Excesses of Magnetic Flux and Angular Momentum in

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

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

Excess Magnetic Flux • Magnetic Flux of Main Sequence Stars • Magnetic Flux of Parent’s Cloud

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

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. Outflo w be reduced to 10 -3 jcl. w o Inflow ® star Outflow tfl u O B-Fields Mass Ang. Mom. Disk

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

Larson 1969, Penston 1969, Hunter 1977, Whitworth & Summers 1985 Dynamical Collapse Hydrostatic Core Accretion-associated Collapse Density increases infinitely Runaway Collapse Shu 1977 Inside-out Collapse

Runaway Collapse – Initial a=pmag/pth=0. 05 -10 – Final 2 p. G 1/2 Sc/Bc=1. 1 -1. 3 vr al. 99 Cuts at the equator Log r • In Isothermal regime, even for magnetized clouds the run-away collapse: Self-similar collapse. • Universality: Nakamura et Log r

• Evolution is as follows: Run-away Collapse (isothermal G=1) ® Increase in Central Density ® Formation of Adiabatic Core(1 st core G=7/5) ® Accretion Phase ®Dissociation of H 2 ®Second Collapse (G~1. 1) ®Second Core(G=5/3) (Larson 1969) Log T 4 ｎ 15 5 Log 10 H 2 1 aba adi 2 tic 3 l r isotherma Log so s i D

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

Run-away Collapse Phase t=0 0. 6 Myr 1 Myr

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

Accretion Phase a=1, W=5 B¹ 0, W¹ 0 300 AU L 10 Run-away Collapse Stage t» 1000 yr

B¹ 0, W¹ 0 Accretion Phase Weak Magnetic Fields (a=0. 1, W=5) 0 yr 2000 yr 4000 yr

Accretion/Outflow Rate 2000 yr 4000 yr 6000 yr • 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. ¤ 4 3 2 1

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

Molecular Outflow Optical Jets L 1551 IRS 5 Optical Jets Edge of Hole made by Molecular Outflow

Jets and Outflows 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 Temperature-Density Relation • Optical jets are formed just outside the second core? 1 tic aba 2 Jets? adi Log T Outflows Temperature-Density Relation 15 2 nd Core 5 Log ｎ 10 4 1 st Core. c o s s i D 3 H 2 isothermal Log r Tohline 1982

Jets and Outflows L 16 rc=1019 H 2 cm-3 sso c. 2 nd Runaway Collapse Di Outflow H 2 L 8 rc=1014. 6 H 2 cm-3 10 R¤ X 256 Jets rc=1021. 3. H 2 cm-3 10 AU rs=104 H 2 cm-3 a=1, w=1/2 10 R¤

Case with a=0. 1 w=0. 3

Microjet around S 106 FIR • H 2 O maser observation • Small scale expanding bow shocks? • No bipolar molecular outflow. • Prediction: Two outflows with different scales Maser spots 25 -40 km/s 4 AU 25 AU Class 0 protostar

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?

Flux Loss • Induction Equation of BFields: s • After • Diffusion speed is larger than free-fall speed. Joule dissipation. M+ Log n. H Nakano, Umebayashi 1986

Flux Loss(II) first core Log T 4 ｎ 15 5 Log 10 H 2 1 second core aba adi 2 tic 3 isotherma Logl r Magnetic Flux in Mrec D c o s s i .

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

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 1/4 1/2 1 L 0 ~ L 23

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

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

B¹ 0, W=0 Accretion Phase Core + Contracting Disk Pseudo. Disk Adiabatic (the first) Core

W¹ 0 , B=0 Accretion Phase A Ring Supported by Centrifugal Force r r W Run-away Collapse Stage W Accretion Stage

Accretion Phase B¹ 0, W¹ 0 Why Does the Outflow Begin in the Accretion Stage? Blandford & Peyne 82 Magneto-Centrifugal Wind Mass Accretion Rate

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

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

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

Summary • In dynamically collapsing clouds, the outflow emerges just after the core formation (t~1000 yr). • In the accretion phase, the centrifugal wind mechanism & magnetic pressure force work efficiently. • In t~7000 yr ( ), the outflow ¤ reaches 2000 AU. Maximum speed reaches

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 2 nd outflow outside the 2 nd (atomic) core explains optical jets.

Parameters • Angular Rotation Speed • Magnetic to thermal pressure ratio

Run-away Collapse Phase L 12 Nest (Self-Similar) Structure Along z-axis r L 5 z

Run-away Collapse • Evolution characterized as self-similar

Magnetocentrifugal Wind Model: Blandford & Peyne 1982 • Consider a particle rotating with rotation speed w = Kepler velocity and assume w is conserved moving along the B-fields. • Along field lines with q<60 deg the particle is accelerated. For q>60 deg decelerated. Effective potential for a particle rotating with w.

Momentum Flux (Observation) Momentum • Low-Mass YSOs (Bontemps et al. 1996) l Luminosity

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

Effective Outflow Speed a=1 a=0. 1 W=5 W=1 W=5

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 Outfl ow O • Contraction vs Outflow? • When outflow begins? • Condition? w o utfl B-Fields Disk Inflow

Momentum Driving Rate 2000 yr 4000 yr 6000 yr • Molecular Outflows (Class 0&1 Objects) show Momentum Outflow Rate (Bontemps et al. 1996) ¤ ¤ ¤

Accretion Phase B¹ 0, W¹ 0 Effect of B-Field Strength • In small a model, toroidal B-fields become dominant against the poloidal ones. • Poloidal B-fields are winding. • Small a and slow rotation lead less effective acceleration.

Angular Momentum Problem • Typical specific angular momentum of T Tauri stars ¤ • Angular momentum of typical molecular cores • Centrifugal Radius ¤

Molecular Outflow L 1551 IRS 5 Saito, Kawabe, Kitamura&Sunada 1996 Optical Jets Snell, Loren, &Plambeck 1980