Transcript Continuous
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 Positron Excess: PAMELA ~1-100GeV • Observed positron flux seems to exceed that expected in the context of secondary positron production. • Similar trend had been observed (AMS, HEAT etc.) (Adriani et al. 2008) • Some primary sources are needed! ATIC/PPB-BETS ~10GeV-3TeV (Chang et al. 2008) Sharp spectral cutoff around ~600GeV m~600GeV dark matter annihilation/decay? H.E.S.S. ~1-10TeV (H.E.S.S. collaboration 2008) Astrophysical source(s)? • Electrons/Positrons are cooled via synchrotron & inverse Compton scattering during the propagation. • electron energy~10GeV1TeV Sources should be within Rd~kpc (< Galactic disk~10kpc) • diffusion time~Rd2/K ~107yr (~birth rate of the source) (Lavalle et al. 2007) • Etot ~1050 erg is needed. Candidates • Pulsars 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… e± propagation • Diffusion equation 2 B( e ) f Q(t , r , e ) f (t , r , e ) K ( e ) f t e injection diffusion cooling (synchrotron, IC) K ( e ) K0 1 e / 3GeV , B( e ) b e2GeV -1s-1, b 1016 Green’s function with respect to r and t (Atoyan+ 1995) 2 Q0 e r 2 G (t , r , e ) 3 / 2 3 1 bt e exp 2 Q e r rdiff diff 1 1 1 e / max 2 K ( e )t , max 1 / bt 1 e / max 1/ 2 rdiff This is just the observed spectrum in the case of a transient point source (e.g. GRB) The case of transient source (e.g. GRB) t=5.6x105yr … age r=1kpc Etot=1x1050erg =1.8 ? Epeak~1/bt ~600GeV Continuous injection (expected in pulsars, MQs, etc.) The spectral peak around Ee~1/bt will be broadened! 2 Q0 (t t ) e r 2 F (t , e ) dt 1 b t exp e 3/ 2 3 r2 r diff 0 diff t Case 1: pulsar-type decay Etot Q0 (t ) Lspindown 0 1 t / 0 2 cf.) 2 0 7.4 103 B / 1012 G P10ms years 2 0 Case 2: exponential decay Q0 (t ) Etot ln 4 0 t ln 4 exp 0 0 Results: Electron/Positron Flux solid line :exponential decay (0~105yr) DE: effect of finite 0 thick: total (source+2nd) pure secondary t=5.6x105yr r=1kpc Etot=2x1050erg =1.4 Emax=3TeV K0=3.2x1028cm2s-1 =0.6 pure source transient source Epeak~1/bt ~600GeV (NK, Ioka and Nojiri in prep.) Spin down time should not be too long? * A significant fraction of observed electrons are emitted recently. t=5.6x105yr r=1kpc Etot=2x1050erg =1.4 Emax=3TeV K0=3.2x1028cm2s-1 =0.6 pure source pulsar type: 0=105yr H.E.S.S. pulsar type: 0=104yr (NK, Ioka and Nojiri in prep.) Young pulsars should not have any contribution? Why so rare? 1. Local birth rate is intrinsically low? 2. HE pairs are confined in the pulsar wind nebula? 3. Most pulsars have lower Etot (<2×1050 erg)? (= P0 >~10msec) 4. 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 =1.4 (NK, Ioka and Nojiri in prep.) Results: Positron Fraction Total contribution from old pulsars (birth rate~1 per 5x105yr) thin solid lines: old pulsars with =1.4 thin dashed lines: =1.6 (NK, Ioka and Nojiri in prep.) Summary • We investigate the effects of continuous electron/positron injection from astrophysical objects on the observed electron/positron spectrum. • Epeak tage of the source • DE @ Epeak the duration of electron injection • Assuming pulsar spin down type injection, high energy tail in the electron spectrum would be enhanced if 0 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.