Analyzing Plasma Jets in Astrophysical Environments: Force-Free Approximations and Simulation Results

2. Contents • Introduction • Force-Free Approximation • Analytical Solutions • Simulations • Conclusions • Future Goals

3. Jets are plasma outflows extended for large distances. They stay collimated for many Mpc in some cases. Are observed in active galactic nuclei (AGN), neutron stars , young stellar object (YSO) etc. Relativistic (AGN, Pulsar etc) Non Relativistic (YSO, u~100-200 Km/s) The first jet observed was from the galaxy M87 in 1918 by Curtis. Center for Magnetic Self Organization in Laboratory and Astrophysical Plasmas Introduction

4. Active Galactic Nuclei Cygnus A(NRAO) 3C273(earthsky.org)

5. Herbig-Haro HH47(esa) Carina Nebula(nasa.gov)

6. Most Important Papers • Tsinganos K.. Magnetohydrodynamic equilibrium. I - Exact solutions of the equations. 1981, ApJ, 245, 764. • Blandford R. D. and Payne D. G.. Hydromagnetic ows from accretion discs and the production of radio jets . 1982, MNRAS, 199, 883. • Contopoulos J., Lovelace R. V. E. Magnetically driven jets and winds: Exact solutions . 1992, ApJ, 429, 139 • Bodo G., Massaglia S., Ferrari A., and Trussoni E.. Kelvin-Helmholtz instability of hydrodynamics supersonic jets . 1994, A&A, 283, 655. • Matsakos T., Tsinganos K., Vlahakis N., Massaglia, Mignone A., Trussoni E.Two-component jet simulations I:Topological stability of analytical MHD out-flow solutions . 2008, A&A, 477, 52. • Mizuno Y., Jose L. Gomez et al. Recollimation shock in magnetized relativisticjets . 2015, ApJ, 809, 38.

8. Force-Free (1) • Relativistic momentum equation • In the force-free limit: - - -Ε<<B Force-Free momentum equation:

9. Force-Free (2) • We apply . We define Ρ as magnetic flux. • Magnetic field - - - • Ampere law • Transfield: • Where β(Ρ) is the current in a cross section at a height Z

10. Force-Free (3) • Non linear equation. • The function β(Ρ) is unknown. • No critical points. • Boundary conditions Ρ(0,z)=P(R,z)=0

11. Dunce's Cap Model • Spherical coordinates • Transfield: • We consider solutions as, where μ=cosθ and. • Finally: • Solutions:

12. Results (1) • We consider small angles • Magnetic Fields: - - - • C4 is calculated from the pressure balance

13. Br Lynden-Bell 2006 Results (2) Bφ Βθ • Lynden-Bell 2006

14. Simulations • All the simulations were executed with the pluto code. • The purpose of the simulation is to create magnetic towers based in Lynden-Bell’s idea. • We consider: - Cylindrical coordinates with axial symmetry - Ideal magnetohydrodynamics in 2 dimensions and 3 components - Negligible gravity - Polytropic gas with γ=5/3 - Non relativistic fluid - Vφ=0initially

15. Problem Set Up • We are based in Dunce's Cap modelas an initial condition. • We consider . • Magnetic fields: • - • - • - • Where Ζο=0.5, wo=10^(-3), C4=2π

16. Problem Set Up (2) • All variables are non dimensional. • Jet pressure Pj=0.0001 • Environment pressure Pa=1/8π • Characteristic velocity Alfven

17. ρj=10, ρa=0.1, Vz=1

18. Recollimation

19. Magnetic Fields

20. Velocities

21. Mach • The • We considerk // Vp • We define

22. Plasma β(1) • The • For β<1 the magnetic field dominates • For β>1 the thermal pressure dominates.

23. Plasma β(2)

24. Energies (1) • Kinetic energy flux: • Thermal energy flux: • Poynting flux: • Kinetic to thermal ratio gives • Kinetic to Poynting ratio gives • Thermal to Poynting ratio gives plasma β

25. Energies(2)

26. ρj=0.1, ρa=1, Vz=5

27. Recollimation

28. Magnetic Fields

29. Velocities

30. Mach

31. Plasma β

32. Energies

33. Conclusions • In all simulations with subfast initial velocities the outflow couldn’t reach superfast velocities. • In the case with η=100 density ratio and superfast initial velocity recollimation shocks appeared. • In the case with η=0.1 and η=1 density ratio and superfast initial velocities Kelvin-Helmholtz instabilities appeared. • In all simulations the initial magnetic energy is converted to thermal energy. • In all simulation the outflow became hydrodynamic. • The Dunce's Cap model is unsuitable to accelerate the outflows in superfast velocities and create magnetic towers. Very interesting solutions for jet propagation - Possible magnetic reconnection.

34. Future Goals • Test the Bessel function solutions. • Make simulations with relativistic velocities. • Use non ideal MHD in order to test the magnetic reconnection hypothesis.

35. Thank you!