Pair production and γ-ray emission in pulsars: A modern view
Andrey Timokhin C. Kalapotharakos, A.Harding, D.Kazanas
NASA Goddard Space Flight Center
Fifth International Fermi Symposium
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 1 / 18 Pulsar: rapidly rotating magnetized neutron star “Electric lighthouse”
Polar Cap
Polar Cap
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 2 / 18 Pulsar: Cosmic Electrical Lighthouse NB: Pulsars are non-thermal emitters
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 3 / 18 Plasma creation in the polar cap Cascades are electromagnetically driven
Magnetosphere
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 4 / 18 Limit cycle: series of discharges No particles extraction from the NS
NS Magnetosphere
• electrons • positrons • γ-rays
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 5 / 18 Free particle extraction from the NS
Particles' "cold" flow - no pairs momenta: p~[0,10]
electrons
Polar cap currents
"hot" flow - pair production
Particles' momenta: p~[0,107]
electrons positrons photons
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 6 / 18 Full cascade
2 1 Synctrotron cascade
0
1 synchrotron photon CR photon pair creation 2 generation # Curvature Radiation 0
neutron star
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 7 / 18 Cascade Efficiency Fraction of particle energy going into synchrotron and curvature radiation
ζsyn ζCR
.6 .9 8.0 .25 13.0 .1 .001
12.5 7.5 .3 .9
.8 c 12.0 7.0 .1 .75 log B logρ 11.5 6.5 .01 .95 .99 .5 11.0 6.0 .95 1 2 3 4 5 6 7 8 6.0 6.5 7.0 7.5 8.0 0 logϵ γ logϵ ±
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 8 / 18 Particle acceleration
logϵ ±, acc 7.8 13.0 11 10− 7.2 13 12.5 10−
15 10− 12.0 8.2 P˙ 7.6 17 log B 10−
11.5 19 10−
21 8.4 10− 11.0 7.4 3 2 1 0 1 10− 10− 10− 10 10 8 P 6.0 6.5 7.0 7.5 8.0
logρ c 7 2/7 1/7 4/7 −1/7 −1/7 ±, acc ' 5 × 10 χa ξj ρc, 7 P B12
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 9 / 18 Multiplicity of polar cap cascade: κ ∼ 105
P=33 ms,ξ=2 P=33 ms,ξ=0.25 P=330 ms,ξ=2 4 4 13.0 4.5 4 4.5 4.5
12.5 5 5 5
12.0 6 5.5 5.5 5.5 log B
11.5
11.0 5 4.5 5 4.5 5 4.5 6.0 6.5 7.0 7.5 8.0 6.0 6.5 7.0 7.5 8.0 6.0 6.5 7.0 7.5 8.0
logρ c logρ c logρ c
Dependence on ρc partially cancels out: small ρ high splitting efficienly, but low primary particle energy • c large ρc low splitting efficienly, but high primary particle energy • → →
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 10 / 18 Discharge: RS flow
NS Magnetosphere bulk of pair-producing particles
• electrons • positrons • γ-rays
Low heating of NS surface • Duty cycle: can be as low as • hgap/RNS ∼ 1/100 (for Crab)
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 11 / 18 Discharge: super-GJ SCLF
bulk of pair-producing particles
NS Magnetosphere
• electrons • positrons • γ-rays
Low heating of NS surface • Duty cycle: ∼ 1/few •
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 12 / 18 PSR J1057-5226: Polar cap emission?
> 0.1 GeV H=14999 J1057-5226, P=0.1971s d = 0.30 pm 0.00, D = 0.31 pm 0.00 PKS 1.4 GHz
300
200 W. Counts / bin
100
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Pulse Phase
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 13 / 18 Electric field in resistive magnetosphere uniform high σ
(Kalapotharakos et al. 2014)
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 14 / 18 Curvature radiation in magnetosphere with non-unifrom σ
2 4 E × B B dγ qecEk 2q γ = + f c L = f − e L v 2 2 2 2 B + E0 B dt mec 3RCRmec
(Kalapotharakos et al. 2014)
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 15 / 18 γ-ray Emitting Regions
(Kalapotharakos et al. 2014)
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 16 / 18 Peak Separation(∆) vs Radio Lag (δ)
(Kalapotharakos et al. 2014)
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 17 / 18 Conclusions
Particles can be accelearted faster and at lower altitudes • γ-ray emission from polar caps is at lower energies • (∼ 10 − 100 MeV) Maximum multiplicity of polar cap cascades κ ∼ 105 • • Maximum multiplicity is not sensitive to pulsar parameters • Plasma distribution is non-uniform • Inclinations angle should be very important factor determining the overall pulsar pair multiplicity
The bulk of γ-ray emission seems to come from the current sheet • region outside the light cylinder
A. Timokhin (GSFC) Pairs and γ-rays in Pulsars Fermi Symposium 18 / 18