Magnetic-Tower Jet Solution for Astrophysical Jets Yoshiaki Kato Center for Computational Sciences, University of Tsukuba Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Outline of my talk Introduction Why we study jets? Connection between accretion disks and astrophysical jets Previous studies of MHD jets and unresolved issues A new study of MHD jets “Magnetic-Tower Jet” Formation of magnetic-tower jets in accretion disks around black holes Formation of magnetic-tower jets in accretion disks around weakly magnetized neutron stars Summary Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
M87 Artistic Animation (HH30, HH34, HH47) VIRGO A Keywords： Accretion Disks B-fields X-ray binaries (SS433) Young stellar objects Why we study jets? The radio sky above an optical 150 kpc photograph of the NRAO site in Green Bank, WV Image courtesy of NRAO/AUI Extended radio sources Synchrotron= are outflows/jets! B-fields + high energy electrons 7 pc http://archive.ncsa.uiuc.edu/Cyberia/NumRel/Movies/SupermassBlkHole.mov non-steady VLA image ~ 0.5 lys X-ray image ~ 3 lys Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
jets Accretion disks are launching pads for astrophysical jets subrelativistic relativistic no jet Jets or corona optically thin disk optically thick disk Accretion Disks & Astrophysical Jets Microquasar ： ” small- Quasars/AGNs” X-ray Binaries Mirabel 2004 Spectral Type of X-ray Binaries (XRBs) Microquasar GRS 1915+105 intensity Schematics of SED VHS/IS HS LS Soft Hard in Black Hole XRBs thermal optically thick disk [cm -2 s -1 keV] Count Rate � > 2 � < 2 non-thermal ii intensity iii hardness jet line y a r � optically thin disk X hardness Jet Lorentz factor Disc inner radius or corona no Energy [keV] jet iv i Tanaka & Lewin 1995 iv i ii iii Fender et al. 2004 Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Previous Study of MHD Jets Large-scale ordered magnetic fields permeating the accretion disks Uchida, Nakamura, Hirose Kudoh, Shibata Magneto-centrifugally driven outflows (Blandford & Payne 1982) Magnetic-pressure Magnetic-pressure driven outflows driven (Uchida & Shibata 1984) Both accelerations may work simultaneously Magneto-centrifugally driven along the magnetic field lines (Kudoh & Shibata 1997) Colors = Density Although the origin of large-scale magnetic fields is not well understood,,,, people frame the existence of large-scale magnetic fields within a paradigm of astrophysical jets Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Cumulative distribution function of the difference in polarization angles between the local B-fields and the CTTS symmetry axis. No-correlation between the direction of large-scale magnetic fields and that of the observed jets in YSOs F . Ménard and G. Duchêne (2004) All samples Random distributions Jet Disk B-fields The existance of large-scale magnetic fields may not be a necessary condition for launching astrophysical jets Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Look at the Sun! Sun creates large-scale magnetic fields by its magnetic activities Solar flare and Coronal Mass Ejections (CMEs) Schematic of CMEs http://svs.gsfc.nasa.gov/vis/a000000/a002500/a002509/ What about the accretion disks? Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
BH Initial Model See Kato, Mineshige, Shibata 2004 for more detail A magnetized rotating torus is in equilibrium around a black hole: ρ ( r, z ) = ρ (40 r s , 0) = ρ 0 Isothermal, hot, low-density corona outside the torus: Colors = density ρ c, 0 = 10 − 5 ρ 0 C s,corona ≈ 0 . 5 − 0 . 9 c B-field is given by vector potential: Initial torus & z rA φ ∝ ρ when ρ > ρ c ! magnetic fields Employ pseudo-Newtonian potential in order to take into account general relativistic gravity r Ψ = − GM r − r s Localized Poloidal B-fields Absorbing boundary at R=2rs plasma- β =10, 100 sphere (b) Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Density is a free parameter Neglect radiative cooling Non-relativistic MHD approximation & Using pseudo-Newtonian potential. Employ anomalous resistivity (Yokoyama & Shibata 1994): Assumptions: Basic Equations (Resistive MHD Equations) ∂ρ ∂ B ∂ t + ∇ · ( ρ v ) = 0 ∂ t = − c ∇ × E ρ d v dt = − ρ ∇ ψ − ∇ p + J × B � v × B + 4 πη ψ = − GM � E = − c 2 J c r − r s c ρ T ds J = c dt = Γ − Λ where s = K ln ( p/ ρ ) 4 π ∇ × B Γ = η | J | 2 : heating term Λ = Q rad : cooling term B = ˜ B ( ρ 0 c 2 ) 1 / 2 p ( ρ 0 c 2 ) r s = c = 1 ρ = ˜ p = ˜ ρρ 0 v d ≡ | J | / ρ 0 for v d < v crit η max = 10 − 3 cr s η max [( v d /v crit ) − 1] 2 for v crit < v d < 2 v crit η = for v d ≥ 2 v crit v crit = 10 − 2 c η max Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Evolution of Magnetic Fields in the Disk and the Jet (Magnetic Coupling between the Disk & the Jet) 1. Before the formation of jets 0 0 2. During the formation of jets log 10 <B 2 > corona / B 2 log 10 <B 2 > corona / B 2 1 1 Toroidal B-field 3 Poloidal B-field 3. After the formation of jets 0 0 2 1 3 2 -1 -1 1 -2 -2 -3 -3 10 100 10 100 r / r s r / r s Jet 0 0 log 10 <B 2 > disk / B 2 Toroidal B-field log 10 <B 2 > disk / B 2 2 Poloidal B-field 2 2 1 3 1 1 3 1 0 0 2 -1 -1 Initial Initial -2 -2 10 100 10 100 Disk r / r s r / r s Initial weak poloidal fields are converted into toroidal fields, and the toroidal fields injected into the jet. Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Magnetic Fields in the Accretion Disks and the Dynamo By transferring the angular Schematic evolution of magnetic fields momentum between the plasma in the accretion disk connected via magnetic field lines, τ B τ S , τ MRI MRI (Balbus & Hawley 1991) creates the radial magnetic fields, Azimuthal magnetic fields are generated by winding up the radial magnetic fields as a result of the differential rotation,,,, * τ MRI MRI ∼ τ s = 1 / Ω ∼ τ K τ MRI ∼ τ ∗ MRI + differential rotation = Time-scales: τ B ∼ H/v A = v s / ( v A Ω ) ∼ βτ K Efficient Dynamo. Even if the initial magnetic field is weak, magnetic pressure can be comparable to gas pressure in a few dynamical time-scale. Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Toroidal (poloidal) fields dominates poloidal (toroidal) field at the rim (core) of the tower. Magnetic-tower is collimated by the external force = it is not collimated by itself! Structure of Magnetic-Tower (Collimation of Magnetic-Tower Jet) Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
B A C D Persistent weak jet / outflow ~ 0.1 c Weak B-field, Cold Corona Persistent strong jet / outflow ~ 0.5 c Strong B-field, Cold Corona No jet / No outflow Filamentary strong Bφ in the disk Weak B-fields, Hot Corona Transient jet / outflow Strong Bφ in the inner region of the disk Strong B-fields, Hot Corona Model dependencies A. Cs=0.91c B. Cs=0.65c C. D. β =100 β =10 Formation, collimation, velocity of the jets depend on the corona Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
Related Works in Magnetic-Tower Jet Solutions Lynden-Bell Proposed a solution of a magnetic-tower (1996) Published Initial Dimension Initial Disk Notes Papers B-fields Turner et al. 2-D Boundary Poloidal Newtonian (1999) Axisymmetric Condition Li et al. 2-D Boundary Magneto- Dipole (2001) Axisymmetric Condition static solution Kudoh et al. 2-D Thick Torus Poloidal Newtonian (2003) Axisymmetric von Rekowski 2-D Thin Disk with Newtonian Poloidal et al. (2003) Axisymmetric Mass Supply α - ω Dynamo Kato et al. 2-D pseudo- Thin Torus Dipole (2004a) Axisymmetric Newtonian Kato et al pseudo- 3-D Thin Torus Poloidal (2004b) Newtonian McKinney et 2-D Full General Thick Torus Poloidal al. (2004) Axisymmetric Relativistic Romanova et 2-D Thin Disk Dipole Newtonian al. (2005) Axisymmetric Workshop on MHD Processes in Galaxies, Accretion disks and in Star Forming Regions @ Chiba Univ. Nov. 17 - 18, 2005
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