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

Pulsar contribution to electron/positron cosmic rays Dmitry Malyshev CCPP, NYU together with Ilias Cholis & Joseph Gelfand arXiv:0903.1310 PRD80:063005(2009 ) Fermi Symposium ‘09

2000 Anomalous flux: Total flux ATIC � Extra source HESS 08 � E 3 F e � � e � � GeV 2 m � 2 s � 1 sr � 1 � 1000 Backgrounds HESS 09 � Fermi � LAT E � F ∼ F 0 E − n e − 500 E br � � 200 n ∼ 2 . 0 − 2 . 5 � � � � � � � � � � � � � � � � � � � ��������� � � � � � � � � � � � � � � � � � � � � � � � � 100 � E � 3.3 E br ∼ 100 GeV − 1 TeV � � � � � 50 � E � 2.2 � Backgrounds: � � 20 10 50 100 500 1000 5000 E � GeV � 100 Primary Total positron ratio PAMELA ∼ E − 3 . 3 � Extra source 50 Secondary background Secondary F e � � F e � ∼ E − 3 . 6 20 F e � � 10 � � � � � � � � � � 100 � � � 5 � � � 2 1 1 5 10 50 100 500 E � GeV �

Propagation Energy loss: ˙ E = b 0 E 2 1 Characteristic cooling time: t = b 0 E For E < 1 TeV the time t > 100 kyr Diffusion: D ( E ) = D 0 E δ (Moscalenko & Strong) Characteristic diffusion distnace: x 2 ∼ D ( E ) t For E > 100 GeV the distance x < 2 kpc

Emission 1 � − 2 � E = E 0 1 + t Magnetic dipole radiation: ˙ τ τ Pulsar time scale: τ < 10 kyr Crab: E 0 ≈ 5 × 10 49 erg τ ≈ 0 . 7 kyr After escaping the magnetosphere the electrons are trapped for some time in Pulsar Wind Nebula. The lifetime of PWNe << 100 kyr. For the purposes of observations ˙ e + e − E = E 0 δ ( t )

Emission 2 From PWNe synchrotron and Gamma rays: Q ∼ η E 0 E − n 0 e − E/E br δ ( t ) Initial energy: E 0 = 10 48 − 10 50 erg ( P = 0 . 02 − 0 . 2 s) Conversion efficiency: η ≈ 0 . 01 − 0 . 1 Index: n 0 ≈ 1 . 0 − 2 . 0 (D.A.Green SNR catalog) Break: E br ≈ 100 GeV − 10 TeV

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 = n 0 + 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 of pulsars.

Flux from ATNF pulsars versus continuous disc source n = 1 . 5 ATNF pulsars 1000 Continuous distribution � GeV 2 m � 2 s � 1 sr � 1 � η = 0 . 065 500 τ = 1 kyr 100 The cutoff is determined 50 by the cooling break from the youngest pulsar E 3 dN dE within the Earth’ s 10 5 diffusion zone. 10 100 1000 10 4 10 5 E � GeV � Fitting the continuous flux to the ATNF pulsars requires the pulsar birth rate N b = 1 . 8 kyr − 1

The flux from ATNF pulsars Total flux ATIC versus Fermi and PAMELA � ATNF pulsars Fermi � � GeV 2 m � 2 s � 1 sr � 1 � Backgrounds HESS 08 � 1000 HESS 09 � δ = 0 . 4 n 0 = 1 . 5 � � � � � � � � � � � η = 0 . 065 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 100 � � � � � � � � � τ = 1 kyr � � � � E 3 dN dE The initial rotational energy 10 for every pulsar is 10 50 100 500 1000 5000 E � GeV � E t 2 200 E 0 = ˙ Total positron ratio PAMELA � ATNF pulsars 100 τ Secondary background 50 where F e � � F e � F e � 20 - current spin-down ˙ � E 10 � 100 � � � � � 5 t = P � � � � � - characteristic 2 ˙ P 2 pulsar age 1 10 20 50 100 200 500 E � GeV �

The crosses and 10 0.60 the areas 0.55 0.95 8 correspond to 0.50 diffusion index ∆ Η� W 0 � � 10 48 erg � � 0.68 6 0.99 the best fits of 0.45 0.99 0.68 � 0.40 4 continuous disc 0.35 0.95 distribution to 2 0.30 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 Fermi and b 0 � � 10 � 16 GeV � 1 s � 1 � b 0 � � 10 � 16 GeV � 1 s � 1 � 2.0 2.0 PAMELA data. 0.95 1.8 1.8 0.68 0.68 injection index n injection index n 0.95 � The best fit � 1.6 1.6 parameters are: 0.99 1.4 1.4 0.99 δ ≈ 0 . 50 ± 0 . 05 n 0 ≈ 1 . 6 ± 0 . 2 1.2 1.2 2 4 6 8 10 12 14 0.30 0.35 0.40 0.45 0.50 0.55 0.60 η E 0 ∼ 5 × 10 48 erg Η� W 0 � � 10 48 erg � diffusion index ∆

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