2% (>100GeV)

e/p selection power: ~105

Summary• We investigate the spectral features of CR e± from co

ntinuous/multiple sources (e.g. pulsars).• Continuous injection from a single source comparison with the ATIC/PPB-BETS data　 peak width ： duration of the source　 TeV tail ： upper limit for the duration (B>~1011G for a puls

ar) may be measured by CALET

• Multiple injections: average flux and its dispersion average e± spectrum should be quite FLAT & SMOOTH. se

en in the Fermi data ATIC/PPB-BETS peak is hardly to produce by multiple pulsar

s, and requires a single (or a few) energetic source(s). spectral cutoff at ~a few TeV seen in the H.E.S.S. data : due t

o the small number of young and nearby sources