1. Excesses of Magnetic Flux and Angular Momentum in Stars National Astronomical Observatory (NAOJ) Kohji Tomisaka

2. Angular Momentum Angular Momentum Problem: j * << j cl Specific angular momentum of a new-born star: is much smaller than that of parent cloud:

3. Excess Magnetic Flux Magnetic Flux of Main Sequence Stars Magnetic Flux of Parent’s Cloud

4. Angular Momentum Transfer Magnetic Braking Alfven Speed Ambient density Column density Free-fall time in ambient matter >1: For super- critical clouds Longer than dynamical time B-Fields do not play a role in angular momentum transfer in a contracting cloud?

5. Angular Momentum Redistribution in Dynamical Collapse In outflows driven by magnetic fields: –The angular momentum is transferred effectively from the disk to the outflow. –If 10 % of inflowing mass is outflowed with having 99.9% of angular momentum, j * would be reduced to 10 -3 j cl. Outflo w Disk B-Fields Outflow Mass Inflow  star Outflow Ang.Mom.

6. Shu’s Inside-out Solution Larson-Penston Solution What we have done. Dynamical contraction of slowly rotating magnetized clouds is studied by ideal MHD numerical simulations with cylindrical symmetry with nested grid. (cf. AMR) Evolution : –Isothermal Run-away Collapse Phase –Adiabatic Accretion Phase Nested Grid Method

7. Runaway CollapseAccretion-associated Collapse Density increases infinitely Inside-out CollapseHydrostatic Core Larson 1969, Penston 1969, Hunter 1977, Whitworth & Summers 1985 Shu 1977 Dynamical Collapse

8. Runaway Collapse In Isothermal regime, even for magnetized clouds the run-away collapse: Self-similar collapse. Universality: Nakamura et al. 99 –Initial  p mag /p th  –Final 2  G 1/2  c  c =1.1  1.3 Log r Log  Log r vrvr Cuts at the equator

9. Evolution is as follows: Run-away Collapse (isothermal  )  Increase in Central Density  Formation of Adiabatic Core(1 st core  )  Accretion Phase  Dissociation of H 2  Second Collapse (  )  Second Core(  ) (Larson 1969) adiabatic H 2 Dissoc. isothermal Log T Log  Log ｎ 510 15 1 2 3 4

10. Angular Momentum OUTFLOW is formed just outside the 1st molecular core. Angular momentum is effectively transported by the outflow motion and the gas with less angular momentum falls into the core.

11. t=0 0.6Myr 1Myr Run-away Collapse Phase

12. Accretion Phase High-density gas becomes adiabatic. –The central core becomes optically thick for thermal radiation from dusts. –Critical density = An adiabatic core is formed. To simulate, a double polytrope is applied –isothermal –adaiabatic

13. Accretion Phase B  0,  0 Run-away Collapse Stage  1000yr L10 300AU  

14. Weak Magnetic Fields (  =0.1,  ) 0 yr 2000 yr 4000 yr B  0,  0 Accretion Phase

15. Accretion/Outflow Rate Inflow Rate is Much Larger than Shu’s Rate (1977). LP Solution: Outflow/Inflow Mass Ratio is Large ~ 50 %. Source Point of Outflow Moves Outward. 6000yr2000yr4000yr 1 2 3 4 

16. Core Formation 7000 yr after Core Formation Mass Specific Angular Momentum Initial High-density region is formed by gases with small j. Run-away Collapse Magnetic torque brings the angular momentum from the disk to the outflow. Outflow brings the angular momentum. Accretion Stage Angular Momentum Problem

17. Molecular OutflowOptical Jets L1551 IRS5 Optical Jets Edge of Hole made by Molecular Outflow

18. Optical Jets Flow velocity: faster than molecular outflow. The width is much smaller. These indicate ‘Optical jets are made and ejected from compact objects.’ The first outflow is ejected just outside the adiabatic (first) core. Jets and Outflows

19. Optical jets are formed just outside the second core? Temperature-Density RelationJets and Outflows Temperature-Density Relation adiabatic H 2 Dissoc. isothermal 1st Core 2nd Core Log T Log  Outflows Jets? Log ｎ 510 15 1 2 3 4 Tohline 1982

20. Outflow Jets Jets and Outflows  s =10 4 H 2 cm -3  =1,  L8 L16 10AU 10R   c =10 14.6 H 2 cm -3  c =10 19 H 2 cm -3  c =10 21.3. H 2 cm -3 H 2 Dissoc. 10R  2nd Runaway Collapse X256

21. Case with  =0.1  =0.3

22. Microjet around S106 FIR H 2 O maser observation Small scale expanding bow shocks? No bipolar molecular outflow. Prediction: Two outflows with different scales 25AU 4AU 25-40km/s Class0 protostar Maser spots

23. Centrifugal Radius Specific angular momentum: Mass Centrifugal radius: For a slow rotator, –No outflow outside the 1 st core? –Jet outside the 2 nd core?

24. Flux Loss Induction Equation of B- Fields: After Diffusion speed is larger than free-fall speed. Joule dissipation. Nakano, Umebayashi 1986 Log n H  M+M+

25. Flux Loss(II) adiabatic H 2 Dissoc. isothermal Log T Log  Log ｎ 510 15 1 2 3 4 first core second core Magnetic Flux in M rec

26. Further Accretion The final magnetic flux can be determined as the magnetic flux when the X- point is formed. If, a star with has Or if dipolar B-fields are formed…… (B), accretion would not increase the magnetic flux further. (A) (B)

27. Numerical Method Ideal MHD + Self- Gravity + Cylindrical Symmetry Collapse: nonhomologous Large Dynamic Range is attained by Nested Grid Method. –Coarse Grids: Global Structure –Fine Grids: Small-Scale Structure Near the Core L0  L23 1 1/2 1/4

28. Initial Condition Cylindrical Isothermal Clouds –Magnetohydrostatic balance in r-direction –uniform in z-direction B-Fields Slowly rotating (~ rigid-body rotation) Added perturbation with of the gravitationally most unstable mode MGR. MGR parameters

29. Accretion Phase (II) Collapse time-scale in the adiabatic core becomes much longer than the infall time. Inflowing gas accretes on to the nearly static core, which grows to a star. Outflow emerges in this phase. Outflow

30. Core + Contracting Disk Pseudo- Disk Accretion Phase B  0,  Adiabatic (the first) Core

31. A Ring Supported by Centrifugal Force Run-away Collapse Stage Accretion Stage Accretion Phase  0, B=0    

32. Why Does the Outflow Begin in the Accretion Stage? B  0,  0 Accretion Phase Blandford & Peyne 82 Mass Accretion RateMagneto-Centrifugal Wind

33. Angular Momentum Distribution (1) Mass measured from the center (2) Angular momentum in (3) Specific Angular momentum distribution Angular Momentum Problem

34. Magnetic Torque, Angular Momentum Inflow/Outflow Rate Mass Initial Torque Inflow Outflow Accretion Phase Inflow Torque Core Formation Inflow Torque

35. In weakly ionized plasma, neutral molecules have only indirect coupling with the B-fields through ionized ions. Neutral-ion collision time When, ambipolar diffusion is important. Assuming (on core formation), rotation period of centrifugal radius: Ambipolar Diffusion? 

36. Summary In dynamically collapsing clouds, the outflow emerges just after the core formation (  yr). In the accretion phase, the centrifugal wind mechanism & magnetic pressure force work efficiently. In  7000 yr ( ), the outflow reaches 2000 AU. Maximum speed reaches 

37. Summary(2) In the process, the angular momentum is transferred from the disk to the outflow and the outflow brings the excess j. This solves the angular momentum problem of new-born stars. The 2nd outflow outside the 2nd (atomic) core explains optical jets.

38. Parameters Angular Rotation Speed Magnetic to thermal pressure ratio

39. Nest (Self-Similar) Structure L5 L12 z  Run-away Collapse Phase Along z-axis

40. Run-away Collapse Evolution characterized as self-similar

41. Magnetocentrifugal Wind Model: Blandford & Peyne 1982 Consider a particle rotating with rotation speed  = Kepler velocity and assume  is conserved moving along the B-fields. Along field lines with  deg the particle is accelerated. For  deg decelerated. Effective potential for a particle rotating with 

42. Momentum Flux (Observation) Low-Mass YSOs (Bontemps et al.1996)  Luminosity Momentum

43. Angular Momentum (1) Mass measured from the center (2) Angular momentum in (3) Specific Angular momentum distribution Angular Momentum Problem

44. Effective Outflow Speed    

45. Outflow Driving Mechanism Rotating Disk + Twisted Magnetic Fields –Centrifugal Wind + Pudritz & Norman 1983; Uchida & Shibata 1985; Shu et al.1994; Ouyed & Pudritz 1997; Kudoh & Shibata 1997 Contraction vs Outflow? When outflow begins? Condition? Outflow Disk B-Fields Outflow Inflow

46. Momentum Driving Rate Molecular Outflows (Class 0&1 Objects) show Momentum Outflow Rate (Bontemps et al.1996)  6000yr2000yr4000yr  

47. Effect of B-Field Strength In small  model, toroidal B-fields become dominant against the poloidal ones. Poloidal B-fields are winding. Small  and slow rotation lead less effective acceleration. B  0,  0 Accretion Phase

48. Angular Momentum Problem Typical specific angular momentum of T Tauri stars Angular momentum of typical molecular cores Centrifugal Radius Angular Momentum Problem  

49. Molecular Outflow Saito, Kawabe, Kitamura&Sunada 1996 L1551 IRS5 Optical Jets Snell, Loren, &Plambeck 1980