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Published on November 15, 2007

Author: brod

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Binary Star Formation and Mass Outflows -MHD Nested Grid Simulation - :  Binary Star Formation and Mass Outflows -MHD Nested Grid Simulation - Masahiro N. Machida (Hokkaido University / National Astronomical Observatory of Japan ) Kohji Tomisaka (National Observatory of Japan) Tomoaki Matsumoto (Hosei University) The international Symposium on New Trend of Physics: Part 2 (2003/3/18) 1.Motivation:  1.Motivation Over 70% of stars are binary or multiple systems (the ratio of the multiples and binaries is 1:5) (Heintz 1969; Abt&Levy 1976; Abt 1983; Duquennoy & Mayor 1991) The ratio of a binary stars increases further in pre-main-sequence stars (Abt 1993; Joy& van Biesbroeck 1994; Cohen&Kuhi 1979; Dyck et al. 1982; Simon et al. 1992; Richichi et al. 1994; Ghez et al. 1993)  ⇒ A star is born as a binary star generally We should study binary star formation process rather than a single star Slide3:  outflow from the pre main sequence star Two optical jets  from the binary Schematic View We study the binary star formation from molecular cloud . observations Slide4:  ★Problem of the star (or binary ) formation   The angular momentum should be largely removed in the evolution course from molecular cloud core (jcloud~1021 cm2s-1)  to the pre-main-sequence star (jTTauri~1016 cm2s-1) When and How is the angular momentum removed ? How is the angular momentum distributed between spin and orbital angular momenta ? The fragmentation in the molecular cloud (binary star formation) When and How dose the molecular cloud fragment ? The condition under which the cloud forms binary and a single star The outflow from the binary system Do two outflows appear from binary system? What form dose the outflow from a binary star have? We studied the binary star formation in order to solve the above problems Slide5:  ◆magnetic field strength:  α=Bc2/(4prcs2)   (the magnetic-to-thermal pressure ratio) ◆rotation:ω (angular speed) ◆Cylindrical magnetized molecular cloud in hydrostatic equilibrium 2.Model    magnetic field line ◆ Central density :rc=100 cm-3 ◆ Temperature:T=10 [K] Slide6:  Scale length Box size:~106 [AU] Total mass:M=~20 Msun 2.Model Perturbations Axisymmetric magnetic field line Parameters Am2=0, 0.01, 0.1, 0.2: non-axisymmetry α=0, 0.01, 0.1, 1, 5 :magnetic field strength ω=0, 0.1, 0.5, 0.7:angular rotation speed we calculate 51 models with different parameters Non-axisymmeric Slide7:  3D Ideal MHD nested grid simulation ◆Hydro:Roe's method, polytrope (isothermal, adiabatic) ◆Self-gravity:Multigrid Iteration Method ◆Nested grid: The generation condition of a new grid :h<λJ /8 (h: mesh length )、 λJ :Jeans length) Jeans length should be expressed with at least 8 grid ◆NAOJ VPP5000 Mesh size:128×128×32×17 (level) ⇒8388608×8388608×2097152 ~1.5×1020 A calculation end if followings fulfilled: Jeans Condition is violated at 17 level of grid isothermal phase adiabatic phase equation of continuity equation of motion Magnetic induction equation Poisson equation Basic equations We calculated density:100 cm-3 (initial)~ 1017 cm-3 (final) scale: 106 AU (initial ) ~ 1 AU (final) equation of state rcri=1010 cm-3 Slide8:  (Am2, a, w)=(0.2, 1, 0.5) Initial state r=102 cm-3 L=1 r=103 cm-3 L=1 r=107 cm-3 L=6 r=109 cm-3 L=9 r=1010 cm-3 L=11 r=1011cm-3 L=12 r=104 cm-3 L=2 r=105 cm-3 L=3 z=0 plane x=0 plane Only After the sufficiently thin disk is formed, the non-axisymmetric perturbation can grow Model with strong magnetic field and high rotation speed 3.Results isothermal phase adiabatic phase Slide9:  Typical Model (Am2, a, w)=(0.01, 0.01, 0.5) Initial state r=102 cm-3 L=1 r=103 cm-3 L=1 r=107 cm-3 L=6 r=109 cm-3 L=9 r=1010 cm-3 L=10 r=1010cm-3 L=10 r=104 cm-3 L=2 r=105 cm-3 L=3 z=0 plane x=0 plane In this model, the non-axisymmetry hardly grow because disk formation time is delayed for weak magnetic field Model with weak magnetic field and high rotation speed isothermal phase adiabatic phase Slide10:  Bar Disk lines: magnetic field line iso-surface: adiabatic core Pole on view Slide11:  Numerical results We obtain various types of the adiabatic cores. Each panel shows the final structure of the adiabatic core for different models. Slide12:  ◆definition of the oblateness and axis-ratio oblateness:thickness of the disk axis ratio:degree of the non-axisymmetry The schematic figures hxy z r z=0 plane Slide13:  1.The non-axisymmetry (ear) dose not grow until the oblateness is over 4 2.The oblateness dose not grow further when eob >4, while the non-axisymmetry continues to grow in the isothermal phase 3.The final non-axisymmetry depends on the disk formation time 4.The magnetic field strength and rotation speed promote the disk formation ◆The evolution of the shape of the central region in the isothermal phase in the eob-ear plane 4 Initial state Slide14:  Two modes of the fragmentation ・The disk is deformed to the ring, and fragmentation occurs in this ring ・Outflow from the ring in early adiabatic phase(wide range, weak) ・Out flow from fragments after fragmentation occur (narrow range、weak)] ・The bar evolves thinner and longer and the fragmentation occurs by Jeans instability ・Outflow from the region enclosed bar in early adiabatic phase(wide-scale, weak) ・Outflow from fragments after fragmentation occur(narrow, very strong)  ⇒ two layer structure, two type outflow co-exist ★Ring fragmentation ★Bar fragmentation macrograph macrograph outflow outflow In this panel, outflow is defined vz>cs Evolution in adiabatic phase Slide15:  ring fragmentation :Am2=0.01 α=0.01 ω=0.5 bar fragmentation :Am2=0.2 α=1.0 ω=0.5 Shape of the magnetic field line (red stream lines) outflow region( blue isovolume) ◆Modes of fragmentation density (false color, contour) velocity (arrows) density (false color, contour) velocity (arrows) Shape of the magnetic field line (red stream lines) outflow region( blue isovolume) Slide16:  ◆Quantitative classifications of the central core By using the axis ratio (ear) and oblateness (eob), the shape of the central region can be classified as follows: core: eob < 4, ear < 4 disk: eob >4, ear <4 (ring: eob >4, ear <4 The same as disk but its density peak is outside. The ring-mode instability appears in some disks in the adiabatic stage ) bar : eob > 4, ear >4 ・isothermal phase:the gas with r>0.1 rmax  ・adiabatic phase:the gas with r>0.1 rmax  core disk ring bar density high low Density distribution at z=0 plane oblateness axis ratio Slide17:  Fragmentation occurs if the oblateness is over 4 at the beginning of the adiabatic phase After fragmentation, some binary fragments results in merger. To survive at the end of the simulation, the axis ratio must be a smaller than 2(ring fragmentation) or greater than 10 (bar fragmentation) The condition for the binary formation is following: ・oblateness >4 ・axis-ratio<2   or axis-ratio > 10 ◆Fragment condition for the oblateness and the axis-ratio at the beginning of the adiabatic phase After fragmentation ×:not merge ×:merge axis ratio oblateness Shape at the fragmentation or calculation end ・□:core ・◇:disk ・○:ring ・△: bar 4 bar →bar fragmentation ring fragmentation ←disk evolutional track Slide18:  Relation between modes of the fragmentation and angular momentum redistribution Bar fragmentation: angular momentum is evenly redistributed into the spin angular momentum and orbital one of the binary fragments Ring fragmentation: mainly redistributed to the orbital angular momentum of the binary fragments spin angular momentum orbital angular momentum 全角運動量 spin angular momentum orbital angular momentum 全角運動量 Bar fragmentation Ring fragmentation t (yr) J J t (yr) Slide19:  Growth of the non-axisymmetry The non-axisymmetric perturbation (bar-mode) grows only after a thin disk is formed The axisymmetric ring mode grows also in this thin disk Fragmentation condition Models which result in fragmentation have sufficiently large oblateness, eob >4 Condition for survival for binary fragments Axis ratio is over 10 or approximately 1 (obleteness is over 4) A much elongated bar or an almost axisymmetric ring forms binary fragments which can survive against mutual merger Two modes of the fragmentation One is from the bar and the other is from the ring Ring fragmentation⇒ j orbital: large, j spin: small, outflow:wide, weak Bar fragmentation ⇒ j orbital: small, j spin: large, outflow:: narrow, strong Two types of outflow: one is driven by the rotation of the fragments and the other is driven by the remnant of the ring or the bar 4.Summary

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