Pulsar contribution to electron/positron cosmic rays Dmitry - - PowerPoint PPT Presentation

Dmitry Malyshev CCPP, NYU Fermi Symposium ‘09

Pulsar contribution to electron/positron cosmic rays

together with Ilias Cholis & Joseph Gelfand

arXiv:0903.1310 PRD80:063005(2009)

• Total positron ratio

Extra source Secondary background

• PAMELA

1 5 10 50 100 500 1 2 5 10 20 50 100 E GeV 100 Fe Fe Fe

• ATIC
• HESS 08
• HESS 09
• FermiLAT

Total flux Extra source Backgrounds E 2.2 E 3.3 10 50 100 500 1000 5000 20 50 100 200 500 1000 2000 E GeV E3 Fe e GeV2 m2 s1 sr1

Anomalous flux: Backgrounds: Primary Secondary

Ebr ∼ 100 GeV − 1 TeV n ∼ 2.0 − 2.5 ∼ E−3.3 ∼ E−3.6 F ∼ F0E−ne−

E Ebr

Propagation Energy loss: Characteristic cooling time:

t = 1 b0E

For E < 1 TeV the time t > 100 kyr Diffusion:

D(E) = D0Eδ

Characteristic diffusion distnace:

x2 ∼ D(E)t

For E > 100 GeV the distance x < 2 kpc

(Moscalenko & Strong)

˙ E = b0E2

Emission 1 Magnetic dipole radiation: Pulsar time scale:

˙ E = E0 τ

• 1 + t

τ −2 τ < 10 kyr

Crab:

τ ≈ 0.7 kyr E0 ≈ 5 × 1049erg

For the purposes of observations ˙

E = E0 δ(t)

After escaping the magnetosphere the electrons are trapped for some time in Pulsar Wind Nebula. The lifetime of PWNe << 100 kyr.

e+e−

Emission 2 From PWNe synchrotron and Gamma rays:

Q ∼ ηE0E−n0e−E/Ebrδ(t)

Initial energy:

E0 = 1048 − 1050erg

Conversion efficiency: Index:

n0 ≈ 1.0 − 2.0 η ≈ 0.01 − 0.1

Break:

Ebr ≈ 100 GeV − 10 TeV

(D.A.Green SNR catalog)

(P = 0.02 − 0.2 s)

Problems

• 1. PWN lifetime << propagation time:

The electrons from observed PWNe cannot reach us. The electrons that reach us come from PWNe that can no longer be observed.

• 2. Degeneracy:

Thus there are at least 6 unconstrained parameters (single pulsar and ISM) to describe 3 parameters of the anomalous flux. For instance, the propagated index of the flux from a disc-like source is n = n0 + 1 + δ 2

What we can do? Use currently observed PWNe to find the distribution of properties Calculate typical spectra Constrain the parameters of ISM & pulsars We will start by comparing the flux from ATNF pulsars and a continuous distribution

• f pulsars.

ATNF pulsars Continuous distribution 10 100 1000 104 105 5 10 50 100 500 1000 E GeV E3 dN dE GeV2 m2 s1 sr1

Flux from ATNF pulsars versus continuous disc source Fitting the continuous flux to the ATNF pulsars requires the pulsar birth rate Nb = 1.8 kyr−1

n = 1.5 η = 0.065 τ = 1 kyr

The cutoff is determined by the cooling break from the youngest pulsar within the Earth’ s diffusion zone.

• Total flux

ATNF pulsars Backgrounds

• ATIC
• Fermi
• HESS 08
• HESS 09

10 50 100 500 1000 5000 10 100 1000 E GeV E3 dN dE GeV2 m2 s1 sr1

• Total positron ratio

ATNF pulsars Secondary background

• PAMELA

10 20 50 100 200 500 1 2 5 10 20 50 100 200 E GeV 100 Fe Fe Fe

The flux from ATNF pulsars versus Fermi and PAMELA The initial rotational energy for every pulsar is

t = P 2 ˙ P

E0 = ˙ E t2 τ where ˙ E

• current spin-down
• characteristic

pulsar age n0 = 1.5 δ = 0.4 η = 0.065 τ = 1 kyr

• 0.68

0.95 0.99

0.5 1.0 1.5 2.0 2.5 3.0 0.30 0.35 0.40 0.45 0.50 0.55 0.60

b0 1016 GeV1 s1 diffusion index ∆

• 0.68

0.95 0.99

0.5 1.0 1.5 2.0 2.5 3.0 2 4 6 8 10

b0 1016 GeV1 s1 ΗW01048 erg

• 0.68

0.95 0.99

0.30 0.35 0.40 0.45 0.50 0.55 0.60 1.2 1.4 1.6 1.8 2.0

diffusion index ∆ injection index n

• 0.68

0.95 0.99

2 4 6 8 10 12 14 1.2 1.4 1.6 1.8 2.0

ΗW01048 erg injection index n

The crosses and the areas correspond to the best fits of continuous disc distribution to Fermi and PAMELA data. The best fit parameters are:

δ ≈ 0.50 ± 0.05 n0 ≈ 1.6 ± 0.2 ηE0 ∼ 5 × 1048 erg

Conclusions

• 1. It is possible to fit both Fermi and PAMELA

with reasonable ISM and pulsar parameters

• 2. Assuming the pulsar origin of electron/

positron fluxes, Fermi&PAMELA can constrain some propagation and pulsar parameters

• 3. It is impossible to “derive” the flux from

the observed properties of pulsars: the corresponding PWNe have disappeared