1. Polarization in Pulsar Wind Nebulae Delia Volpi In collaboration with: L. Del Zanna - E. Amato - N. Bucciantini Dipartimento di Astronomia e Scienza dello Spazio-Università degli Studi di Firenze-Italy

2. Observations: optical and X-ray

3. RELATIVISTIC MHD Models

4. IDEAL RMHD EQUATIONS ECHO: GRMHD 3-D VERSION (Del Zanna et al., 2007, A&A, 473, 11)

5. Numerical model 2-D (axysimmetric) RMHD shock capturing code in spherical coordinates (Del Zanna et al., 2002, 2003, 2004) Initial cold ultrarelativistic Pulsar Wind with v radial and r -2 +SNR+ISM Lorentz factor (conservation of energy along streamlines) : Anisotropic energy flux: Toroidal field: Space and time evolution of RMHD equations+ maximum particle energy (Lorentz factor) equation with adiabatic and synchrotron losses averaged on the pitch angle: (b = /2) w= c 2 +4p

6. Synchrotron emission recipes Emitting particles isotropic distribution function at termination shock (TS = 0) (Kennel & Coroniti, 1984b): Post-shock distribution function (obtained from conservation of particlesnumber along streamlines and under condition of 0.5): spectral index

7. Synchrotron emission recipes Emission coefficient in observers fixed frame: Relativistic corrections: Cut-off frequency for synchrotron burn-off (evolved in the code from the maximum particle energy): observer direction versor optical or X-ray frequency of observation

8. Synchrotron emission recipes Surface brightness: Stokes parameters (linear polarization): Polarization fraction ( ) and polarization direction ( P ): Spectral index ( ) for two frequencies ( 1, 2 ) and integrated spectra (F ): local polarization position angle between emitted electric field and Z d=distance of emitting object

9. Wind magnetization Runs with effective =0.02 (averaged over ) A ( =0.025, b=10) B ( =0.1, b=1)

10. Results: flow structure maps RunA: a) Stronger pinching forces smaller wind zone; b) Equipartition near TS; c) Larger magnetized region particles loose most of their energy nearer to TS; d) Less complex magnetization map. Supersonic jets and equatorial outflow: v 0.5-0.7c (as in Crab Nebula-Hester-2002, Vela-Pavlov 2003). =0.025, b=10 narrow striped wind region =0.1, b=1 large striped wind region

11. Results: surface brightness maps =0.025, b=10 narrow striped wind region =0.1, b=1 large striped wind region

12. HIGH RESOLUTION POLARIZATION MAPS TOY MODEL UNIFORM EMITTING TORUS WITH B TOROIDAL AND V RADIAL : ANGLE SWING INCREASES WITH V AND BIGGER IN THE FRONT v=0.2C θ =90° - - v=0.5c θ =75° -- v=0.8c θ =60°=>INFORMATION ABOUT FLOW VELOCITY POLARIZATION FRACTION=>MAXIMUM EVERYWHERE SAME EFFECT WITH A KC FLOW

13. Results: optical polarization maps Synchrotron emission linear polarization Polarization fraction: B poloidal Normalization against ( +1)/( +5/3) 70% Along polar axis: higher polarized fraction (projected B line of sight) Outer regions: depolarization (opposite signs of projected B along line of sight) Polarization direction: v flow Ticks: ortogonal to B, lenght proportional to Π (Schmidt, 1979) Polarization angle swing (deviation of vector direction) in brighter arcs, v c, strong Doppler boost Bigger effect in the front side Origin of the knot????? RunB: more complex structure slow velocity =0.1, b=1 large striped wind region =0.025, b=10 narrow striped wind region

14. Results: X-ray polarization maps =0.025, b=10 narrow striped wind region =0.1, b=1 large striped wind region

15. Results: spectral index maps Values of Crab Nebula Optical maps obtained with: 1 =5364Å, 2 =9241Å (Veron-Cetty & Woltjer, 1993) X-ray maps obtained with: h 1 =0.5keV, h 2 =8keV (Mori et al., 2004) Spectral index grows from inner to outer regions RunA: X-ray simulated spectral index maps similar to ones of Crab Nebula (Mori et al, 2004) = + 1 =0.025, b=10 narrow striped wind region =0.1, b=1 large striped wind region

16. MAGIC Telescope (J.Albert et al., Arxiv:0705.3244v1, 2007) Crab Nebula: gamma-ray standard candle target of new instruments Emission: accelerated electrons+target photons (CMB+FIR+sync) HESS: TeV frequencies; GLAST: 20MeV-300GeV Disantangle magnetic field and distribution function+adronic component

17. Synchrotron and IC emission recipes Primordial isotropic radio-emitting population (A&A,1996): Accelerated wind population at TS (A&A,1996): Evolved distribution function (Del Zanna et al., 2006): Integration between spectral power per unit of frequency and distribution function: synchrotron=> monochromatic frequency IC => respect to ε and ν, total differential cross section, 3 targets (FIR, CMB, SYNC) (Blumenthal and Gould, 1970)

18. Results: IC Multislopes Disconnetted areas in maximum particle energy IC emission in excess Energy map: Compression around TS of B. Parameter? Distribution function? =0.025, b=10 narrow striped wind region

19. Results: IC Size reduction with increasing frequency: along y-axis Jet and torus visible for radio electron distribution, no observational counterpart =0.025, b=10 narrow striped wind region

20. Results: IC Time-variability: gamma-rays similar to X-rays. =0.025, b=10 narrow striped wind region

21. Conclusions Spectra: well reproduced from radio to X-ray. Excess in gamma-ray due to compression of B around TS (flux vortices). Brightness maps: jet-torus structure in gamma-rays as in X-rays (high resolution). Observed dimensions. Gamma-ray (as X-ray) time-variability is well reproduced by MHD motions. COMPLETE SET OF DIAGNOSTIC TOOLS FOR PWNe AND OTHER EMITTING SOURCES (AGN, GRB) Future work: direct evolution of the distribution function; investigation of the parameter space; applications to other PWNe (different evolution stages) and other non-thermal emitting sources (AGN, GRB). Paper: Simulated synchrotron emission from Pulsar Wind Nebulae (L.Del Zanna, D.Volpi, E.Amato, N.Bucciantini, A&A, 453, 621-633, 2006) Paper: Non-thermal emission from relativistic MHD simulations of pulsar wind nebulae: from synchrotron to inverse Compton, D.Volpi, L. Del Zanna, E. Amato, N. Bucciantini, A&A, 2008, 485, 337

22. WHICH KIND OF CONTINUUM EMISSION FROM RADIO TO SOFT-GAMMA ? CRAB NEBULA: SAME FRACTION AND POSITION ANGLE OF POLARIZATION FROM RADIO TO X-RAYS=> SIGNATURE OF SYNCHROTRON EMISSION OPTICAL (SHKLOVSKY, 1952- DOMBROVSKY, 1954) SYNCHROTRON EMISSION=> LINEAR POLARIZATION WITH A MAXIMUM OF 80% IMPORTANCE OF POLARIZATION: 1)GEOMETRY OF THE SOURCE (PULSAR WIND) 2)PROPERTIES OF THE SOURCE=>MAGNETIC FIELD STRENGHT AND DIRECTION 3) ACCELERATION OF PARTICLES OBTAIN SYNTHETIC MAPS FROM NUMERICAL SIMULATIONS AND COMPARE WITH OBSERVATIONS: STUDY OF POLARIZATION

23. IC emission recipes Integration between distribution function (primordial and wind) and power per unit of frequency respect to ε and ν (Blumenthal&Gould, 1970) Incident photon density per unit of frequency: IC from CMB target IC from FIR target IC from SYN target