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Constraints on Ultra-High Energy Cosmic Ray Acceleration in Pulsars in the Local Universe

Constraints on Ultra-High Energy Cosmic Ray Acceleration in Pulsars in the Local Universe. Elisabete M. de Gouveia Dal Pino & Alex Lazarian IAG – Universidade de São Paulo University of Wisconsin - Madison. PROLOGUE.

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Constraints on Ultra-High Energy Cosmic Ray Acceleration in Pulsars in the Local Universe

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  1. Constraints on Ultra-High Energy Cosmic Ray Acceleration in Pulsars in the Local Universe Elisabete M. de Gouveia Dal Pino & Alex Lazarian IAG – Universidade de São Paulo University of Wisconsin - Madison

  2. PROLOGUE • Origin of UHECRs with E  1020 eV (AGASA, Fly’s Eye, Haverah Park, Yakutsk): challenge for the understanding of their nature and sources. • If UHECRs are protons: affected by GZK energy cutoff - 5 x 1019 eV - (due to photomeson production off interactions with CMBR), UNLESS originated at  50 Mpc (e.g., Medina Tanco, de Gouveia Dal Pino & Horvath 1997). • If UHECRs are protons from nearby sources: arrival directions should point toward their sources (little deflected by intergalactic and Galactic B-fields (e.g. Stanev 1997; Medina Tanco, de Gouveia Dal Pino & Horvath 1998).

  3.  Data: no significant large-scale anisotropy in the distribution related to Galactic disk; Some clusters of events point to the supergalactic plane. • Figure 1: Observed arrival directions of UHECRs with energies > 1019 eV (Takeda et al. ) : • (a) equatorial • (b) galactic-coordinates •  : E ~ (1 to 4) x 1019 eV, • : E ~ (4 to 10) x 1019 eV; • : E  1020 eV. • Galactic and supergalactic planes shown by dotted curves. GC : galactic center

  4. Source Candidates • Several source candidates and acceleration mechanisms invoked (e.g., reviews by Olinto 2000, 2001; Watson 2001; and this Workshop). • Among potential Zevatrons: pulsars with B > 1012 G: • UHECRs could be accelerated byinduced e.m.f. across open B-lines: but E-fields can be shorted by pair production, or particles loose energy by curvature radiation.

  5. To overcome these difficulties: We have suggested (de Gouveia Dal Pino & Lazarian, ApJL, 536, 2000; ApJ, 560, 2001): UHECR events could be mostly protons accelerated in reconnection sites just above the magnetosphere of newborn millisecond pulsars originated by accretion-induced collapse (AIC) of white dwarfs  Also we find that in order to obtain the observed UHECR flux: we need the integrated contribution due to AICs from all galaxieswithin the local Universe: i.e., within the volume not affected by the GZK effect (RG ~ 50 Mpc)  naturally provides isotropic distribution of events.

  6. At Rx: the equatorial flow divert into a funnel inflow along the closed field-lines toward the star, and a centrifugally driven wind outflow THE MODEL B-lines of the star encouter those opened by the wind and those trapped by the funnel inflow emanating from the RX: reconnection region (helmet streamer) UHECRs: accelerated in theHelmet Streamer. The accretion flow spins up the star and confines the magnetosphere to a radius RX (Arons 1993).

  7. How could the particles be accelerated? • Potential acceleration mechanisms: • 1st-order Fermi • one-shot acceleration by induced electric field Reconnection site: upper and lower parts of the flow move towards each other and particles see the lower part to approach with 2vrec  Helmet Streamer <E/E> = 8vrec/3c

  8. However: SYNCHROTRON LOSSES In the UHE regime, the amount of energy lost by particle of E  1020 eV when deflected by angle  in very strong B(1013 G) (de Gouveia Dal Pino & Lazarian, ApJ, 2001): E  1011  E20 sin E  the back and forth bouncing of protons in reconnection site entails proihibitive synchrotron losses:  Fermi does NOT provide required efficiency for UHECRs

  9. ONE-SHOT UHECR ACCELERATION Particles CAN be accelerated to UHEs by induced electric field (p ) in the reconnection site But: for particles to be able to escape without suffering any significant deflection in B  B just above the Alfvén surface:  must be predominantly toroidal

  10. Condition to accelerate particles of charge Ze to energies E by electric field in the reconnection site gives: • E  Ze B vrecLx/c • This condition + fast reconnection (Rx/Rx 1) + field geometry imply: • B13 0.8 E20 Z-12.5k-4/3  Pulsars with spin 4 x 103 s-1 * > 102 s-1 and 1012 G < B* 1015 G and: are able to accelerate particles to energies E20  1.

  11. The rate of magnetic energy extracted from reconnection site: •  <1:the reconnection efficiency factor WB 3 x 1046 erg s-1 B1322.5k8/3 And the Particle-Spectrum is obtained from: dN/dt  N(E) dE/d* d* /dt f -1 Or: • N(E)  2 x 1033 GeV-1 B13-1/2 Z-1/2 E20-3/2 • f: fraction of * -1 : duration of acceleration

  12. UHECR FLUX • Number of AIC-pulsars in our Galaxy: limited by very small rate (Fryer et al. 1999):AIC-1 ~ 10-5 yr-1 • Integrated contribution due to AICs from all galaxies within volume not affected by the GZK effect (RG ~ 50 Mpc), gives an UHECR flux F(E)  N(E) nGAIC-1RG at E20 1: F(E)  3 x 10-29 GeV-1 cm-2 s-1B13-1/2 Z-1/2 E20-3/2 AIC,5-1 nG,0.01 R50 • Observed data (e.g.,Takeda et al.) gives • F(E)obs 4 x 10-30 GeV-1 cm-2 s-1 • so that efficiency of converting magnetic energy into UHECR should be:F(E)obs / F(E)  0.1

  13. SUMMARY •  We have proposed that the UHECRs: accelerated in reconnection sites just above magnetosphere of newborn millisecond AIC-pulsars of galaxies within the local Universe (50 Mpc) through one-shot acceleration in induced electric field (de Gouveia Dal Pino & Lazarian, ApJL, 536, 2000; ApJ, 560, 2001) •  AIC-pulsars with surface magnetic fields 1012 G < B* 1015 G, and spin periods 1 ms  P* < 60 ms, are able to accelerate particles to energies E 1020 eV. •  Produce a particle-spectrum: N(E)  E-3/2 •  The calculated efficiency of converting magnetic into UHECR flux should be F(E)obs / F(E)  0.1. • Synchrotron losses: important constraints on B-geometry of any UHECR accelerators with strong B’s.

  14. TO BE SOLVED YET •  Induced electric field saturation due to e : depend on details on MHD pulsar wind outer regions 

  15. FURTHER RECENT WORK •  Acceleration in neutron star MHD winds (Blasi, Epstein & Olinto 2000) •  Very recentnon-ideal MHD pulsar wind models (Birk et al. 2001; Kirk & Lyubarsky 2001): • have also pointed out importance of magnetic reconnection on accelerating winds •  Birk et al. (2001): reconnection of toroidal fields driven by plasma inertia in extragalactic jets •  Kirk & Lyubarsky (2001): magnetic reconnection in stripes of toroidal field near equator of pulsar winds: significant to accelerate particles even in isolated pulsars  Any case: attention must be paid: synchrotron losses

  16. FIM

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