Shota Kisaka (ICRR, Univ. of Tokyo) with Norita Kawanaka (Hebrew Univ. of Jerusalem) Toshio Terasawa (ICRR, Univ. of Tokyo) Takayuki Saito (MPI)

Shota Kisaka (ICRR, Univ. of Tokyo) with Norita Kawanaka (Hebrew Univ. of Jerusalem) Toshio Terasawa (ICRR, Univ. of Tokyo) Takayuki Saito (MPI)

Outline 1. IntroducHon 2. AcceleraHon region : Pairstarved MSPs 3. Emission region : subtev emission region

Structure of pulsar magnetosphere RotaHng magnet Unipolar induchon E screening Magnetosphere Basic concept (Goldreich & Julian 1969) Light cylinder Null line Closed zone To maintain the forcefree condihon, following processes work in some regions. ParHcle accelerahon ParHcle supply (parhcle creahon) E screening (ρ & J adjustment)

Structure of pulsar magnetosphere RotaHng magnet Unipolar induchon E screening Magnetosphere Basic concept (Goldreich & Julian 1969) Light cylinder Null line Closed zone To maintain the forcefree condihon, following processes work in some regions. ParHcle accelerahon GeV γray ParHcle supply (parhcle creahon) IR ~ Xray E screening (ρ & J adjustment) Radio?

Structure of pulsar magnetosphere RotaHng magnet Unipolar induchon E screening Magnetosphere Basic concept (Goldreich & Julian 1969) Light cylinder Null line Closed zone To maintain the forcefree condihon, following processes work in some regions. ParHcle accelerahon GeV γray (e ± CR?) ParHcle supply (parhcle creahon) IR ~ Xray (& TeV γray?) E screening (ρ & J adjustment) Radio?

Problems Outer gap model cannot reproduce observed γray light curves in some millisecond pulsars (MSPs). VERITAS and MAGIC detected subtev pulsed emission from Crab pulsar.

Unusual γray light curve Two MSPs show unusual light curves that the γray peak lead the radio peak. Young γray pulsars do not show such light curves. γray Radio Guillemot (2009)

PairStarved Polar Cap (1/2) Muslimov & Harding (2004) suggest that most MSPs can not produce pairs through curvature radiahon. In this case, parhcle accelerahon can occur in almost open field volume (PairStarved Polar Cap model). Pair death line for curvature radiahon Harding (2009)

PairStarved Polar Cap (2/2) The model that have extended parhcle accelerahon region can explain observed light curves. γray Radio model Venter(2009), Johnson (2012)

However, the existence of pairstarved MSPs suggests that radio emission mechanisms should be insensihve to the parhcle number density down to subgj one. Therefore, further verificahon is important. CondiHons for radioemiing region In general, people have believed the condihons of a primary beam with γ b ~10 7 and n b ~n GJ, and a secondary e ± with γ p ~1010 3 and n p ~10 3 10 5 n GJ in the radioemiing region. LyuHkov (1999)

AcceleraHon AssumpHons In the wind region, the energy equiparhhon between B and e ±. the flux conservahon of B and e ±. Typical energy is related to the number of parhcles. ε e = e V max κ 1 50κ 1 TeV κ : mulhplicity Ω : angular velocity

PropagaHon of e ± cosmic ray Diffusion coefficient Cooling funchon Source funchon AssumpHons MSPs are single populahon. Source funchon is monoenergehc distribuhon. Spectrum f ave (ε e )= t0 0 dt i ddiff (ε e,ε e,i) 0 2πrdrf(t 0,r,ε e ; t i )R R ~ 3 10 9 kpc 2 yr 1 : local birth rate

Result for κ=1 (ε e =50TeV) Flux e 3 e [m -2 s -1 sr -1 GeV 2 ] 10 3 10 2 10 1 std. 25% std. 10% std. ATIC HESS(08) PPB-BETS Fermi HESS(09) e ± total flux 100% 25% 10% FracHon of pairstarved MSPs 10 0 10 1 10 2 10 3 10 4 10 5 Energy e [GeV] SK & Kawanaka (2012) Large peak form in 1050 TeV range and may be detectable by CALET and CTA.

SubTeV pulse model Outer gap Cold wind Aleksic et al. (2011) Aharonian et al. (2012) Do SubTeV emission regions locate inside the light cylinder? or outside?

γb absorphon Lee et al. (2010) ~0.5R lc ~0.35R lc The value of the last escaping radius for a 400(120) GeV photon is 0.5(0.35) R lc.

Geometrical modeling AssumpHons MagneHc field RotaHng dipole Emission direchon Along the parhcle trajectory Emission region r null < r < R lc (Outward) Emissivity Constant We focus on the peak phases of the light curve. Parameters MagneHc colahtude : f Ξr pc /r pc,0 InclinaHon angle : α Viewing angle : ζ ζ α μ r null : Distance to null surface R lc : Light cylinder radius f =1.0 f <1.0 f >1.0 r pc,0

Emission region in outer gap The distance distribuhon from NS to emission regions r/r lc r/r lc 1 0.8 0.6 0.8 0.4 0.6 0.4 0.2 0.2 0 0.5 0.4 0 0.2 0.4 0.6 0.8 1 0.3 0.2 0 0.2 0.4 0.6 0.8 1 Peaks include photons emi ed from relahvely far region.

Emission region in outer gap The distance distribuhon from NS to emission regions r/r lc r/r lc 1 0.8 0.6 0.8 0.4 0.6 0.4 0.2 0.2 0 0.5 0.4 0 0.2 0.4 0.6 0.8 1 0.3 0.2 0 0.2 0.4 0.6 0.8 1 Peaks include photons emi ed from relahvely far region. All photons at leading side of second peak come from the closest region in the magnetosphere.

000 000 000 000 000 r/r lc Where should we focus on? 0 0 0.2 0.4 0.6 0.8 1 0.8 The distance 0.6 0.4 0.2 0.5 0.4 0.3 0.2 light curve distribuhon from NS to emission regions 0 0.2 0.4 0.6 0.8 1 0.1 Phase of second peak : φ_peak Phase where photons from outer region are included : φ_out 0 Phase where photons from the closest region are included : φ_in 1 : φ_peak φ_out 2 : φ_peak φ_in 0.9 0.95 1 1.05

Where should we focus on? 1 : φ_peak φ_out 0.05 2 : φ_peak φ_in 0.14 relative phase 0-0.05-0.1 relative phase 0.12 0.1 0.08 0.06-0.15 0.9 0.95 1 1.05 1.1 MagneHc altitude colahtude f 0.04 0.9 0.95 1 1.05 1.1 MagneHc colahtude f We can exclude the photons from outer region when we use photons in phase < φ_peak 0.05. Photons from the closest region from NS are included in phase φ_peak (0.05 0.15).

Constraint for outer gap model The minimum distance of emission region r/r lc 0.5 0.4 0.3 0.2 0.1 0 0.9 0.95 1 1.05 1.1 MagneHc colahtude f ~400GeV r > ~0.5R lc Outer gap can not explain this energy of photons. ~120GeV r > ~0.35R lc 35 < α < 45, ζ~80, f~0.95.

Prospects 1. If the spectrum have the powerlaw component outer gap Constraint for geometrical parameters. 2. If the spectrum show the strong cutoff outer gap Constraint for the alhtude of emission region. cold wind Constraint for the anisotropy of the parhcle distribuhon in pulsar wind. 3. If the spectrum do not have the powerlaw component outer gap Constraint for the condihon of IC. cold wind Constraint for the anisotropy of the parhcle distribuhon in pulsar wind.

Summary Outer gap model cannot reproduce observed γray light curve in some MSPs. CTA can detect the evidence of the existence of pairstarved MSPs in the e ± cosmic ray spectrum. VERITAS and MAGIC detected subtev emission from Crab pulsar. CTA can restrict the emission region using the spectrum at the phase of the bridge.