＠ FAN3 22 June 2012

1.To give the theoretical proof of the outer gap (the mechanism has been proposed) 2.To look for other particle acceleration sites; polar cap, & slot gap to be confirmed, and look for other possibilities? 3.To study the pulsar wind formation via particle simulation, the main problems to be challenged are

黄色系 Ｐ１ メインピーク一つ 緑系 Ｐ１＋Ｐ２ ２ピーク＋ブリッジ Ｍ型 青系 Ｐ１＋Ｐ２＋Ｐ３以上 ４４サンプル From “The First Fermi Large Area Telescope Catalog of Gamma-ray Pulsars, Abdo et al., astro- ph/ v2 Although pulse profiles have some varieties,

Two-pole caustic (TPC) geometry (Dyks & Rudak, 2003) Double peak and bridge emission can be understood if emission is along the last open field lines; due to multi-ply superposition of photon arrival times: caustic. Favors Slot gap / Outer gap Closed field (dead zone) Open field region Observation (Vela) model Caustic in human life

Double pulses and spectrum support the outer gap model  to give the proof of the outer gap.

After Ray & Parkinson 2010 Astro-ph Third peak, may not be caustic 3 rd peak, 4 th,,,,,many components are observed and shall be observed in the future.  look for other acceleration sites by simulation.

The rotation power is mostly carried off by the pulsar wind.  formation of the pulsar wind. Q1 how much fraction of the wind energy is carried by electromagnetic flux (Poynting flux), and how much by kinetic energy of particles; acceleration efficiency Q2 where the wind acceleration takes place; near the l.c. or gradually in a long distance to the nebula. X-ray image of Crab Nebula, which is exited by the pulsar wind, but the contents of the wind is not certain

Model: NS  magnetized electrically conducting sphere; B=10^12 G, rotating wiht P= 0.1sec v B V + - Electric potential difference appears between the poles and the equator. Rotating magnet has emf  charge separation

＋ ＋ ー ー ー ＋ B V F

Release of rotational energy (in reality ]: how? Note ∂B /∂t =0 Unipolar inductor: rotating magnet produces emf

φ=(Ωμ/cR^3) [(x^2+y^2)cos χ – zx sin χ] v B V + - Electric potential difference appears between the poles and the equator. For oblique rotator, potential difference becomes

current magnetic field By forming a closed current circuit, one can extract energy: one can light the lamp. As a back reation, electromagnetic breaking on the magnet causes spin-down: Thus rotational energy of the neutron star is extracted.

The rate of energy loss L_rot is (by dimensional analysis within the classical physics) One can estimate μ by this relation.

current magnetic field hν/c or γmc Angular momentum is lost by photons  back reaction on the emitting material make mutual mo.  extraction possible One must notice that the circuit experiences a force in such a direction that the circuit is force to corotate with the star. Thus the circuit and the plasma around the neutron star have strong tendency of corotation. If the ciruit corotates with the star, no mutual motion, no extraction of emf. Co-rotation speed becomes c

If the lever-arm distance is c/Ω, angular momentum is properly lost. Summary: The extraction of rotation energy can be kept continuously by emission of photons and particles near and beyond the light cylinder with levar-arm distance of c/Ω. As a corollaly, the polar cap and any other radiations well within LC cannot be a dominant emission site. I think that most of the rotation power is emitted tangentially from the light cylinder by a mixture of photons and relativistic particles, called the pulsar wind.

Breaking index Younger pulsars may have worse efficiency (?) n < 3 ?

If there is enough plasma, it corotates with the star. However, because of relativity principle, the corotation is limited within the LC. In 1973, Holloway thought that if some plasma is leaked from the LC, there appears a gap in the corotation region. (Holloway N.J.,1973 Nat. Phys. Sci 246, 6) Eq. of motion: Co-rotation electric field BC; rigid rotation of the star; star is a good conductor Drift is corotation; for oblique rotator

The corotation electric field is supported by the “corotation charge density”, GJ density In number density, “quasi-neutral plasma?” This charge density is difficult to realize in the pulsar magnetosphere because of large gravity and because source of plasma is limited. We do not have quasi- neutral plasma in the pulsar magnetosphere as far as electron-positron pair creation, which we shall discuss later, takes place.

Let us suppose somewhat idealized situation where the electric field is the corotaional one (no field-aligned comp.) and therefore the charge density is GJ. The plasma is supported against gravitational force from the star so that the plasma is completely charge separated. Let us add a perturbation that some plasma is leaked from LC by say centrifugal force. Holloway 1973 Deficiency of plasma within the LC manifests itself as a gap round the boundary between the negative and positive GJ density. strong charge separation causes gaps Positive GJ GJ negative

electrons positrons star Light cylinder For the first time, the particle simulation is applied for this situation by Krause-Polstorf and Michel (1985). Gap Field-aligned Electric field Gap These pictures are reproduced by our code.

In the gap, GJ density is not filled, and the electric field deviates from the co-rotation filed. Inertial force, non-EM forces must balance EM force; Particle acceleration Evacuated space (Gap) is unstable against pair creation. As a result, Holloway gap creates pairs continuously or quasi-periodically. This is the outer gap.

By many authors, the gap structure is calculated but is affected by many factors: e.g., geometry of back ground magnetic field, soft-photon field, radiation process taken into account, boundary conditions for the electric field. (Hirotani & Shibata 1999, Takata Shibata & Hirotani 2004, Hirotani 2008, Takata Wang & Cheng 2010,,,,) One can in principle calculate the structure of the outer gap if sufficient conditions are given.

However, we do not think the outer gap structure can be determined as far as it is local model. We always have free parameter, which must be free to adjust with the surroundings, especially the pulsar wind. More specifically the total current and current distribution in the gap is controlled by the pulsar wind. Thus the model must be global, and the outer gap must be solved together with the wind.  Particle simulation. (Wada & Shibata 2007, Wada & Shibata 2011, Yuki & Shibata 2012)

For the case of axisymmetry, Special purpose computer for Astrononomical N-body Problem Plasmas are represented by several tens of thousands of super-particles. (number of particles are not fixed, but particles are added suitably from the stellar surface or because of pair creation.) Cal.Domain is 3D (60RL)^3 60RL We iteratively solve the equation of mo. and EM field

Special purpose computer for Astrononomical N-body Problem

With this method, the corotation boundary (i.e. emf of the star) is strictly satisfied, For the magnetic field, we use In general, surface charge on the star exists, but it is replaced by simulation particles (free emission) until no surface charge is emitted from the stellar surface. with

Treatment for pair creation: Gap is unstable against e+e- pair creation A simple treatment B γ ＋ B  e+ ＋ e- γ ＋ X-ray  e+ ＋ e- Two photon pair creation Unscreened Gap Electric field If E > Ec, n=f * int(E/Ec) pairs are created (on the spot approx.)

NS 1.Particles flows 2.(m, q) are chosen so that any plasma drift motions are tracked correctly. 3.Radiation drag force is taken into account in the lowest order approximation. Curvature radiation

＊ Outer gap is formed with continuous pair creation & E// just aboe Ec Paris are separated in the gap by E// ＊ outgoing flow  LC ＊ ingoing flow  Star ＊ Outer gap is formed with continuous pair creation & E// just aboe Ec Paris are separated in the gap by E// ＊ outgoing flow  LC ＊ ingoing flow  Star The outer gap is proven by the particle simulation. Ingredients are eq. of mo., Maxwell’s eq., BC rotating NS and pair creatoin if E//>Ec The outgoing flow rotate with high Lorentz factor, so that curvature radiation carries off the angular momentum. Back reaction of the curvature radiation is in –φ direction  cross drift motion. Rotating plasmas makes toroidal current to open some magnetic flux. Particles on the open magnetic flux flows out along the magnetic field.

In going flow from the outer gap fall on to the star. If this continues, the star is charged up and up. So steady state is reached by emission of pariticles from the polar cap. There must be accelerating field to extract particles from the polar cap.

E// map E// is just above Ec: necessary minimum for pair creation.

Map of Φ(Non-corotational electric potential) Dead zone Current neutral dead zone If Φ=0, the potential is as the same as the star, Co-rotation and E // =0 E // = -B ・∇ Φ The non-corotaion potential Φ = φ - Ωxr ・Ａ is constant on the star, it is set to be zero.

Map of Φ(Non-corotational electric potential) Dead zone Current neutral dead zone We find another dead zone in the middle latitudes. This dead zone locates on the field lines which separates the outgoing current and ingoing current. Let us call this dead zone the current neutral dead zone.

Light cylinder Super- rotatoin

Discussion The ploidal current loop is such that it start from the star, go through the outer gap, goes to the nebula, and go back to the star in higher latitudes. We have two dead zones: One is the dead zone in the equatorial closed magnetic flux. The other extends along the separatrix of the oppositely directed currents.

Discussion Φ = 0 in the dead zone. The outer gap is sandwiched by two dead zone. Therefore, previous boundary conditions used for the outer gap is correct.

Discussion The polar current is surrounded by the current neutral zone; Inside of hollow cone of the current neutral zone. If there is slot- gap, it resides above the current neutral dead zone.

Discussion Some particles leak due to radiation drag drift. It is noticeable that E is larger than B in this region.

Map o f E/B （ Uzdensky, 2003 ） Udzdenski の force free 解 light cylinder

PIC simulation for an axisymetric Y- point 初期の磁力線 （ Uzdensky, 2003 ） Magnetic reconnection takes place t ～ 4 x 10^5 ⊿ t Z / R LC での磁力線 赤道面 R / R LC Z / R LC ⇒ heating and acceleretion

Discussion Flow out of magnetic islands with pairs. Thin current sheet with outgoing positrons and backward electron beam along last open field line  another component

Future work Number of particles must be still larger (now Ndot = 0.7 GJ Electric field in the polar flow has not been resolved.) Gamma-ray coming into the screened region also make pairs. These pair must be included. Oblique rotator (not Grape,  PIC) Realistic pair creation process (include photons) GR effect near the star.