1. 分子雲コアからの連星形成過程 とアウトフロー 町田正博 ( 北大・理 ／ 国立天文台 ) 富阪幸治 ( 国立天文台 ) 、 松本倫明 ( 法政 大 ）

2. 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 ⇒ A star is born as a binary star generally  We should study binary star formation process rather than a single star

3. molecular cloud outflow from the pre main sequence star Two optical jets ｆｒｏｍ ｔｈｅ ｂｉｎａｒｙ ？ orbital rotation spin Outflow Schematic View We study the binary star formation from molecular cloud. observations

4. ★ Problem of the star (or binary ) formation ★ Problem of the star (or binary ) formation  The angular momentum should be largely removed in the evolution course from molecular cloud core (j cloud ～ 10 21 cm 2 s -1 ) to the pre-main- sequence star (j TTauri ～ 10 16 cm 2 s -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 We studied the binary star formation in order to solve the above problems

5. X Z Y ◆ magnetic field strength ： α=B c 2 /(4prc s 2 ) （ the magnetic-to-thermal pressure ratio ） ◆ rotation ： ω (angular speed) rotate ◆ Cylindrical magnetized molecular cloud in hydrostatic equilibrium 2.Model 2.Model magnetic field line ◆ Central density ： r c =100 cm -3 ◆ Temperature ： T=10 [K]

6. X Z Y rotate  Scale length  Box size ：～ 10 6 [AU]  Total mass ： M= ～ 20 M sun H= ～ 10 6 [AU] M= ～ 20 M sun 2.Model  Perturbations  Axisymmetric magnetic field line  Parameters A m2 =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: rotation speed we calculate 51 models with different parameters  Non-axisymmeric

7.  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<λ J /8 (h: mesh length ) 、 λ J :Jeans length) Jeans length should be expressed with at least 8 grid ◆ NAOJ VPP5000 L=1 L=2 L=3 Nested grid Mesh size ： 128×128×32×17 (level) ⇒ 8388608 × 8388608×2097152 ～ 1.5×10 20 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)~ 10 17 cm -3 (final) scale: 10 6 AU (initial ) ~ 1 AU (final) equation of state r cri = 10 10 cm -3

8. (A m2, a, w)=(0.2, 1, 0.5) Initial state r=10 2 cm -3 L=1 r=10 3 cm -3 L=1 r=10 7 cm -3 L=6 r=10 9 cm -3 L=9 r=10 10 cm -3 L=11 r=10 11 cm -3 L=12 r=10 4 cm -3 L=2 r=10 5 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 phaseadiabatic phase

9. Numerical results We obtain various types of the adiabatic cores. Each panel shows the final structure of the adiabatic core for different models.

10. ◆ definition of the oblateness and axis-ratio  oblateness ： thickness of the disk  axis ratio ： degree of the non-axisymmetry z x ｈｚｈｚ x y ｈ long ｈ short The schematic figures h xy z r z=0 plane

11. 1.The non-axisymmetry ( e ar ) dose not grow until the oblateness is over 4 2.The oblateness dose not grow further when  ob > 4, while the non-axisymmetry  ar 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 e ob - e ar plane prolate sphere round disk bar 10 1 1 4 Initial state

12. 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 outflow In this panel, outflow is defined v z >c s Evolution in adiabatic phase

13. ring fragmentation ring fragmentation ： A m2 =0.01 α=0.01 ω=0.5 bar fragmentation bar fragmentation ： A m2 =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) Shape of the magnetic field line (red stream lines) outflow region( blue isovolume )

14. ◆ Quantitative classifications of the central core By using the axis ratio ( e ar ) and oblateness ( e ob ), the shape of the central region can be classified as follows:  core: e ob < 4, e ar < 4  disk: e ob >4, e ar <4  （ ring: e ob >4, e ar <4 The same as disk but its density peak is outside. The ring-mode instability appears in some disks in the adiabatic stage )  bar : e ob > 4, e ar >4 ・ isothermal phase ： the gas with r>0.1 r max ・ adiabatic phase ： the gas with r>0.1 r max corediskring bar density high low Density distribution at z=0 plane ε ax ε ob Core Disk or Ring Bar No 4 4 0 oblateness axis ratio

15.  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 10 Fragment condition for the oblateness and the axis-ratio at the beginning of the adiabatic phase ◆ Fragment condition for the oblateness and the axis-ratio at the beginning of the adiabatic phase Fragmented region 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 Survive to form binary

16. Growth of the non-axisymmetry Growth of the non-axisymmetry The non-axisymmetric perturbation (bar-mode) grows only after a thin disk is formed The non-axisymmetric perturbation (bar-mode) grows only after a thin disk is formed The axisymmetric ring mode grows also in this thin disk The axisymmetric ring mode grows also in this thin disk Fragmentation condition Fragmentation condition Models which result in fragmentation have sufficiently large oblateness, Models which result in fragmentation have sufficiently large oblateness, e ob >4 Condition for survival for binary fragments Condition for survival for binary fragments Axis ratio is over 10 or approximately 1 (obleteness is over 4) 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 A much elongated bar or an almost axisymmetric ring forms binary fragments which can survive against mutual merger Two modes of the fragmentation Two modes of the fragmentation One is from the bar and the other is from the ring One is from the bar and the other is from the ring Ring fragmentation ⇒ j orbital: large, j spin: small, outflow ： wide, weak Ring fragmentation ⇒ j orbital: large, j spin: small, outflow ： wide, weak Bar fragmentation ⇒ j orbital: small, j spin: large, outflow:: narrow, strong 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 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

17. Typical Model (A m2, a, w)=(0.01, 0.01, 0.5) Initial state r=10 2 cm -3 L=1 r=10 3 cm -3 L=1 r=10 7 cm -3 L=6 r=10 9 cm -3 L=9 r=10 10 cm -3 L=10 r=10 4 cm -3 L=2 r=10 5 cm -3 L=3 z=0 plane x=0 plane In this model, t he non- axisymmetry hardly grow because disk formation time is delayed for weak magnetic field Model with weak magnetic field and high rotation speed isothermal phaseadiabatic phase

18. Bar Disk lines: magnetic field line iso-surface: adiabatic core Pole on view

19. 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 orbital rotation spin rotation t (yr) J J