Axisymmetric Pulsar Magnetosphere with Particle Method III: Dipole - PowerPoint PPT Presentation

Axisymmetric Pulsar Magnetosphere with Particle Method III: Dipole and Quadrupole magnetic field case Tomohide Wada* ( National Astronomical Observatory Japan ) Kotaro Fujisawa ( University of Tokyo ) Shinpei Shibata ( Yamagata university ) email: tomohide.wada @ nao.ac.jp 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

Rotation powered pulsars electron Gamma-ray beam < 10% of L sd Pulsar wind ～ L sd positron magnetosphere Crab nebula: pulsar image credit: NASA 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong Pulsar is identified highly magnetized(10 12 G) and rapidly rotating(P<1sec) neutron star and one of the brightest source of gamma-ray. Pulsar exists inside the nebula as a central engine. The rotational energy of star is released by radiation & plasma. synchrotron nebula accelerated plasma(Lorentz factor=10 7 ) L sd ; spin down luminosity

Outline of presentation 1. Axisymmetric magnetosphere model 2. Effect of Quadrupole B field 3. Outline of particle simulation(method) 4. Results 5. Summary How does pulsar release the rotational energy by accelerated plasma and HE-radiation? Fermi observation has been important for pulsar. Outer gap, Slot gap, Polar cap.... How are the gap(s?) formed? higher order component of poloidal magnetic field 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

Dipole & Quadrupole B field Rotating magnetized star induces unipolar electric field. Dipole; term B 1 Kojima Y & Kisaka S MNRAS 2012; Evolution(decay) stellar magnetic field by hall drift effect Quadrupole; term B 2 B n ; surface field intensity at pole R 0 ; stellar radius θ; colatitude r; radius of spherical coordinate P n ; Legendre polynomial function P 1n ; Associated Legendre polynomial function Pulsar is one of the greatest accelerator of plasma. Neutron equatorial plane Anti-symmetry to equatorial plane Symmetry to equatorial plane B.C. vacuum solution of B is given by steady condition, analytical Suppose axial symmetry & →Possibility of multipolar poloidal B(higher order of dipole) field dominant phase. star 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong magnetic field line e n i l d l e fi c i r t c e l e

Dipole + Quadrupole B field case Quadrupole B dominant case; B 1 =2B 0 polar cap + dipole Quadrupole Magnetic stream function in spherical coordinate This function is constant along a B line, and then ; light radius last closed line Polar cap radius Quadrupole B field changes the area of polar cap ～ 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

Magnetic neutral region(MNR) equatorial plane B field intensity on B quad <B dip B quad >B dip -> null surface(NS) light radius, Goldreich-Julian space charge density is given, Suppose force-free condition and consider only inside Goldreich-Julian space charge density • NS of dipole case is maybe Eperp acceleration? → not magnetized region pole • MNR above the south NS is added modified and another poloidal plane 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong ; e n i l d l e d fi a null surface u q B B + p i d B null surface; dipole case

Pulsar magnetosphere -Synchrotron radiation present case. accelerated plasma in CR photon by primary For simplicity, we treat only solve below effects at once. To understand the structure of pulsar magnetosphere, we have to hereafter, X-gamma -Photon collision process hereafter, B-gamma -Magnetic pair creation process -Inverse Compton scattering (Curvature radiation; CR) Acceleration -Bremsstrahlung -magnetic dissipation(recconection) modifies stellar EB field - magnetospheric charge & current -radiation drag -inertia -drift motion -Eperp acceleration(if it is needed) -Eparallel acceleration Pair creation Radiation 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

Outline of our particle method positive charge (yellow volume) gamma-ray emitting region 4 we finally obtain the steady magnetosphere. Solving static fields and motion of particle iteratively, (magenta curves) magnetic field line negative charge 3 1. calculate surface charge density 2 1 6. repeat 1-5 until steady state is obtained 5. delete particle outside of the outer boundary gamma collision) 4. Gamma-ray photons by CR are estimated by E // and converts into e+e-(X- position of particle and solve 3-D equation of motion for each particles 3. calculate fields (stellar field plus field by space charge and current) at the 2. replace surface charge density with simulation particle 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

Solving acceleration And therefore, it has no singular surface at light cylinder. We gave up to find singular surface light cylinder -> + maxwell’s eqs But it usually needs a large computational time. Because of solving EOM, the nature at LC is determined by basic eqs. To solve pulsar equation, some constraint or boundary condition Particle method with axisymmetric model - -steady condition (time independent) -axial symmetry Axisymmetric force-free model is imposed at light cylinder. Usually, it is difficult to solve. analytical solution...

Basic equations (with steady condition) Equation of motion(3D) ; field by particle ; stellar field stellar fields(2D)+magnetospheric field(3D) ; stellar field B.C. guiding center of particle Magnetic field equations in steady state and EOM iteratively. To obtain steady solution, we solve Maxwell’s negative charge B.C. positive charge E ij B ij B B drag force radiation gamma-ray E // Electric field ; field by particle

Radiation model -CR, SR, IC process and the gamma-rays For simplicity, we treat only CR -> might be simple system -CR, SR, IC Old PSR (but may emits gamma-ray) -> complicated system Young PSR ～10 5 yr -> time evolution of spectra energy spectrum of various age pulsar n γ ,ε γ ρ,j,E,B Thompson 2004 ～10 3 yr SR

Treatment of pair creation 1 propagating direction of gamma-ray emitting region E // >E cr If photon moves out numerical outer boundary(10R l ), it removed. outer boundary 1 ;perpendicular component 1 2 2 3 4 gamma-ray photons l p of magnetic field for B-gamma X-gamma numerically, mean free path is estimated with lp x f, where f is robability distribution function given by random number ; c o l l i s i o n a n g l e ; Thomson cross section

Overview of result 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong

Result; B dip case +charge structure similar middle latitudes plasma is gap in main source of Outer gap model Cheng K S et al ApJ 1987b poloidal plane particle distribution on gaps & wind steady solution Our particle method reconstruct rotation period time normalized by -charge 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong This is a conventional model for acceleration of plasma

time normalized by rotation period/2 months e- Main source of plasma is also outer gaps, It is a same global feature (wind & gaps) in previous work (e.g., WS2011) But the system had not become perfectly steady, It needs more calculation time. Preliminary result! rotation period OG OG charge distribution on poloidal plane Result; B dip & B quad case light cylinder -charge +charge e+ 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong dead zone e n o z d a e d dead zone d a e d e n o z

light cylinder dead zone 2 star last closed line open zone 1 open zone 2 dead zone north-pole south-pole dead zone 1 light cylinder drops are obtained! Different potential Available maximum voltage in force-free limit with B dip +B quad case free limit with dipole case Open field line voltage in force- colatitude (degree) Asymmetry of Available Voltage neutron 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong 1 e n o z d a e d dead zone 2

Summary テキスト 2013-07-09 4th Fermi Asian Network(FAN) workshop@university of Hong Kong We demonstrated the particle simulation for axisymmetric pulsar magnetosphere. Steady outflow of accelerated plasma & local accelerating regions(in middle latitudes) The effect of quadrupole stellar magnetic field 1. Asymmetry of Charge & Current distribution around the equatorial surface, especially in the vicinity of star. 2. If B quad become dominant, MNR & another dead zone is formed. In the future work, we will try to taking account to magnetic pair creation process, and then -Super GJ-space charge density region formed around MNR? or E perp acceleration? -asymmetric beam radiation from north and south hemisphere.

Acknowledgement FOUR-DIMENSIONAL DIGITAL UNIVERSE PROJECT I would like to thank Syota Kisaka and Junpei Takata for insightful suggestion and fruitful discussion. And I am grateful for all the help and discussion for everyone in the workshop. Numerical simulation and visualization of the result were carried out on system at Center for Computational Astrophysics(CfCA), NAOJ and supported by Four-dimensional digital universe project(4D2U). -CfCA: http://www.cfca.jp -4D2U: http://www.4d2u.nao.ac.jp/

End Thanks!